%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX166^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:37 AM UTC 2026
% Result : Theorem 6.44s 1.36s
% Output : Refutation 6.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX166^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:09:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.41 % (3054299)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.76/0.41 % (3054309)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1220218814:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.76/0.41 % (3054310)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.76/0.41 % (3054310)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
% 0.76/0.41 % (3054308)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3487443997:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.76/0.41 % (3054306)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2787612599:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.76/0.41 % (3054304)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=154531038:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.76/0.41 % (3054305)lrs+10_16_si=on:nwc=1.5:random_seed=1908317561:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.76/0.41 % (3054307)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=2559282162: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)
% 0.76/0.41 % (3054310)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=3425875445:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.76/0.41 % (3054306)Instruction limit reached!
% 0.76/0.41 % (3054306)------------------------------
% 0.76/0.41 % (3054306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.41 % (3054306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.41 % (3054306)CaDiCaL version: 2.1.3
% 0.76/0.41 % (3054306)Termination reason: Instruction limit
% 0.76/0.41 % (3054306)Termination phase: shuffling
% 0.76/0.41 % (3054306)Time elapsed: 0.003 s
% 0.76/0.41 % (3054306)Peak memory usage: 10 MB
% 0.76/0.41 % (3054306)Instructions burned: 6 (million)
% 0.76/0.41 % (3054305)Instruction limit reached!
% 0.76/0.41 % (3054305)------------------------------
% 0.76/0.41 % (3054305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.41 % (3054305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.41 % (3054305)CaDiCaL version: 2.1.3
% 0.76/0.41 % (3054305)Termination reason: Instruction limit
% 0.76/0.41 % (3054305)Termination phase: shuffling
% 0.76/0.41 % (3054305)Time elapsed: 0.008 s
% 0.76/0.41 % (3054305)Peak memory usage: 10 MB
% 0.76/0.41 % (3054305)Instructions burned: 19 (million)
% 0.76/0.41 % (3054309)Instruction limit reached!
% 0.76/0.41 % (3054309)------------------------------
% 0.76/0.41 % (3054309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.41 % (3054309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.41 % (3054309)CaDiCaL version: 2.1.3
% 0.76/0.41 % (3054309)Termination reason: Instruction limit
% 0.76/0.41 % (3054309)Termination phase: Preprocessing 3
% 0.76/0.41 % (3054308)Instruction limit reached!
% 0.76/0.41 % (3054308)------------------------------
% 0.76/0.41 % (3054308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.41 % (3054309)Time elapsed: 0.018 s
% 0.76/0.41 % (3054309)Peak memory usage: 12 MB
% 0.76/0.41 % (3054308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.41 % (3054309)Instructions burned: 78 (million)
% 0.76/0.41 % (3054308)CaDiCaL version: 2.1.3
% 0.76/0.41 % (3054308)Termination reason: Instruction limit
% 0.76/0.41 % (3054308)Termination phase: Property scanning
% 0.76/0.41 % (3054308)Time elapsed: 0.011 s
% 0.76/0.41 % (3054308)Peak memory usage: 10 MB
% 0.76/0.41 % (3054308)Instructions burned: 27 (million)
% 0.76/0.41 % (3054318)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3071402637:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.41 % (3054318)Instruction limit reached!
% 0.76/0.41 % (3054318)------------------------------
% 0.76/0.41 % (3054318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (3054318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (3054318)CaDiCaL version: 2.1.3
% 0.76/0.44 % (3054318)Termination reason: Instruction limit
% 0.76/0.44 % (3054318)Termination phase: shuffling
% 0.76/0.44 % (3054318)Time elapsed: 0.003 s
% 0.76/0.44 % (3054318)Peak memory usage: 10 MB
% 0.76/0.44 % (3054318)Instructions burned: 5 (million)
% 0.76/0.44 % (3054319)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1227042029:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.76/0.44 % (3054304)Instruction limit reached!
% 0.76/0.44 % (3054304)------------------------------
% 0.76/0.44 % (3054304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (3054304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (3054304)CaDiCaL version: 2.1.3
% 0.76/0.44 % (3054304)Termination reason: Instruction limit
% 0.76/0.44 % (3054304)Termination phase: Preprocessing 3
% 0.76/0.44 % (3054304)Time elapsed: 0.028 s
% 0.76/0.44 % (3054304)Peak memory usage: 12 MB
% 0.76/0.44 % (3054304)Instructions burned: 91 (million)
% 0.76/0.44 % (3054321)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3251393185:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.76/0.44 % (3054319)Instruction limit reached!
% 0.76/0.44 % (3054319)------------------------------
% 0.76/0.44 % (3054319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (3054319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (3054319)CaDiCaL version: 2.1.3
% 0.76/0.44 % (3054319)Termination reason: Instruction limit
% 0.76/0.44 % (3054319)Termination phase: shuffling
% 0.76/0.44 % (3054319)Time elapsed: 0.003 s
% 0.76/0.44 % (3054319)Peak memory usage: 10 MB
% 0.76/0.44 % (3054319)Instructions burned: 6 (million)
% 0.76/0.44 % (3054321)Instruction limit reached!
% 0.76/0.44 % (3054321)------------------------------
% 0.76/0.44 % (3054321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (3054321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (3054321)CaDiCaL version: 2.1.3
% 0.76/0.44 % (3054321)Termination reason: Instruction limit
% 0.76/0.44 % (3054321)Termination phase: shuffling
% 0.76/0.44 % (3054321)Time elapsed: 0.006 s
% 0.76/0.44 % (3054321)Peak memory usage: 10 MB
% 0.76/0.44 % (3054321)Instructions burned: 14 (million)
% 0.76/0.44 % (3054325)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=1265239653:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.76/0.44 % (3054324)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
% 0.76/0.44 % (3054324)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.44 % (3054320)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.44 % (3054324)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3028892980:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.76/0.44 % (3054327)lrs+10_1_si=on:cs=on:random_seed=4245391507:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.76/0.44 % (3054328)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.76/0.44 % (3054320)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3681183041:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.76/0.44 % (3054327)Instruction limit reached!
% 0.76/0.44 % (3054327)------------------------------
% 0.76/0.44 % (3054327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (3054327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (3054327)CaDiCaL version: 2.1.3
% 0.76/0.44 % (3054327)Termination reason: Instruction limit
% 0.76/0.44 % (3054327)Termination phase: shuffling
% 0.76/0.46 % (3054327)Time elapsed: 0.005 s
% 0.76/0.46 % (3054327)Peak memory usage: 10 MB
% 0.76/0.46 % (3054327)Instructions burned: 11 (million)
% 0.76/0.46 % (3054328)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=3857528676:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.46 % (3054325)Instruction limit reached!
% 0.76/0.46 % (3054325)------------------------------
% 0.76/0.46 % (3054325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.46 % (3054325)CaDiCaL version: 2.1.3
% 0.76/0.46 % (3054325)Termination reason: Instruction limit
% 0.76/0.46 % (3054325)Termination phase: Saturation
% 0.76/0.46 % (3054325)Time elapsed: 0.019 s
% 0.76/0.46 % (3054325)Peak memory usage: 12 MB
% 0.76/0.46 % (3054325)Instructions burned: 87 (million)
% 0.76/0.46 % (3054328)Instruction limit reached!
% 0.76/0.46 % (3054328)------------------------------
% 0.76/0.46 % (3054328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.46 % (3054328)CaDiCaL version: 2.1.3
% 0.76/0.46 % (3054328)Termination reason: Instruction limit
% 0.76/0.46 % (3054328)Termination phase: shuffling
% 0.76/0.46 % (3054328)Time elapsed: 0.002 s
% 0.76/0.46 % (3054328)Peak memory usage: 10 MB
% 0.76/0.46 % (3054328)Instructions burned: 3 (million)
% 0.76/0.46 % (3054324)Instruction limit reached!
% 0.76/0.46 % (3054324)------------------------------
% 0.76/0.46 % (3054324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.46 % (3054324)CaDiCaL version: 2.1.3
% 0.76/0.46 % (3054324)Termination reason: Instruction limit
% 0.76/0.46 % (3054324)Termination phase: shuffling
% 0.76/0.46 % (3054324)Time elapsed: 0.012 s
% 0.76/0.46 % (3054324)Peak memory usage: 10 MB
% 0.76/0.46 % (3054324)Instructions burned: 28 (million)
% 0.76/0.46 % (3054320)Instruction limit reached!
% 0.76/0.46 % (3054320)------------------------------
% 0.76/0.46 % (3054320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.46 % (3054320)CaDiCaL version: 2.1.3
% 0.76/0.46 % (3054320)Termination reason: Instruction limit
% 0.76/0.46 % (3054320)Termination phase: shuffling
% 0.76/0.46 % (3054320)Time elapsed: 0.009 s
% 0.76/0.46 % (3054320)Peak memory usage: 9 MB
% 0.76/0.46 % (3054320)Instructions burned: 11 (million)
% 0.76/0.46 % (3054335)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=856926316:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.76/0.46 % (3054310)Instruction limit reached!
% 0.76/0.46 % (3054310)------------------------------
% 0.76/0.46 % (3054310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.46 % (3054310)CaDiCaL version: 2.1.3
% 0.76/0.46 % (3054310)Termination reason: Instruction limit
% 0.76/0.46 % (3054310)Termination phase: Property scanning
% 0.76/0.46 % (3054310)Time elapsed: 0.069 s
% 0.76/0.46 % (3054310)Peak memory usage: 13 MB
% 0.76/0.46 % (3054310)Instructions burned: 159 (million)
% 0.76/0.46 % (3054333)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=587404049:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.76/0.46 % (3054336)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2562384993:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.76/0.46 % (3054337)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4128223775:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.76/0.46 % (3054338)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3936961371:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.76/0.46 % (3054337)Instruction limit reached!
% 0.76/0.46 % (3054337)------------------------------
% 0.76/0.46 % (3054337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.46 % (3054337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054337)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054337)Termination reason: Instruction limit
% 1.45/0.51 % (3054337)Termination phase: shuffling
% 1.45/0.51 % (3054337)Time elapsed: 0.006 s
% 1.45/0.51 % (3054337)Peak memory usage: 10 MB
% 1.45/0.51 % (3054337)Instructions burned: 14 (million)
% 1.45/0.51 % (3054336)Instruction limit reached!
% 1.45/0.51 % (3054336)------------------------------
% 1.45/0.51 % (3054336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054336)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054336)Termination reason: Instruction limit
% 1.45/0.51 % (3054336)Termination phase: Property scanning
% 1.45/0.51 % (3054336)Time elapsed: 0.011 s
% 1.45/0.51 % (3054336)Peak memory usage: 10 MB
% 1.45/0.51 % (3054336)Instructions burned: 25 (million)
% 1.45/0.51 % (3054340)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3128251406:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.45/0.51 % (3054333)Instruction limit reached!
% 1.45/0.51 % (3054333)------------------------------
% 1.45/0.51 % (3054333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054333)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054333)Termination reason: Instruction limit
% 1.45/0.51 % (3054333)Termination phase: Property scanning
% 1.45/0.51 % (3054333)Time elapsed: 0.016 s
% 1.45/0.51 % (3054333)Peak memory usage: 11 MB
% 1.45/0.51 % (3054333)Instructions burned: 38 (million)
% 1.45/0.51 % (3054340)Instruction limit reached!
% 1.45/0.51 % (3054340)------------------------------
% 1.45/0.51 % (3054340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054340)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054340)Termination reason: Instruction limit
% 1.45/0.51 % (3054340)Termination phase: shuffling
% 1.45/0.51 % (3054340)Time elapsed: 0.007 s
% 1.45/0.51 % (3054340)Peak memory usage: 10 MB
% 1.45/0.51 % (3054340)Instructions burned: 16 (million)
% 1.45/0.51 % (3054347)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2492769798:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.45/0.51 % (3054346)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3935247071: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)
% 1.45/0.51 % (3054348)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=624263197:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.45/0.51 % (3054346)Instruction limit reached!
% 1.45/0.51 % (3054346)------------------------------
% 1.45/0.51 % (3054346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054346)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054346)Termination reason: Instruction limit
% 1.45/0.51 % (3054346)Termination phase: shuffling
% 1.45/0.51 % (3054346)Time elapsed: 0.002 s
% 1.45/0.51 % (3054346)Peak memory usage: 10 MB
% 1.45/0.51 % (3054346)Instructions burned: 4 (million)
% 1.45/0.51 % (3054349)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4100924277:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.45/0.51 % (3054347)Instruction limit reached!
% 1.45/0.51 % (3054347)------------------------------
% 1.45/0.51 % (3054347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054347)CaDiCaL version: 2.1.3
% 1.45/0.51 % (3054347)Termination reason: Instruction limit
% 1.45/0.51 % (3054347)Termination phase: shuffling
% 1.45/0.51 % (3054347)Time elapsed: 0.012 s
% 1.45/0.51 % (3054347)Peak memory usage: 10 MB
% 1.45/0.51 % (3054347)Instructions burned: 28 (million)
% 1.45/0.51 % (3054348)Instruction limit reached!
% 1.45/0.51 % (3054348)------------------------------
% 1.45/0.51 % (3054348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.51 % (3054348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.51 % (3054348)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054348)Termination reason: Instruction limit
% 2.01/0.58 % (3054348)Termination phase: Property scanning
% 2.01/0.58 % (3054348)Time elapsed: 0.011 s
% 2.01/0.58 % (3054348)Peak memory usage: 10 MB
% 2.01/0.58 % (3054348)Instructions burned: 25 (million)
% 2.01/0.58 % (3054353)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
% 2.01/0.58 % (3054353)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.01/0.58 % (3054335)Instruction limit reached!
% 2.01/0.58 % (3054335)------------------------------
% 2.01/0.58 % (3054335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.58 % (3054335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.58 % (3054335)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054335)Termination reason: Instruction limit
% 2.01/0.58 % (3054335)Termination phase: Saturation
% 2.01/0.58 % (3054335)Time elapsed: 0.059 s
% 2.01/0.58 % (3054335)Peak memory usage: 15 MB
% 2.01/0.58 % (3054335)Instructions burned: 251 (million)
% 2.01/0.58 % (3054353)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=1329984606:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.01/0.58 % (3054355)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.01/0.58 % (3054353)Instruction limit reached!
% 2.01/0.58 % (3054353)------------------------------
% 2.01/0.58 % (3054353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.58 % (3054353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.58 % (3054353)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054353)Termination reason: Instruction limit
% 2.01/0.58 % (3054353)Termination phase: shuffling
% 2.01/0.58 % (3054353)Time elapsed: 0.007 s
% 2.01/0.58 % (3054353)Peak memory usage: 10 MB
% 2.01/0.58 % (3054353)Instructions burned: 16 (million)
% 2.01/0.58 % (3054357)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4034533649:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.01/0.58 % (3054355)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=899703190:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.01/0.58 % (3054356)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=3608919134:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.01/0.58 % (3054357)Instruction limit reached!
% 2.01/0.58 % (3054357)------------------------------
% 2.01/0.58 % (3054357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.58 % (3054357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.58 % (3054357)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054357)Termination reason: Instruction limit
% 2.01/0.58 % (3054357)Termination phase: shuffling
% 2.01/0.58 % (3054357)Time elapsed: 0.002 s
% 2.01/0.58 % (3054357)Peak memory usage: 10 MB
% 2.01/0.58 % (3054357)Instructions burned: 8 (million)
% 2.01/0.58 % (3054349)Instruction limit reached!
% 2.01/0.58 % (3054349)------------------------------
% 2.01/0.58 % (3054349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.58 % (3054349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.58 % (3054349)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054349)Termination reason: Instruction limit
% 2.01/0.58 % (3054349)Termination phase: Preprocessing 3
% 2.01/0.58 % (3054349)Time elapsed: 0.027 s
% 2.01/0.58 % (3054349)Peak memory usage: 11 MB
% 2.01/0.58 % (3054349)Instructions burned: 61 (million)
% 2.01/0.58 % (3054355)Instruction limit reached!
% 2.01/0.58 % (3054355)------------------------------
% 2.01/0.58 % (3054355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.58 % (3054355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.58 % (3054355)CaDiCaL version: 2.1.3
% 2.01/0.58 % (3054355)Termination reason: Instruction limit
% 2.01/0.58 % (3054355)Termination phase: shuffling
% 2.01/0.58 % (3054355)Time elapsed: 0.005 s
% 2.01/0.58 % (3054355)Peak memory usage: 10 MB
% 2.32/0.65 % (3054355)Instructions burned: 10 (million)
% 2.32/0.65 % (3054363)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3575287815:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.32/0.65 % (3054356)Instruction limit reached!
% 2.32/0.65 % (3054356)------------------------------
% 2.32/0.65 % (3054356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.65 % (3054356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.65 % (3054356)CaDiCaL version: 2.1.3
% 2.32/0.65 % (3054356)Termination reason: Instruction limit
% 2.32/0.65 % (3054356)Termination phase: Property scanning
% 2.32/0.65 % (3054356)Time elapsed: 0.014 s
% 2.32/0.65 % (3054356)Peak memory usage: 10 MB
% 2.32/0.65 % (3054356)Instructions burned: 32 (million)
% 2.32/0.65 % (3054360)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3276808320:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.32/0.65 % (3054363)Instruction limit reached!
% 2.32/0.65 % (3054363)------------------------------
% 2.32/0.65 % (3054363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.65 % (3054363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.65 % (3054363)CaDiCaL version: 2.1.3
% 2.32/0.65 % (3054363)Termination reason: Instruction limit
% 2.32/0.65 % (3054363)Termination phase: shuffling
% 2.32/0.65 % (3054363)Time elapsed: 0.005 s
% 2.32/0.65 % (3054363)Peak memory usage: 10 MB
% 2.32/0.65 % (3054363)Instructions burned: 22 (million)
% 2.32/0.65 % (3054364)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=875655666:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.32/0.65 % (3054365)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2036299304:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.32/0.65 % (3054374)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2158424177:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.32/0.65 % (3054360)Instruction limit reached!
% 2.32/0.65 % (3054360)------------------------------
% 2.32/0.65 % (3054360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.65 % (3054360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.65 % (3054360)CaDiCaL version: 2.1.3
% 2.32/0.65 % (3054360)Termination reason: Instruction limit
% 2.32/0.65 % (3054360)Termination phase: shuffling
% 2.32/0.65 % (3054360)Time elapsed: 0.011 s
% 2.32/0.65 % (3054360)Peak memory usage: 10 MB
% 2.32/0.65 % (3054360)Instructions burned: 24 (million)
% 2.32/0.65 % (3054372)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=198561328:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.32/0.65 % (3054374)Instruction limit reached!
% 2.32/0.65 % (3054374)------------------------------
% 2.32/0.65 % (3054374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.65 % (3054374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.65 % (3054374)CaDiCaL version: 2.1.3
% 2.32/0.65 % (3054374)Termination reason: Instruction limit
% 2.32/0.65 % (3054374)Termination phase: Preprocessing 2
% 2.32/0.65 % (3054374)Time elapsed: 0.010 s
% 2.32/0.65 % (3054374)Peak memory usage: 11 MB
% 2.32/0.65 % (3054374)Instructions burned: 43 (million)
% 2.32/0.65 % (3054382)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.32/0.65 % (3054382)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2674960256:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.32/0.65 % (3054387)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=394044191:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.32/0.65 % (3054382)Instruction limit reached!
% 2.32/0.65 % (3054382)------------------------------
% 2.32/0.65 % (3054382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.65 % (3054382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.65 % (3054382)CaDiCaL version: 2.1.3
% 2.32/0.65 % (3054382)Termination reason: Instruction limit
% 2.32/0.65 % (3054382)Termination phase: shuffling
% 2.48/0.74 % (3054382)Time elapsed: 0.004 s
% 2.48/0.74 % (3054382)Peak memory usage: 10 MB
% 2.48/0.74 % (3054382)Instructions burned: 9 (million)
% 2.48/0.74 % (3054393)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=2948947949: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)
% 2.48/0.74 % (3054365)Instruction limit reached!
% 2.48/0.74 % (3054365)------------------------------
% 2.48/0.74 % (3054365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054365)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054365)Termination reason: Instruction limit
% 2.48/0.74 % (3054365)Termination phase: Function definition elimination
% 2.48/0.74 % (3054365)Time elapsed: 0.062 s
% 2.48/0.74 % (3054365)Peak memory usage: 13 MB
% 2.48/0.74 % (3054365)Instructions burned: 144 (million)
% 2.48/0.74 % (3054387)Instruction limit reached!
% 2.48/0.74 % (3054387)------------------------------
% 2.48/0.74 % (3054387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054387)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054387)Termination reason: Instruction limit
% 2.48/0.74 % (3054387)Termination phase: Saturation
% 2.48/0.74 % (3054387)Time elapsed: 0.045 s
% 2.48/0.74 % (3054387)Peak memory usage: 13 MB
% 2.48/0.74 % (3054387)Instructions burned: 185 (million)
% 2.48/0.74 % (3054338)Instruction limit reached!
% 2.48/0.74 % (3054338)------------------------------
% 2.48/0.74 % (3054338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054338)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054338)Termination reason: Instruction limit
% 2.48/0.74 % (3054338)Termination phase: Saturation
% 2.48/0.74 % (3054338)Time elapsed: 0.152 s
% 2.48/0.74 % (3054338)Peak memory usage: 16 MB
% 2.48/0.74 % (3054338)Instructions burned: 327 (million)
% 2.48/0.74 % (3054405)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.48/0.74 % (3054405)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4196187031:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.48/0.74 % (3054410)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1900272129:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.48/0.74 % (3054405)Instruction limit reached!
% 2.48/0.74 % (3054405)------------------------------
% 2.48/0.74 % (3054405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054405)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054405)Termination reason: Instruction limit
% 2.48/0.74 % (3054405)Termination phase: shuffling
% 2.48/0.74 % (3054405)Time elapsed: 0.004 s
% 2.48/0.74 % (3054405)Peak memory usage: 10 MB
% 2.48/0.74 % (3054405)Instructions burned: 8 (million)
% 2.48/0.74 % (3054410)Instruction limit reached!
% 2.48/0.74 % (3054410)------------------------------
% 2.48/0.74 % (3054410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054410)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054410)Termination reason: Instruction limit
% 2.48/0.74 % (3054410)Termination phase: Property scanning
% 2.48/0.74 % (3054410)Time elapsed: 0.006 s
% 2.48/0.74 % (3054410)Peak memory usage: 10 MB
% 2.48/0.74 % (3054410)Instructions burned: 26 (million)
% 2.48/0.74 % (3054372)Instruction limit reached!
% 2.48/0.74 % (3054372)------------------------------
% 2.48/0.74 % (3054372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.48/0.74 % (3054372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/0.74 % (3054372)CaDiCaL version: 2.1.3
% 2.48/0.74 % (3054372)Termination reason: Instruction limit
% 2.48/0.74 % (3054372)Termination phase: Property scanning
% 2.48/0.74 % (3054372)Time elapsed: 0.081 s
% 2.48/0.74 % (3054372)Peak memory usage: 13 MB
% 2.48/0.74 % (3054372)Instructions burned: 194 (million)
% 2.48/0.74 % (3054413)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1512278300:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 3.34/0.82 % (3054423)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=822295450: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)
% 3.34/0.82 % (3054413)Instruction limit reached!
% 3.34/0.82 % (3054413)------------------------------
% 3.34/0.82 % (3054413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.82 % (3054413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.82 % (3054413)CaDiCaL version: 2.1.3
% 3.34/0.82 % (3054413)Termination reason: Instruction limit
% 3.34/0.82 % (3054413)Termination phase: shuffling
% 3.34/0.82 % (3054413)Time elapsed: 0.009 s
% 3.34/0.82 % (3054413)Peak memory usage: 10 MB
% 3.34/0.82 % (3054413)Instructions burned: 20 (million)
% 3.34/0.82 % (3054421)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=2287679013:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.34/0.82 % (3054426)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=3971245185: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)
% 3.34/0.82 % (3054393)Instruction limit reached!
% 3.34/0.82 % (3054393)------------------------------
% 3.34/0.82 % (3054393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.82 % (3054393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.82 % (3054393)CaDiCaL version: 2.1.3
% 3.34/0.82 % (3054393)Termination reason: Instruction limit
% 3.34/0.82 % (3054393)Termination phase: Property scanning
% 3.34/0.82 % (3054393)Time elapsed: 0.073 s
% 3.34/0.82 % (3054393)Peak memory usage: 13 MB
% 3.34/0.82 % (3054393)Instructions burned: 171 (million)
% 3.34/0.82 % (3054434)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1780414897:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.34/0.82 % (3054426)Instruction limit reached!
% 3.34/0.82 % (3054426)------------------------------
% 3.34/0.82 % (3054426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.82 % (3054426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.82 % (3054426)CaDiCaL version: 2.1.3
% 3.34/0.82 % (3054426)Termination reason: Instruction limit
% 3.34/0.82 % (3054426)Termination phase: SInE selection
% 3.34/0.82 % (3054426)Time elapsed: 0.019 s
% 3.34/0.82 % (3054426)Peak memory usage: 10 MB
% 3.34/0.82 % (3054426)Instructions burned: 45 (million)
% 3.34/0.82 % (3054446)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=867864920: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)
% 3.34/0.82 % (3054455)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.34/0.82 % (3054446)Instruction limit reached!
% 3.34/0.82 % (3054446)------------------------------
% 3.34/0.82 % (3054446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.82 % (3054446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/0.82 % (3054446)CaDiCaL version: 2.1.3
% 3.34/0.82 % (3054446)Termination reason: Instruction limit
% 3.34/0.82 % (3054446)Termination phase: shuffling
% 3.34/0.82 % (3054446)Time elapsed: 0.009 s
% 3.34/0.82 % (3054446)Peak memory usage: 10 MB
% 3.34/0.82 % (3054446)Instructions burned: 22 (million)
% 3.34/0.82 % (3054455)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=426117081:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.34/0.82 % (3054464)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3418932792:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.34/0.82 % (3054307)Instruction limit reached!
% 3.34/0.82 % (3054307)------------------------------
% 3.34/0.82 % (3054307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.34/0.82 % (3054307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054307)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054307)Termination reason: Instruction limit
% 4.05/0.94 % (3054307)Termination phase: Saturation
% 4.05/0.94 % (3054307)Time elapsed: 0.336 s
% 4.05/0.94 % (3054307)Peak memory usage: 19 MB
% 4.05/0.94 % (3054307)Instructions burned: 635 (million)
% 4.05/0.94 % (3054464)Instruction limit reached!
% 4.05/0.94 % (3054464)------------------------------
% 4.05/0.94 % (3054464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/0.94 % (3054464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054464)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054464)Termination reason: Instruction limit
% 4.05/0.94 % (3054464)Termination phase: shuffling
% 4.05/0.94 % (3054464)Time elapsed: 0.006 s
% 4.05/0.94 % (3054464)Peak memory usage: 10 MB
% 4.05/0.94 % (3054464)Instructions burned: 13 (million)
% 4.05/0.94 % (3054469)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=2870488302:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.05/0.94 % (3054471)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1980367250:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 4.05/0.94 % (3054471)Instruction limit reached!
% 4.05/0.94 % (3054471)------------------------------
% 4.05/0.94 % (3054471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/0.94 % (3054471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054471)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054471)Termination reason: Instruction limit
% 4.05/0.94 % (3054471)Termination phase: Preprocessing 3
% 4.05/0.94 % (3054471)Time elapsed: 0.024 s
% 4.05/0.94 % (3054471)Peak memory usage: 11 MB
% 4.05/0.94 % (3054471)Instructions burned: 52 (million)
% 4.05/0.94 % (3054469)Instruction limit reached!
% 4.05/0.94 % (3054469)------------------------------
% 4.05/0.94 % (3054469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/0.94 % (3054469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054469)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054469)Termination reason: Instruction limit
% 4.05/0.94 % (3054469)Termination phase: SInE selection
% 4.05/0.94 % (3054469)Time elapsed: 0.028 s
% 4.05/0.94 % (3054469)Peak memory usage: 11 MB
% 4.05/0.94 % (3054469)Instructions burned: 67 (million)
% 4.05/0.94 % (3054455)Instruction limit reached!
% 4.05/0.94 % (3054455)------------------------------
% 4.05/0.94 % (3054455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/0.94 % (3054455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054455)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054455)Termination reason: Instruction limit
% 4.05/0.94 % (3054455)Termination phase: Saturation
% 4.05/0.94 % (3054455)Time elapsed: 0.084 s
% 4.05/0.94 % (3054455)Peak memory usage: 14 MB
% 4.05/0.94 % (3054455)Instructions burned: 200 (million)
% 4.05/0.94 % (3054487)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1756865844:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 4.05/0.94 % (3054488)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=411734215:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.05/0.94 % (3054434)Refutation not found, incomplete strategy
% 4.05/0.94 % (3054434)------------------------------
% 4.05/0.94 % (3054434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.05/0.94 % (3054434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/0.94 % (3054434)CaDiCaL version: 2.1.3
% 4.05/0.94 % (3054434)Termination reason: Refutation not found, incomplete strategy
% 4.05/0.94 % (3054434)Time elapsed: 0.125 s
% 4.05/0.94 % (3054434)Peak memory usage: 16 MB
% 4.05/0.94 % (3054434)Instructions burned: 271 (million)
% 4.05/0.94 % (3054434)------------------------------
% 4.05/0.94 % (3054434)------------------------------
% 4.05/0.94 % (3054490)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=1299972314:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.05/0.94 % (3054487)Instruction limit reached!
% 4.05/0.94 % (3054487)------------------------------
% 4.05/0.94 % (3054487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054487)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054487)Termination reason: Instruction limit
% 6.07/1.21 % (3054487)Termination phase: Property scanning
% 6.07/1.21 % (3054487)Time elapsed: 0.022 s
% 6.07/1.21 % (3054487)Peak memory usage: 10 MB
% 6.07/1.21 % (3054487)Instructions burned: 32 (million)
% 6.07/1.21 % (3054500)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3702558502:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 6.07/1.21 % (3054490)Instruction limit reached!
% 6.07/1.21 % (3054490)------------------------------
% 6.07/1.21 % (3054490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054490)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054490)Termination reason: Instruction limit
% 6.07/1.21 % (3054490)Termination phase: Property scanning
% 6.07/1.21 % (3054490)Time elapsed: 0.016 s
% 6.07/1.21 % (3054490)Peak memory usage: 10 MB
% 6.07/1.21 % (3054490)Instructions burned: 36 (million)
% 6.07/1.21 % (3054421)Instruction limit reached!
% 6.07/1.21 % (3054421)------------------------------
% 6.07/1.21 % (3054421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054421)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054421)Termination reason: Instruction limit
% 6.07/1.21 % (3054421)Termination phase: Saturation
% 6.07/1.21 % (3054421)Time elapsed: 0.171 s
% 6.07/1.21 % (3054421)Peak memory usage: 15 MB
% 6.07/1.21 % (3054421)Instructions burned: 319 (million)
% 6.07/1.21 % (3054507)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.07/1.21 % (3054507)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2694607441:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 6.07/1.21 % (3054512)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=5167230:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 6.07/1.21 % (3054513)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2971437408:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 6.07/1.21 % (3054500)Instruction limit reached!
% 6.07/1.21 % (3054500)------------------------------
% 6.07/1.21 % (3054500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054500)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054500)Termination reason: Instruction limit
% 6.07/1.21 % (3054500)Termination phase: Preprocessing 3
% 6.07/1.21 % (3054500)Time elapsed: 0.030 s
% 6.07/1.21 % (3054500)Peak memory usage: 12 MB
% 6.07/1.21 % (3054500)Instructions burned: 69 (million)
% 6.07/1.21 % (3054488)Instruction limit reached!
% 6.07/1.21 % (3054488)------------------------------
% 6.07/1.21 % (3054488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054488)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054488)Termination reason: Instruction limit
% 6.07/1.21 % (3054488)Termination phase: Property scanning
% 6.07/1.21 % (3054488)Time elapsed: 0.062 s
% 6.07/1.21 % (3054488)Peak memory usage: 12 MB
% 6.07/1.21 % (3054488)Instructions burned: 137 (million)
% 6.07/1.21 % (3054522)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=183573762:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 6.07/1.21 % (3054521)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1549934457:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 6.07/1.21 % (3054513)Instruction limit reached!
% 6.07/1.21 % (3054513)------------------------------
% 6.07/1.21 % (3054513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.07/1.21 % (3054513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.07/1.21 % (3054513)CaDiCaL version: 2.1.3
% 6.07/1.21 % (3054513)Termination reason: Instruction limit
% 6.07/1.21 % (3054513)Termination phase: Property scanning
% 6.07/1.21 % (3054513)Time elapsed: 0.043 s
% 6.07/1.21 % (3054513)Peak memory usage: 13 MB
% 6.44/1.36 % (3054513)Instructions burned: 96 (million)
% 6.44/1.36 % (3054423)Instruction limit reached!
% 6.44/1.36 % (3054423)------------------------------
% 6.44/1.36 % (3054423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054423)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054423)Termination reason: Instruction limit
% 6.44/1.36 % (3054423)Termination phase: Saturation
% 6.44/1.36 % (3054423)Time elapsed: 0.241 s
% 6.44/1.36 % (3054423)Peak memory usage: 19 MB
% 6.44/1.36 % (3054423)Instructions burned: 854 (million)
% 6.44/1.36 % (3054534)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1687527854:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 6.44/1.36 % (3054533)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2115451385:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 6.44/1.36 % (3054507)Instruction limit reached!
% 6.44/1.36 % (3054507)------------------------------
% 6.44/1.36 % (3054507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054507)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054507)Termination reason: Instruction limit
% 6.44/1.36 % (3054507)Termination phase: Saturation
% 6.44/1.36 % (3054507)Time elapsed: 0.084 s
% 6.44/1.36 % (3054507)Peak memory usage: 12 MB
% 6.44/1.36 % (3054507)Instructions burned: 180 (million)
% 6.44/1.36 % (3054534)Instruction limit reached!
% 6.44/1.36 % (3054534)------------------------------
% 6.44/1.36 % (3054534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054534)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054534)Termination reason: Instruction limit
% 6.44/1.36 % (3054534)Termination phase: Saturation
% 6.44/1.36 % (3054534)Time elapsed: 0.032 s
% 6.44/1.36 % (3054534)Peak memory usage: 13 MB
% 6.44/1.36 % (3054534)Instructions burned: 132 (million)
% 6.44/1.36 % (3054547)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2887055980:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 6.44/1.36 % (3054512)Instruction limit reached!
% 6.44/1.36 % (3054512)------------------------------
% 6.44/1.36 % (3054512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054512)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054512)Termination reason: Instruction limit
% 6.44/1.36 % (3054512)Termination phase: Saturation
% 6.44/1.36 % (3054512)Time elapsed: 0.107 s
% 6.44/1.36 % (3054512)Peak memory usage: 15 MB
% 6.44/1.36 % (3054512)Instructions burned: 247 (million)
% 6.44/1.36 % (3054547)Instruction limit reached!
% 6.44/1.36 % (3054547)------------------------------
% 6.44/1.36 % (3054547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054547)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054547)Termination reason: Instruction limit
% 6.44/1.36 % (3054547)Termination phase: Property scanning
% 6.44/1.36 % (3054547)Time elapsed: 0.022 s
% 6.44/1.36 % (3054547)Peak memory usage: 10 MB
% 6.44/1.36 % (3054547)Instructions burned: 44 (million)
% 6.44/1.36 % (3054548)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4105314782:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 6.44/1.36 % (3054554)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=119129138:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.44/1.36 % (3054567)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2381343408:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 6.44/1.36 % (3054567)Instruction limit reached!
% 6.44/1.36 % (3054567)------------------------------
% 6.44/1.36 % (3054567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054567)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054567)Termination reason: Instruction limit
% 6.44/1.36 % (3054567)Termination phase: Property scanning
% 6.44/1.36 % (3054567)Time elapsed: 0.024 s
% 6.44/1.36 % (3054567)Peak memory usage: 13 MB
% 6.44/1.36 % (3054567)Instructions burned: 99 (million)
% 6.44/1.36 % (3054577)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=811556518:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 6.44/1.36 % (3054577)Instruction limit reached!
% 6.44/1.36 % (3054577)------------------------------
% 6.44/1.36 % (3054577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054577)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054577)Termination reason: Instruction limit
% 6.44/1.36 % (3054577)Termination phase: Property scanning
% 6.44/1.36 % (3054577)Time elapsed: 0.015 s
% 6.44/1.36 % (3054577)Peak memory usage: 11 MB
% 6.44/1.36 % (3054577)Instructions burned: 67 (million)
% 6.44/1.36 % (3054580)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1235104660:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 6.44/1.36 % (3054580)Instruction limit reached!
% 6.44/1.36 % (3054580)------------------------------
% 6.44/1.36 % (3054580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054580)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054580)Termination reason: Instruction limit
% 6.44/1.36 % (3054580)Termination phase: Saturation
% 6.44/1.36 % (3054580)Time elapsed: 0.024 s
% 6.44/1.36 % (3054580)Peak memory usage: 12 MB
% 6.44/1.36 % (3054580)Instructions burned: 107 (million)
% 6.44/1.36 % (3054584)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3268012988:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 6.44/1.36 % (3054521)Instruction limit reached!
% 6.44/1.36 % (3054521)------------------------------
% 6.44/1.36 % (3054521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054521)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054521)Termination reason: Instruction limit
% 6.44/1.36 % (3054521)Termination phase: Saturation
% 6.44/1.36 % (3054521)Time elapsed: 0.264 s
% 6.44/1.36 % (3054521)Peak memory usage: 14 MB
% 6.44/1.36 % (3054521)Instructions burned: 427 (million)
% 6.44/1.36 % (3054364)Instruction limit reached!
% 6.44/1.36 % (3054364)------------------------------
% 6.44/1.36 % (3054364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054364)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054364)Termination reason: Instruction limit
% 6.44/1.36 % (3054364)Termination phase: Saturation
% 6.44/1.36 % (3054364)Time elapsed: 0.596 s
% 6.44/1.36 % (3054364)Peak memory usage: 14 MB
% 6.44/1.36 % (3054364)Instructions burned: 1241 (million)
% 6.44/1.36 % (3054590)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2725862549:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.44/1.36 % (3054592)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=623323289:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 6.44/1.36 % (3054533)Instruction limit reached!
% 6.44/1.36 % (3054533)------------------------------
% 6.44/1.36 % (3054533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054533)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054533)Termination reason: Instruction limit
% 6.44/1.36 % (3054533)Termination phase: Saturation
% 6.44/1.36 % (3054533)Time elapsed: 0.341 s
% 6.44/1.36 % (3054533)Peak memory usage: 18 MB
% 6.44/1.36 % (3054533)Instructions burned: 516 (million)
% 6.44/1.36 % (3054602)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=3118662795:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 6.44/1.36 % (3054602)Instruction limit reached!
% 6.44/1.36 % (3054602)------------------------------
% 6.44/1.36 % (3054602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054602)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054602)Termination reason: Instruction limit
% 6.44/1.36 % (3054602)Termination phase: Property scanning
% 6.44/1.36 % (3054602)Time elapsed: 0.027 s
% 6.44/1.36 % (3054602)Peak memory usage: 10 MB
% 6.44/1.36 % (3054602)Instructions burned: 34 (million)
% 6.44/1.36 % (3054554) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3054299-3054554"...
% 6.44/1.36 % (3054606)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1894200233:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 6.44/1.36 % (3054606)Instruction limit reached!
% 6.44/1.36 % (3054606)------------------------------
% 6.44/1.36 % (3054606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.36 % (3054606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.36 % (3054606)CaDiCaL version: 2.1.3
% 6.44/1.36 % (3054606)Termination reason: Instruction limit
% 6.44/1.36 % (3054606)Termination phase: Preprocessing 3
% 6.44/1.36 % (3054606)Time elapsed: 0.075 s
% 6.44/1.36 % (3054606)Peak memory usage: 13 MB
% 6.44/1.36 % (3054606)Instructions burned: 91 (million)
% 6.44/1.36 % (3054554)...printing done.
% 6.44/1.36 % (3054554)Refutation found. Thanks to Tanya!
% 6.44/1.36 % SZS status Theorem for theBenchmark
% 6.44/1.36 % SZS output start Proof for theBenchmark
% 6.44/1.36 thf(type_def_5, type, term: $tType).
% 6.44/1.36 thf(type_def_6, type, subst: $tType).
% 6.44/1.36 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.44/1.36 thf(type_def_8, type, d_term: $tType).
% 6.44/1.36 thf(type_def_9, type, d_subst: $tType).
% 6.44/1.36 thf(func_def_0, type, one: term).
% 6.44/1.36 thf(func_def_1, type, ap: (term > term > term)).
% 6.44/1.36 thf(func_def_2, type, lam: (term > term)).
% 6.44/1.36 thf(func_def_3, type, sub: (term > subst > term)).
% 6.44/1.36 thf(func_def_4, type, id: subst).
% 6.44/1.36 thf(func_def_5, type, sh: subst).
% 6.44/1.36 thf(func_def_6, type, push: (term > subst > subst)).
% 6.44/1.36 thf(func_def_7, type, comp: (subst > subst > subst)).
% 6.44/1.36 thf(func_def_8, type, var: (term > $o)).
% 6.44/1.36 thf(func_def_9, type, pushprop_lem1v2: $o).
% 6.44/1.36 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 6.44/1.36 thf(func_def_11, type, axmap: $o).
% 6.44/1.36 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 6.44/1.36 thf(func_def_13, type, shinj: $o).
% 6.44/1.36 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 6.44/1.36 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 6.44/1.36 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 6.44/1.36 thf(func_def_17, type, induction2lem: $o).
% 6.44/1.36 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 6.44/1.36 thf(func_def_19, type, axvarshift: $o).
% 6.44/1.36 thf(func_def_20, type, hoasapinj2: $o).
% 6.44/1.36 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 6.44/1.36 thf(func_def_22, type, hoasapinj1: $o).
% 6.44/1.36 thf(func_def_23, type, ulamvar1: $o).
% 6.44/1.36 thf(func_def_24, type, induction2lem_lthm: $o).
% 6.44/1.36 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 6.44/1.36 thf(func_def_26, type, apnotvar: $o).
% 6.44/1.36 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 6.44/1.36 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 6.44/1.36 thf(func_def_29, type, hoasinduction_lthm: $o).
% 6.44/1.36 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 6.44/1.36 thf(func_def_31, type, hoaslaminj: $o).
% 6.44/1.36 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 6.44/1.36 thf(func_def_33, type, induction2lem_gthm: $o).
% 6.44/1.36 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 6.44/1.36 thf(func_def_35, type, hoasinduction_lem3: $o).
% 6.44/1.36 thf(func_def_36, type, hoasinduction_lem2: $o).
% 6.44/1.36 thf(func_def_37, type, termmset_lthm: $o).
% 6.44/1.36 thf(func_def_38, type, hoasinduction_lem1: $o).
% 6.44/1.36 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 6.44/1.36 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 6.44/1.36 thf(func_def_41, type, hoasapnotvar: $o).
% 6.44/1.36 thf(func_def_42, type, hoasinduction_lem0: $o).
% 6.44/1.36 thf(func_def_43, type, hoasinduction: $o).
% 6.44/1.36 thf(func_def_44, type, hoasinduction_gthm: $o).
% 6.44/1.36 thf(func_def_45, type, axapp: $o).
% 6.44/1.36 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 6.44/1.36 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 6.44/1.36 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 6.44/1.36 thf(func_def_49, type, ulamvarind: $o).
% 6.44/1.36 thf(func_def_50, type, induction: $o).
% 6.44/1.36 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 6.44/1.36 thf(func_def_52, type, termmset_gthm: $o).
% 6.44/1.36 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 6.44/1.36 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 6.44/1.36 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 6.44/1.36 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 6.44/1.36 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 6.44/1.36 thf(func_def_58, type, pushprop_lem2v2: $o).
% 6.44/1.36 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 6.44/1.36 thf(func_def_60, type, axclos: $o).
% 6.44/1.36 thf(func_def_61, type, axassoc: $o).
% 6.44/1.36 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 6.44/1.36 thf(func_def_63, type, pushprop_lthm: $o).
% 6.44/1.36 thf(func_def_64, type, apinj2: $o).
% 6.44/1.36 thf(func_def_65, type, apinj1: $o).
% 6.44/1.36 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 6.44/1.36 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 6.44/1.36 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 6.44/1.36 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 6.44/1.36 thf(func_def_70, type, axvarcons: $o).
% 6.44/1.36 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 6.44/1.36 thf(func_def_72, type, axscons: $o).
% 6.44/1.36 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 6.44/1.36 thf(func_def_74, type, axidr: $o).
% 6.44/1.36 thf(func_def_75, type, pushprop_lem1: $o).
% 6.44/1.36 thf(func_def_76, type, laminj: $o).
% 6.44/1.36 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 6.44/1.36 thf(func_def_78, type, pushprop_lem0: $o).
% 6.44/1.36 thf(func_def_79, type, pushprop_gthm: $o).
% 6.44/1.36 thf(func_def_80, type, axabs: $o).
% 6.44/1.36 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 6.44/1.36 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 6.44/1.36 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 6.44/1.36 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 6.44/1.36 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 6.44/1.36 thf(func_def_86, type, lamnotap: $o).
% 6.44/1.36 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 6.44/1.36 thf(func_def_88, type, hoaslamnotvar: $o).
% 6.44/1.36 thf(func_def_89, type, axidl: $o).
% 6.44/1.36 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 6.44/1.36 thf(func_def_91, type, induction2_lthm: $o).
% 6.44/1.36 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 6.44/1.36 thf(func_def_93, type, substmonoid_lthm: $o).
% 6.44/1.36 thf(func_def_94, type, pushprop: $o).
% 6.44/1.36 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 6.44/1.36 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 6.44/1.36 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 6.44/1.36 thf(func_def_98, type, substmonoid: $o).
% 6.44/1.36 thf(func_def_99, type, lamnotvar: $o).
% 6.44/1.36 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 6.44/1.36 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 6.44/1.36 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 6.44/1.36 thf(func_def_103, type, induction2_gthm: $o).
% 6.44/1.36 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 6.44/1.36 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_106, type, hoaslamnotap: $o).
% 6.44/1.36 thf(func_def_107, type, substmonoid_gthm: $o).
% 6.44/1.36 thf(func_def_108, type, ulamvarsh: $o).
% 6.44/1.36 thf(func_def_109, type, induction2: $o).
% 6.44/1.36 thf(func_def_110, type, pushprop_lem3v2: $o).
% 6.44/1.36 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 6.44/1.36 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 6.44/1.36 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 6.44/1.36 thf(func_def_114, type, axshiftcons: $o).
% 6.44/1.36 thf(func_def_115, type, termmset: $o).
% 6.44/1.36 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 6.44/1.36 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 6.44/1.36 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 6.44/1.36 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 6.44/1.36 thf(func_def_120, type, axvarid: $o).
% 6.44/1.36 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 6.44/1.36 thf(func_def_122, type, d2term: (d_term > term)).
% 6.44/1.36 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 6.44/1.36 thf(func_def_124, type, d_one: d_term).
% 6.44/1.36 thf(func_def_125, type, d_id: d_subst).
% 6.44/1.36 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.44/1.36 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 6.44/1.36 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 6.44/1.36 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 6.44/1.36 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.44/1.36 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.44/1.36 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 6.44/1.36 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 6.44/1.36 thf(func_def_137, type, vIMP: ($o > $o > $o)).
% 6.44/1.36 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_139, type, sP1: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_140, type, sP2: $o).
% 6.44/1.36 thf(func_def_141, type, sP3: $o).
% 6.44/1.36 thf(func_def_142, type, sP4: $o).
% 6.44/1.36 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_145, type, sP7: $o).
% 6.44/1.36 thf(func_def_146, type, sP8: $o).
% 6.44/1.36 thf(func_def_147, type, sP9: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_148, type, sP10: $o).
% 6.44/1.36 thf(func_def_149, type, sP11: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_150, type, sP12: $o).
% 6.44/1.36 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_152, type, sP14: $o).
% 6.44/1.36 thf(func_def_153, type, sP15: $o).
% 6.44/1.36 thf(func_def_154, type, sP16: $o).
% 6.44/1.36 thf(func_def_155, type, sP17: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_156, type, sP18: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_157, type, sP19: $o).
% 6.44/1.36 thf(func_def_158, type, sP20: $o).
% 6.44/1.36 thf(func_def_159, type, sP21: $o).
% 6.44/1.36 thf(func_def_160, type, sP22: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_161, type, sP23: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_162, type, sP24: $o).
% 6.44/1.36 thf(func_def_163, type, sP25: $o).
% 6.44/1.36 thf(func_def_164, type, sP26: $o).
% 6.44/1.36 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_166, type, sP28: $o).
% 6.44/1.36 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_168, type, sP30: $o).
% 6.44/1.36 thf(func_def_169, type, sP31: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_170, type, sP32: $o).
% 6.44/1.36 thf(func_def_171, type, sP33: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_172, type, sP34: $o).
% 6.44/1.36 thf(func_def_173, type, sP35: $o).
% 6.44/1.36 thf(func_def_174, type, sP36: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_176, type, sP38: $o).
% 6.44/1.36 thf(func_def_177, type, sP39: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_180, type, sP42: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_182, type, sP44: $o).
% 6.44/1.36 thf(func_def_183, type, sP45: $o).
% 6.44/1.36 thf(func_def_184, type, sP46: $o).
% 6.44/1.36 thf(func_def_185, type, sP47: $o).
% 6.44/1.36 thf(func_def_186, type, sP48: $o).
% 6.44/1.36 thf(func_def_187, type, sP49: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_189, type, sP51: ((term > $o) > $o)).
% 6.44/1.36 thf(func_def_190, type, sP52: $o).
% 6.44/1.36 thf(func_def_191, type, sP53: $o).
% 6.44/1.36 thf(func_def_192, type, sP54: $o).
% 6.44/1.36 thf(func_def_193, type, sP55: $o).
% 6.44/1.36 thf(func_def_194, type, sP56: $o).
% 6.44/1.36 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 6.44/1.36 thf(func_def_196, type, sP58: $o).
% 6.44/1.36 thf(func_def_197, type, sK59: term).
% 6.44/1.36 thf(func_def_198, type, sK60: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_199, type, sK61: (term > $o)).
% 6.44/1.36 thf(func_def_200, type, sK62: term).
% 6.44/1.36 thf(func_def_201, type, sK63: ((term > $o) > term > term)).
% 6.44/1.36 thf(func_def_202, type, sK64: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_203, type, sK65: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_206, type, sK68: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_208, type, sK70: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_209, type, sK71: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_210, type, sK72: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_211, type, sK73: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_212, type, sK74: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_213, type, sK75: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_214, type, sK76: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_215, type, sK77: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_216, type, sK78: (term > subst > term > term)).
% 6.44/1.36 thf(func_def_217, type, sK79: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_218, type, sK80: (term > $o)).
% 6.44/1.36 thf(func_def_219, type, sK81: term).
% 6.44/1.36 thf(func_def_220, type, sK82: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_221, type, sK83: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_222, type, sK84: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_223, type, sK85: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_224, type, sK86: term).
% 6.44/1.36 thf(func_def_225, type, sK87: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_226, type, sK88: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_227, type, sK89: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_228, type, sK90: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_229, type, sK91: (term > (term > $o) > term)).
% 6.44/1.36 thf(func_def_230, type, sK92: term).
% 6.44/1.36 thf(func_def_231, type, sK93: term).
% 6.44/1.36 thf(func_def_232, type, sK94: (subst > term > term)).
% 6.44/1.36 thf(func_def_233, type, sK95: subst).
% 6.44/1.36 thf(func_def_234, type, sK96: (subst > term > term)).
% 6.44/1.36 thf(func_def_235, type, sK97: subst).
% 6.44/1.36 thf(func_def_236, type, sK98: term).
% 6.44/1.36 thf(func_def_237, type, sK99: subst).
% 6.44/1.36 thf(func_def_238, type, sK100: term).
% 6.44/1.36 thf(func_def_239, type, sK101: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_240, type, sK102: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_241, type, sK103: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_242, type, sK104: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_243, type, sK105: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_244, type, sK106: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_245, type, sK107: term).
% 6.44/1.36 thf(func_def_246, type, sK108: term).
% 6.44/1.36 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > term > $o)).
% 6.44/1.36 thf(func_def_248, type, sK110: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_249, type, sK111: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_250, type, sK112: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_251, type, sK113: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_252, type, sK114: term).
% 6.44/1.36 thf(func_def_253, type, sK115: (term > $o)).
% 6.44/1.36 thf(func_def_254, type, sK116: (term > term)).
% 6.44/1.36 thf(func_def_255, type, sK117: term).
% 6.44/1.36 thf(func_def_256, type, sK118: term).
% 6.44/1.36 thf(func_def_257, type, sK119: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_267, type, sK129: ((term > $o) > term > term)).
% 6.44/1.36 thf(func_def_268, type, sK130: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_270, type, sK132: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_271, type, sK133: term).
% 6.44/1.36 thf(func_def_272, type, sK134: (term > $o)).
% 6.44/1.36 thf(func_def_273, type, sK135: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_274, type, sK136: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_275, type, sK137: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_276, type, sK138: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_277, type, sK139: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_278, type, sK140: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_281, type, sK143: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_282, type, sK144: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_283, type, sK145: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_284, type, sK146: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_286, type, sK148: term).
% 6.44/1.36 thf(func_def_287, type, sK149: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_288, type, sK150: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_290, type, sK152: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_291, type, sK153: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > term > term)).
% 6.44/1.36 thf(func_def_293, type, sK155: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_294, type, sK156: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_296, type, sK158: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_297, type, sK159: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_298, type, sK160: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_299, type, sK161: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_300, type, sK162: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_302, type, sK164: term).
% 6.44/1.36 thf(func_def_303, type, sK165: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_304, type, sK166: term).
% 6.44/1.36 thf(func_def_305, type, sK167: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_306, type, sK168: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_307, type, sK169: (term > $o)).
% 6.44/1.36 thf(func_def_308, type, sK170: term).
% 6.44/1.36 thf(func_def_309, type, sK171: (term > term)).
% 6.44/1.36 thf(func_def_310, type, sK172: term).
% 6.44/1.36 thf(func_def_311, type, sK173: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_319, type, sK181: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_320, type, sK182: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_322, type, sK184: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_323, type, sK185: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_324, type, sK186: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_325, type, sK187: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_327, type, sK189: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_329, type, sK191: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_330, type, sK192: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_331, type, sK193: term).
% 6.44/1.36 thf(func_def_332, type, sK194: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_333, type, sK195: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_334, type, sK196: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_335, type, sK197: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_336, type, sK198: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_337, type, sK199: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_342, type, sK204: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_343, type, sK205: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_344, type, sK206: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_345, type, sK207: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_346, type, sK208: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_347, type, sK209: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_348, type, sK210: term).
% 6.44/1.36 thf(func_def_349, type, sK211: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_350, type, sK212: ((subst > term > subst > $o) > term > term)).
% 6.44/1.36 thf(func_def_351, type, sK213: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_352, type, sK214: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_353, type, sK215: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_354, type, sK216: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_355, type, sK217: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_356, type, sK218: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_357, type, sK219: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_358, type, sK220: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_359, type, sK221: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_360, type, sK222: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_361, type, sK223: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_362, type, sK224: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_363, type, sK225: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_364, type, sK226: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_365, type, sK227: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_366, type, sK228: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_367, type, sK229: term).
% 6.44/1.36 thf(func_def_368, type, sK230: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_369, type, sK231: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_370, type, sK232: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_371, type, sK233: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_372, type, sK234: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_374, type, sK236: (term > $o)).
% 6.44/1.36 thf(func_def_375, type, sK237: term).
% 6.44/1.36 thf(func_def_376, type, sK238: (term > term)).
% 6.44/1.36 thf(func_def_377, type, sK239: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_378, type, sK240: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_379, type, sK241: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_380, type, sK242: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_381, type, sK243: subst).
% 6.44/1.36 thf(func_def_382, type, sK244: (term > $o)).
% 6.44/1.36 thf(func_def_383, type, sK245: term).
% 6.44/1.36 thf(func_def_384, type, sK246: (term > term)).
% 6.44/1.36 thf(func_def_385, type, sK247: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_386, type, sK248: ((term > $o) > subst > term)).
% 6.44/1.36 thf(func_def_387, type, sK249: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_388, type, sK250: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_389, type, sK251: term).
% 6.44/1.36 thf(func_def_390, type, sK252: term).
% 6.44/1.36 thf(func_def_391, type, sK253: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_397, type, sK259: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_398, type, sK260: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_399, type, sK261: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_400, type, sK262: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_402, type, sK264: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_403, type, sK265: term).
% 6.44/1.36 thf(func_def_404, type, sK266: ((subst > term > term) > term > subst)).
% 6.44/1.36 thf(func_def_405, type, sK267: ((subst > term > term) > term > subst)).
% 6.44/1.36 thf(func_def_406, type, sK268: ((subst > term > term) > term > term)).
% 6.44/1.36 thf(func_def_407, type, sK269: ((subst > term > term) > term > term)).
% 6.44/1.36 thf(func_def_408, type, sK270: ((subst > term > term) > term > subst)).
% 6.44/1.36 thf(func_def_409, type, sK271: ((subst > term > term) > term > subst)).
% 6.44/1.36 thf(func_def_410, type, sK272: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_411, type, sK273: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_412, type, sK274: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_413, type, sK275: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_414, type, sK276: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_415, type, sK277: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_416, type, sK278: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_417, type, sK279: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_418, type, sK280: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_419, type, sK281: ((subst > term > subst > $o) > term > $o)).
% 6.44/1.36 thf(func_def_420, type, sK282: term).
% 6.44/1.36 thf(func_def_421, type, sK283: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_422, type, sK284: term).
% 6.44/1.36 thf(func_def_423, type, sK285: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_424, type, sK286: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_425, type, sK287: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_427, type, sK289: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_428, type, sK290: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_429, type, sK291: (term > $o)).
% 6.44/1.36 thf(func_def_430, type, sK292: term).
% 6.44/1.36 thf(func_def_431, type, sK293: (term > term)).
% 6.44/1.36 thf(func_def_432, type, sK294: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_433, type, sK295: (term > (term > $o) > term)).
% 6.44/1.36 thf(func_def_434, type, sK296: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_435, type, sK297: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_436, type, sK298: (term > $o)).
% 6.44/1.36 thf(func_def_437, type, sK299: term).
% 6.44/1.36 thf(func_def_438, type, sK300: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_439, type, sK301: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_440, type, sK302: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_441, type, sK303: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_442, type, sK304: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_443, type, sK305: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_444, type, sK306: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_445, type, sK307: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_446, type, sK308: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_447, type, sK309: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_449, type, sK311: term).
% 6.44/1.36 thf(func_def_450, type, sK312: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_451, type, sK313: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_452, type, sK314: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_453, type, sK315: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_454, type, sK316: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_455, type, sK317: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_456, type, sK318: ((subst > term > subst > $o) > term > term)).
% 6.44/1.36 thf(func_def_457, type, sK319: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_458, type, sK320: ((term > $o) > subst > term)).
% 6.44/1.36 thf(func_def_459, type, sK321: term).
% 6.44/1.36 thf(func_def_460, type, sK322: subst).
% 6.44/1.36 thf(func_def_461, type, sK323: (term > $o)).
% 6.44/1.36 thf(func_def_462, type, sK324: term).
% 6.44/1.36 thf(func_def_463, type, sK325: (term > term)).
% 6.44/1.36 thf(func_def_464, type, sK326: (term > $o)).
% 6.44/1.36 thf(func_def_465, type, sK327: term).
% 6.44/1.36 thf(func_def_466, type, sK328: (term > term)).
% 6.44/1.36 thf(func_def_467, type, sK329: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_468, type, sK330: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_469, type, sK331: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_470, type, sK332: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_471, type, sK333: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_472, type, sK334: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_473, type, sK335: term).
% 6.44/1.36 thf(func_def_474, type, sK336: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_475, type, sK337: (term > $o)).
% 6.44/1.36 thf(func_def_476, type, sK338: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_477, type, sK339: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_478, type, sK340: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_479, type, sK341: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_480, type, sK342: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_481, type, sK343: ((term > $o) > term > term)).
% 6.44/1.36 thf(func_def_482, type, sK344: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_483, type, sK345: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_484, type, sK346: term).
% 6.44/1.36 thf(func_def_485, type, sK347: term).
% 6.44/1.36 thf(func_def_486, type, sK348: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_487, type, sK349: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_489, type, sK351: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_490, type, sK352: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_491, type, sK353: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_492, type, sK354: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_493, type, sK355: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_494, type, sK356: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_495, type, sK357: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_496, type, sK358: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_497, type, sK359: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_498, type, sK360: term).
% 6.44/1.36 thf(func_def_499, type, sK361: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_500, type, sK362: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_501, type, sK363: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_502, type, sK364: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_503, type, sK365: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_504, type, sK366: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_505, type, sK367: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_506, type, sK368: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_508, type, sK370: (term > $o)).
% 6.44/1.36 thf(func_def_509, type, sK371: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_510, type, sK372: term).
% 6.44/1.36 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.44/1.36 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_520, type, sK382: (term > (term > $o) > term)).
% 6.44/1.36 thf(func_def_521, type, sK383: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_522, type, sK384: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_523, type, sK385: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_524, type, sK386: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_526, type, sK388: term).
% 6.44/1.36 thf(func_def_527, type, sK389: term).
% 6.44/1.36 thf(func_def_528, type, sK390: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_529, type, sK391: (term > $o)).
% 6.44/1.36 thf(func_def_530, type, sK392: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_532, type, sK394: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_534, type, sK396: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_535, type, sK397: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_538, type, sK400: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_541, type, sK403: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_542, type, sK404: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_543, type, sK405: term).
% 6.44/1.36 thf(func_def_544, type, sK406: subst).
% 6.44/1.36 thf(func_def_545, type, sK407: (term > $o)).
% 6.44/1.36 thf(func_def_546, type, sK408: term).
% 6.44/1.36 thf(func_def_547, type, sK409: subst).
% 6.44/1.36 thf(func_def_548, type, sK410: term).
% 6.44/1.36 thf(func_def_549, type, sK411: subst).
% 6.44/1.36 thf(func_def_550, type, sK412: subst).
% 6.44/1.36 thf(func_def_551, type, sK413: (term > $o)).
% 6.44/1.36 thf(func_def_552, type, sK414: term).
% 6.44/1.36 thf(func_def_553, type, sK415: (term > term)).
% 6.44/1.36 thf(func_def_554, type, sK416: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_555, type, sK417: ((term > $o) > subst > term)).
% 6.44/1.36 thf(func_def_556, type, sK418: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_557, type, sK419: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_558, type, sK420: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_559, type, sK421: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_560, type, sK422: term).
% 6.44/1.36 thf(func_def_561, type, sK423: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_562, type, sK424: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_563, type, sK425: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_565, type, sK427: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_566, type, sK428: term).
% 6.44/1.36 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > term > term)).
% 6.44/1.36 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_569, type, sK431: (term > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_570, type, sK432: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_571, type, sK433: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_572, type, sK434: term).
% 6.44/1.36 thf(func_def_573, type, sK435: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_574, type, sK436: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_575, type, sK437: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_576, type, sK438: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_577, type, sK439: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_578, type, sK440: term).
% 6.44/1.36 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_585, type, sK447: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_588, type, sK450: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_589, type, sK451: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_590, type, sK452: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_591, type, sK453: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_592, type, sK454: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_593, type, sK455: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst > term > term)).
% 6.44/1.36 thf(func_def_595, type, sK457: subst).
% 6.44/1.36 thf(func_def_596, type, sK458: term).
% 6.44/1.36 thf(func_def_597, type, sK459: (subst > d_subst)).
% 6.44/1.36 thf(func_def_598, type, sK460: ((subst > term > subst > $o) > term > $o)).
% 6.44/1.36 thf(func_def_599, type, sK461: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_600, type, sK462: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_601, type, sK463: term).
% 6.44/1.36 thf(func_def_602, type, sK464: (term > subst > term > term)).
% 6.44/1.36 thf(func_def_603, type, sK465: ((term > $o) > term > subst > (term > $o) > term)).
% 6.44/1.36 thf(func_def_604, type, sK466: subst).
% 6.44/1.36 thf(func_def_605, type, sK467: term).
% 6.44/1.36 thf(func_def_606, type, sK468: (term > $o)).
% 6.44/1.36 thf(func_def_607, type, sK469: subst).
% 6.44/1.36 thf(func_def_608, type, sK470: term).
% 6.44/1.36 thf(func_def_609, type, sK471: (term > $o)).
% 6.44/1.36 thf(func_def_610, type, sK472: ((term > $o) > term > subst > term > $o)).
% 6.44/1.36 thf(func_def_611, type, sK473: subst).
% 6.44/1.36 thf(func_def_612, type, sK474: term).
% 6.44/1.36 thf(func_def_613, type, sK475: (term > $o)).
% 6.44/1.36 thf(func_def_614, type, sK476: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_615, type, sK477: term).
% 6.44/1.36 thf(func_def_616, type, sK478: (term > subst > term > term)).
% 6.44/1.36 thf(func_def_617, type, sK479: term).
% 6.44/1.36 thf(func_def_618, type, sK480: term).
% 6.44/1.36 thf(func_def_619, type, sK481: term).
% 6.44/1.36 thf(func_def_620, type, sK482: term).
% 6.44/1.36 thf(func_def_621, type, sK483: term).
% 6.44/1.36 thf(func_def_622, type, sK484: term).
% 6.44/1.36 thf(func_def_623, type, sK485: term).
% 6.44/1.36 thf(func_def_624, type, sK486: (term > $o)).
% 6.44/1.36 thf(func_def_625, type, sK487: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_626, type, sK488: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_627, type, sK489: subst).
% 6.44/1.36 thf(func_def_628, type, sK490: (subst > term > (term > $o) > (term > $o) > term)).
% 6.44/1.36 thf(func_def_629, type, sK491: (term > $o)).
% 6.44/1.36 thf(func_def_630, type, sK492: (term > $o)).
% 6.44/1.36 thf(func_def_631, type, sK493: term).
% 6.44/1.36 thf(func_def_632, type, sK494: subst).
% 6.44/1.36 thf(func_def_633, type, sK495: term).
% 6.44/1.36 thf(func_def_634, type, sK496: term).
% 6.44/1.36 thf(func_def_635, type, sK497: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_636, type, sK498: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_637, type, sK499: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_638, type, sK500: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_639, type, sK501: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_640, type, sK502: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_641, type, sK503: (subst > term > term)).
% 6.44/1.36 thf(func_def_642, type, sK504: (subst > term > term)).
% 6.44/1.36 thf(func_def_643, type, sK505: subst).
% 6.44/1.36 thf(func_def_644, type, sK506: term).
% 6.44/1.36 thf(func_def_645, type, sK507: subst).
% 6.44/1.36 thf(func_def_646, type, sK508: (term > $o)).
% 6.44/1.36 thf(func_def_647, type, sK509: term).
% 6.44/1.36 thf(func_def_648, type, sK510: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_649, type, sK511: (term > (term > $o) > subst > term > $o)).
% 6.44/1.36 thf(func_def_650, type, sK512: subst).
% 6.44/1.36 thf(func_def_651, type, sK513: subst).
% 6.44/1.36 thf(func_def_652, type, sK514: subst).
% 6.44/1.36 thf(func_def_653, type, sK515: term).
% 6.44/1.36 thf(func_def_654, type, sK516: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_655, type, sK517: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_656, type, sK518: (term > subst > term > term)).
% 6.44/1.36 thf(func_def_657, type, sK519: term).
% 6.44/1.36 thf(func_def_658, type, sK520: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_659, type, sK521: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_660, type, sK522: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_661, type, sK523: term).
% 6.44/1.36 thf(func_def_662, type, sK524: term).
% 6.44/1.36 thf(func_def_663, type, sK525: term).
% 6.44/1.36 thf(func_def_664, type, sK526: term).
% 6.44/1.36 thf(func_def_665, type, sK527: term).
% 6.44/1.36 thf(func_def_666, type, sK528: term).
% 6.44/1.36 thf(func_def_667, type, sK529: term).
% 6.44/1.36 thf(func_def_668, type, sK530: term).
% 6.44/1.36 thf(func_def_669, type, sK531: term).
% 6.44/1.36 thf(func_def_670, type, sK532: (term > $o)).
% 6.44/1.36 thf(func_def_671, type, sK533: (term > $o)).
% 6.44/1.36 thf(func_def_672, type, sK534: subst).
% 6.44/1.36 thf(func_def_673, type, sK535: term).
% 6.44/1.36 thf(func_def_674, type, sK536: term).
% 6.44/1.36 thf(func_def_675, type, sK537: term).
% 6.44/1.36 thf(func_def_676, type, sK538: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_677, type, sK539: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_678, type, sK540: (term > subst > term > term)).
% 6.44/1.36 thf(func_def_679, type, sK541: (term > $o)).
% 6.44/1.36 thf(func_def_680, type, sK542: subst).
% 6.44/1.36 thf(func_def_681, type, sK543: term).
% 6.44/1.36 thf(func_def_682, type, sK544: (term > $o)).
% 6.44/1.36 thf(func_def_683, type, sK545: term).
% 6.44/1.36 thf(func_def_684, type, sK546: term).
% 6.44/1.36 thf(func_def_685, type, sK547: subst).
% 6.44/1.36 thf(func_def_686, type, sK548: term).
% 6.44/1.36 thf(func_def_687, type, sK549: subst).
% 6.44/1.36 thf(func_def_688, type, sK550: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_689, type, sK551: ((term > $o) > term)).
% 6.44/1.36 thf(func_def_690, type, sK552: ((subst > term > subst > $o) > term > $o)).
% 6.44/1.36 thf(func_def_691, type, sK553: (term > d_term)).
% 6.44/1.36 thf(func_def_692, type, sK554: term).
% 6.44/1.36 thf(func_def_693, type, sK555: term).
% 6.44/1.36 thf(func_def_694, type, sK556: term).
% 6.44/1.36 thf(func_def_695, type, sK557: term).
% 6.44/1.36 thf(func_def_696, type, sK558: term).
% 6.44/1.36 thf(func_def_697, type, sK559: term).
% 6.44/1.36 thf(func_def_698, type, sK560: term).
% 6.44/1.36 thf(func_def_699, type, sK561: term).
% 6.44/1.36 thf(func_def_700, type, sK562: term).
% 6.44/1.36 thf(func_def_701, type, sK563: term).
% 6.44/1.36 thf(func_def_702, type, sK564: (subst > term > term)).
% 6.44/1.36 thf(func_def_703, type, sK565: term).
% 6.44/1.36 thf(func_def_704, type, sK566: term).
% 6.44/1.36 thf(func_def_705, type, sK567: ((subst > term > term) > term)).
% 6.44/1.36 thf(func_def_706, type, sK568: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_707, type, sK569: ((subst > term > term) > subst)).
% 6.44/1.36 thf(func_def_708, type, sK570: subst).
% 6.44/1.36 thf(func_def_709, type, sK571: subst).
% 6.44/1.36 thf(func_def_710, type, sK572: subst).
% 6.44/1.36 thf(func_def_711, type, sK573: subst).
% 6.44/1.36 thf(func_def_712, type, sK574: subst).
% 6.44/1.36 thf(func_def_713, type, sK575: term).
% 6.44/1.36 thf(func_def_714, type, sK576: subst).
% 6.44/1.36 thf(func_def_715, type, sK577: term).
% 6.44/1.36 thf(func_def_716, type, sK578: term).
% 6.44/1.36 thf(func_def_717, type, sK579: term).
% 6.44/1.36 thf(func_def_718, type, sK580: term).
% 6.44/1.36 thf(func_def_719, type, sK581: term).
% 6.44/1.36 thf(func_def_720, type, sK582: term).
% 6.44/1.36 thf(func_def_721, type, sK583: term).
% 6.44/1.36 thf(func_def_722, type, sK584: term).
% 6.44/1.36 thf(func_def_723, type, sK585: term).
% 6.44/1.36 thf(func_def_724, type, sK586: term).
% 6.44/1.36 thf(func_def_725, type, sK587: term).
% 6.44/1.36 thf(func_def_726, type, sK588: term).
% 6.44/1.36 thf(func_def_727, type, sK589: term).
% 6.44/1.36 thf(func_def_728, type, sK590: term).
% 6.44/1.36 thf(func_def_729, type, sF591: $o).
% 6.44/1.36 thf(func_def_730, type, sK592: (subst > term > subst > $o)).
% 6.44/1.36 thf(func_def_731, type, sK593: term).
% 6.44/1.36 thf(func_def_732, type, sK594: term).
% 6.44/1.36 thf(func_def_733, type, sK595: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_734, type, sK596: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_735, type, sK597: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_736, type, sK598: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_737, type, sK599: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_738, type, sK600: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_739, type, sK601: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_740, type, sK602: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_741, type, sK603: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_742, type, sK604: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_743, type, sK605: ((subst > term > subst > $o) > term)).
% 6.44/1.36 thf(func_def_744, type, sK606: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_745, type, sK607: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_746, type, sK608: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(func_def_747, type, sK609: ((subst > term > subst > $o) > subst)).
% 6.44/1.36 thf(f1,axiom,(
% 6.44/1.36 (shinj <=> ! [X15 : term,X13 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15))) & pushprop & pushprop_lem0_gthm & pushprop_lem3v2_lthm & (hoaslaminj <=> ! [X32 : subst,X33 : term,X18 : (subst > term > term),X31 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (one = ((d2term @ d_one))) & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & hoasinduction_lem3b_gthm & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X38 : subst,X36 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X39 : subst,X40 : term,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapnotvar_lthm & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [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))))) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) & hoasinduction_lem1v2 & pushprop_lem2v2_gthm & hoasinduction_lem3a_gthm & (! [X46 : term,X47 : term,X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & hoaslamnotvar_lthm & pushprop_lthm & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,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))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))))) & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ~ulamvar1 & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X33 : term,X32 : subst,X31 : (subst > term > term),X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((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) & (pushprop_lem1v2 <=> ! [X14 : subst,X10 : (term > $o),X11 : (term > $o),X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & axapp & (hoasinduction_lem3v2 <=> ! [X11 : (term > $o),X48 : term,X10 : (subst > term > subst > $o)] : (~ ! [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))) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & (sh = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & induction2lem_gthm & (apinj2 <=> ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & (! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_no_psi_cond) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (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)))))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) <=> hoasinduction_lthm_3) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoasinduction_lem1_lthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & pushprop_lem2v2_lthm & hoasapinj2_gthm & hoasinduction_lem1_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (induction2lem <=> ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X15 : term,X13 : term,X20 : term,X19 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)) <=> hoasapinj2) & ulamvarind & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (apinj1 <=> ! [X19 : term,X15 : term,X13 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15))) & ! [X1 : d_term] : (X1 = d_one) & pushprop_lem1_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3aa <=> ! [X42 : 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,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & axclos & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & (! [X19 : term,X13 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & hoaslamnotap_gthm & hoaslamnotvar & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapnotvar & hoasinduction_lem3_gthm & induction2_gthm & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X14 : subst,X25 : 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,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & apnotvar & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & hoaslaminj_gthm & axassoc & hoasapnotvar_gthm & ulamvarsh & substmonoid_gthm & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (hoasinduction_lem2v2 <=> ! [X11 : (term > $o),X44 : term,X45 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~(X11 @ X44) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (laminj <=> ! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & pushprop_lthm_orig & axvarshift & ! [X5 : d_subst] : (X5 = d_id) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & lamnotvar & hoasinduction_lem2_gthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X14 : subst,X26 : (term > $o),X10 : (term > $o),X13 : term,X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) <=> hoasinduction_lem2) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) <=> substmonoid) & (! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction) & (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [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)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (hoasapinj2_lthm <=> (! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & hoasinduction_lem1v2_gthm & ~lamnotap & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X21)) => ! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))))))) <=> induction2lem_lthm) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [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))) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id)))) <=> hoasinduction_lem3_lthm) & axmap & (! [X26 : (term > $o),X15 : term,X13 : term,X10 : (term > $o),X14 : subst] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))))) <=> hoasinduction_lem3a_lthm) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) <=> hoasinduction_lem3v2_lthm) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => ! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))))) <=> induction2_lthm) & termmset_gthm & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_gthm & hoasinduction_lem1 & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & (! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) <=> hoasinduction_lem3a) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & hoasinduction_lem3v2_gthm & axabs & (! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [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)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) <=> hoasinduction_lem3v2a) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & hoaslamnotap_lthm & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X14 : subst,X11 : (term > $o),X10 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one)))) & (induction <=> ! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))))) & (pushprop_lem0 <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (id = ((d2subst @ d_id))) & pushprop_gthm & pushprop_lem3v2 & hoasapinj1_gthm & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))),
% 6.44/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 6.44/1.36 thf(f2,conjecture,(
% 6.44/1.36 (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X3 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X3 : subst,X2 : term,X4 : subst,X1 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => ! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (ap @ X2 @ X5) @ id)))))) = hoasinduction_lem2)),
% 6.44/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2)).
% 6.44/1.36 thf(f3,negated_conjecture,(
% 6.44/1.36 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X3 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X3 : subst,X2 : term,X4 : subst,X1 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => ! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (ap @ X2 @ X5) @ id)))))) = hoasinduction_lem2)),
% 6.44/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 6.44/1.36 thf(f4,plain,(
% 6.44/1.36 (shinj <=> ! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1))) & pushprop & pushprop_lem0_gthm & pushprop_lem3v2_lthm & (hoaslaminj <=> ! [X2 : subst,X3 : term,X4 : (subst > term > term),X5 : (subst > term > term)] : ((((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ~ ! [X6 : subst,X7 : term,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6)))) | ~ ! [X9 : term,X10 : subst,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))))) & ! [X12 : d_subst,X13 : d_subst] : ((((d2subst @ X13)) = ((d2subst @ X12))) => (X12 = X13)) & (one = ((d2term @ d_one))) & ((! [X14 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X16 : subst,X17 : term] : (((X15 @ X16 @ X17)) = ((sub @ X14 @ (push @ X17 @ X16)))) => (! [X18 : term] : (((sub @ X18 @ id)) = X18) => ! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : ((X20 @ (lam @ X21)) | ~ ! [X22 : term] : (((X19 @ id @ X22 @ id)) = ((X20 @ X22))) | ~ ! [X23 : term] : ((X20 @ (sub @ X21 @ (push @ X23 @ id))) | ~(X20 @ X23)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X25 : subst,X26 : term,X27 : subst] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) | (X19 @ id @ (lam @ (X24 @ sh @ one)) @ id) | ~ ! [X28 : term] : ((X19 @ id @ (X24 @ id @ X28) @ id) | ~(X19 @ id @ X28 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & hoasinduction_lem3b_gthm & (hoasinduction_lem3aaa <=> ! [X29 : term,X30 : (subst > term > subst > $o)] : (~ ! [X31 : term] : ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id) | ~(X30 @ id @ X31 @ id)) | ~ ! [X32 : (subst > term > term),X33 : term] : (~ ! [X34 : subst,X35 : subst,X36 : term] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) | ~ ! [X37 : term] : ((X30 @ id @ (X32 @ id @ X37) @ id) | ~(X30 @ id @ X37 @ id)) | ~ ! [X38 : subst,X39 : term,X40 : subst] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) | (X30 @ id @ (lam @ (X32 @ sh @ one)) @ id)) | (X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))) & (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> axvarcons) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapnotvar_lthm & (hoasinduction_lthm <=> (! [X43 : (term > $o),X44 : term] : (~ ! [X45 : term] : ((X43 @ X45) | ~(var @ X45)) | ~ ! [X46 : term,X47 : term] : (~(X43 @ X47) | ~(X43 @ X46) | (X43 @ (ap @ X47 @ X46))) | (X43 @ X44) | ~ ! [X48 : term] : (~ ! [X49 : term] : ((X43 @ (sub @ X48 @ (push @ X49 @ id))) | ~(X43 @ X49)) | (X43 @ (lam @ X48)))) => (! [X50 : (subst > term > subst > $o),X51 : term,X52 : term] : (~ ! [X53 : term,X54 : term] : (~(X50 @ id @ X54 @ id) | ~(X50 @ id @ X53 @ id) | (X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) | ~(X50 @ id @ X51 @ id) | ~(X50 @ id @ X52 @ id) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : (~(X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57) | (X50 @ X56 @ X58 @ (comp @ X55 @ X57))) | (X50 @ id @ (ap @ X51 @ X52) @ id) | ~ ! [X59 : subst,X60 : subst,X61 : term,X62 : subst] : ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59) | ~(X50 @ X62 @ X61 @ (comp @ X60 @ X59)))) => (! [X63 : (subst > term > subst > $o),X64 : term] : ((X63 @ id @ (lam @ X64) @ id) | ~ ! [X65 : subst,X66 : subst,X67 : term,X68 : subst] : ((X63 @ X66 @ X67 @ (comp @ X65 @ X68)) | ~(X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) | ~ ! [X69 : term] : (~(X63 @ id @ X69 @ id) | (X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id)) | ~ ! [X70 : (subst > term > term)] : ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id) | ~ ! [X71 : term] : ((X63 @ id @ (X70 @ id @ X71) @ id) | ~(X63 @ id @ X71 @ id)) | ~ ! [X72 : term,X73 : subst,X74 : subst] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) = ((sub @ (X70 @ X74 @ X72) @ X73)))) | ~ ! [X75 : term,X76 : subst,X77 : subst,X78 : subst] : (~(X63 @ X78 @ X75 @ (comp @ X76 @ X77)) | (X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77))) => ! [X79 : (subst > term > subst > $o),X80 : term] : (~ ! [X81 : term] : ((X79 @ id @ X81 @ id) | ~(var @ (sub @ X81 @ id))) | ~ ! [X82 : (subst > term > term)] : (~ ! [X83 : subst,X84 : subst,X85 : term] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83))) | ~ ! [X86 : term] : ((X79 @ id @ (X82 @ id @ X86) @ id) | ~(X79 @ id @ X86 @ id)) | (X79 @ id @ (lam @ (X82 @ sh @ one)) @ id)) | (X79 @ id @ X80 @ id) | ~ ! [X87 : term,X88 : term] : (~(X79 @ id @ X87 @ id) | ~(X79 @ id @ X88 @ id) | (X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)) | ~ ! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : ((X79 @ X90 @ X91 @ (comp @ X92 @ X89)) | ~(X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) | ~ ! [X93 : subst,X94 : subst,X95 : term,X96 : subst] : (~(X79 @ X94 @ X95 @ (comp @ X93 @ X96)) | (X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96))))))) & hoasinduction_lem1v2 & pushprop_lem2v2_gthm & hoasinduction_lem3a_gthm & (! [X97 : term,X98 : term,X99 : (subst > term > term)] : (~ ! [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))) | (((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98)))) <=> hoaslamnotap) & (axidl <=> ! [X103 : subst] : (((comp @ id @ X103)) = X103)) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & hoaslamnotvar_lthm & pushprop_lthm & (hoasinduction_no_psi_cond_lthm <=> (! [X106 : (subst > term > subst > $o)] : ~ ! [X107 : (term > $o)] : ~ ! [X108 : term] : (((X106 @ id @ X108 @ id)) = ((X107 @ X108))) => (! [X109 : term,X110 : (term > $o)] : (~ ! [X111 : term] : (~ ! [X112 : term] : (~(X110 @ X112) | (X110 @ (sub @ X111 @ (push @ X112 @ id)))) | (X110 @ (lam @ X111))) | ~ ! [X113 : term,X114 : term] : ((X110 @ (ap @ X114 @ X113)) | ~(X110 @ X114) | ~(X110 @ X113)) | (X110 @ X109) | ~ ! [X115 : term] : (~(var @ X115) | (X110 @ X115))) => (! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X117 : term,X118 : (term > $o),X119 : (subst > term > subst > $o)] : ((X118 @ (lam @ X117)) | ~ ! [X120 : (subst > term > term)] : ((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id) | ~ ! [X121 : term,X122 : subst,X123 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) = ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122)))) | ~ ! [X124 : term] : (~(X119 @ id @ X124 @ id) | (X119 @ id @ (X120 @ id @ X124) @ id))) | ~ ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) | ~ ! [X126 : term] : ((X118 @ (sub @ X117 @ (push @ X126 @ id))) | ~(X118 @ X126))) => ! [X127 : (subst > term > subst > $o),X128 : term] : (~ ! [X129 : term,X130 : term] : (~(X127 @ id @ X129 @ id) | ~(X127 @ id @ X130 @ id) | (X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)) | (X127 @ id @ X128 @ id) | ~ ! [X131 : (subst > term > term)] : ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id) | ~ ! [X132 : term] : (~(X127 @ id @ X132 @ id) | (X127 @ id @ (X131 @ id @ X132) @ id)) | ~ ! [X133 : subst,X134 : term,X135 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133))))))))))) & (induction2 <=> ! [X136 : term,X137 : (term > $o)] : (~ ! [X138 : term,X139 : term] : (~(X137 @ X138) | ~(X137 @ X139) | (X137 @ (ap @ X139 @ X138))) | ~ ! [X140 : term] : (~ ! [X141 : term] : ((X137 @ (sub @ X140 @ (push @ X141 @ id))) | ~(X137 @ X141)) | (X137 @ (lam @ X140))) | ~ ! [X142 : term] : (~(var @ X142) | (X137 @ X142)) | (X137 @ X136))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ~ulamvar1 & ((! [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X145 : term,X146 : subst] : (((comp @ sh @ (push @ X145 @ X146))) = X146) => (! [X147 : term,X148 : term] : ((X147 = X148) | (((lam @ X147)) != ((lam @ X148)))) => ! [X149 : term,X150 : subst,X151 : (subst > term > term),X152 : (subst > term > term)] : (~ ! [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X151 @ X154 @ X155) @ X153)) = ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one)))) | (((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ~ ! [X156 : subst,X157 : term,X158 : subst] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) = ((sub @ (X152 @ X156 @ X157) @ X158))))))) <=> hoaslaminj_lthm) & (pushprop_lem1v2 <=> ! [X159 : subst,X160 : (term > $o),X161 : (term > $o),X162 : term] : (~(X160 @ X162) | (X161 @ one) | ~ ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163))))) & axapp & (hoasinduction_lem3v2 <=> ! [X164 : (term > $o),X165 : term,X166 : (subst > term > subst > $o)] : (~ ! [X167 : (subst > term > term)] : ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id) | ~ ! [X168 : subst,X169 : term,X170 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) | ~ ! [X171 : term] : (~(X166 @ id @ X171 @ id) | (X166 @ id @ (X167 @ id @ X171) @ id))) | ~ ! [X172 : term,X173 : subst,X174 : subst,X175 : subst] : (~(X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174) | (X166 @ X173 @ X172 @ (comp @ X175 @ X174))) | (X164 @ (lam @ X165)) | ~ ! [X176 : term] : ((X164 @ (sub @ X165 @ (push @ X176 @ id))) | ~(X164 @ X176)) | ~ ! [X177 : subst,X178 : subst,X179 : subst,X180 : term] : ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179) | ~(X166 @ X178 @ X180 @ (comp @ X177 @ X179))) | ~ ! [X181 : term] : (((X164 @ X181)) = ((X166 @ id @ X181 @ id))))) & (hoasapinj1_lthm <=> (! [X182 : term] : (((sub @ X182 @ id)) = X182) => (! [X183 : term,X184 : term,X185 : term,X186 : term] : ((((ap @ X183 @ X186)) != ((ap @ X185 @ X184))) | (X183 = X185)) => ! [X187 : term,X188 : term,X189 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190))))) & (sh = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & induction2lem_gthm & (apinj2 <=> ! [X191 : term,X192 : term,X193 : term,X194 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (! [X195 : term,X196 : (subst > term > subst > $o)] : ((X196 @ id @ X195 @ id) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~(X196 @ id @ X198 @ id) | (X196 @ id @ (X197 @ id @ X198) @ id)) | (X196 @ id @ (lam @ (X197 @ sh @ one)) @ id) | ~ ! [X199 : subst,X200 : term,X201 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))) | ~ ! [X202 : term,X203 : term] : ((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id) | ~(X196 @ id @ X203 @ id) | ~(X196 @ id @ X202 @ id))) <=> hoasinduction_no_psi_cond) & (! [X204 : term] : (((sub @ X204 @ id)) = X204) <=> axvarid) & ((! [X205 : (subst > term > subst > $o)] : ~ ! [X206 : (term > $o)] : ~ ! [X207 : term] : (((X205 @ id @ X207 @ id)) = ((X206 @ X207))) => (! [X208 : term,X209 : (term > $o)] : (~ ! [X210 : term] : ((X209 @ X210) | ~(var @ X210)) | ~ ! [X211 : term] : (~ ! [X212 : term] : ((X209 @ (sub @ X211 @ (push @ X212 @ id))) | ~(X209 @ X212)) | (X209 @ (lam @ X211))) | ~ ! [X213 : term,X214 : term] : (~(X209 @ X214) | (X209 @ (ap @ X214 @ X213)) | ~(X209 @ X213)) | (X209 @ X208)) => (! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X216 : (term > $o),X217 : term,X218 : (subst > term > subst > $o)] : (~ ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) | (X216 @ (lam @ X217)) | ~ ! [X220 : term] : ((X216 @ (sub @ X217 @ (push @ X220 @ id))) | ~(X216 @ X220)) | ~ ! [X221 : (subst > term > term)] : (~ ! [X222 : term] : (~(X218 @ id @ X222 @ id) | (X218 @ id @ (X221 @ id @ X222) @ id)) | (X218 @ id @ (lam @ (X221 @ sh @ one)) @ id) | ~ ! [X223 : subst,X224 : subst,X225 : term] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) = ((sub @ (X221 @ X223 @ X225) @ X224))))) => ! [X226 : term,X227 : (subst > term > subst > $o)] : ((X227 @ id @ X226 @ id) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : ((X227 @ X228 @ X231 @ (comp @ X229 @ X230)) | ~(X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) | ~ ! [X232 : term] : ((X227 @ id @ X232 @ id) | ~(var @ (sub @ X232 @ id))) | ~ ! [X233 : term,X234 : term] : (~(X227 @ id @ X233 @ id) | ~(X227 @ id @ X234 @ id) | (X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) | ~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term] : ((X227 @ id @ (X235 @ id @ X236) @ id) | ~(X227 @ id @ X236 @ id)) | (X227 @ id @ (lam @ (X235 @ sh @ one)) @ id) | ~ ! [X237 : subst,X238 : term,X239 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237)))) | ~ ! [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242) | ~(X227 @ X240 @ X241 @ (comp @ X243 @ X242)))))))) <=> hoasinduction_lthm_3) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & hoasinduction_lem1_lthm & (! [X246 : term] : ~ ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & pushprop_lem2v2_lthm & hoasapinj2_gthm & hoasinduction_lem1_gthm & (! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id))) <=> hoasinduction_lem0) & (induction2lem <=> ! [X251 : (term > $o),X252 : subst,X253 : term] : (~ ! [X254 : term] : ((X251 @ (lam @ X254)) | ~ ! [X255 : term] : ((X251 @ (sub @ X254 @ (push @ X255 @ id))) | ~(X251 @ X255))) | ~ ! [X256 : term,X257 : term] : (~(X251 @ X257) | (X251 @ (ap @ X256 @ X257)) | ~(X251 @ X256)) | ~ ! [X258 : term] : (~(var @ X258) | (X251 @ (sub @ X258 @ X252))) | (X251 @ (sub @ X253 @ X252)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X259 : term,X260 : term,X261 : term,X262 : term] : ((((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))) | (X261 = X262)) <=> hoasapinj2) & ulamvarind & ((^[X263 : subst, X264 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (apinj1 <=> ! [X265 : term,X266 : term,X267 : term,X268 : term] : ((((ap @ X266 @ X268)) != ((ap @ X267 @ X265))) | (X266 = X267))) & ! [X269 : d_term] : (d_one = X269) & pushprop_lem1_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3aa <=> ! [X270 : term,X271 : (subst > term > subst > $o)] : (~ ! [X272 : (subst > term > term)] : (~ ! [X273 : term] : (~(X271 @ id @ X273 @ id) | (X271 @ id @ (X272 @ id @ X273) @ id)) | (X271 @ id @ (lam @ (X272 @ sh @ one)) @ id) | ~ ! [X274 : subst,X275 : term,X276 : subst] : (((sub @ (X272 @ X274 @ X275) @ X276)) = ((X272 @ (comp @ X274 @ X276) @ (sub @ X275 @ X276))))) | ~ ! [X277 : term] : (~(X271 @ id @ X277 @ id) | (X271 @ id @ (sub @ X270 @ (push @ X277 @ id)) @ id)) | (X271 @ id @ (lam @ (sub @ X270 @ (push @ one @ sh))) @ id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & axclos & (! [X278 : term] : ~ ! [X279 : (subst > term > term)] : ~ ! [X280 : subst,X281 : term] : (((X279 @ X280 @ X281)) = ((sub @ X278 @ (push @ X281 @ X280)))) <=> hoasinduction_lem3v2_f) & (! [X282 : term,X283 : term,X284 : term,X285 : term] : ((X283 = X285) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X285 @ id) @ X284)))) <=> hoasapinj1) & hoaslamnotap_gthm & hoaslamnotvar & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapnotvar & hoasinduction_lem3_gthm & induction2_gthm & (hoasinduction_lem3 <=> ! [X286 : term,X287 : (subst > term > subst > $o)] : ((X287 @ id @ (lam @ X286) @ id) | ~ ! [X288 : term] : (~(X287 @ id @ X288 @ id) | (X287 @ id @ (sub @ X286 @ (push @ X288 @ id)) @ id)) | ~ ! [X289 : subst,X290 : subst,X291 : subst,X292 : term] : ((X287 @ X289 @ X292 @ (comp @ X291 @ X290)) | ~(X287 @ (comp @ X289 @ X291) @ (sub @ X292 @ X291) @ X290)) | ~ ! [X293 : (subst > term > term)] : (~ ! [X294 : subst,X295 : subst,X296 : term] : (((sub @ (X293 @ X294 @ X296) @ X295)) = ((X293 @ (comp @ X294 @ X295) @ (sub @ X296 @ X295)))) | ~ ! [X297 : term] : ((X287 @ id @ (X293 @ id @ X297) @ id) | ~(X287 @ id @ X297 @ id)) | (X287 @ id @ (lam @ (X293 @ sh @ one)) @ id)) | ~ ! [X298 : subst,X299 : subst,X300 : term,X301 : subst] : ((X287 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301) @ X298) | ~(X287 @ X299 @ X300 @ (comp @ X301 @ X298))))) & apnotvar & (! [X302 : term] : (((sub @ X302 @ id)) = X302) <=> termmset) & hoaslaminj_gthm & axassoc & hoasapnotvar_gthm & ulamvarsh & substmonoid_gthm & (pushprop_p_and_p_prime = (^[X303 : term, X304 : subst, X305 : (term > $o), X306 : (term > $o)] : (! [X307 : term] : (((X306 @ X307)) = ((X305 @ (sub @ X307 @ (push @ X303 @ X304)))))))) & (hoasinduction_lem2v2 <=> ! [X308 : (term > $o),X309 : term,X310 : term,X311 : (subst > term > subst > $o)] : (~ ! [X312 : term,X313 : term] : (~(X311 @ id @ X313 @ id) | ~(X311 @ id @ X312 @ id) | (X311 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id)) | ~ ! [X314 : subst,X315 : subst,X316 : subst,X317 : term] : ((X311 @ X314 @ X317 @ (comp @ X315 @ X316)) | ~(X311 @ (comp @ X314 @ X315) @ (sub @ X317 @ X315) @ X316)) | (X308 @ (ap @ X309 @ X310)) | ~(X308 @ X310) | ~ ! [X318 : term] : (((X308 @ X318)) = ((X311 @ id @ X318 @ id))) | ~(X308 @ X309) | ~ ! [X319 : term,X320 : subst,X321 : subst,X322 : subst] : (~(X311 @ X320 @ X319 @ (comp @ X321 @ X322)) | (X311 @ (comp @ X320 @ X321) @ (sub @ X319 @ X321) @ X322)))) & (laminj <=> ! [X323 : term,X324 : term] : ((((lam @ X324)) != ((lam @ X323))) | (X323 = X324))) & (hoasinduction_p_and_p_prime = (^[X325 : (subst > term > subst > $o), X326 : (term > $o)] : (! [X327 : term] : (((X325 @ id @ X327 @ id)) = ((X326 @ X327)))))) & pushprop_lthm_orig & axvarshift & ! [X328 : d_subst] : (d_id = X328) & (hoasinduction_lem0_lthm <=> ! [X329 : (subst > term > subst > $o)] : ~ ! [X330 : (term > $o)] : ~ ! [X331 : term] : (((X330 @ X331)) = ((X329 @ id @ X331 @ id)))) & lamnotvar & hoasinduction_lem2_gthm & ((! [X332 : subst,X333 : term] : (((sub @ one @ (push @ X333 @ X332))) = X333) => (! [X334 : subst,X335 : term] : (((comp @ sh @ (push @ X335 @ X334))) = X334) => ! [X336 : subst,X337 : (term > $o),X338 : (term > $o),X339 : term,X340 : term] : (~(X338 @ X339) | (X337 @ (sub @ X339 @ (push @ X340 @ X336)))))) <=> pushprop_lem1_lthm) & ! [X341 : d_term,X342 : d_term] : ((((d2term @ X342)) = ((d2term @ X341))) => (X341 = X342)) & (! [X343 : term,X344 : term,X345 : (subst > term > subst > $o)] : (~(X345 @ id @ X343 @ id) | ~(X345 @ id @ X344 @ id) | ~ ! [X346 : subst,X347 : subst,X348 : subst,X349 : term] : ((X345 @ X348 @ X349 @ (comp @ X347 @ X346)) | ~(X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347) @ X346)) | ~ ! [X350 : term,X351 : subst,X352 : subst,X353 : subst] : ((X345 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X353) | ~(X345 @ X352 @ X350 @ (comp @ X351 @ X353))) | (X345 @ id @ (ap @ X344 @ X343) @ id) | ~ ! [X354 : term,X355 : term] : (~(X345 @ id @ X354 @ id) | ~(X345 @ id @ X355 @ id) | (X345 @ id @ (ap @ (sub @ X354 @ id) @ X355) @ id))) <=> hoasinduction_lem2) & ((! [X356 : subst] : (((comp @ id @ X356)) = X356) & ! [X357 : subst] : (((comp @ X357 @ id)) = X357)) <=> substmonoid) & (! [X358 : term,X359 : (subst > term > subst > $o)] : (~ ! [X360 : term,X361 : term] : (~(X359 @ id @ X361 @ id) | ~(X359 @ id @ X360 @ id) | (X359 @ id @ (ap @ (sub @ X360 @ id) @ X361) @ id)) | (X359 @ id @ X358 @ id) | ~ ! [X362 : (subst > term > term)] : ((X359 @ id @ (lam @ (X362 @ sh @ one)) @ id) | ~ ! [X363 : subst,X364 : term,X365 : subst] : (((sub @ (X362 @ X363 @ X364) @ X365)) = ((X362 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365)))) | ~ ! [X366 : term] : ((X359 @ id @ (X362 @ id @ X366) @ id) | ~(X359 @ id @ X366 @ id))) | ~ ! [X367 : term] : ((X359 @ id @ X367 @ id) | ~(var @ (sub @ X367 @ id))) | ~ ! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (~(X359 @ (comp @ X370 @ X369) @ (sub @ X371 @ X369) @ X368) | (X359 @ X370 @ X371 @ (comp @ X369 @ X368))) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : ((X359 @ (comp @ X374 @ X372) @ (sub @ X375 @ X372) @ X373) | ~(X359 @ X374 @ X375 @ (comp @ X372 @ X373)))) <=> hoasinduction) & (! [X376 : (subst > term > subst > $o),X377 : term] : ((X376 @ id @ (lam @ (sub @ X377 @ (push @ one @ sh))) @ id) | ~ ! [X378 : (subst > term > term)] : (~ ! [X379 : term] : ((X376 @ id @ (X378 @ id @ X379) @ id) | ~(X376 @ id @ X379 @ id)) | ~ ! [X380 : subst,X381 : term,X382 : subst] : (((X378 @ (comp @ X380 @ X382) @ (sub @ X381 @ X382))) = ((sub @ (X378 @ X380 @ X381) @ X382))) | (X376 @ id @ (lam @ (X378 @ sh @ one)) @ id)) | ~ ! [X383 : term] : (~(X376 @ id @ X383 @ id) | (X376 @ id @ (sub @ X377 @ (push @ X383 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & (axscons <=> ! [X384 : subst] : (((push @ (sub @ one @ X384) @ (comp @ sh @ X384))) = X384)) & (hoasapinj2_lthm <=> (! [X385 : term,X386 : term,X387 : term,X388 : term] : ((X386 = X388) | (((ap @ X387 @ X388)) != ((ap @ X385 @ X386)))) => ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X392) | (((ap @ (sub @ X390 @ id) @ X389)) != ((ap @ (sub @ X391 @ id) @ X392)))))) & hoasinduction_lem1v2_gthm & ~lamnotap & ((! [X393 : subst,X394 : term] : (((sub @ one @ (push @ X394 @ X393))) = X394) => (! [X395 : term,X396 : subst] : (((comp @ sh @ (push @ X395 @ X396))) = X396) => (! [X397 : subst] : (((comp @ X397 @ id)) = X397) => (! [X398 : (term > $o),X399 : term] : (~ ! [X400 : term] : (~(X398 @ X400) | (X398 @ (lam @ X400))) | ~ ! [X401 : term] : (~(var @ X401) | (X398 @ X401)) | ~ ! [X402 : term,X403 : term] : ((X398 @ (ap @ X402 @ X403)) | ~(X398 @ X403) | ~(X398 @ X402)) | (X398 @ X399)) => ! [X404 : term,X405 : (term > $o),X406 : subst] : (~ ! [X407 : term,X408 : term] : ((X405 @ (ap @ X408 @ X407)) | ~(X405 @ X408) | ~(X405 @ X407)) | (X405 @ (sub @ X404 @ X406)) | ~ ! [X409 : term] : ((X405 @ (lam @ X409)) | ~ ! [X410 : term] : ((X405 @ (sub @ X409 @ (push @ X410 @ id))) | ~(X405 @ X410))) | ~ ! [X411 : term] : ((X405 @ (sub @ X411 @ X406)) | ~(var @ X411))))))) <=> induction2lem_lthm) & ((! [X412 : term] : (((sub @ X412 @ id)) = X412) => (! [X413 : term,X414 : (subst > term > subst > $o)] : (~ ! [X415 : term] : (~(X414 @ id @ X415 @ id) | (X414 @ id @ (sub @ X413 @ (push @ X415 @ id)) @ id)) | (X414 @ id @ (lam @ (sub @ X413 @ (push @ one @ sh))) @ id) | ~ ! [X416 : (subst > term > term)] : ((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) | ~ ! [X417 : term] : (~(X414 @ id @ X417 @ id) | (X414 @ id @ (X416 @ id @ X417) @ id)) | ~ ! [X418 : subst,X419 : term,X420 : subst] : (((X416 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420))) = ((sub @ (X416 @ X418 @ X419) @ X420))))) => ! [X421 : (subst > term > subst > $o),X422 : term] : (~ ! [X423 : subst,X424 : subst,X425 : subst,X426 : term] : ((X421 @ X424 @ X426 @ (comp @ X425 @ X423)) | ~(X421 @ (comp @ X424 @ X425) @ (sub @ X426 @ X425) @ X423)) | ~ ! [X427 : (subst > term > term)] : ((X421 @ id @ (lam @ (X427 @ sh @ one)) @ id) | ~ ! [X428 : subst,X429 : subst,X430 : term] : (((X427 @ (comp @ X428 @ X429) @ (sub @ X430 @ X429))) = ((sub @ (X427 @ X428 @ X430) @ X429))) | ~ ! [X431 : term] : (~(X421 @ id @ X431 @ id) | (X421 @ id @ (X427 @ id @ X431) @ id))) | ~ ! [X432 : subst,X433 : subst,X434 : term,X435 : subst] : (~(X421 @ X435 @ X434 @ (comp @ X433 @ X432)) | (X421 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433) @ X432)) | ~ ! [X436 : term] : ((X421 @ id @ (sub @ X422 @ (push @ X436 @ id)) @ id) | ~(X421 @ id @ X436 @ id)) | (X421 @ id @ (lam @ X422) @ id)))) <=> hoasinduction_lem3_lthm) & axmap & (! [X437 : (term > $o),X438 : term,X439 : term,X440 : (term > $o),X441 : subst] : ((X437 @ (sub @ X439 @ (push @ X438 @ X441))) | ~(X440 @ X439)) <=> pushprop_lem1) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((! [X442 : term] : (((sub @ X442 @ id)) = X442) => (! [X443 : (subst > term > subst > $o),X444 : term] : (~ ! [X445 : (subst > term > term)] : (~ ! [X446 : term] : (~(X443 @ id @ X446 @ id) | (X443 @ id @ (X445 @ id @ X446) @ id)) | (X443 @ id @ (lam @ (X445 @ sh @ one)) @ id) | ~ ! [X447 : subst,X448 : subst,X449 : term] : (((X445 @ (comp @ X448 @ X447) @ (sub @ X449 @ X447))) = ((sub @ (X445 @ X448 @ X449) @ X447)))) | (X443 @ id @ (lam @ (sub @ X444 @ (push @ one @ sh))) @ id) | ~ ! [X450 : term] : ((X443 @ id @ (sub @ X444 @ (push @ X450 @ id)) @ id) | ~(X443 @ id @ X450 @ id))) => ! [X451 : term,X452 : (subst > term > subst > $o)] : ((X452 @ id @ (lam @ X451) @ id) | ~ ! [X453 : (subst > term > term)] : (~ ! [X454 : subst,X455 : subst,X456 : term] : (((sub @ (X453 @ X454 @ X456) @ X455)) = ((X453 @ (comp @ X454 @ X455) @ (sub @ X456 @ X455)))) | (X452 @ id @ (lam @ (X453 @ sh @ one)) @ id) | ~ ! [X457 : term] : (~(X452 @ id @ X457 @ id) | (X452 @ id @ (X453 @ id @ X457) @ id))) | ~ ! [X458 : term] : ((X452 @ id @ (sub @ X451 @ (push @ X458 @ id)) @ id) | ~(X452 @ id @ X458 @ id))))) <=> hoasinduction_lem3a_lthm) & (termmset_lthm <=> (! [X459 : term] : (((sub @ X459 @ id)) = X459) => ! [X460 : term] : (((sub @ X460 @ id)) = X460))) & ((! [X461 : term] : (((sub @ X461 @ id)) = X461) => ! [X462 : term,X463 : (subst > term > subst > $o),X464 : (term > $o)] : (~ ! [X465 : subst,X466 : term,X467 : subst,X468 : subst] : ((X463 @ X467 @ X466 @ (comp @ X465 @ X468)) | ~(X463 @ (comp @ X467 @ X465) @ (sub @ X466 @ X465) @ X468)) | (X464 @ (lam @ X462)) | ~ ! [X469 : subst,X470 : term,X471 : subst,X472 : subst] : ((X463 @ (comp @ X469 @ X471) @ (sub @ X470 @ X471) @ X472) | ~(X463 @ X469 @ X470 @ (comp @ X471 @ X472))) | ~ ! [X473 : (subst > term > term)] : ((X463 @ id @ (lam @ (X473 @ sh @ one)) @ id) | ~ ! [X474 : subst,X475 : term,X476 : subst] : (((X473 @ (comp @ X476 @ X474) @ (sub @ X475 @ X474))) = ((sub @ (X473 @ X476 @ X475) @ X474))) | ~ ! [X477 : term] : ((X463 @ id @ (X473 @ id @ X477) @ id) | ~(X463 @ id @ X477 @ id))) | ~ ! [X478 : term] : ((X464 @ (sub @ X462 @ (push @ X478 @ id))) | ~(X464 @ X478)) | ~ ! [X479 : term] : (((X463 @ id @ X479 @ id)) = ((X464 @ X479))))) <=> hoasinduction_lem3v2_lthm) & ((! [X480 : term] : (((sub @ X480 @ id)) = X480) => (! [X481 : subst,X482 : (term > $o),X483 : term] : (~ ! [X484 : term] : (~ ! [X485 : term] : ((X482 @ (sub @ X484 @ (push @ X485 @ id))) | ~(X482 @ X485)) | (X482 @ (lam @ X484))) | (X482 @ (sub @ X483 @ X481)) | ~ ! [X486 : term] : (~(var @ X486) | (X482 @ (sub @ X486 @ X481))) | ~ ! [X487 : term,X488 : term] : ((X482 @ (ap @ X487 @ X488)) | ~(X482 @ X487) | ~(X482 @ X488))) => ! [X489 : term,X490 : (term > $o)] : ((X490 @ X489) | ~ ! [X491 : term] : (~(var @ X491) | (X490 @ X491)) | ~ ! [X492 : term,X493 : term] : (~(X490 @ X492) | (X490 @ (ap @ X493 @ X492)) | ~(X490 @ X493)) | ~ ! [X494 : term] : ((X490 @ (lam @ X494)) | ~ ! [X495 : term] : (~(X490 @ X495) | (X490 @ (sub @ X494 @ (push @ X495 @ id)))))))) <=> induction2_lthm) & termmset_gthm & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & (! [X496 : term] : ~ ! [X497 : (subst > term > term)] : ~ ! [X498 : term,X499 : subst] : (((sub @ X496 @ (push @ X498 @ X499))) = ((X497 @ X499 @ X498))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_gthm & hoasinduction_lem1 & (! [X500 : term] : ~ ! [X501 : (subst > term > term)] : (((sub @ X500 @ (push @ one @ sh))) != ((X501 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & (! [X502 : term,X503 : (subst > term > subst > $o)] : ((X503 @ id @ (lam @ X502) @ id) | ~ ! [X504 : term] : (~(X503 @ id @ X504 @ id) | (X503 @ id @ (sub @ X502 @ (push @ X504 @ id)) @ id)) | ~ ! [X505 : (subst > term > term)] : (~ ! [X506 : subst,X507 : term,X508 : subst] : (((sub @ (X505 @ X506 @ X507) @ X508)) = ((X505 @ (comp @ X506 @ X508) @ (sub @ X507 @ X508)))) | (X503 @ id @ (lam @ (X505 @ sh @ one)) @ id) | ~ ! [X509 : term] : (~(X503 @ id @ X509 @ id) | (X503 @ id @ (X505 @ id @ X509) @ id)))) <=> hoasinduction_lem3a) & ((! [X510 : subst] : (((comp @ id @ X510)) = X510) => (! [X511 : subst] : (((comp @ X511 @ id)) = X511) => (! [X512 : subst] : (((comp @ X512 @ id)) = X512) & ! [X513 : subst] : (((comp @ id @ X513)) = X513)))) <=> substmonoid_lthm) & hoasinduction_lem3v2_gthm & axabs & (! [X514 : (term > $o),X515 : subst,X516 : term] : ~ ! [X517 : (term > $o)] : ~ ! [X518 : term] : (((X517 @ X518)) = ((X514 @ (sub @ X518 @ (push @ X516 @ X515))))) <=> pushprop_lem0_lthm) & (! [X519 : (term > $o),X520 : (subst > term > subst > $o),X521 : term] : ((X519 @ (lam @ X521)) | ~ ! [X522 : (subst > term > term)] : (~ ! [X523 : term] : (~(X520 @ id @ X523 @ id) | (X520 @ id @ (X522 @ id @ X523) @ id)) | ~ ! [X524 : term,X525 : subst,X526 : subst] : (((X522 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525))) = ((sub @ (X522 @ X526 @ X524) @ X525))) | (X520 @ id @ (lam @ (X522 @ sh @ one)) @ id)) | ~ ! [X527 : term] : (((X519 @ X527)) = ((X520 @ id @ X527 @ id))) | ~ ! [X528 : term] : ((X519 @ (sub @ X521 @ (push @ X528 @ id))) | ~(X519 @ X528))) <=> hoasinduction_lem3v2a) & (axshiftcons <=> ! [X529 : term,X530 : subst] : (((comp @ sh @ (push @ X529 @ X530))) = X530)) & hoaslamnotap_lthm & (pushprop_lem1v2_lthm <=> (! [X531 : term,X532 : subst] : (((sub @ one @ (push @ X531 @ X532))) = X531) => ! [X533 : term,X534 : subst,X535 : (term > $o),X536 : (term > $o)] : (~ ! [X537 : term] : (((X535 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X533 @ X534))))) | ~(X536 @ X533) | (X535 @ one)))) & (induction <=> ! [X538 : term,X539 : (term > $o)] : ((X539 @ X538) | ~ ! [X540 : term] : (~(var @ X540) | (X539 @ X540)) | ~ ! [X541 : term] : (~(X539 @ X541) | (X539 @ (lam @ X541))) | ~ ! [X542 : term,X543 : term] : (~(X539 @ X542) | ~(X539 @ X543) | (X539 @ (ap @ X542 @ X543))))) & (pushprop_lem0 <=> ! [X544 : (term > $o),X545 : term,X546 : subst] : ~ ! [X547 : (term > $o)] : ~ ! [X548 : term] : (((X544 @ (sub @ X548 @ (push @ X545 @ X546)))) = ((X547 @ X548)))) & (id = ((d2subst @ d_id))) & pushprop_gthm & pushprop_lem3v2 & hoasapinj1_gthm & (axidr <=> ! [X549 : subst] : (((comp @ X549 @ id)) = X549))),
% 6.44/1.36 inference(rectify,[],[f1])).
% 6.44/1.36 thf(f5,plain,(
% 6.44/1.36 (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & (pushprop = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoaslaminj = $true) <=> ! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (~ ! [X8 : subst,X7 : term,X6 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6)))) | ~ ! [X11 : subst,X10 : subst,X9 : term] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))))) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) = ((d2subst @ X12))) => (X12 = X13)) & (one = ((d2term @ d_one))) & ((! [X14 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X17 : term,X16 : subst] : (((X15 @ X16 @ X17)) = ((sub @ X14 @ (push @ X17 @ X16)))) => (! [X18 : term] : (((sub @ X18 @ id)) = X18) => ! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : (($true = ((X20 @ (lam @ X21)))) | ~ ! [X22 : term] : (((X19 @ id @ X22 @ id)) = ((X20 @ X22))) | ~ ! [X23 : term] : (($true = ((X20 @ (sub @ X21 @ (push @ X23 @ id))))) | ~ (((X20 @ X23)) = $true)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) | ($true = ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) | ~ ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ~ ($true = ((X19 @ id @ X28 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X29 : term,X30 : (subst > term > subst > $o)] : (~ ! [X31 : term] : (($true = ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id))) | ~ ($true = ((X30 @ id @ X31 @ id)))) | ~ ! [X32 : (subst > term > term),X33 : term] : (~ ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) | ~ ! [X37 : term] : (($true = ((X30 @ id @ (X32 @ id @ X37) @ id))) | ~ ($true = ((X30 @ id @ X37 @ id)))) | ~ ! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) | ($true = ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id)))) | ($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))))) & (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X43 : (term > $o),X44 : term] : (~ ! [X45 : term] : (($true = ((X43 @ X45))) | ~ (((var @ X45)) = $true)) | ~ ! [X46 : term,X47 : term] : (~ ($true = ((X43 @ X47))) | ~ (((X43 @ X46)) = $true) | ($true = ((X43 @ (ap @ X47 @ X46))))) | (((X43 @ X44)) = $true) | ~ ! [X48 : term] : (~ ! [X49 : term] : (($true = ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) | ~ (((X43 @ X49)) = $true)) | (((X43 @ (lam @ X48))) = $true))) => (! [X50 : (subst > term > subst > $o),X51 : term,X52 : term] : (~ ! [X53 : term,X54 : term] : (~ ($true = ((X50 @ id @ X54 @ id))) | ~ ($true = ((X50 @ id @ X53 @ id))) | (((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true)) | ~ ($true = ((X50 @ id @ X51 @ id))) | ~ ($true = ((X50 @ id @ X52 @ id))) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : (~ ($true = ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57))) | ($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57))))) | ($true = ((X50 @ id @ (ap @ X51 @ X52) @ id))) | ~ ! [X59 : subst,X60 : subst,X61 : term,X62 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ~ ($true = ((X50 @ X62 @ X61 @ (comp @ X60 @ X59)))))) => (! [X63 : (subst > term > subst > $o),X64 : term] : (($true = ((X63 @ id @ (lam @ X64) @ id))) | ~ ! [X65 : subst,X66 : subst,X67 : term,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | ~ (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) = $true)) | ~ ! [X69 : term] : (~ (((X63 @ id @ X69 @ id)) = $true) | ($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id)))) | ~ ! [X70 : (subst > term > term)] : (($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X71 : term] : ((((X63 @ id @ (X70 @ id @ X71) @ id)) = $true) | ~ ($true = ((X63 @ id @ X71 @ id)))) | ~ ! [X73 : subst,X72 : term,X74 : subst] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) = ((sub @ (X70 @ X74 @ X72) @ X73)))) | ~ ! [X75 : term,X76 : subst,X77 : subst,X78 : subst] : (~ ($true = ((X63 @ X78 @ X75 @ (comp @ X76 @ X77)))) | (((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true))) => ! [X79 : (subst > term > subst > $o),X80 : term] : (~ ! [X81 : term] : (($true = ((X79 @ id @ X81 @ id))) | ~ (((var @ (sub @ X81 @ id))) = $true)) | ~ ! [X82 : (subst > term > term)] : (~ ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83))) | ~ ! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | ~ (((X79 @ id @ X86 @ id)) = $true)) | ($true = ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id)))) | ($true = ((X79 @ id @ X80 @ id))) | ~ ! [X87 : term,X88 : term] : (~ ($true = ((X79 @ id @ X87 @ id))) | ~ (((X79 @ id @ X88 @ id)) = $true) | ($true = ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)))) | ~ ! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : ((((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) = $true) | ~ (((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) = $true)) | ~ ! [X93 : subst,X94 : subst,X95 : term,X96 : subst] : (~ ($true = ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) | ($true = ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96))))))))) & (hoasinduction_lem1v2 = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X98 : term,X97 : term,X99 : (subst > term > term)] : (~ ! [X100 : term,X102 : subst,X101 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))) | (((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98)))) <=> (hoaslamnotap = $true)) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X106 : (subst > term > subst > $o)] : ~ ! [X107 : (term > $o)] : ~ ! [X108 : term] : (((X106 @ id @ X108 @ id)) = ((X107 @ X108))) => (! [X109 : term,X110 : (term > $o)] : (~ ! [X111 : term] : (~ ! [X112 : term] : (~ ($true = ((X110 @ X112))) | ($true = ((X110 @ (sub @ X111 @ (push @ X112 @ id)))))) | ($true = ((X110 @ (lam @ X111))))) | ~ ! [X113 : term,X114 : term] : (($true = ((X110 @ (ap @ X114 @ X113)))) | ~ (((X110 @ X114)) = $true) | ~ ($true = ((X110 @ X113)))) | (((X110 @ X109)) = $true) | ~ ! [X115 : term] : (~ ($true = ((var @ X115))) | ($true = ((X110 @ X115))))) => (! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X117 : term,X118 : (term > $o),X119 : (subst > term > subst > $o)] : (($true = ((X118 @ (lam @ X117)))) | ~ ! [X120 : (subst > term > term)] : ((((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ~ ! [X123 : subst,X121 : term,X122 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) = ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122)))) | ~ ! [X124 : term] : (~ ($true = ((X119 @ id @ X124 @ id))) | ($true = ((X119 @ id @ (X120 @ id @ X124) @ id))))) | ~ ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) | ~ ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ~ ($true = ((X118 @ X126))))) => ! [X127 : (subst > term > subst > $o),X128 : term] : (~ ! [X129 : term,X130 : term] : (~ ($true = ((X127 @ id @ X129 @ id))) | ~ ($true = ((X127 @ id @ X130 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)))) | ($true = ((X127 @ id @ X128 @ id))) | ~ ! [X131 : (subst > term > term)] : (($true = ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ~ ! [X132 : term] : (~ ($true = ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id)))) | ~ ! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133))))))))))) & ((induction2 = $true) <=> ! [X136 : term,X137 : (term > $o)] : (~ ! [X138 : term,X139 : term] : (~ ($true = ((X137 @ X138))) | ~ ($true = ((X137 @ X139))) | ($true = ((X137 @ (ap @ X139 @ X138))))) | ~ ! [X140 : term] : (~ ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ ($true = ((X137 @ X141)))) | ($true = ((X137 @ (lam @ X140))))) | ~ ! [X142 : term] : (~ (((var @ X142)) = $true) | ($true = ((X137 @ X142)))) | ($true = ((X137 @ X136))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ~ (ulamvar1 = $true) & ((hoaslaminj_lthm = $true) <=> (! [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) = X146) => (! [X148 : term,X147 : term] : ((X147 = X148) | (((lam @ X147)) != ((lam @ X148)))) => ! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : (~ ! [X156 : subst,X158 : subst,X157 : term] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) = ((sub @ (X152 @ X156 @ X157) @ X158))) | (((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ~ ! [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) = ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one))))))))) & ((pushprop_lem1v2 = $true) <=> ! [X159 : subst,X160 : (term > $o),X161 : (term > $o),X162 : term] : (~ ($true = ((X160 @ X162))) | (((X161 @ one)) = $true) | ~ ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163))))) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X164 : (term > $o),X165 : term,X166 : (subst > term > subst > $o)] : (~ ! [X167 : (subst > term > term)] : (($true = ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))) | ~ ! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) | ~ ! [X171 : term] : (~ (((X166 @ id @ X171 @ id)) = $true) | (((X166 @ id @ (X167 @ id @ X171) @ id)) = $true))) | ~ ! [X172 : term,X173 : subst,X174 : subst,X175 : subst] : (~ ($true = ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174))) | ($true = ((X166 @ X173 @ X172 @ (comp @ X175 @ X174))))) | ($true = ((X164 @ (lam @ X165)))) | ~ ! [X176 : term] : (($true = ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) | ~ (((X164 @ X176)) = $true)) | ~ ! [X177 : subst,X178 : subst,X179 : subst,X180 : term] : (($true = ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179))) | ~ ($true = ((X166 @ X178 @ X180 @ (comp @ X177 @ X179))))) | ~ ! [X181 : term] : (((X164 @ X181)) = ((X166 @ id @ X181 @ id))))) & ((hoasapinj1_lthm = $true) <=> (! [X182 : term] : (((sub @ X182 @ id)) = X182) => (! [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 = X185) | (((ap @ X183 @ X186)) != ((ap @ X185 @ X184)))) => ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190))))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (! [X195 : term,X196 : (subst > term > subst > $o)] : (($true = ((X196 @ id @ X195 @ id))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~ ($true = ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id)))) | (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))) | ~ ! [X202 : term,X203 : term] : ((((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) = $true) | ~ ($true = ((X196 @ id @ X203 @ id))) | ~ ($true = ((X196 @ id @ X202 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & ((! [X205 : (subst > term > subst > $o)] : ~ ! [X206 : (term > $o)] : ~ ! [X207 : term] : (((X205 @ id @ X207 @ id)) = ((X206 @ X207))) => (! [X208 : term,X209 : (term > $o)] : (~ ! [X210 : term] : (($true = ((X209 @ X210))) | ~ ($true = ((var @ X210)))) | ~ ! [X211 : term] : (~ ! [X212 : term] : (($true = ((X209 @ (sub @ X211 @ (push @ X212 @ id))))) | ~ ($true = ((X209 @ X212)))) | ($true = ((X209 @ (lam @ X211))))) | ~ ! [X213 : term,X214 : term] : (~ ($true = ((X209 @ X214))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ~ ($true = ((X209 @ X213)))) | ($true = ((X209 @ X208)))) => (! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X216 : (term > $o),X217 : term,X218 : (subst > term > subst > $o)] : (~ ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) | ($true = ((X216 @ (lam @ X217)))) | ~ ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ~ ($true = ((X216 @ X220)))) | ~ ! [X221 : (subst > term > term)] : (~ ! [X222 : term] : (~ (((X218 @ id @ X222 @ id)) = $true) | (((X218 @ id @ (X221 @ id @ X222) @ id)) = $true)) | ($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ~ ! [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) = ((sub @ (X221 @ X223 @ X225) @ X224))))) => ! [X226 : term,X227 : (subst > term > subst > $o)] : ((((X227 @ id @ X226 @ id)) = $true) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : (($true = ((X227 @ X228 @ X231 @ (comp @ X229 @ X230)))) | ~ (((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) = $true)) | ~ ! [X232 : term] : (($true = ((X227 @ id @ X232 @ id))) | ~ ($true = ((var @ (sub @ X232 @ id))))) | ~ ! [X233 : term,X234 : term] : (~ ($true = ((X227 @ id @ X233 @ id))) | ~ ($true = ((X227 @ id @ X234 @ id))) | (((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) = $true)) | ~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term] : (($true = ((X227 @ id @ (X235 @ id @ X236) @ id))) | ~ (((X227 @ id @ X236 @ id)) = $true)) | (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237)))) | ~ ! [X240 : subst,X241 : term,X242 : subst,X243 : subst] : (($true = ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242))) | ~ (((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ~ ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh))))) & (pushprop_lem2v2_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ((induction2lem = $true) <=> ! [X251 : (term > $o),X252 : subst,X253 : term] : (~ ! [X254 : term] : (($true = ((X251 @ (lam @ X254)))) | ~ ! [X255 : term] : ((((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true) | ~ ($true = ((X251 @ X255))))) | ~ ! [X256 : term,X257 : term] : (~ (((X251 @ X257)) = $true) | ($true = ((X251 @ (ap @ X256 @ X257)))) | ~ ($true = ((X251 @ X256)))) | ~ ! [X258 : term] : (~ (((var @ X258)) = $true) | ($true = ((X251 @ (sub @ X258 @ X252))))) | (((X251 @ (sub @ X253 @ X252))) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (ulamvarind = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((apinj1 = $true) <=> ! [X265 : term,X266 : term,X267 : term,X268 : term] : ((((ap @ X266 @ X268)) != ((ap @ X267 @ X265))) | (X266 = X267))) & ! [X269 : d_term] : (d_one = X269) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X270 : term,X271 : (subst > term > subst > $o)] : (~ ! [X272 : (subst > term > term)] : (~ ! [X273 : term] : (~ ($true = ((X271 @ id @ X273 @ id))) | ($true = ((X271 @ id @ (X272 @ id @ X273) @ id)))) | ($true = ((X271 @ id @ (lam @ (X272 @ sh @ one)) @ id))) | ~ ! [X274 : subst,X275 : term,X276 : subst] : (((sub @ (X272 @ X274 @ X275) @ X276)) = ((X272 @ (comp @ X274 @ X276) @ (sub @ X275 @ X276))))) | ~ ! [X277 : term] : (~ ($true = ((X271 @ id @ X277 @ id))) | ($true = ((X271 @ id @ (sub @ X270 @ (push @ X277 @ id)) @ id)))) | ($true = ((X271 @ id @ (lam @ (sub @ X270 @ (push @ one @ sh))) @ id))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (axclos = $true) & (! [X278 : term] : ~ ! [X279 : (subst > term > term)] : ~ ! [X280 : subst,X281 : term] : (((X279 @ X280 @ X281)) = ((sub @ X278 @ (push @ X281 @ X280)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X282 : term,X283 : term,X284 : term,X285 : term] : ((X283 = X285) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X285 @ id) @ X284)))) <=> (hoasapinj1 = $true)) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X286 : term,X287 : (subst > term > subst > $o)] : ((((X287 @ id @ (lam @ X286) @ id)) = $true) | ~ ! [X288 : term] : (~ (((X287 @ id @ X288 @ id)) = $true) | ($true = ((X287 @ id @ (sub @ X286 @ (push @ X288 @ id)) @ id)))) | ~ ! [X289 : subst,X290 : subst,X291 : subst,X292 : term] : ((((X287 @ X289 @ X292 @ (comp @ X291 @ X290))) = $true) | ~ (((X287 @ (comp @ X289 @ X291) @ (sub @ X292 @ X291) @ X290)) = $true)) | ~ ! [X293 : (subst > term > term)] : (~ ! [X294 : subst,X295 : subst,X296 : term] : (((sub @ (X293 @ X294 @ X296) @ X295)) = ((X293 @ (comp @ X294 @ X295) @ (sub @ X296 @ X295)))) | ~ ! [X297 : term] : ((((X287 @ id @ (X293 @ id @ X297) @ id)) = $true) | ~ ($true = ((X287 @ id @ X297 @ id)))) | (((X287 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true)) | ~ ! [X298 : subst,X299 : subst,X300 : term,X301 : subst] : ((((X287 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301) @ X298)) = $true) | ~ ($true = ((X287 @ X299 @ X300 @ (comp @ X301 @ X298))))))) & (apnotvar = $true) & (! [X302 : term] : (((sub @ X302 @ id)) = X302) <=> (termmset = $true)) & (hoaslaminj_gthm = $true) & (axassoc = $true) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & (substmonoid_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)))))))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X308 : (term > $o),X309 : term,X310 : term,X311 : (subst > term > subst > $o)] : (~ ! [X312 : term,X313 : term] : (~ ($true = ((X311 @ id @ X313 @ id))) | ~ (((X311 @ id @ X312 @ id)) = $true) | (((X311 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id)) = $true)) | ~ ! [X314 : subst,X315 : subst,X316 : subst,X317 : term] : (($true = ((X311 @ X314 @ X317 @ (comp @ X315 @ X316)))) | ~ ($true = ((X311 @ (comp @ X314 @ X315) @ (sub @ X317 @ X315) @ X316)))) | ($true = ((X308 @ (ap @ X309 @ X310)))) | ~ ($true = ((X308 @ X310))) | ~ ! [X318 : term] : (((X308 @ X318)) = ((X311 @ id @ X318 @ id))) | ~ ($true = ((X308 @ X309))) | ~ ! [X319 : term,X320 : subst,X321 : subst,X322 : subst] : (~ (((X311 @ X320 @ X319 @ (comp @ X321 @ X322))) = $true) | ($true = ((X311 @ (comp @ X320 @ X321) @ (sub @ X319 @ X321) @ X322)))))) & ((laminj = $true) <=> ! [X323 : term,X324 : term] : ((((lam @ X324)) != ((lam @ X323))) | (X323 = X324))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lthm_orig = $true) & (axvarshift = $true) & ! [X328 : d_subst] : (d_id = X328) & ((hoasinduction_lem0_lthm = $true) <=> ! [X329 : (subst > term > subst > $o)] : ~ ! [X330 : (term > $o)] : ~ ! [X331 : term] : (((X330 @ X331)) = ((X329 @ id @ X331 @ id)))) & (lamnotvar = $true) & (hoasinduction_lem2_gthm = $true) & ((! [X332 : subst,X333 : term] : (((sub @ one @ (push @ X333 @ X332))) = X333) => (! [X334 : subst,X335 : term] : (((comp @ sh @ (push @ X335 @ X334))) = X334) => ! [X336 : subst,X337 : (term > $o),X338 : (term > $o),X339 : term,X340 : term] : (~ (((X338 @ X339)) = $true) | ($true = ((X337 @ (sub @ X339 @ (push @ X340 @ X336)))))))) <=> (pushprop_lem1_lthm = $true)) & ! [X341 : d_term,X342 : d_term] : ((((d2term @ X342)) = ((d2term @ X341))) => (X341 = X342)) & (! [X343 : term,X344 : term,X345 : (subst > term > subst > $o)] : (~ ($true = ((X345 @ id @ X343 @ id))) | ~ ($true = ((X345 @ id @ X344 @ id))) | ~ ! [X346 : subst,X347 : subst,X348 : subst,X349 : term] : (($true = ((X345 @ X348 @ X349 @ (comp @ X347 @ X346)))) | ~ ($true = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347) @ X346)))) | ~ ! [X350 : term,X351 : subst,X352 : subst,X353 : subst] : (($true = ((X345 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X353))) | ~ ($true = ((X345 @ X352 @ X350 @ (comp @ X351 @ X353))))) | (((X345 @ id @ (ap @ X344 @ X343) @ id)) = $true) | ~ ! [X354 : term,X355 : term] : (~ ($true = ((X345 @ id @ X354 @ id))) | ~ ($true = ((X345 @ id @ X355 @ id))) | (((X345 @ id @ (ap @ (sub @ X354 @ id) @ X355) @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & ((! [X356 : subst] : (((comp @ id @ X356)) = X356) & ! [X357 : subst] : (((comp @ X357 @ id)) = X357)) <=> (substmonoid = $true)) & (! [X358 : term,X359 : (subst > term > subst > $o)] : (~ ! [X360 : term,X361 : term] : (~ (((X359 @ id @ X361 @ id)) = $true) | ~ ($true = ((X359 @ id @ X360 @ id))) | ($true = ((X359 @ id @ (ap @ (sub @ X360 @ id) @ X361) @ id)))) | (((X359 @ id @ X358 @ id)) = $true) | ~ ! [X362 : (subst > term > term)] : ((((X359 @ id @ (lam @ (X362 @ sh @ one)) @ id)) = $true) | ~ ! [X363 : subst,X364 : term,X365 : subst] : (((sub @ (X362 @ X363 @ X364) @ X365)) = ((X362 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365)))) | ~ ! [X366 : term] : (($true = ((X359 @ id @ (X362 @ id @ X366) @ id))) | ~ ($true = ((X359 @ id @ X366 @ id))))) | ~ ! [X367 : term] : ((((X359 @ id @ X367 @ id)) = $true) | ~ ($true = ((var @ (sub @ X367 @ id))))) | ~ ! [X368 : subst,X369 : subst,X370 : subst,X371 : term] : (~ ($true = ((X359 @ (comp @ X370 @ X369) @ (sub @ X371 @ X369) @ X368))) | ($true = ((X359 @ X370 @ X371 @ (comp @ X369 @ X368))))) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : ((((X359 @ (comp @ X374 @ X372) @ (sub @ X375 @ X372) @ X373)) = $true) | ~ ($true = ((X359 @ X374 @ X375 @ (comp @ X372 @ X373)))))) <=> (hoasinduction = $true)) & (! [X376 : (subst > term > subst > $o),X377 : term] : ((((X376 @ id @ (lam @ (sub @ X377 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X378 : (subst > term > term)] : (~ ! [X379 : term] : ((((X376 @ id @ (X378 @ id @ X379) @ id)) = $true) | ~ ($true = ((X376 @ id @ X379 @ id)))) | ~ ! [X380 : subst,X381 : term,X382 : subst] : (((X378 @ (comp @ X380 @ X382) @ (sub @ X381 @ X382))) = ((sub @ (X378 @ X380 @ X381) @ X382))) | ($true = ((X376 @ id @ (lam @ (X378 @ sh @ one)) @ id)))) | ~ ! [X383 : term] : (~ ($true = ((X376 @ id @ X383 @ id))) | ($true = ((X376 @ id @ (sub @ X377 @ (push @ X383 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axscons = $true) <=> ! [X384 : subst] : (((push @ (sub @ one @ X384) @ (comp @ sh @ X384))) = X384)) & ((hoasapinj2_lthm = $true) <=> (! [X385 : term,X386 : term,X387 : term,X388 : term] : ((X386 = X388) | (((ap @ X387 @ X388)) != ((ap @ X385 @ X386)))) => ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X392) | (((ap @ (sub @ X390 @ id) @ X389)) != ((ap @ (sub @ X391 @ id) @ X392)))))) & (hoasinduction_lem1v2_gthm = $true) & ~ (lamnotap = $true) & ((! [X393 : subst,X394 : term] : (((sub @ one @ (push @ X394 @ X393))) = X394) => (! [X395 : term,X396 : subst] : (((comp @ sh @ (push @ X395 @ X396))) = X396) => (! [X397 : subst] : (((comp @ X397 @ id)) = X397) => (! [X398 : (term > $o),X399 : term] : (~ ! [X400 : term] : (~ ($true = ((X398 @ X400))) | ($true = ((X398 @ (lam @ X400))))) | ~ ! [X401 : term] : (~ ($true = ((var @ X401))) | (((X398 @ X401)) = $true)) | ~ ! [X402 : term,X403 : term] : (($true = ((X398 @ (ap @ X402 @ X403)))) | ~ ($true = ((X398 @ X403))) | ~ (((X398 @ X402)) = $true)) | ($true = ((X398 @ X399)))) => ! [X404 : term,X405 : (term > $o),X406 : subst] : (~ ! [X407 : term,X408 : term] : (($true = ((X405 @ (ap @ X408 @ X407)))) | ~ (((X405 @ X408)) = $true) | ~ (((X405 @ X407)) = $true)) | ($true = ((X405 @ (sub @ X404 @ X406)))) | ~ ! [X409 : term] : ((((X405 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : (($true = ((X405 @ (sub @ X409 @ (push @ X410 @ id))))) | ~ ($true = ((X405 @ X410))))) | ~ ! [X411 : term] : ((((X405 @ (sub @ X411 @ X406))) = $true) | ~ (((var @ X411)) = $true))))))) <=> (induction2lem_lthm = $true)) & ((! [X412 : term] : (((sub @ X412 @ id)) = X412) => (! [X413 : term,X414 : (subst > term > subst > $o)] : (~ ! [X415 : term] : (~ (((X414 @ id @ X415 @ id)) = $true) | (((X414 @ id @ (sub @ X413 @ (push @ X415 @ id)) @ id)) = $true)) | (((X414 @ id @ (lam @ (sub @ X413 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X416 : (subst > term > term)] : (($true = ((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id))) | ~ ! [X417 : term] : (~ (((X414 @ id @ X417 @ id)) = $true) | ($true = ((X414 @ id @ (X416 @ id @ X417) @ id)))) | ~ ! [X418 : subst,X419 : term,X420 : subst] : (((X416 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420))) = ((sub @ (X416 @ X418 @ X419) @ X420))))) => ! [X421 : (subst > term > subst > $o),X422 : term] : (~ ! [X423 : subst,X424 : subst,X425 : subst,X426 : term] : ((((X421 @ X424 @ X426 @ (comp @ X425 @ X423))) = $true) | ~ ($true = ((X421 @ (comp @ X424 @ X425) @ (sub @ X426 @ X425) @ X423)))) | ~ ! [X427 : (subst > term > term)] : (($true = ((X421 @ id @ (lam @ (X427 @ sh @ one)) @ id))) | ~ ! [X428 : subst,X429 : subst,X430 : term] : (((X427 @ (comp @ X428 @ X429) @ (sub @ X430 @ X429))) = ((sub @ (X427 @ X428 @ X430) @ X429))) | ~ ! [X431 : term] : (~ ($true = ((X421 @ id @ X431 @ id))) | ($true = ((X421 @ id @ (X427 @ id @ X431) @ id))))) | ~ ! [X432 : subst,X433 : subst,X434 : term,X435 : subst] : (~ (((X421 @ X435 @ X434 @ (comp @ X433 @ X432))) = $true) | ($true = ((X421 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433) @ X432)))) | ~ ! [X436 : term] : (($true = ((X421 @ id @ (sub @ X422 @ (push @ X436 @ id)) @ id))) | ~ ($true = ((X421 @ id @ X436 @ id)))) | (((X421 @ id @ (lam @ X422) @ id)) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & (axmap = $true) & (! [X437 : (term > $o),X438 : term,X439 : term,X440 : (term > $o),X441 : subst] : (($true = ((X437 @ (sub @ X439 @ (push @ X438 @ X441))))) | ~ (((X440 @ X439)) = $true)) <=> (pushprop_lem1 = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ((! [X442 : term] : (((sub @ X442 @ id)) = X442) => (! [X443 : (subst > term > subst > $o),X444 : term] : (~ ! [X445 : (subst > term > term)] : (~ ! [X446 : term] : (~ ($true = ((X443 @ id @ X446 @ id))) | (((X443 @ id @ (X445 @ id @ X446) @ id)) = $true)) | ($true = ((X443 @ id @ (lam @ (X445 @ sh @ one)) @ id))) | ~ ! [X447 : subst,X448 : subst,X449 : term] : (((X445 @ (comp @ X448 @ X447) @ (sub @ X449 @ X447))) = ((sub @ (X445 @ X448 @ X449) @ X447)))) | (((X443 @ id @ (lam @ (sub @ X444 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X450 : term] : (($true = ((X443 @ id @ (sub @ X444 @ (push @ X450 @ id)) @ id))) | ~ ($true = ((X443 @ id @ X450 @ id))))) => ! [X451 : term,X452 : (subst > term > subst > $o)] : (($true = ((X452 @ id @ (lam @ X451) @ id))) | ~ ! [X453 : (subst > term > term)] : (~ ! [X454 : subst,X455 : subst,X456 : term] : (((sub @ (X453 @ X454 @ X456) @ X455)) = ((X453 @ (comp @ X454 @ X455) @ (sub @ X456 @ X455)))) | (((X452 @ id @ (lam @ (X453 @ sh @ one)) @ id)) = $true) | ~ ! [X457 : term] : (~ (((X452 @ id @ X457 @ id)) = $true) | ($true = ((X452 @ id @ (X453 @ id @ X457) @ id))))) | ~ ! [X458 : term] : (($true = ((X452 @ id @ (sub @ X451 @ (push @ X458 @ id)) @ id))) | ~ ($true = ((X452 @ id @ X458 @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X459 : term] : (((sub @ X459 @ id)) = X459) => ! [X460 : term] : (((sub @ X460 @ id)) = X460))) & ((! [X461 : term] : (((sub @ X461 @ id)) = X461) => ! [X462 : term,X463 : (subst > term > subst > $o),X464 : (term > $o)] : (~ ! [X465 : subst,X466 : term,X467 : subst,X468 : subst] : ((((X463 @ X467 @ X466 @ (comp @ X465 @ X468))) = $true) | ~ ($true = ((X463 @ (comp @ X467 @ X465) @ (sub @ X466 @ X465) @ X468)))) | ($true = ((X464 @ (lam @ X462)))) | ~ ! [X469 : subst,X470 : term,X471 : subst,X472 : subst] : (($true = ((X463 @ (comp @ X469 @ X471) @ (sub @ X470 @ X471) @ X472))) | ~ ($true = ((X463 @ X469 @ X470 @ (comp @ X471 @ X472))))) | ~ ! [X473 : (subst > term > term)] : (($true = ((X463 @ id @ (lam @ (X473 @ sh @ one)) @ id))) | ~ ! [X474 : subst,X475 : term,X476 : subst] : (((X473 @ (comp @ X476 @ X474) @ (sub @ X475 @ X474))) = ((sub @ (X473 @ X476 @ X475) @ X474))) | ~ ! [X477 : term] : (($true = ((X463 @ id @ (X473 @ id @ X477) @ id))) | ~ ($true = ((X463 @ id @ X477 @ id))))) | ~ ! [X478 : term] : (($true = ((X464 @ (sub @ X462 @ (push @ X478 @ id))))) | ~ (((X464 @ X478)) = $true)) | ~ ! [X479 : term] : (((X463 @ id @ X479 @ id)) = ((X464 @ X479))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((! [X480 : term] : (((sub @ X480 @ id)) = X480) => (! [X481 : subst,X482 : (term > $o),X483 : term] : (~ ! [X484 : term] : (~ ! [X485 : term] : ((((X482 @ (sub @ X484 @ (push @ X485 @ id)))) = $true) | ~ (((X482 @ X485)) = $true)) | ($true = ((X482 @ (lam @ X484))))) | (((X482 @ (sub @ X483 @ X481))) = $true) | ~ ! [X486 : term] : (~ ($true = ((var @ X486))) | ($true = ((X482 @ (sub @ X486 @ X481))))) | ~ ! [X487 : term,X488 : term] : ((((X482 @ (ap @ X487 @ X488))) = $true) | ~ (((X482 @ X487)) = $true) | ~ (((X482 @ X488)) = $true))) => ! [X489 : term,X490 : (term > $o)] : (($true = ((X490 @ X489))) | ~ ! [X491 : term] : (~ ($true = ((var @ X491))) | ($true = ((X490 @ X491)))) | ~ ! [X492 : term,X493 : term] : (~ ($true = ((X490 @ X492))) | ($true = ((X490 @ (ap @ X493 @ X492)))) | ~ (((X490 @ X493)) = $true)) | ~ ! [X494 : term] : ((((X490 @ (lam @ X494))) = $true) | ~ ! [X495 : term] : (~ ($true = ((X490 @ X495))) | (((X490 @ (sub @ X494 @ (push @ X495 @ id)))) = $true)))))) <=> (induction2_lthm = $true)) & (termmset_gthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X496 : term] : ~ ! [X497 : (subst > term > term)] : ~ ! [X498 : term,X499 : subst] : (((sub @ X496 @ (push @ X498 @ X499))) = ((X497 @ X499 @ X498))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (! [X500 : term] : ~ ! [X501 : (subst > term > term)] : (((sub @ X500 @ (push @ one @ sh))) != ((X501 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X502 : term,X503 : (subst > term > subst > $o)] : ((((X503 @ id @ (lam @ X502) @ id)) = $true) | ~ ! [X504 : term] : (~ ($true = ((X503 @ id @ X504 @ id))) | ($true = ((X503 @ id @ (sub @ X502 @ (push @ X504 @ id)) @ id)))) | ~ ! [X505 : (subst > term > term)] : (~ ! [X506 : subst,X507 : term,X508 : subst] : (((sub @ (X505 @ X506 @ X507) @ X508)) = ((X505 @ (comp @ X506 @ X508) @ (sub @ X507 @ X508)))) | (((X503 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true) | ~ ! [X509 : term] : (~ ($true = ((X503 @ id @ X509 @ id))) | ($true = ((X503 @ id @ (X505 @ id @ X509) @ id)))))) <=> (hoasinduction_lem3a = $true)) & ((! [X510 : subst] : (((comp @ id @ X510)) = X510) => (! [X511 : subst] : (((comp @ X511 @ id)) = X511) => (! [X512 : subst] : (((comp @ X512 @ id)) = X512) & ! [X513 : subst] : (((comp @ id @ X513)) = X513)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (axabs = $true) & (! [X514 : (term > $o),X515 : subst,X516 : term] : ~ ! [X517 : (term > $o)] : ~ ! [X518 : term] : (((X517 @ X518)) = ((X514 @ (sub @ X518 @ (push @ X516 @ X515))))) <=> (pushprop_lem0_lthm = $true)) & (! [X519 : (term > $o),X520 : (subst > term > subst > $o),X521 : term] : ((((X519 @ (lam @ X521))) = $true) | ~ ! [X522 : (subst > term > term)] : (~ ! [X523 : term] : (~ (((X520 @ id @ X523 @ id)) = $true) | (((X520 @ id @ (X522 @ id @ X523) @ id)) = $true)) | ~ ! [X524 : term,X525 : subst,X526 : subst] : (((X522 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525))) = ((sub @ (X522 @ X526 @ X524) @ X525))) | (((X520 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true)) | ~ ! [X527 : term] : (((X519 @ X527)) = ((X520 @ id @ X527 @ id))) | ~ ! [X528 : term] : ((((X519 @ (sub @ X521 @ (push @ X528 @ id)))) = $true) | ~ ($true = ((X519 @ X528))))) <=> (hoasinduction_lem3v2a = $true)) & ((axshiftcons = $true) <=> ! [X529 : term,X530 : subst] : (((comp @ sh @ (push @ X529 @ X530))) = X530)) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X531 : term,X532 : subst] : (((sub @ one @ (push @ X531 @ X532))) = X531) => ! [X533 : term,X534 : subst,X535 : (term > $o),X536 : (term > $o)] : (~ ! [X537 : term] : (((X535 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X533 @ X534))))) | ~ ($true = ((X536 @ X533))) | (((X535 @ one)) = $true)))) & ((induction = $true) <=> ! [X538 : term,X539 : (term > $o)] : (($true = ((X539 @ X538))) | ~ ! [X540 : term] : (~ ($true = ((var @ X540))) | (((X539 @ X540)) = $true)) | ~ ! [X541 : term] : (~ (((X539 @ X541)) = $true) | ($true = ((X539 @ (lam @ X541))))) | ~ ! [X542 : term,X543 : term] : (~ (((X539 @ X542)) = $true) | ~ (((X539 @ X543)) = $true) | ($true = ((X539 @ (ap @ X542 @ X543))))))) & ((pushprop_lem0 = $true) <=> ! [X544 : (term > $o),X545 : term,X546 : subst] : ~ ! [X547 : (term > $o)] : ~ ! [X548 : term] : (((X544 @ (sub @ X548 @ (push @ X545 @ X546)))) = ((X547 @ X548)))) & (((d2subst @ d_id)) = id) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj1_gthm = $true) & ((axidr = $true) <=> ! [X549 : subst] : (((comp @ X549 @ id)) = X549))),
% 6.44/1.36 inference(fool_elimination,[],[f4])).
% 6.44/1.36 thf(f6,plain,(
% 6.44/1.36 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X1 @ X4 @ (comp @ X2 @ X3)) => (X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) => (! [X5 : subst,X6 : term,X7 : subst,X8 : subst] : ((X0 @ (comp @ X8 @ X7) @ (sub @ X6 @ X7) @ X5) => (X0 @ X8 @ X6 @ (comp @ X7 @ X5))) => (! [X9 : term,X10 : term] : ((X0 @ id @ X9 @ id) => ((X0 @ id @ X10 @ id) => (X0 @ id @ (hoasap @ id @ X9 @ id @ X10) @ id))) => ! [X11 : term,X12 : term] : ((X0 @ id @ X11 @ id) => ((X0 @ id @ X12 @ id) => (X0 @ id @ (ap @ X11 @ X12) @ id)))))) = hoasinduction_lem2)),
% 6.44/1.36 inference(rectify,[],[f3])).
% 6.44/1.36 thf(f7,plain,(
% 6.44/1.36 ~ (hoasinduction_lem2 = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))))),
% 6.44/1.36 inference(fool_elimination,[],[f6])).
% 6.44/1.36 thf(f8,plain,(
% 6.44/1.36 (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & (pushprop = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoaslaminj = $true) <=> ! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (~ ! [X8 : subst,X7 : term,X6 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6)))) | ~ ! [X11 : subst,X10 : subst,X9 : term] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))))) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) = ((d2subst @ X12))) => (X12 = X13)) & (one = ((d2term @ d_one))) & ((! [X14 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X17 : term,X16 : subst] : (((X15 @ X16 @ X17)) = ((sub @ X14 @ (push @ X17 @ X16)))) => (! [X18 : term] : (((sub @ X18 @ id)) = X18) => ! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : (($true = ((X20 @ (lam @ X21)))) | ~ ! [X22 : term] : (((X19 @ id @ X22 @ id)) = ((X20 @ X22))) | ~ ! [X23 : term] : (($true = ((X20 @ (sub @ X21 @ (push @ X23 @ id))))) | ~ (((X20 @ X23)) = $true)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) | ($true = ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) | ~ ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ~ ($true = ((X19 @ id @ X28 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X29 : term,X30 : (subst > term > subst > $o)] : (~ ! [X31 : term] : (($true = ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id))) | ~ ($true = ((X30 @ id @ X31 @ id)))) | ~ ! [X32 : (subst > term > term),X33 : term] : (~ ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) | ~ ! [X37 : term] : (($true = ((X30 @ id @ (X32 @ id @ X37) @ id))) | ~ ($true = ((X30 @ id @ X37 @ id)))) | ~ ! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) | ($true = ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id)))) | ($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))))) & (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X43 : (term > $o),X44 : term] : (~ ! [X45 : term] : (($true = ((X43 @ X45))) | ~ (((var @ X45)) = $true)) | ~ ! [X46 : term,X47 : term] : (~ ($true = ((X43 @ X47))) | ~ (((X43 @ X46)) = $true) | ($true = ((X43 @ (ap @ X47 @ X46))))) | (((X43 @ X44)) = $true) | ~ ! [X48 : term] : (~ ! [X49 : term] : (($true = ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) | ~ (((X43 @ X49)) = $true)) | (((X43 @ (lam @ X48))) = $true))) => (! [X50 : (subst > term > subst > $o),X51 : term,X52 : term] : (~ ! [X53 : term,X54 : term] : (~ ($true = ((X50 @ id @ X54 @ id))) | ~ ($true = ((X50 @ id @ X53 @ id))) | (((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true)) | ~ ($true = ((X50 @ id @ X51 @ id))) | ~ ($true = ((X50 @ id @ X52 @ id))) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : (~ ($true = ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57))) | ($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57))))) | ($true = ((X50 @ id @ (ap @ X51 @ X52) @ id))) | ~ ! [X59 : subst,X60 : subst,X61 : term,X62 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ~ ($true = ((X50 @ X62 @ X61 @ (comp @ X60 @ X59)))))) => (! [X63 : (subst > term > subst > $o),X64 : term] : (($true = ((X63 @ id @ (lam @ X64) @ id))) | ~ ! [X65 : subst,X66 : subst,X67 : term,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | ~ (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) = $true)) | ~ ! [X69 : term] : (~ (((X63 @ id @ X69 @ id)) = $true) | ($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id)))) | ~ ! [X70 : (subst > term > term)] : (($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X71 : term] : ((((X63 @ id @ (X70 @ id @ X71) @ id)) = $true) | ~ ($true = ((X63 @ id @ X71 @ id)))) | ~ ! [X73 : subst,X72 : term,X74 : subst] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) = ((sub @ (X70 @ X74 @ X72) @ X73)))) | ~ ! [X75 : term,X76 : subst,X77 : subst,X78 : subst] : (~ ($true = ((X63 @ X78 @ X75 @ (comp @ X76 @ X77)))) | (((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true))) => ! [X79 : (subst > term > subst > $o),X80 : term] : (~ ! [X81 : term] : (($true = ((X79 @ id @ X81 @ id))) | ~ (((var @ (sub @ X81 @ id))) = $true)) | ~ ! [X82 : (subst > term > term)] : (~ ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83))) | ~ ! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | ~ (((X79 @ id @ X86 @ id)) = $true)) | ($true = ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id)))) | ($true = ((X79 @ id @ X80 @ id))) | ~ ! [X87 : term,X88 : term] : (~ ($true = ((X79 @ id @ X87 @ id))) | ~ (((X79 @ id @ X88 @ id)) = $true) | ($true = ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)))) | ~ ! [X89 : subst,X90 : subst,X91 : term,X92 : subst] : ((((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) = $true) | ~ (((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) = $true)) | ~ ! [X93 : subst,X94 : subst,X95 : term,X96 : subst] : (~ ($true = ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) | ($true = ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96))))))))) & (hoasinduction_lem1v2 = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X98 : term,X97 : term,X99 : (subst > term > term)] : (~ ! [X100 : term,X102 : subst,X101 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))) | (((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98)))) <=> (hoaslamnotap = $true)) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X106 : (subst > term > subst > $o)] : ~ ! [X107 : (term > $o)] : ~ ! [X108 : term] : (((X106 @ id @ X108 @ id)) = ((X107 @ X108))) => (! [X109 : term,X110 : (term > $o)] : (~ ! [X111 : term] : (~ ! [X112 : term] : (~ ($true = ((X110 @ X112))) | ($true = ((X110 @ (sub @ X111 @ (push @ X112 @ id)))))) | ($true = ((X110 @ (lam @ X111))))) | ~ ! [X113 : term,X114 : term] : (($true = ((X110 @ (ap @ X114 @ X113)))) | ~ (((X110 @ X114)) = $true) | ~ ($true = ((X110 @ X113)))) | (((X110 @ X109)) = $true) | ~ ! [X115 : term] : (~ ($true = ((var @ X115))) | ($true = ((X110 @ X115))))) => (! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X117 : term,X118 : (term > $o),X119 : (subst > term > subst > $o)] : (($true = ((X118 @ (lam @ X117)))) | ~ ! [X120 : (subst > term > term)] : ((((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ~ ! [X123 : subst,X121 : term,X122 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) = ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122)))) | ~ ! [X124 : term] : (~ ($true = ((X119 @ id @ X124 @ id))) | ($true = ((X119 @ id @ (X120 @ id @ X124) @ id))))) | ~ ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) | ~ ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ~ ($true = ((X118 @ X126))))) => ! [X127 : (subst > term > subst > $o),X128 : term] : (~ ! [X129 : term,X130 : term] : (~ ($true = ((X127 @ id @ X129 @ id))) | ~ ($true = ((X127 @ id @ X130 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)))) | ($true = ((X127 @ id @ X128 @ id))) | ~ ! [X131 : (subst > term > term)] : (($true = ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ~ ! [X132 : term] : (~ ($true = ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id)))) | ~ ! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133))))))))))) & ((induction2 = $true) <=> ! [X136 : term,X137 : (term > $o)] : (~ ! [X138 : term,X139 : term] : (~ ($true = ((X137 @ X138))) | ~ ($true = ((X137 @ X139))) | ($true = ((X137 @ (ap @ X139 @ X138))))) | ~ ! [X140 : term] : (~ ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ ($true = ((X137 @ X141)))) | ($true = ((X137 @ (lam @ X140))))) | ~ ! [X142 : term] : (~ (((var @ X142)) = $true) | ($true = ((X137 @ X142)))) | ($true = ((X137 @ X136))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ~ (ulamvar1 = $true) & ((hoaslaminj_lthm = $true) <=> (! [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) = X146) => (! [X148 : term,X147 : term] : ((X147 = X148) | (((lam @ X147)) != ((lam @ X148)))) => ! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : (~ ! [X156 : subst,X158 : subst,X157 : term] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) = ((sub @ (X152 @ X156 @ X157) @ X158))) | (((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ~ ! [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) = ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one))))))))) & ((pushprop_lem1v2 = $true) <=> ! [X159 : subst,X160 : (term > $o),X161 : (term > $o),X162 : term] : (~ ($true = ((X160 @ X162))) | (((X161 @ one)) = $true) | ~ ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163))))) & (axapp = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X164 : (term > $o),X165 : term,X166 : (subst > term > subst > $o)] : (~ ! [X167 : (subst > term > term)] : (($true = ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))) | ~ ! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) | ~ ! [X171 : term] : (~ (((X166 @ id @ X171 @ id)) = $true) | (((X166 @ id @ (X167 @ id @ X171) @ id)) = $true))) | ~ ! [X172 : term,X173 : subst,X174 : subst,X175 : subst] : (~ ($true = ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174))) | ($true = ((X166 @ X173 @ X172 @ (comp @ X175 @ X174))))) | ($true = ((X164 @ (lam @ X165)))) | ~ ! [X176 : term] : (($true = ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) | ~ (((X164 @ X176)) = $true)) | ~ ! [X177 : subst,X178 : subst,X179 : subst,X180 : term] : (($true = ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179))) | ~ ($true = ((X166 @ X178 @ X180 @ (comp @ X177 @ X179))))) | ~ ! [X181 : term] : (((X164 @ X181)) = ((X166 @ id @ X181 @ id))))) & ((hoasapinj1_lthm = $true) <=> (! [X182 : term] : (((sub @ X182 @ id)) = X182) => (! [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 = X185) | (((ap @ X183 @ X186)) != ((ap @ X185 @ X184)))) => ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190))))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (! [X195 : term,X196 : (subst > term > subst > $o)] : (($true = ((X196 @ id @ X195 @ id))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~ ($true = ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id)))) | (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))) | ~ ! [X202 : term,X203 : term] : ((((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) = $true) | ~ ($true = ((X196 @ id @ X203 @ id))) | ~ ($true = ((X196 @ id @ X202 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & ((! [X205 : (subst > term > subst > $o)] : ~ ! [X206 : (term > $o)] : ~ ! [X207 : term] : (((X205 @ id @ X207 @ id)) = ((X206 @ X207))) => (! [X208 : term,X209 : (term > $o)] : (~ ! [X210 : term] : (($true = ((X209 @ X210))) | ~ ($true = ((var @ X210)))) | ~ ! [X211 : term] : (~ ! [X212 : term] : (($true = ((X209 @ (sub @ X211 @ (push @ X212 @ id))))) | ~ ($true = ((X209 @ X212)))) | ($true = ((X209 @ (lam @ X211))))) | ~ ! [X213 : term,X214 : term] : (~ ($true = ((X209 @ X214))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ~ ($true = ((X209 @ X213)))) | ($true = ((X209 @ X208)))) => (! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X216 : (term > $o),X217 : term,X218 : (subst > term > subst > $o)] : (~ ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) | ($true = ((X216 @ (lam @ X217)))) | ~ ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ~ ($true = ((X216 @ X220)))) | ~ ! [X221 : (subst > term > term)] : (~ ! [X222 : term] : (~ (((X218 @ id @ X222 @ id)) = $true) | (((X218 @ id @ (X221 @ id @ X222) @ id)) = $true)) | ($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ~ ! [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) = ((sub @ (X221 @ X223 @ X225) @ X224))))) => ! [X226 : term,X227 : (subst > term > subst > $o)] : ((((X227 @ id @ X226 @ id)) = $true) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : (($true = ((X227 @ X228 @ X231 @ (comp @ X229 @ X230)))) | ~ (((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) = $true)) | ~ ! [X232 : term] : (($true = ((X227 @ id @ X232 @ id))) | ~ ($true = ((var @ (sub @ X232 @ id))))) | ~ ! [X233 : term,X234 : term] : (~ ($true = ((X227 @ id @ X233 @ id))) | ~ ($true = ((X227 @ id @ X234 @ id))) | (((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) = $true)) | ~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term] : (($true = ((X227 @ id @ (X235 @ id @ X236) @ id))) | ~ (((X227 @ id @ X236 @ id)) = $true)) | (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237)))) | ~ ! [X240 : subst,X241 : term,X242 : subst,X243 : subst] : (($true = ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242))) | ~ (((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ~ ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh))))) & (pushprop_lem2v2_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ((induction2lem = $true) <=> ! [X251 : (term > $o),X252 : subst,X253 : term] : (~ ! [X254 : term] : (($true = ((X251 @ (lam @ X254)))) | ~ ! [X255 : term] : ((((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true) | ~ ($true = ((X251 @ X255))))) | ~ ! [X256 : term,X257 : term] : (~ (((X251 @ X257)) = $true) | ($true = ((X251 @ (ap @ X256 @ X257)))) | ~ ($true = ((X251 @ X256)))) | ~ ! [X258 : term] : (~ (((var @ X258)) = $true) | ($true = ((X251 @ (sub @ X258 @ X252))))) | (((X251 @ (sub @ X253 @ X252))) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (ulamvarind = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((apinj1 = $true) <=> ! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265))) & ! [X267 : d_term] : (d_one = X267) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X268 : term,X269 : (subst > term > subst > $o)] : (~ ! [X270 : (subst > term > term)] : (~ ! [X271 : term] : (~ ($true = ((X269 @ id @ X271 @ id))) | ($true = ((X269 @ id @ (X270 @ id @ X271) @ id)))) | ($true = ((X269 @ id @ (lam @ (X270 @ sh @ one)) @ id))) | ~ ! [X273 : term,X274 : subst,X272 : subst] : (((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274))) = ((sub @ (X270 @ X272 @ X273) @ X274)))) | ~ ! [X275 : term] : (~ (((X269 @ id @ X275 @ id)) = $true) | (((X269 @ id @ (sub @ X268 @ (push @ X275 @ id)) @ id)) = $true)) | ($true = ((X269 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (axclos = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X276 : term] : ~ ! [X277 : (subst > term > term)] : ~ ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278))))) & ((hoasapinj1 = $true) <=> ! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280))))) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X284 : term,X285 : (subst > term > subst > $o)] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ~ ! [X286 : term] : (~ ($true = ((X285 @ id @ X286 @ id))) | ($true = ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id)))) | ~ ! [X287 : subst,X288 : subst,X289 : subst,X290 : term] : ((((X285 @ X287 @ X290 @ (comp @ X289 @ X288))) = $true) | ~ ($true = ((X285 @ (comp @ X287 @ X289) @ (sub @ X290 @ X289) @ X288)))) | ~ ! [X291 : (subst > term > term)] : (~ ! [X294 : term,X293 : subst,X292 : subst] : (((sub @ (X291 @ X292 @ X294) @ X293)) = ((X291 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) | ~ ! [X295 : term] : (($true = ((X285 @ id @ (X291 @ id @ X295) @ id))) | ~ ($true = ((X285 @ id @ X295 @ id)))) | ($true = ((X285 @ id @ (lam @ (X291 @ sh @ one)) @ id)))) | ~ ! [X296 : subst,X297 : subst,X298 : term,X299 : subst] : ((((X285 @ (comp @ X297 @ X299) @ (sub @ X298 @ X299) @ X296)) = $true) | ~ ($true = ((X285 @ X297 @ X298 @ (comp @ X299 @ X296))))))) & (apnotvar = $true) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) <=> (termmset = $true)) & (hoaslaminj_gthm = $true) & (axassoc = $true) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & (substmonoid_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)))))))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X301 : (term > $o),X302 : term,X303 : term,X304 : (subst > term > subst > $o)] : (~ ! [X305 : term,X306 : term] : (~ ($true = ((X304 @ id @ X306 @ id))) | ~ ($true = ((X304 @ id @ X305 @ id))) | (((X304 @ id @ (ap @ (sub @ X305 @ id) @ X306) @ id)) = $true)) | ~ ! [X307 : subst,X308 : subst,X309 : subst,X310 : term] : (($true = ((X304 @ X307 @ X310 @ (comp @ X308 @ X309)))) | ~ (((X304 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309)) = $true)) | ($true = ((X301 @ (ap @ X302 @ X303)))) | ~ ($true = ((X301 @ X303))) | ~ ! [X311 : term] : (((X301 @ X311)) = ((X304 @ id @ X311 @ id))) | ~ ($true = ((X301 @ X302))) | ~ ! [X312 : term,X313 : subst,X314 : subst,X315 : subst] : (~ ($true = ((X304 @ X313 @ X312 @ (comp @ X314 @ X315)))) | (((X304 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314) @ X315)) = $true)))) & ((laminj = $true) <=> ! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lthm_orig = $true) & (axvarshift = $true) & ! [X318 : d_subst] : (d_id = X318) & ((hoasinduction_lem0_lthm = $true) <=> ! [X319 : (subst > term > subst > $o)] : ~ ! [X320 : (term > $o)] : ~ ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id)))) & (lamnotvar = $true) & (hoasinduction_lem2_gthm = $true) & ((! [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) = X323) => (! [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) = X324) => ! [X326 : subst,X327 : (term > $o),X328 : (term > $o),X329 : term,X330 : term] : (~ (((X328 @ X329)) = $true) | ($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326)))))))) <=> (pushprop_lem1_lthm = $true)) & ! [X331 : d_term,X332 : d_term] : ((((d2term @ X331)) = ((d2term @ X332))) => (X331 = X332)) & (! [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (~ (((X335 @ id @ X333 @ id)) = $true) | ~ ($true = ((X335 @ id @ X334 @ id))) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : (($true = ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) | ~ (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) = $true)) | ~ ! [X340 : term,X341 : subst,X342 : subst,X343 : subst] : ((((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) = $true) | ~ ($true = ((X335 @ X342 @ X340 @ (comp @ X341 @ X343))))) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true) | ~ ! [X344 : term,X345 : term] : (~ (((X335 @ id @ X344 @ id)) = $true) | ~ (((X335 @ id @ X345 @ id)) = $true) | ($true = ((X335 @ id @ (ap @ (sub @ X344 @ id) @ X345) @ id))))) <=> (hoasinduction_lem2 = $true)) & ((substmonoid = $true) <=> (! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346))) & (! [X348 : term,X349 : (subst > term > subst > $o)] : (~ ! [X350 : term,X351 : term] : (~ ($true = ((X349 @ id @ X351 @ id))) | ~ ($true = ((X349 @ id @ X350 @ id))) | ($true = ((X349 @ id @ (ap @ (sub @ X350 @ id) @ X351) @ id)))) | (((X349 @ id @ X348 @ id)) = $true) | ~ ! [X352 : (subst > term > term)] : ((((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) = $true) | ~ ! [X355 : subst,X354 : term,X353 : subst] : (((X352 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X353 @ X354) @ X355))) | ~ ! [X356 : term] : (($true = ((X349 @ id @ (X352 @ id @ X356) @ id))) | ~ (((X349 @ id @ X356 @ id)) = $true))) | ~ ! [X357 : term] : ((((X349 @ id @ X357 @ id)) = $true) | ~ ($true = ((var @ (sub @ X357 @ id))))) | ~ ! [X358 : subst,X359 : subst,X360 : subst,X361 : term] : (~ (((X349 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359) @ X358)) = $true) | ($true = ((X349 @ X360 @ X361 @ (comp @ X359 @ X358))))) | ~ ! [X362 : subst,X363 : subst,X364 : subst,X365 : term] : ((((X349 @ (comp @ X364 @ X362) @ (sub @ X365 @ X362) @ X363)) = $true) | ~ ($true = ((X349 @ X364 @ X365 @ (comp @ X362 @ X363)))))) <=> (hoasinduction = $true)) & (! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : (subst > term > term)] : (~ ! [X369 : term] : (($true = ((X366 @ id @ (X368 @ id @ X369) @ id))) | ~ ($true = ((X366 @ id @ X369 @ id)))) | ~ ! [X371 : term,X370 : subst,X372 : subst] : (((X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) = ((sub @ (X368 @ X370 @ X371) @ X372))) | ($true = ((X366 @ id @ (lam @ (X368 @ sh @ one)) @ id)))) | ~ ! [X373 : term] : (~ ($true = ((X366 @ id @ X373 @ id))) | ($true = ((X366 @ id @ (sub @ X367 @ (push @ X373 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axscons = $true) <=> ! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374)) & ((hoasapinj2_lthm = $true) <=> (! [X378 : term,X375 : term,X376 : term,X377 : term] : ((((ap @ X377 @ X378)) != ((ap @ X375 @ X376))) | (X376 = X378)) => ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379)))))) & (hoasinduction_lem1v2_gthm = $true) & ~ (lamnotap = $true) & ((! [X383 : subst,X384 : term] : (((sub @ one @ (push @ X384 @ X383))) = X384) => (! [X386 : subst,X385 : term] : (((comp @ sh @ (push @ X385 @ X386))) = X386) => (! [X387 : subst] : (((comp @ X387 @ id)) = X387) => (! [X388 : (term > $o),X389 : term] : (~ ! [X390 : term] : (~ (((X388 @ X390)) = $true) | (((X388 @ (lam @ X390))) = $true)) | ~ ! [X391 : term] : (~ ($true = ((var @ X391))) | ($true = ((X388 @ X391)))) | ~ ! [X392 : term,X393 : term] : (($true = ((X388 @ (ap @ X392 @ X393)))) | ~ (((X388 @ X393)) = $true) | ~ ($true = ((X388 @ X392)))) | (((X388 @ X389)) = $true)) => ! [X394 : term,X395 : (term > $o),X396 : subst] : (~ ! [X397 : term,X398 : term] : ((((X395 @ (ap @ X398 @ X397))) = $true) | ~ ($true = ((X395 @ X398))) | ~ ($true = ((X395 @ X397)))) | ($true = ((X395 @ (sub @ X394 @ X396)))) | ~ ! [X399 : term] : ((((X395 @ (lam @ X399))) = $true) | ~ ! [X400 : term] : (($true = ((X395 @ (sub @ X399 @ (push @ X400 @ id))))) | ~ (((X395 @ X400)) = $true))) | ~ ! [X401 : term] : (($true = ((X395 @ (sub @ X401 @ X396)))) | ~ ($true = ((var @ X401))))))))) <=> (induction2lem_lthm = $true)) & ((! [X402 : term] : (((sub @ X402 @ id)) = X402) => (! [X403 : term,X404 : (subst > term > subst > $o)] : (~ ! [X405 : term] : (~ ($true = ((X404 @ id @ X405 @ id))) | ($true = ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)))) | ($true = ((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id))) | ~ ! [X406 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true) | ~ ! [X407 : term] : (~ ($true = ((X404 @ id @ X407 @ id))) | ($true = ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ~ ! [X410 : subst,X409 : term,X408 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X406 @ X408 @ X409) @ X410))))) => ! [X411 : (subst > term > subst > $o),X412 : term] : (~ ! [X413 : subst,X414 : subst,X415 : subst,X416 : term] : (($true = ((X411 @ X414 @ X416 @ (comp @ X415 @ X413)))) | ~ ($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X416 @ X415) @ X413)))) | ~ ! [X417 : (subst > term > term)] : (($true = ((X411 @ id @ (lam @ (X417 @ sh @ one)) @ id))) | ~ ! [X418 : subst,X419 : subst,X420 : term] : (((X417 @ (comp @ X418 @ X419) @ (sub @ X420 @ X419))) = ((sub @ (X417 @ X418 @ X420) @ X419))) | ~ ! [X421 : term] : (~ ($true = ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (X417 @ id @ X421) @ id))))) | ~ ! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : (~ ($true = ((X411 @ X425 @ X424 @ (comp @ X423 @ X422)))) | (((X411 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423) @ X422)) = $true)) | ~ ! [X426 : term] : (($true = ((X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))) | ~ ($true = ((X411 @ id @ X426 @ id)))) | ($true = ((X411 @ id @ (lam @ X412) @ id)))))) <=> (hoasinduction_lem3_lthm = $true)) & (axmap = $true) & (! [X427 : (term > $o),X428 : term,X429 : term,X430 : (term > $o),X431 : subst] : (($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431))))) | ~ ($true = ((X430 @ X429)))) <=> (pushprop_lem1 = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ((! [X432 : term] : (((sub @ X432 @ id)) = X432) => (! [X433 : (subst > term > subst > $o),X434 : term] : (~ ! [X435 : (subst > term > term)] : (~ ! [X436 : term] : (~ (((X433 @ id @ X436 @ id)) = $true) | ($true = ((X433 @ id @ (X435 @ id @ X436) @ id)))) | (((X433 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true) | ~ ! [X437 : subst,X439 : term,X438 : subst] : (((sub @ (X435 @ X438 @ X439) @ X437)) = ((X435 @ (comp @ X438 @ X437) @ (sub @ X439 @ X437))))) | (((X433 @ id @ (lam @ (sub @ X434 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X440 : term] : (($true = ((X433 @ id @ (sub @ X434 @ (push @ X440 @ id)) @ id))) | ~ (((X433 @ id @ X440 @ id)) = $true))) => ! [X441 : term,X442 : (subst > term > subst > $o)] : (($true = ((X442 @ id @ (lam @ X441) @ id))) | ~ ! [X443 : (subst > term > term)] : (~ ! [X444 : subst,X445 : subst,X446 : term] : (((sub @ (X443 @ X444 @ X446) @ X445)) = ((X443 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445)))) | ($true = ((X442 @ id @ (lam @ (X443 @ sh @ one)) @ id))) | ~ ! [X447 : term] : (~ (((X442 @ id @ X447 @ id)) = $true) | ($true = ((X442 @ id @ (X443 @ id @ X447) @ id))))) | ~ ! [X448 : term] : (($true = ((X442 @ id @ (sub @ X441 @ (push @ X448 @ id)) @ id))) | ~ ($true = ((X442 @ id @ X448 @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X449 : term] : (((sub @ X449 @ id)) = X449) => ! [X450 : term] : (((sub @ X450 @ id)) = X450))) & ((! [X451 : term] : (((sub @ X451 @ id)) = X451) => ! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (~ ! [X455 : subst,X456 : term,X457 : subst,X458 : subst] : ((((X453 @ X457 @ X456 @ (comp @ X455 @ X458))) = $true) | ~ ($true = ((X453 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455) @ X458)))) | ($true = ((X454 @ (lam @ X452)))) | ~ ! [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (($true = ((X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461) @ X462))) | ~ (((X453 @ X459 @ X460 @ (comp @ X461 @ X462))) = $true)) | ~ ! [X463 : (subst > term > term)] : (($true = ((X453 @ id @ (lam @ (X463 @ sh @ one)) @ id))) | ~ ! [X465 : term,X464 : subst,X466 : subst] : (((X463 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X463 @ X466 @ X465) @ X464))) | ~ ! [X467 : term] : ((((X453 @ id @ (X463 @ id @ X467) @ id)) = $true) | ~ (((X453 @ id @ X467 @ id)) = $true))) | ~ ! [X468 : term] : ((((X454 @ (sub @ X452 @ (push @ X468 @ id)))) = $true) | ~ ($true = ((X454 @ X468)))) | ~ ! [X469 : term] : (((X454 @ X469)) = ((X453 @ id @ X469 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((! [X470 : term] : (((sub @ X470 @ id)) = X470) => (! [X471 : subst,X472 : (term > $o),X473 : term] : (~ ! [X474 : term] : (~ ! [X475 : term] : ((((X472 @ (sub @ X474 @ (push @ X475 @ id)))) = $true) | ~ (((X472 @ X475)) = $true)) | (((X472 @ (lam @ X474))) = $true)) | ($true = ((X472 @ (sub @ X473 @ X471)))) | ~ ! [X476 : term] : (~ (((var @ X476)) = $true) | ($true = ((X472 @ (sub @ X476 @ X471))))) | ~ ! [X477 : term,X478 : term] : (($true = ((X472 @ (ap @ X477 @ X478)))) | ~ ($true = ((X472 @ X477))) | ~ (((X472 @ X478)) = $true))) => ! [X479 : term,X480 : (term > $o)] : ((((X480 @ X479)) = $true) | ~ ! [X481 : term] : (~ (((var @ X481)) = $true) | ($true = ((X480 @ X481)))) | ~ ! [X482 : term,X483 : term] : (~ ($true = ((X480 @ X482))) | (((X480 @ (ap @ X483 @ X482))) = $true) | ~ (((X480 @ X483)) = $true)) | ~ ! [X484 : term] : ((((X480 @ (lam @ X484))) = $true) | ~ ! [X485 : term] : (~ (((X480 @ X485)) = $true) | ($true = ((X480 @ (sub @ X484 @ (push @ X485 @ id)))))))))) <=> (induction2_lthm = $true)) & (termmset_gthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X486 : term] : ~ ! [X487 : (subst > term > term)] : ~ ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (! [X490 : term] : ~ ! [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) != ((X491 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X492 : term,X493 : (subst > term > subst > $o)] : (($true = ((X493 @ id @ (lam @ X492) @ id))) | ~ ! [X494 : term] : (~ (((X493 @ id @ X494 @ id)) = $true) | ($true = ((X493 @ id @ (sub @ X492 @ (push @ X494 @ id)) @ id)))) | ~ ! [X495 : (subst > term > term)] : (~ ! [X496 : subst,X497 : term,X498 : subst] : (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X495 @ X496 @ X497) @ X498))) | (((X493 @ id @ (lam @ (X495 @ sh @ one)) @ id)) = $true) | ~ ! [X499 : term] : (~ (((X493 @ id @ X499 @ id)) = $true) | (((X493 @ id @ (X495 @ id @ X499) @ id)) = $true)))) <=> (hoasinduction_lem3a = $true)) & ((substmonoid_lthm = $true) <=> (! [X500 : subst] : (((comp @ id @ X500)) = X500) => (! [X501 : subst] : (((comp @ X501 @ id)) = X501) => (! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502))))) & (hoasinduction_lem3v2_gthm = $true) & (axabs = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X506 : term,X505 : subst,X504 : (term > $o)] : ~ ! [X507 : (term > $o)] : ~ ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (! [X509 : (term > $o),X510 : (subst > term > subst > $o),X511 : term] : ((((X509 @ (lam @ X511))) = $true) | ~ ! [X512 : (subst > term > term)] : (~ ! [X513 : term] : (~ ($true = ((X510 @ id @ X513 @ id))) | ($true = ((X510 @ id @ (X512 @ id @ X513) @ id)))) | ~ ! [X516 : subst,X514 : term,X515 : subst] : (((X512 @ (comp @ X516 @ X515) @ (sub @ X514 @ X515))) = ((sub @ (X512 @ X516 @ X514) @ X515))) | ($true = ((X510 @ id @ (lam @ (X512 @ sh @ one)) @ id)))) | ~ ! [X517 : term] : (((X509 @ X517)) = ((X510 @ id @ X517 @ id))) | ~ ! [X518 : term] : (($true = ((X509 @ (sub @ X511 @ (push @ X518 @ id))))) | ~ ($true = ((X509 @ X518))))) <=> (hoasinduction_lem3v2a = $true)) & ((axshiftcons = $true) <=> ! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520)) & (hoaslamnotap_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) = X521) => ! [X523 : term,X524 : subst,X525 : (term > $o),X526 : (term > $o)] : (~ ! [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) = ((X525 @ X527))) | ~ (((X526 @ X523)) = $true) | (((X525 @ one)) = $true)))) & ((induction = $true) <=> ! [X528 : term,X529 : (term > $o)] : ((((X529 @ X528)) = $true) | ~ ! [X530 : term] : (~ ($true = ((var @ X530))) | (((X529 @ X530)) = $true)) | ~ ! [X531 : term] : (~ (((X529 @ X531)) = $true) | ($true = ((X529 @ (lam @ X531))))) | ~ ! [X532 : term,X533 : term] : (~ (((X529 @ X532)) = $true) | ~ ($true = ((X529 @ X533))) | ($true = ((X529 @ (ap @ X532 @ X533))))))) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ~ ! [X537 : (term > $o)] : ~ ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = id) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj1_gthm = $true) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) <=> (axidr = $true))),
% 6.44/1.36 inference(rectify,[],[f5])).
% 6.44/1.36 thf(f9,plain,(
% 6.44/1.36 (! [X269 : (subst > term > subst > $o),X268 : term] : (~ ! [X275 : term] : ((((X269 @ id @ X275 @ id)) != $true) | (((X269 @ id @ (sub @ X268 @ (push @ X275 @ id)) @ id)) = $true)) | ($true = ((X269 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id))) | ~ ! [X270 : (subst > term > term)] : (~ ! [X271 : term] : (($true != ((X269 @ id @ X271 @ id))) | ($true = ((X269 @ id @ (X270 @ id @ X271) @ id)))) | ~ ! [X273 : term,X274 : subst,X272 : subst] : (((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274))) = ((sub @ (X270 @ X272 @ X273) @ X274))) | ($true = ((X269 @ id @ (lam @ (X270 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((substmonoid_lthm = $true) <=> (! [X500 : subst] : (((comp @ id @ X500)) = X500) => (! [X501 : subst] : (((comp @ X501 @ id)) = X501) => (! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502))))) & ((hoasinduction_lthm = $true) <=> (! [X43 : (term > $o),X44 : term] : (~ ! [X48 : term] : ((((X43 @ (lam @ X48))) = $true) | ~ ! [X49 : term] : (($true = ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) | (((X43 @ X49)) != $true))) | ~ ! [X47 : term,X46 : term] : ((((X43 @ X46)) != $true) | ($true != ((X43 @ X47))) | ($true = ((X43 @ (ap @ X47 @ X46))))) | (((X43 @ X44)) = $true) | ~ ! [X45 : term] : (($true = ((X43 @ X45))) | (((var @ X45)) != $true))) => (! [X50 : (subst > term > subst > $o),X52 : term,X51 : term] : (~ ! [X62 : subst,X59 : subst,X61 : term,X60 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ($true != ((X50 @ X62 @ X61 @ (comp @ X60 @ X59))))) | ($true = ((X50 @ id @ (ap @ X51 @ X52) @ id))) | ~ ! [X56 : subst,X55 : subst,X57 : subst,X58 : term] : (($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57)))) | ($true != ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57)))) | ($true != ((X50 @ id @ X52 @ id))) | ($true != ((X50 @ id @ X51 @ id))) | ~ ! [X53 : term,X54 : term] : ((((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true) | ($true != ((X50 @ id @ X54 @ id))) | ($true != ((X50 @ id @ X53 @ id))))) => (! [X63 : (subst > term > subst > $o),X64 : term] : (~ ! [X70 : (subst > term > term)] : (~ ! [X71 : term] : ((((X63 @ id @ (X70 @ id @ X71) @ id)) = $true) | ($true != ((X63 @ id @ X71 @ id)))) | ($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X73 : subst,X72 : term,X74 : subst] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) = ((sub @ (X70 @ X74 @ X72) @ X73)))) | ($true = ((X63 @ id @ (lam @ X64) @ id))) | ~ ! [X69 : term] : (($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id))) | (((X63 @ id @ X69 @ id)) != $true)) | ~ ! [X75 : term,X77 : subst,X78 : subst,X76 : subst] : ((((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true) | ($true != ((X63 @ X78 @ X75 @ (comp @ X76 @ X77))))) | ~ ! [X66 : subst,X67 : term,X65 : subst,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) != $true))) => ! [X80 : term,X79 : (subst > term > subst > $o)] : (~ ! [X96 : subst,X95 : term,X93 : subst,X94 : subst] : (($true != ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) | ($true = ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96)))) | ~ ! [X81 : term] : (($true = ((X79 @ id @ X81 @ id))) | (((var @ (sub @ X81 @ id))) != $true)) | ~ ! [X82 : (subst > term > term)] : (~ ! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | (((X79 @ id @ X86 @ id)) != $true)) | ~ ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83))) | ($true = ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id)))) | ~ ! [X91 : term,X92 : subst,X89 : subst,X90 : subst] : ((((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) != $true) | (((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) = $true)) | ~ ! [X88 : term,X87 : term] : ((((X79 @ id @ X88 @ id)) != $true) | ($true = ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id))) | ($true != ((X79 @ id @ X87 @ id)))) | ($true = ((X79 @ id @ X80 @ id)))))))) & ((termmset_lthm = $true) <=> (! [X449 : term] : (((sub @ X449 @ id)) = X449) => ! [X450 : term] : (((sub @ X450 @ id)) = X450))) & (hoasinduction_lem2v2_gthm = $true) & (one = ((d2term @ d_one))) & ((! [X14 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X17 : term,X16 : subst] : (((X15 @ X16 @ X17)) = ((sub @ X14 @ (push @ X17 @ X16)))) => (! [X18 : term] : (((sub @ X18 @ id)) = X18) => ! [X19 : (subst > term > subst > $o),X21 : term,X20 : (term > $o)] : (($true = ((X20 @ (lam @ X21)))) | ~ ! [X22 : term] : (((X19 @ id @ X22 @ id)) = ((X20 @ X22))) | ~ ! [X23 : term] : ((((X20 @ X23)) != $true) | ($true = ((X20 @ (sub @ X21 @ (push @ X23 @ id)))))) | ~ ! [X24 : (subst > term > term)] : (($true = ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) | ~ ! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) | ~ ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ($true != ((X19 @ id @ X28 @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X486 : term] : ~ ! [X487 : (subst > term > term)] : ~ ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (apnotvar = $true) & (induction2lem_gthm = $true) & ((induction2lem = $true) <=> ! [X252 : subst,X253 : term,X251 : (term > $o)] : (~ ! [X258 : term] : (($true = ((X251 @ (sub @ X258 @ X252)))) | (((var @ X258)) != $true)) | ~ ! [X254 : term] : (($true = ((X251 @ (lam @ X254)))) | ~ ! [X255 : term] : (($true != ((X251 @ X255))) | (((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true))) | ~ ! [X256 : term,X257 : term] : (($true != ((X251 @ X256))) | (((X251 @ X257)) != $true) | ($true = ((X251 @ (ap @ X256 @ X257))))) | (((X251 @ (sub @ X253 @ X252))) = $true))) & (hoaslamnotvar = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (pushprop_lthm_orig = $true) & (! [X490 : term] : ~ ! [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) != ((X491 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (termmset_gthm = $true) & (lamnotap != $true) & (pushprop_lem1_gthm = $true) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (! [X493 : (subst > term > subst > $o),X492 : term] : (~ ! [X495 : (subst > term > term)] : (~ ! [X496 : subst,X497 : term,X498 : subst] : (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X495 @ X496 @ X497) @ X498))) | ~ ! [X499 : term] : ((((X493 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X493 @ id @ X499 @ id)) != $true)) | (((X493 @ id @ (lam @ (X495 @ sh @ one)) @ id)) = $true)) | ($true = ((X493 @ id @ (lam @ X492) @ id))) | ~ ! [X494 : term] : (($true = ((X493 @ id @ (sub @ X492 @ (push @ X494 @ id)) @ id))) | (((X493 @ id @ X494 @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & (! [X284 : term,X285 : (subst > term > subst > $o)] : (~ ! [X290 : term,X288 : subst,X287 : subst,X289 : subst] : ((((X285 @ X287 @ X290 @ (comp @ X289 @ X288))) = $true) | ($true != ((X285 @ (comp @ X287 @ X289) @ (sub @ X290 @ X289) @ X288)))) | ~ ! [X298 : term,X296 : subst,X297 : subst,X299 : subst] : (($true != ((X285 @ X297 @ X298 @ (comp @ X299 @ X296)))) | (((X285 @ (comp @ X297 @ X299) @ (sub @ X298 @ X299) @ X296)) = $true)) | ~ ! [X286 : term] : (($true = ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) | ($true != ((X285 @ id @ X286 @ id)))) | (((X285 @ id @ (lam @ X284) @ id)) = $true) | ~ ! [X291 : (subst > term > term)] : (($true = ((X285 @ id @ (lam @ (X291 @ sh @ one)) @ id))) | ~ ! [X294 : term,X293 : subst,X292 : subst] : (((sub @ (X291 @ X292 @ X294) @ X293)) = ((X291 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) | ~ ! [X295 : term] : (($true != ((X285 @ id @ X295 @ id))) | ($true = ((X285 @ id @ (X291 @ id @ X295) @ id)))))) <=> (hoasinduction_lem3 = $true)) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((axscons = $true) <=> ! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : (~ ! [X373 : term] : (($true = ((X366 @ id @ (sub @ X367 @ (push @ X373 @ id)) @ id))) | ($true != ((X366 @ id @ X373 @ id)))) | (((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : (subst > term > term)] : (~ ! [X369 : term] : (($true != ((X366 @ id @ X369 @ id))) | ($true = ((X366 @ id @ (X368 @ id @ X369) @ id)))) | ($true = ((X366 @ id @ (lam @ (X368 @ sh @ one)) @ id))) | ~ ! [X371 : term,X370 : subst,X372 : subst] : (((X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) = ((sub @ (X368 @ X370 @ X371) @ X372)))))) & ((hoaslaminj = $true) <=> ! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (~ ! [X8 : subst,X7 : term,X6 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6)))) | ~ ! [X11 : subst,X10 : subst,X9 : term] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))))) & (ulamvarsh = $true) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ~ ! [X537 : (term > $o)] : ~ ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X303 : term,X301 : (term > $o),X304 : (subst > term > subst > $o),X302 : term] : (($true != ((X301 @ X302))) | ~ ! [X312 : term,X314 : subst,X313 : subst,X315 : subst] : (($true != ((X304 @ X313 @ X312 @ (comp @ X314 @ X315)))) | (((X304 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314) @ X315)) = $true)) | ($true = ((X301 @ (ap @ X302 @ X303)))) | ~ ! [X305 : term,X306 : term] : (($true != ((X304 @ id @ X306 @ id))) | ($true != ((X304 @ id @ X305 @ id))) | (((X304 @ id @ (ap @ (sub @ X305 @ id) @ X306) @ id)) = $true)) | ~ ! [X311 : term] : (((X301 @ X311)) = ((X304 @ id @ X311 @ id))) | ~ ! [X307 : subst,X310 : term,X309 : subst,X308 : subst] : (($true = ((X304 @ X307 @ X310 @ (comp @ X308 @ X309)))) | (((X304 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309)) != $true)) | ($true != ((X301 @ X303))))) & (pushprop_lthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) = X146) => (! [X148 : term,X147 : term] : ((X147 = X148) | (((lam @ X147)) != ((lam @ X148)))) => ! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : (~ ! [X156 : subst,X158 : subst,X157 : term] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) = ((sub @ (X152 @ X156 @ X157) @ X158))) | (((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ~ ! [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) = ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one))))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X451 : term] : (((sub @ X451 @ id)) = X451) => ! [X453 : (subst > term > subst > $o),X452 : term,X454 : (term > $o)] : (~ ! [X469 : term] : (((X454 @ X469)) = ((X453 @ id @ X469 @ id))) | ~ ! [X459 : subst,X461 : subst,X460 : term,X462 : subst] : ((((X453 @ X459 @ X460 @ (comp @ X461 @ X462))) != $true) | ($true = ((X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461) @ X462)))) | ~ ! [X463 : (subst > term > term)] : (($true = ((X453 @ id @ (lam @ (X463 @ sh @ one)) @ id))) | ~ ! [X467 : term] : ((((X453 @ id @ X467 @ id)) != $true) | (((X453 @ id @ (X463 @ id @ X467) @ id)) = $true)) | ~ ! [X465 : term,X464 : subst,X466 : subst] : (((X463 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X463 @ X466 @ X465) @ X464)))) | ~ ! [X455 : subst,X458 : subst,X456 : term,X457 : subst] : ((((X453 @ X457 @ X456 @ (comp @ X455 @ X458))) = $true) | ($true != ((X453 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455) @ X458)))) | ($true = ((X454 @ (lam @ X452)))) | ~ ! [X468 : term] : (($true != ((X454 @ X468))) | (((X454 @ (sub @ X452 @ (push @ X468 @ id)))) = $true))))) & ((hoasapinj2_lthm = $true) <=> (! [X378 : term,X375 : term,X376 : term,X377 : term] : ((((ap @ X377 @ X378)) != ((ap @ X375 @ X376))) | (X376 = X378)) => ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X276 : term] : ~ ! [X277 : (subst > term > term)] : ~ ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278))))) & ((hoasapinj1 = $true) <=> ! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280))))) & (hoaslamnotvar_lthm = $true) & (! [X529 : (term > $o),X528 : term] : ((((X529 @ X528)) = $true) | ~ ! [X530 : term] : ((((X529 @ X530)) = $true) | ($true != ((var @ X530)))) | ~ ! [X531 : term] : (($true = ((X529 @ (lam @ X531)))) | (((X529 @ X531)) != $true)) | ~ ! [X532 : term,X533 : term] : (($true != ((X529 @ X533))) | ($true = ((X529 @ (ap @ X532 @ X533)))) | (((X529 @ X532)) != $true))) <=> (induction = $true)) & ((apinj1 = $true) <=> ! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) = X521) => ! [X526 : (term > $o),X523 : term,X524 : subst,X525 : (term > $o)] : ((((X525 @ one)) = $true) | (((X526 @ X523)) != $true) | ~ ! [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) = ((X525 @ X527)))))) & (pushprop_lem2v2 = $true) & (axapp = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (lamnotvar = $true) & (! [X510 : (subst > term > subst > $o),X509 : (term > $o),X511 : term] : ((((X509 @ (lam @ X511))) = $true) | ~ ! [X512 : (subst > term > term)] : (~ ! [X513 : term] : (($true = ((X510 @ id @ (X512 @ id @ X513) @ id))) | ($true != ((X510 @ id @ X513 @ id)))) | ~ ! [X516 : subst,X514 : term,X515 : subst] : (((X512 @ (comp @ X516 @ X515) @ (sub @ X514 @ X515))) = ((sub @ (X512 @ X516 @ X514) @ X515))) | ($true = ((X510 @ id @ (lam @ (X512 @ sh @ one)) @ id)))) | ~ ! [X517 : term] : (((X509 @ X517)) = ((X510 @ id @ X517 @ id))) | ~ ! [X518 : term] : (($true != ((X509 @ X518))) | ($true = ((X509 @ (sub @ X511 @ (push @ X518 @ id))))))) <=> (hoasinduction_lem3v2a = $true)) & (! [X161 : (term > $o),X162 : term,X159 : subst,X160 : (term > $o)] : (~ ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163))) | (((X161 @ one)) = $true) | ($true != ((X160 @ X162)))) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X319 : (subst > term > subst > $o)] : ~ ! [X320 : (term > $o)] : ~ ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id)))) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem3_gthm = $true) & (! [X348 : term,X349 : (subst > term > subst > $o)] : (~ ! [X352 : (subst > term > term)] : ((((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) = $true) | ~ ! [X355 : subst,X354 : term,X353 : subst] : (((X352 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X353 @ X354) @ X355))) | ~ ! [X356 : term] : ((((X349 @ id @ X356 @ id)) != $true) | ($true = ((X349 @ id @ (X352 @ id @ X356) @ id))))) | (((X349 @ id @ X348 @ id)) = $true) | ~ ! [X357 : term] : ((((X349 @ id @ X357 @ id)) = $true) | ($true != ((var @ (sub @ X357 @ id))))) | ~ ! [X359 : subst,X358 : subst,X361 : term,X360 : subst] : ((((X349 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359) @ X358)) != $true) | ($true = ((X349 @ X360 @ X361 @ (comp @ X359 @ X358))))) | ~ ! [X362 : subst,X363 : subst,X365 : term,X364 : subst] : (($true != ((X349 @ X364 @ X365 @ (comp @ X362 @ X363)))) | (((X349 @ (comp @ X364 @ X362) @ (sub @ X365 @ X362) @ X363)) = $true)) | ~ ! [X350 : term,X351 : term] : (($true != ((X349 @ id @ X350 @ id))) | ($true != ((X349 @ id @ X351 @ id))) | ($true = ((X349 @ id @ (ap @ (sub @ X350 @ id) @ X351) @ id))))) <=> (hoasinduction = $true)) & ((laminj = $true) <=> ! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317))) & (axclos = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_gthm = $true) & (! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ~ ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346))) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem1_lthm = $true) & (! [X30 : (subst > term > subst > $o),X29 : term] : (($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))) | ~ ! [X31 : term] : (($true = ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id))) | ($true != ((X30 @ id @ X31 @ id)))) | ~ ! [X33 : term,X32 : (subst > term > term)] : (($true = ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id))) | ~ ! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) | ~ ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) | ~ ! [X37 : term] : (($true != ((X30 @ id @ X37 @ id))) | ($true = ((X30 @ id @ (X32 @ id @ X37) @ id)))))) <=> (hoasinduction_lem3aaa = $true)) & ((! [X402 : term] : (((sub @ X402 @ id)) = X402) => (! [X404 : (subst > term > subst > $o),X403 : term] : (($true = ((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id))) | ~ ! [X405 : term] : (($true != ((X404 @ id @ X405 @ id))) | ($true = ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)))) | ~ ! [X406 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true) | ~ ! [X407 : term] : (($true = ((X404 @ id @ (X406 @ id @ X407) @ id))) | ($true != ((X404 @ id @ X407 @ id)))) | ~ ! [X410 : subst,X409 : term,X408 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X406 @ X408 @ X409) @ X410))))) => ! [X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (lam @ X412) @ id))) | ~ ! [X417 : (subst > term > term)] : (~ ! [X418 : subst,X419 : subst,X420 : term] : (((X417 @ (comp @ X418 @ X419) @ (sub @ X420 @ X419))) = ((sub @ (X417 @ X418 @ X420) @ X419))) | ~ ! [X421 : term] : (($true != ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (X417 @ id @ X421) @ id)))) | ($true = ((X411 @ id @ (lam @ (X417 @ sh @ one)) @ id)))) | ~ ! [X426 : term] : (($true != ((X411 @ id @ X426 @ id))) | ($true = ((X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id)))) | ~ ! [X424 : term,X423 : subst,X425 : subst,X422 : subst] : ((((X411 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423) @ X422)) = $true) | ($true != ((X411 @ X425 @ X424 @ (comp @ X423 @ X422))))) | ~ ! [X414 : subst,X413 : subst,X415 : subst,X416 : term] : (($true != ((X411 @ (comp @ X414 @ X415) @ (sub @ X416 @ X415) @ X413))) | ($true = ((X411 @ X414 @ X416 @ (comp @ X415 @ X413)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslaminj_gthm = $true) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) = ((d2subst @ X12))) => (X12 = X13)) & ((hoasinduction_lthm_3 = $true) <=> (! [X205 : (subst > term > subst > $o)] : ~ ! [X206 : (term > $o)] : ~ ! [X207 : term] : (((X205 @ id @ X207 @ id)) = ((X206 @ X207))) => (! [X209 : (term > $o),X208 : term] : (~ ! [X210 : term] : (($true != ((var @ X210))) | ($true = ((X209 @ X210)))) | ~ ! [X213 : term,X214 : term] : (($true != ((X209 @ X213))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ($true != ((X209 @ X214)))) | ($true = ((X209 @ X208))) | ~ ! [X211 : term] : (($true = ((X209 @ (lam @ X211)))) | ~ ! [X212 : term] : (($true != ((X209 @ X212))) | ($true = ((X209 @ (sub @ X211 @ (push @ X212 @ id)))))))) => (! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X216 : (term > $o),X217 : term,X218 : (subst > term > subst > $o)] : (~ ! [X221 : (subst > term > term)] : (~ ! [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) = ((sub @ (X221 @ X223 @ X225) @ X224))) | ~ ! [X222 : term] : ((((X218 @ id @ X222 @ id)) != $true) | (((X218 @ id @ (X221 @ id @ X222) @ id)) = $true)) | ($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id)))) | ~ ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) | ~ ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ($true != ((X216 @ X220)))) | ($true = ((X216 @ (lam @ X217))))) => ! [X226 : term,X227 : (subst > term > subst > $o)] : (~ ! [X229 : subst,X231 : term,X230 : subst,X228 : subst] : (($true = ((X227 @ X228 @ X231 @ (comp @ X229 @ X230)))) | (((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) != $true)) | ~ ! [X235 : (subst > term > term)] : (~ ! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237))) | ~ ! [X236 : term] : ((((X227 @ id @ X236 @ id)) != $true) | ($true = ((X227 @ id @ (X235 @ id @ X236) @ id)))) | (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true)) | ~ ! [X232 : term] : (($true = ((X227 @ id @ X232 @ id))) | ($true != ((var @ (sub @ X232 @ id))))) | ~ ! [X234 : term,X233 : term] : ((((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) = $true) | ($true != ((X227 @ id @ X233 @ id))) | ($true != ((X227 @ id @ X234 @ id)))) | ~ ! [X242 : subst,X240 : subst,X241 : term,X243 : subst] : (($true = ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242))) | (((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) != $true)) | (((X227 @ id @ X226 @ id)) = $true))))))) & (hoasapnotvar = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axabs = $true) & (ulamvar1 != $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ! [X267 : d_term] : (d_one = X267) & (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)))))))))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X506 : term,X505 : subst,X504 : (term > $o)] : ~ ! [X507 : (term > $o)] : ~ ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & ((! [X470 : term] : (((sub @ X470 @ id)) = X470) => (! [X471 : subst,X472 : (term > $o),X473 : term] : (($true = ((X472 @ (sub @ X473 @ X471)))) | ~ ! [X474 : term] : (~ ! [X475 : term] : ((((X472 @ X475)) != $true) | (((X472 @ (sub @ X474 @ (push @ X475 @ id)))) = $true)) | (((X472 @ (lam @ X474))) = $true)) | ~ ! [X478 : term,X477 : term] : (($true != ((X472 @ X477))) | ($true = ((X472 @ (ap @ X477 @ X478)))) | (((X472 @ X478)) != $true)) | ~ ! [X476 : term] : (($true = ((X472 @ (sub @ X476 @ X471)))) | (((var @ X476)) != $true))) => ! [X480 : (term > $o),X479 : term] : (~ ! [X481 : term] : ((((var @ X481)) != $true) | ($true = ((X480 @ X481)))) | ~ ! [X482 : term,X483 : term] : (($true != ((X480 @ X482))) | (((X480 @ X483)) != $true) | (((X480 @ (ap @ X483 @ X482))) = $true)) | (((X480 @ X479)) = $true) | ~ ! [X484 : term] : ((((X480 @ (lam @ X484))) = $true) | ~ ! [X485 : term] : (($true = ((X480 @ (sub @ X484 @ (push @ X485 @ id))))) | (((X480 @ X485)) != $true)))))) <=> (induction2_lthm = $true)) & ((axshiftcons = $true) <=> ! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520)) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X383 : subst,X384 : term] : (((sub @ one @ (push @ X384 @ X383))) = X384) => (! [X386 : subst,X385 : term] : (((comp @ sh @ (push @ X385 @ X386))) = X386) => (! [X387 : subst] : (((comp @ X387 @ id)) = X387) => (! [X388 : (term > $o),X389 : term] : (~ ! [X390 : term] : ((((X388 @ (lam @ X390))) = $true) | (((X388 @ X390)) != $true)) | ~ ! [X393 : term,X392 : term] : ((((X388 @ X393)) != $true) | ($true != ((X388 @ X392))) | ($true = ((X388 @ (ap @ X392 @ X393))))) | ~ ! [X391 : term] : (($true = ((X388 @ X391))) | ($true != ((var @ X391)))) | (((X388 @ X389)) = $true)) => ! [X396 : subst,X394 : term,X395 : (term > $o)] : (~ ! [X398 : term,X397 : term] : (($true != ((X395 @ X397))) | ($true != ((X395 @ X398))) | (((X395 @ (ap @ X398 @ X397))) = $true)) | ~ ! [X399 : term] : ((((X395 @ (lam @ X399))) = $true) | ~ ! [X400 : term] : (($true = ((X395 @ (sub @ X399 @ (push @ X400 @ id))))) | (((X395 @ X400)) != $true))) | ~ ! [X401 : term] : (($true = ((X395 @ (sub @ X401 @ X396)))) | ($true != ((var @ X401)))) | ($true = ((X395 @ (sub @ X394 @ X396)))))))))) & (! [X98 : term,X97 : term,X99 : (subst > term > term)] : (~ ! [X100 : term,X102 : subst,X101 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))) | (((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98)))) <=> (hoaslamnotap = $true)) & (ulamvarind = $true) & (! [X195 : term,X196 : (subst > term > subst > $o)] : (~ ! [X202 : term,X203 : term] : (($true != ((X196 @ id @ X202 @ id))) | (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) = $true) | ($true != ((X196 @ id @ X203 @ id)))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199)))) | (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : (($true != ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id))))) | ($true = ((X196 @ id @ X195 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X164 : (term > $o),X166 : (subst > term > subst > $o),X165 : term] : (~ ! [X176 : term] : (($true = ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) | (((X164 @ X176)) != $true)) | ~ ! [X178 : subst,X177 : subst,X179 : subst,X180 : term] : (($true != ((X166 @ X178 @ X180 @ (comp @ X177 @ X179)))) | ($true = ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179)))) | ~ ! [X174 : subst,X173 : subst,X172 : term,X175 : subst] : (($true = ((X166 @ X173 @ X172 @ (comp @ X175 @ X174)))) | ($true != ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174)))) | ~ ! [X181 : term] : (((X164 @ X181)) = ((X166 @ id @ X181 @ id))) | ($true = ((X164 @ (lam @ X165)))) | ~ ! [X167 : (subst > term > term)] : (~ ! [X171 : term] : ((((X166 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X166 @ id @ X171 @ id)) != $true)) | ~ ! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) | ($true = ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1v2 = $true) & (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & ! [X331 : d_term,X332 : d_term] : ((((d2term @ X331)) = ((d2term @ X332))) => (X331 = X332)) & (hoasapinj1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) <=> (axidr = $true)) & (induction2_gthm = $true) & (((d2subst @ d_id)) = id) & ((! [X432 : term] : (((sub @ X432 @ id)) = X432) => (! [X433 : (subst > term > subst > $o),X434 : term] : ((((X433 @ id @ (lam @ (sub @ X434 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X435 : (subst > term > term)] : (~ ! [X437 : subst,X439 : term,X438 : subst] : (((sub @ (X435 @ X438 @ X439) @ X437)) = ((X435 @ (comp @ X438 @ X437) @ (sub @ X439 @ X437)))) | (((X433 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true) | ~ ! [X436 : term] : ((((X433 @ id @ X436 @ id)) != $true) | ($true = ((X433 @ id @ (X435 @ id @ X436) @ id))))) | ~ ! [X440 : term] : ((((X433 @ id @ X440 @ id)) != $true) | ($true = ((X433 @ id @ (sub @ X434 @ (push @ X440 @ id)) @ id))))) => ! [X442 : (subst > term > subst > $o),X441 : term] : (~ ! [X448 : term] : (($true != ((X442 @ id @ X448 @ id))) | ($true = ((X442 @ id @ (sub @ X441 @ (push @ X448 @ id)) @ id)))) | ($true = ((X442 @ id @ (lam @ X441) @ id))) | ~ ! [X443 : (subst > term > term)] : (~ ! [X444 : subst,X445 : subst,X446 : term] : (((sub @ (X443 @ X444 @ X446) @ X445)) = ((X443 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445)))) | ~ ! [X447 : term] : (($true = ((X442 @ id @ (X443 @ id @ X447) @ id))) | (((X442 @ id @ X447 @ id)) != $true)) | ($true = ((X442 @ id @ (lam @ (X443 @ sh @ one)) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X318 : d_subst] : (d_id = X318) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) <=> (termmset = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X182 : term] : (((sub @ X182 @ id)) = X182) => (! [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 = X185) | (((ap @ X183 @ X186)) != ((ap @ X185 @ X184)))) => ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190))))) & ((hoasinduction_lem2 = $true) <=> ! [X335 : (subst > term > subst > $o),X334 : term,X333 : term] : ((((X335 @ id @ X333 @ id)) != $true) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : (($true = ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) | (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) != $true)) | ~ ! [X343 : subst,X342 : subst,X341 : subst,X340 : term] : ((((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) = $true) | ($true != ((X335 @ X342 @ X340 @ (comp @ X341 @ X343))))) | ($true != ((X335 @ id @ X334 @ id))) | ~ ! [X345 : term,X344 : term] : ((((X335 @ id @ X345 @ id)) != $true) | (((X335 @ id @ X344 @ id)) != $true) | ($true = ((X335 @ id @ (ap @ (sub @ X344 @ id) @ X345) @ id)))))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & (((d2subst @ d_id)) = sh) & (hoasapnotvar_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) = X323) => (! [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) = X324) => ! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true))))) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X106 : (subst > term > subst > $o)] : ~ ! [X107 : (term > $o)] : ~ ! [X108 : term] : (((X106 @ id @ X108 @ id)) = ((X107 @ X108))) => (! [X110 : (term > $o),X109 : term] : (~ ! [X115 : term] : (($true != ((var @ X115))) | ($true = ((X110 @ X115)))) | (((X110 @ X109)) = $true) | ~ ! [X111 : term] : (~ ! [X112 : term] : (($true != ((X110 @ X112))) | ($true = ((X110 @ (sub @ X111 @ (push @ X112 @ id)))))) | ($true = ((X110 @ (lam @ X111))))) | ~ ! [X113 : term,X114 : term] : ((((X110 @ X114)) != $true) | ($true = ((X110 @ (ap @ X114 @ X113)))) | ($true != ((X110 @ X113))))) => (! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X117 : term,X118 : (term > $o),X119 : (subst > term > subst > $o)] : (~ ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X123 : subst,X121 : term,X122 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) = ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122)))) | ~ ! [X124 : term] : (($true != ((X119 @ id @ X124 @ id))) | ($true = ((X119 @ id @ (X120 @ id @ X124) @ id)))) | (((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true)) | ($true = ((X118 @ (lam @ X117)))) | ~ ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ($true != ((X118 @ X126))))) => ! [X128 : term,X127 : (subst > term > subst > $o)] : (($true = ((X127 @ id @ X128 @ id))) | ~ ! [X131 : (subst > term > term)] : (($true = ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) | ~ ! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133)))) | ~ ! [X132 : term] : (($true != ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id))))) | ~ ! [X129 : term,X130 : term] : (($true = ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id))) | ($true != ((X127 @ id @ X129 @ id))) | ($true != ((X127 @ id @ X130 @ id))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) <=> ! [X137 : (term > $o),X136 : term] : (~ ! [X138 : term,X139 : term] : (($true != ((X137 @ X139))) | ($true = ((X137 @ (ap @ X139 @ X138)))) | ($true != ((X137 @ X138)))) | ~ ! [X140 : term] : (~ ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ($true != ((X137 @ X141)))) | ($true = ((X137 @ (lam @ X140))))) | ~ ! [X142 : term] : ((((var @ X142)) != $true) | ($true = ((X137 @ X142)))) | ($true = ((X137 @ X136))))) & (axvarshift = $true) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true)),
% 6.44/1.36 inference(flattening,[],[f8])).
% 6.44/1.36 thf(f10,plain,(
% 6.44/1.36 (hoasinduction_lem2 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))))),
% 6.44/1.36 inference(flattening,[],[f7])).
% 6.44/1.36 thf(f11,plain,(
% 6.44/1.36 (! [X268 : term,X269 : (subst > term > subst > $o)] : (? [X270 : (subst > term > term)] : (($true != ((X269 @ id @ (lam @ (X270 @ sh @ one)) @ id))) & ! [X273 : term,X274 : subst,X272 : subst] : (((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274))) = ((sub @ (X270 @ X272 @ X273) @ X274))) & ! [X271 : term] : (($true != ((X269 @ id @ X271 @ id))) | ($true = ((X269 @ id @ (X270 @ id @ X271) @ id))))) | ($true = ((X269 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id))) | ? [X275 : term] : ((((X269 @ id @ X275 @ id)) = $true) & (((X269 @ id @ (sub @ X268 @ (push @ X275 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa = $true)) & ((substmonoid_lthm = $true) <=> (((! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501)) | ? [X500 : subst] : (((comp @ id @ X500)) != X500))) & ((hoasinduction_lthm = $true) <=> (((! [X80 : term,X79 : (subst > term > subst > $o)] : (? [X82 : (subst > term > term)] : (! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | (((X79 @ id @ X86 @ id)) != $true)) & ($true != ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id))) & ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83)))) | ($true = ((X79 @ id @ X80 @ id))) | ? [X81 : term] : ((((var @ (sub @ X81 @ id))) = $true) & ($true != ((X79 @ id @ X81 @ id)))) | ? [X96 : subst,X94 : subst,X93 : subst,X95 : term] : (($true = ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) & ($true != ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96)))) | ? [X87 : term,X88 : term] : ((((X79 @ id @ X88 @ id)) = $true) & ($true = ((X79 @ id @ X87 @ id))) & ($true != ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)))) | ? [X90 : subst,X91 : term,X92 : subst,X89 : subst] : ((((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) = $true) & (((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) != $true))) | ? [X63 : (subst > term > subst > $o),X64 : term] : (! [X66 : subst,X67 : term,X65 : subst,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) != $true)) & ($true != ((X63 @ id @ (lam @ X64) @ id))) & ! [X70 : (subst > term > term)] : (($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ? [X71 : term] : (($true = ((X63 @ id @ X71 @ id))) & (((X63 @ id @ (X70 @ id @ X71) @ id)) != $true)) | ? [X73 : subst,X74 : subst,X72 : term] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) != ((sub @ (X70 @ X74 @ X72) @ X73)))) & ! [X69 : term] : (($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id))) | (((X63 @ id @ X69 @ id)) != $true)) & ! [X75 : term,X77 : subst,X78 : subst,X76 : subst] : ((((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true) | ($true != ((X63 @ X78 @ X75 @ (comp @ X76 @ X77))))))) | ? [X52 : term,X50 : (subst > term > subst > $o),X51 : term] : (! [X62 : subst,X59 : subst,X61 : term,X60 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ($true != ((X50 @ X62 @ X61 @ (comp @ X60 @ X59))))) & ! [X56 : subst,X55 : subst,X57 : subst,X58 : term] : (($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57)))) | ($true != ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57)))) & ($true != ((X50 @ id @ (ap @ X51 @ X52) @ id))) & ($true = ((X50 @ id @ X52 @ id))) & ! [X53 : term,X54 : term] : ((((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true) | ($true != ((X50 @ id @ X54 @ id))) | ($true != ((X50 @ id @ X53 @ id)))) & ($true = ((X50 @ id @ X51 @ id))))) | ? [X43 : (term > $o),X44 : term] : ((((X43 @ X44)) != $true) & ! [X48 : term] : (? [X49 : term] : (($true != ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) & (((X43 @ X49)) = $true)) | (((X43 @ (lam @ X48))) = $true)) & ! [X45 : term] : (($true = ((X43 @ X45))) | (((var @ X45)) != $true)) & ! [X47 : term,X46 : term] : ((((X43 @ X46)) != $true) | ($true != ((X43 @ X47))) | ($true = ((X43 @ (ap @ X47 @ X46)))))))) & ((? [X449 : term] : (((sub @ X449 @ id)) != X449) | ! [X450 : term] : (((sub @ X450 @ id)) = X450)) <=> (termmset_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (one = ((d2term @ d_one))) & (((! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : (? [X22 : term] : (((X19 @ id @ X22 @ id)) != ((X20 @ X22))) | ($true = ((X20 @ (lam @ X21)))) | ? [X24 : (subst > term > term)] : (! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) & ($true != ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) & ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ($true != ((X19 @ id @ X28 @ id))))) | ? [X23 : term] : (($true != ((X20 @ (sub @ X21 @ (push @ X23 @ id))))) & (((X20 @ X23)) = $true))) | ? [X18 : term] : (((sub @ X18 @ id)) != X18)) | ? [X14 : term] : ! [X15 : (subst > term > term)] : ? [X16 : subst,X17 : term] : (((X15 @ X16 @ X17)) != ((sub @ X14 @ (push @ X17 @ X16))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X486 : term] : ? [X487 : (subst > term > term)] : ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489))))) & (apnotvar = $true) & (induction2lem_gthm = $true) & ((induction2lem = $true) <=> ! [X252 : subst,X251 : (term > $o),X253 : term] : (? [X254 : term] : (! [X255 : term] : (($true != ((X251 @ X255))) | (((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true)) & ($true != ((X251 @ (lam @ X254))))) | ? [X258 : term] : (($true != ((X251 @ (sub @ X258 @ X252)))) & (((var @ X258)) = $true)) | ? [X257 : term,X256 : term] : (($true != ((X251 @ (ap @ X256 @ X257)))) & ($true = ((X251 @ X256))) & (((X251 @ X257)) = $true)) | (((X251 @ (sub @ X253 @ X252))) = $true))) & (hoaslamnotvar = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X490 : term] : ? [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) = ((X491 @ sh @ one)))) & (termmset_gthm = $true) & (lamnotap != $true) & (pushprop_lem1_gthm = $true) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (! [X492 : term,X493 : (subst > term > subst > $o)] : (? [X494 : term] : (($true != ((X493 @ id @ (sub @ X492 @ (push @ X494 @ id)) @ id))) & (((X493 @ id @ X494 @ id)) = $true)) | ? [X495 : (subst > term > term)] : ((((X493 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X499 : term] : ((((X493 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X493 @ id @ X499 @ id)) != $true)) & ! [X496 : subst,X497 : term,X498 : subst] : (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X495 @ X496 @ X497) @ X498)))) | ($true = ((X493 @ id @ (lam @ X492) @ id)))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X284 : term,X285 : (subst > term > subst > $o)] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & ($true = ((X285 @ id @ X286 @ id)))) | ? [X290 : term,X288 : subst,X289 : subst,X287 : subst] : ((((X285 @ X287 @ X290 @ (comp @ X289 @ X288))) != $true) & ($true = ((X285 @ (comp @ X287 @ X289) @ (sub @ X290 @ X289) @ X288)))) | ? [X298 : term,X299 : subst,X297 : subst,X296 : subst] : ((((X285 @ (comp @ X297 @ X299) @ (sub @ X298 @ X299) @ X296)) != $true) & ($true = ((X285 @ X297 @ X298 @ (comp @ X299 @ X296))))) | ? [X291 : (subst > term > term)] : (($true != ((X285 @ id @ (lam @ (X291 @ sh @ one)) @ id))) & ! [X294 : term,X293 : subst,X292 : subst] : (((sub @ (X291 @ X292 @ X294) @ X293)) = ((X291 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) & ! [X295 : term] : (($true != ((X285 @ id @ X295 @ id))) | ($true = ((X285 @ id @ (X291 @ id @ X295) @ id))))))) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((axscons = $true) <=> ! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : (? [X373 : term] : (($true = ((X366 @ id @ X373 @ id))) & ($true != ((X366 @ id @ (sub @ X367 @ (push @ X373 @ id)) @ id)))) | (((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : (subst > term > term)] : (($true != ((X366 @ id @ (lam @ (X368 @ sh @ one)) @ id))) & ! [X371 : term,X370 : subst,X372 : subst] : (((X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) = ((sub @ (X368 @ X370 @ X371) @ X372))) & ! [X369 : term] : (($true != ((X366 @ id @ X369 @ id))) | ($true = ((X366 @ id @ (X368 @ id @ X369) @ id))))))) & (! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (? [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) != ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ? [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) != ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))) <=> (hoaslaminj = $true)) & (ulamvarsh = $true) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) <=> (pushprop_lem0 = $true)) & (! [X302 : term,X303 : term,X304 : (subst > term > subst > $o),X301 : (term > $o)] : (($true != ((X301 @ X302))) | ? [X306 : term,X305 : term] : (($true = ((X304 @ id @ X305 @ id))) & ($true = ((X304 @ id @ X306 @ id))) & (((X304 @ id @ (ap @ (sub @ X305 @ id) @ X306) @ id)) != $true)) | ($true != ((X301 @ X303))) | ? [X311 : term] : (((X301 @ X311)) != ((X304 @ id @ X311 @ id))) | ? [X315 : subst,X314 : subst,X313 : subst,X312 : term] : (($true = ((X304 @ X313 @ X312 @ (comp @ X314 @ X315)))) & (((X304 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314) @ X315)) != $true)) | ? [X310 : term,X307 : subst,X309 : subst,X308 : subst] : (($true != ((X304 @ X307 @ X310 @ (comp @ X308 @ X309)))) & (((X304 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309)) = $true)) | ($true = ((X301 @ (ap @ X302 @ X303))))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : ((((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ? [X157 : term,X156 : subst,X158 : subst] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) != ((sub @ (X152 @ X156 @ X157) @ X158))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one)))) | ? [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) != ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153))))) | ? [X147 : term,X148 : term] : ((((lam @ X147)) = ((lam @ X148))) & (X147 != X148))) | ? [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) != X146)) | ? [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) != X144))) & ((? [X451 : term] : (((sub @ X451 @ id)) != X451) | ! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (($true = ((X454 @ (lam @ X452)))) | ? [X463 : (subst > term > term)] : (($true != ((X453 @ id @ (lam @ (X463 @ sh @ one)) @ id))) & ! [X467 : term] : ((((X453 @ id @ X467 @ id)) != $true) | (((X453 @ id @ (X463 @ id @ X467) @ id)) = $true)) & ! [X465 : term,X464 : subst,X466 : subst] : (((X463 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X463 @ X466 @ X465) @ X464)))) | ? [X468 : term] : (($true = ((X454 @ X468))) & (((X454 @ (sub @ X452 @ (push @ X468 @ id)))) != $true)) | ? [X460 : term,X462 : subst,X459 : subst,X461 : subst] : (($true != ((X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461) @ X462))) & (((X453 @ X459 @ X460 @ (comp @ X461 @ X462))) = $true)) | ? [X469 : term] : (((X454 @ X469)) != ((X453 @ id @ X469 @ id))) | ? [X457 : subst,X458 : subst,X456 : term,X455 : subst] : ((((X453 @ X457 @ X456 @ (comp @ X455 @ X458))) != $true) & ($true = ((X453 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455) @ X458)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 != X378) & (((ap @ X377 @ X378)) = ((ap @ X375 @ X376)))) | ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X276 : term] : ? [X277 : (subst > term > term)] : ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278))))) & ((hoasapinj1 = $true) <=> ! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280))))) & (hoaslamnotvar_lthm = $true) & ((induction = $true) <=> ! [X528 : term,X529 : (term > $o)] : (? [X533 : term,X532 : term] : (($true = ((X529 @ X533))) & (((X529 @ X532)) = $true) & ($true != ((X529 @ (ap @ X532 @ X533))))) | ? [X530 : term] : ((((X529 @ X530)) != $true) & ($true = ((var @ X530)))) | ? [X531 : term] : ((((X529 @ X531)) = $true) & ($true != ((X529 @ (lam @ X531))))) | (((X529 @ X528)) = $true))) & ((apinj1 = $true) <=> ! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265))) & ((! [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (? [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) != ((X525 @ X527))) | (((X526 @ X523)) != $true) | (((X525 @ one)) = $true)) | ? [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) != X521)) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2 = $true) & (axapp = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (lamnotvar = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X511 : term,X510 : (subst > term > subst > $o),X509 : (term > $o)] : ((((X509 @ (lam @ X511))) = $true) | ? [X517 : term] : (((X509 @ X517)) != ((X510 @ id @ X517 @ id))) | ? [X518 : term] : (($true != ((X509 @ (sub @ X511 @ (push @ X518 @ id))))) & ($true = ((X509 @ X518)))) | ? [X512 : (subst > term > term)] : (! [X516 : subst,X514 : term,X515 : subst] : (((X512 @ (comp @ X516 @ X515) @ (sub @ X514 @ X515))) = ((sub @ (X512 @ X516 @ X514) @ X515))) & ($true != ((X510 @ id @ (lam @ (X512 @ sh @ one)) @ id))) & ! [X513 : term] : (($true = ((X510 @ id @ (X512 @ id @ X513) @ id))) | ($true != ((X510 @ id @ X513 @ id))))))) & (! [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true != ((X160 @ X162))) | (((X161 @ one)) = $true) | ? [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) != ((X161 @ X163)))) <=> (pushprop_lem1v2 = $true)) & (! [X319 : (subst > term > subst > $o)] : ? [X320 : (term > $o)] : ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) <=> ! [X349 : (subst > term > subst > $o),X348 : term] : ((((X349 @ id @ X348 @ id)) = $true) | ? [X364 : subst,X363 : subst,X362 : subst,X365 : term] : ((((X349 @ (comp @ X364 @ X362) @ (sub @ X365 @ X362) @ X363)) != $true) & ($true = ((X349 @ X364 @ X365 @ (comp @ X362 @ X363))))) | ? [X350 : term,X351 : term] : (($true = ((X349 @ id @ X350 @ id))) & ($true = ((X349 @ id @ X351 @ id))) & ($true != ((X349 @ id @ (ap @ (sub @ X350 @ id) @ X351) @ id)))) | ? [X357 : term] : ((((X349 @ id @ X357 @ id)) != $true) & ($true = ((var @ (sub @ X357 @ id))))) | ? [X360 : subst,X359 : subst,X358 : subst,X361 : term] : ((((X349 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359) @ X358)) = $true) & ($true != ((X349 @ X360 @ X361 @ (comp @ X359 @ X358))))) | ? [X352 : (subst > term > term)] : (! [X355 : subst,X354 : term,X353 : subst] : (((X352 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X353 @ X354) @ X355))) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true) & ! [X356 : term] : ((((X349 @ id @ X356 @ id)) != $true) | ($true = ((X349 @ id @ (X352 @ id @ X356) @ id))))))) & ((laminj = $true) <=> ! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317))) & (axclos = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_gthm = $true) & (! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ? [X247 : (subst > term > term)] : (((X247 @ sh @ one)) = ((sub @ X246 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346))) & (pushprop = $true) & (hoasinduction_lem1v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem1_lthm = $true) & (! [X30 : (subst > term > subst > $o),X29 : term] : (? [X31 : term] : (($true = ((X30 @ id @ X31 @ id))) & ($true != ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id)))) | ? [X33 : term,X32 : (subst > term > term)] : (! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) & ($true != ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id))) & ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) & ! [X37 : term] : (($true != ((X30 @ id @ X37 @ id))) | ($true = ((X30 @ id @ (X32 @ id @ X37) @ id))))) | ($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (((! [X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (lam @ X412) @ id))) | ? [X414 : subst,X415 : subst,X416 : term,X413 : subst] : (($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X416 @ X415) @ X413))) & ($true != ((X411 @ X414 @ X416 @ (comp @ X415 @ X413))))) | ? [X417 : (subst > term > term)] : (! [X418 : subst,X419 : subst,X420 : term] : (((X417 @ (comp @ X418 @ X419) @ (sub @ X420 @ X419))) = ((sub @ (X417 @ X418 @ X420) @ X419))) & ($true != ((X411 @ id @ (lam @ (X417 @ sh @ one)) @ id))) & ! [X421 : term] : (($true != ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (X417 @ id @ X421) @ id))))) | ? [X423 : subst,X424 : term,X425 : subst,X422 : subst] : ((((X411 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423) @ X422)) != $true) & ($true = ((X411 @ X425 @ X424 @ (comp @ X423 @ X422))))) | ? [X426 : term] : (($true = ((X411 @ id @ X426 @ id))) & ($true != ((X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))))) | ? [X404 : (subst > term > subst > $o),X403 : term] : (! [X405 : term] : (($true != ((X404 @ id @ X405 @ id))) | ($true = ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)))) & ($true != ((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id))) & ! [X406 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true) | ? [X407 : term] : (($true = ((X404 @ id @ X407 @ id))) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X409 : term,X410 : subst,X408 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) != ((sub @ (X406 @ X408 @ X409) @ X410)))))) | ? [X402 : term] : (((sub @ X402 @ id)) != X402)) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslaminj_gthm = $true) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) != ((d2subst @ X12))) | (X12 = X13)) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X226 : term,X227 : (subst > term > subst > $o)] : (? [X234 : term,X233 : term] : ((((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) != $true) & ($true = ((X227 @ id @ X234 @ id))) & ($true = ((X227 @ id @ X233 @ id)))) | ? [X235 : (subst > term > term)] : (! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237))) & ! [X236 : term] : ((((X227 @ id @ X236 @ id)) != $true) | ($true = ((X227 @ id @ (X235 @ id @ X236) @ id)))) & (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true)) | ? [X243 : subst,X242 : subst,X241 : term,X240 : subst] : ((((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) = $true) & ($true != ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242)))) | ? [X229 : subst,X231 : term,X228 : subst,X230 : subst] : ((((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) = $true) & ($true != ((X227 @ X228 @ X231 @ (comp @ X229 @ X230))))) | (((X227 @ id @ X226 @ id)) = $true) | ? [X232 : term] : (($true = ((var @ (sub @ X232 @ id)))) & ($true != ((X227 @ id @ X232 @ id))))) | ? [X218 : (subst > term > subst > $o),X217 : term,X216 : (term > $o)] : (($true != ((X216 @ (lam @ X217)))) & ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ($true != ((X216 @ X220)))) & ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) & ! [X221 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ? [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) != ((sub @ (X221 @ X223 @ X225) @ X224))) | ? [X222 : term] : ((((X218 @ id @ X222 @ id)) = $true) & (((X218 @ id @ (X221 @ id @ X222) @ id)) != $true))))) | ? [X215 : term] : (((sub @ X215 @ id)) != X215)) | ? [X208 : term,X209 : (term > $o)] : (! [X213 : term,X214 : term] : (($true != ((X209 @ X213))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ($true != ((X209 @ X214)))) & ! [X210 : term] : (($true != ((var @ X210))) | ($true = ((X209 @ X210)))) & ! [X211 : term] : (($true = ((X209 @ (lam @ X211)))) | ? [X212 : term] : (($true = ((X209 @ X212))) & ($true != ((X209 @ (sub @ X211 @ (push @ X212 @ id))))))) & ($true != ((X209 @ X208))))) | ? [X205 : (subst > term > subst > $o)] : ! [X206 : (term > $o)] : ? [X207 : term] : (((X205 @ id @ X207 @ id)) != ((X206 @ X207))))) & (hoasapnotvar = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axabs = $true) & (ulamvar1 != $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ? [X249 : (term > $o)] : ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ! [X267 : d_term] : (d_one = X267) & (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)))))))))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X505 : subst,X504 : (term > $o),X506 : term] : ? [X507 : (term > $o)] : ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (((! [X480 : (term > $o),X479 : term] : ((((X480 @ X479)) = $true) | ? [X482 : term,X483 : term] : ((((X480 @ X483)) = $true) & (((X480 @ (ap @ X483 @ X482))) != $true) & ($true = ((X480 @ X482)))) | ? [X481 : term] : ((((var @ X481)) = $true) & ($true != ((X480 @ X481)))) | ? [X484 : term] : ((((X480 @ (lam @ X484))) != $true) & ! [X485 : term] : (($true = ((X480 @ (sub @ X484 @ (push @ X485 @ id))))) | (((X480 @ X485)) != $true)))) | ? [X471 : subst,X472 : (term > $o),X473 : term] : (! [X474 : term] : (? [X475 : term] : ((((X472 @ (sub @ X474 @ (push @ X475 @ id)))) != $true) & (((X472 @ X475)) = $true)) | (((X472 @ (lam @ X474))) = $true)) & ! [X476 : term] : (($true = ((X472 @ (sub @ X476 @ X471)))) | (((var @ X476)) != $true)) & ! [X478 : term,X477 : term] : (($true != ((X472 @ X477))) | ($true = ((X472 @ (ap @ X477 @ X478)))) | (((X472 @ X478)) != $true)) & ($true != ((X472 @ (sub @ X473 @ X471)))))) | ? [X470 : term] : (((sub @ X470 @ id)) != X470)) <=> (induction2_lthm = $true)) & ((axshiftcons = $true) <=> ! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520)) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X396 : subst,X395 : (term > $o),X394 : term] : (? [X399 : term] : ((((X395 @ (lam @ X399))) != $true) & ! [X400 : term] : (($true = ((X395 @ (sub @ X399 @ (push @ X400 @ id))))) | (((X395 @ X400)) != $true))) | ? [X398 : term,X397 : term] : (($true = ((X395 @ X397))) & ($true = ((X395 @ X398))) & (((X395 @ (ap @ X398 @ X397))) != $true)) | ? [X401 : term] : (($true = ((var @ X401))) & ($true != ((X395 @ (sub @ X401 @ X396))))) | ($true = ((X395 @ (sub @ X394 @ X396))))) | ? [X388 : (term > $o),X389 : term] : (! [X391 : term] : (($true = ((X388 @ X391))) | ($true != ((var @ X391)))) & ! [X390 : term] : ((((X388 @ (lam @ X390))) = $true) | (((X388 @ X390)) != $true)) & (((X388 @ X389)) != $true) & ! [X393 : term,X392 : term] : ((((X388 @ X393)) != $true) | ($true != ((X388 @ X392))) | ($true = ((X388 @ (ap @ X392 @ X393))))))) | ? [X387 : subst] : (((comp @ X387 @ id)) != X387)) | ? [X385 : term,X386 : subst] : (((comp @ sh @ (push @ X385 @ X386))) != X386)) | ? [X383 : subst,X384 : term] : (((sub @ one @ (push @ X384 @ X383))) != X384))) & ((hoaslamnotap = $true) <=> ! [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98))) | ? [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) != ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))))) & (ulamvarind = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X195 : term,X196 : (subst > term > subst > $o)] : (? [X202 : term,X203 : term] : (($true = ((X196 @ id @ X203 @ id))) & (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) != $true) & ($true = ((X196 @ id @ X202 @ id)))) | ($true = ((X196 @ id @ X195 @ id))) | ? [X197 : (subst > term > term)] : (! [X198 : term] : (($true != ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id)))) & (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true) & ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))) & (! [X164 : (term > $o),X166 : (subst > term > subst > $o),X165 : term] : (? [X180 : term,X179 : subst,X178 : subst,X177 : subst] : (($true != ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179))) & ($true = ((X166 @ X178 @ X180 @ (comp @ X177 @ X179))))) | ? [X181 : term] : (((X164 @ X181)) != ((X166 @ id @ X181 @ id))) | ($true = ((X164 @ (lam @ X165)))) | ? [X167 : (subst > term > term)] : (! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) & ($true != ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))) & ! [X171 : term] : ((((X166 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X166 @ id @ X171 @ id)) != $true))) | ? [X174 : subst,X175 : subst,X173 : subst,X172 : term] : (($true != ((X166 @ X173 @ X172 @ (comp @ X175 @ X174)))) & ($true = ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174)))) | ? [X176 : term] : (($true != ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) & (((X164 @ X176)) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1v2 = $true) & (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & ! [X332 : d_term,X331 : d_term] : ((((d2term @ X331)) != ((d2term @ X332))) | (X331 = X332)) & (hoasapinj1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) <=> (axidr = $true)) & (induction2_gthm = $true) & (((d2subst @ d_id)) = id) & (((! [X441 : term,X442 : (subst > term > subst > $o)] : (? [X448 : term] : (($true = ((X442 @ id @ X448 @ id))) & ($true != ((X442 @ id @ (sub @ X441 @ (push @ X448 @ id)) @ id)))) | ? [X443 : (subst > term > term)] : (! [X447 : term] : (($true = ((X442 @ id @ (X443 @ id @ X447) @ id))) | (((X442 @ id @ X447 @ id)) != $true)) & ! [X444 : subst,X445 : subst,X446 : term] : (((sub @ (X443 @ X444 @ X446) @ X445)) = ((X443 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445)))) & ($true != ((X442 @ id @ (lam @ (X443 @ sh @ one)) @ id)))) | ($true = ((X442 @ id @ (lam @ X441) @ id)))) | ? [X433 : (subst > term > subst > $o),X434 : term] : (! [X440 : term] : ((((X433 @ id @ X440 @ id)) != $true) | ($true = ((X433 @ id @ (sub @ X434 @ (push @ X440 @ id)) @ id)))) & (((X433 @ id @ (lam @ (sub @ X434 @ (push @ one @ sh))) @ id)) != $true) & ! [X435 : (subst > term > term)] : (? [X439 : term,X438 : subst,X437 : subst] : (((sub @ (X435 @ X438 @ X439) @ X437)) != ((X435 @ (comp @ X438 @ X437) @ (sub @ X439 @ X437)))) | (((X433 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true) | ? [X436 : term] : ((((X433 @ id @ X436 @ id)) = $true) & ($true != ((X433 @ id @ (X435 @ id @ X436) @ id))))))) | ? [X432 : term] : (((sub @ X432 @ id)) != X432)) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X318 : d_subst] : (d_id = X318) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) <=> (termmset = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190)) | ? [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 != X185) & (((ap @ X183 @ X186)) = ((ap @ X185 @ X184))))) | ? [X182 : term] : (((sub @ X182 @ id)) != X182))) & ((hoasinduction_lem2 = $true) <=> ! [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (($true != ((X335 @ id @ X334 @ id))) | ? [X336 : subst,X339 : term,X338 : subst,X337 : subst] : (($true != ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) & (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) = $true)) | ? [X341 : subst,X343 : subst,X340 : term,X342 : subst] : (($true = ((X335 @ X342 @ X340 @ (comp @ X341 @ X343)))) & (((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) != $true)) | ? [X345 : term,X344 : term] : ((((X335 @ id @ X344 @ id)) = $true) & (((X335 @ id @ X345 @ id)) = $true) & ($true != ((X335 @ id @ (ap @ (sub @ X344 @ id) @ X345) @ id)))) | (((X335 @ id @ X333 @ id)) != $true) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & (((d2subst @ d_id)) = sh) & (hoasapnotvar_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true)) | ? [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) != X324)) | ? [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) != X323))) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((((! [X128 : term,X127 : (subst > term > subst > $o)] : (? [X129 : term,X130 : term] : (($true = ((X127 @ id @ X129 @ id))) & ($true = ((X127 @ id @ X130 @ id))) & ($true != ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)))) | ? [X131 : (subst > term > term)] : (! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133)))) & ($true != ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) & ! [X132 : term] : (($true != ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id))))) | ($true = ((X127 @ id @ X128 @ id)))) | ? [X119 : (subst > term > subst > $o),X118 : (term > $o),X117 : term] : (($true != ((X118 @ (lam @ X117)))) & ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) & ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ($true != ((X118 @ X126)))) & ! [X120 : (subst > term > term)] : ((((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ? [X124 : term] : (($true = ((X119 @ id @ X124 @ id))) & ($true != ((X119 @ id @ (X120 @ id @ X124) @ id)))) | ? [X122 : subst,X121 : term,X123 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) != ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))))))) | ? [X116 : term] : (((sub @ X116 @ id)) != X116)) | ? [X110 : (term > $o),X109 : term] : (! [X115 : term] : (($true != ((var @ X115))) | ($true = ((X110 @ X115)))) & (((X110 @ X109)) != $true) & ! [X113 : term,X114 : term] : ((((X110 @ X114)) != $true) | ($true = ((X110 @ (ap @ X114 @ X113)))) | ($true != ((X110 @ X113)))) & ! [X111 : term] : (? [X112 : term] : (($true != ((X110 @ (sub @ X111 @ (push @ X112 @ id))))) & ($true = ((X110 @ X112)))) | ($true = ((X110 @ (lam @ X111))))))) | ? [X106 : (subst > term > subst > $o)] : ! [X107 : (term > $o)] : ? [X108 : term] : (((X106 @ id @ X108 @ id)) != ((X107 @ X108)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X137 : (term > $o),X136 : term] : (? [X140 : term] : (($true != ((X137 @ (lam @ X140)))) & ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ($true != ((X137 @ X141))))) | ? [X139 : term,X138 : term] : (($true = ((X137 @ X139))) & ($true != ((X137 @ (ap @ X139 @ X138)))) & ($true = ((X137 @ X138)))) | ($true = ((X137 @ X136))) | ? [X142 : term] : (($true != ((X137 @ X142))) & (((var @ X142)) = $true))) <=> (induction2 = $true)) & (axvarshift = $true) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true)),
% 6.44/1.37 inference(ennf_transformation,[],[f9])).
% 6.44/1.37 thf(f12,plain,(
% 6.44/1.37 (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & ((? [X451 : term] : (((sub @ X451 @ id)) != X451) | ! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (($true = ((X454 @ (lam @ X452)))) | ? [X463 : (subst > term > term)] : (($true != ((X453 @ id @ (lam @ (X463 @ sh @ one)) @ id))) & ! [X467 : term] : ((((X453 @ id @ X467 @ id)) != $true) | (((X453 @ id @ (X463 @ id @ X467) @ id)) = $true)) & ! [X465 : term,X464 : subst,X466 : subst] : (((X463 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X463 @ X466 @ X465) @ X464)))) | ? [X468 : term] : (($true = ((X454 @ X468))) & (((X454 @ (sub @ X452 @ (push @ X468 @ id)))) != $true)) | ? [X460 : term,X462 : subst,X459 : subst,X461 : subst] : (($true != ((X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461) @ X462))) & (((X453 @ X459 @ X460 @ (comp @ X461 @ X462))) = $true)) | ? [X469 : term] : (((X454 @ X469)) != ((X453 @ id @ X469 @ id))) | ? [X457 : subst,X458 : subst,X456 : term,X455 : subst] : ((((X453 @ X457 @ X456 @ (comp @ X455 @ X458))) != $true) & ($true = ((X453 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455) @ X458)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X319 : (subst > term > subst > $o)] : ? [X320 : (term > $o)] : ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X490 : term] : ? [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) = ((X491 @ sh @ one)))) & ((? [X14 : term] : ! [X15 : (subst > term > term)] : ? [X16 : subst,X17 : term] : (((X15 @ X16 @ X17)) != ((sub @ X14 @ (push @ X17 @ X16)))) | ! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : (? [X22 : term] : (((X19 @ id @ X22 @ id)) != ((X20 @ X22))) | ($true = ((X20 @ (lam @ X21)))) | ? [X24 : (subst > term > term)] : (! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) & ($true != ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) & ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ($true != ((X19 @ id @ X28 @ id))))) | ? [X23 : term] : (($true != ((X20 @ (sub @ X21 @ (push @ X23 @ id))))) & (((X20 @ X23)) = $true))) | ? [X18 : term] : (((sub @ X18 @ id)) != X18)) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (? [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) != ((X525 @ X527))) | (((X526 @ X523)) != $true) | (((X525 @ one)) = $true)) | ? [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) != X521)) <=> (pushprop_lem1v2_lthm = $true)) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ? [X247 : (subst > term > term)] : (((X247 @ sh @ one)) = ((sub @ X246 @ (push @ one @ sh))))) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & ((hoaslaminj_lthm = $true) <=> (? [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) != X144) | ? [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) != X146) | ! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : ((((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ? [X157 : term,X156 : subst,X158 : subst] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) != ((sub @ (X152 @ X156 @ X157) @ X158))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one)))) | ? [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) != ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153))))) | ? [X147 : term,X148 : term] : ((((lam @ X147)) = ((lam @ X148))) & (X147 != X148)))) & ! [X267 : d_term] : (d_one = X267) & (hoasapinj2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X205 : (subst > term > subst > $o)] : ! [X206 : (term > $o)] : ? [X207 : term] : (((X205 @ id @ X207 @ id)) != ((X206 @ X207))) | ? [X208 : term,X209 : (term > $o)] : (! [X213 : term,X214 : term] : (($true != ((X209 @ X213))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ($true != ((X209 @ X214)))) & ! [X210 : term] : (($true != ((var @ X210))) | ($true = ((X209 @ X210)))) & ! [X211 : term] : (($true = ((X209 @ (lam @ X211)))) | ? [X212 : term] : (($true = ((X209 @ X212))) & ($true != ((X209 @ (sub @ X211 @ (push @ X212 @ id))))))) & ($true != ((X209 @ X208)))) | ! [X226 : term,X227 : (subst > term > subst > $o)] : (? [X234 : term,X233 : term] : ((((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) != $true) & ($true = ((X227 @ id @ X234 @ id))) & ($true = ((X227 @ id @ X233 @ id)))) | ? [X235 : (subst > term > term)] : (! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237))) & ! [X236 : term] : ((((X227 @ id @ X236 @ id)) != $true) | ($true = ((X227 @ id @ (X235 @ id @ X236) @ id)))) & (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true)) | ? [X243 : subst,X242 : subst,X241 : term,X240 : subst] : ((((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) = $true) & ($true != ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242)))) | ? [X229 : subst,X231 : term,X228 : subst,X230 : subst] : ((((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) = $true) & ($true != ((X227 @ X228 @ X231 @ (comp @ X229 @ X230))))) | (((X227 @ id @ X226 @ id)) = $true) | ? [X232 : term] : (($true = ((var @ (sub @ X232 @ id)))) & ($true != ((X227 @ id @ X232 @ id))))) | ? [X218 : (subst > term > subst > $o),X217 : term,X216 : (term > $o)] : (($true != ((X216 @ (lam @ X217)))) & ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ($true != ((X216 @ X220)))) & ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) & ! [X221 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ? [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) != ((sub @ (X221 @ X223 @ X225) @ X224))) | ? [X222 : term] : ((((X218 @ id @ X222 @ id)) = $true) & (((X218 @ id @ (X221 @ id @ X222) @ id)) != $true)))) | ? [X215 : term] : (((sub @ X215 @ id)) != X215))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) <=> (termmset = $true)) & (pushprop_lthm = $true) & (! [X492 : term,X493 : (subst > term > subst > $o)] : (? [X494 : term] : (($true != ((X493 @ id @ (sub @ X492 @ (push @ X494 @ id)) @ id))) & (((X493 @ id @ X494 @ id)) = $true)) | ? [X495 : (subst > term > term)] : ((((X493 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X499 : term] : ((((X493 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X493 @ id @ X499 @ id)) != $true)) & ! [X496 : subst,X497 : term,X498 : subst] : (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X495 @ X496 @ X497) @ X498)))) | ($true = ((X493 @ id @ (lam @ X492) @ id)))) <=> (hoasinduction_lem3a = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X52 : term,X50 : (subst > term > subst > $o),X51 : term] : (! [X62 : subst,X59 : subst,X61 : term,X60 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ($true != ((X50 @ X62 @ X61 @ (comp @ X60 @ X59))))) & ! [X56 : subst,X55 : subst,X57 : subst,X58 : term] : (($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57)))) | ($true != ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57)))) & ($true != ((X50 @ id @ (ap @ X51 @ X52) @ id))) & ($true = ((X50 @ id @ X52 @ id))) & ! [X53 : term,X54 : term] : ((((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true) | ($true != ((X50 @ id @ X54 @ id))) | ($true != ((X50 @ id @ X53 @ id)))) & ($true = ((X50 @ id @ X51 @ id)))) | ! [X80 : term,X79 : (subst > term > subst > $o)] : (? [X82 : (subst > term > term)] : (! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | (((X79 @ id @ X86 @ id)) != $true)) & ($true != ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id))) & ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83)))) | ($true = ((X79 @ id @ X80 @ id))) | ? [X81 : term] : ((((var @ (sub @ X81 @ id))) = $true) & ($true != ((X79 @ id @ X81 @ id)))) | ? [X96 : subst,X94 : subst,X93 : subst,X95 : term] : (($true = ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) & ($true != ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96)))) | ? [X87 : term,X88 : term] : ((((X79 @ id @ X88 @ id)) = $true) & ($true = ((X79 @ id @ X87 @ id))) & ($true != ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)))) | ? [X90 : subst,X91 : term,X92 : subst,X89 : subst] : ((((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) = $true) & (((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) != $true))) | ? [X63 : (subst > term > subst > $o),X64 : term] : (! [X66 : subst,X67 : term,X65 : subst,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) != $true)) & ($true != ((X63 @ id @ (lam @ X64) @ id))) & ! [X70 : (subst > term > term)] : (($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ? [X71 : term] : (($true = ((X63 @ id @ X71 @ id))) & (((X63 @ id @ (X70 @ id @ X71) @ id)) != $true)) | ? [X73 : subst,X74 : subst,X72 : term] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) != ((sub @ (X70 @ X74 @ X72) @ X73)))) & ! [X69 : term] : (($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id))) | (((X63 @ id @ X69 @ id)) != $true)) & ! [X75 : term,X77 : subst,X78 : subst,X76 : subst] : ((((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true) | ($true != ((X63 @ X78 @ X75 @ (comp @ X76 @ X77)))))) | ? [X43 : (term > $o),X44 : term] : ((((X43 @ X44)) != $true) & ! [X48 : term] : (? [X49 : term] : (($true != ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) & (((X43 @ X49)) = $true)) | (((X43 @ (lam @ X48))) = $true)) & ! [X45 : term] : (($true = ((X43 @ X45))) | (((var @ X45)) != $true)) & ! [X47 : term,X46 : term] : ((((X43 @ X46)) != $true) | ($true != ((X43 @ X47))) | ($true = ((X43 @ (ap @ X47 @ X46))))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X284 : term,X285 : (subst > term > subst > $o)] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & ($true = ((X285 @ id @ X286 @ id)))) | ? [X290 : term,X288 : subst,X289 : subst,X287 : subst] : ((((X285 @ X287 @ X290 @ (comp @ X289 @ X288))) != $true) & ($true = ((X285 @ (comp @ X287 @ X289) @ (sub @ X290 @ X289) @ X288)))) | ? [X298 : term,X299 : subst,X297 : subst,X296 : subst] : ((((X285 @ (comp @ X297 @ X299) @ (sub @ X298 @ X299) @ X296)) != $true) & ($true = ((X285 @ X297 @ X298 @ (comp @ X299 @ X296))))) | ? [X291 : (subst > term > term)] : (($true != ((X285 @ id @ (lam @ (X291 @ sh @ one)) @ id))) & ! [X294 : term,X293 : subst,X292 : subst] : (((sub @ (X291 @ X292 @ X294) @ X293)) = ((X291 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) & ! [X295 : term] : (($true != ((X285 @ id @ X295 @ id))) | ($true = ((X285 @ id @ (X291 @ id @ X295) @ id))))))) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (axabs = $true) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & (axvarshift = $true) & ((induction = $true) <=> ! [X528 : term,X529 : (term > $o)] : (? [X533 : term,X532 : term] : (($true = ((X529 @ X533))) & (((X529 @ X532)) = $true) & ($true != ((X529 @ (ap @ X532 @ X533))))) | ? [X530 : term] : ((((X529 @ X530)) != $true) & ($true = ((var @ X530)))) | ? [X531 : term] : ((((X529 @ X531)) = $true) & ($true != ((X529 @ (lam @ X531))))) | (((X529 @ X528)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : (? [X373 : term] : (($true = ((X366 @ id @ X373 @ id))) & ($true != ((X366 @ id @ (sub @ X367 @ (push @ X373 @ id)) @ id)))) | (((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : (subst > term > term)] : (($true != ((X366 @ id @ (lam @ (X368 @ sh @ one)) @ id))) & ! [X371 : term,X370 : subst,X372 : subst] : (((X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) = ((sub @ (X368 @ X370 @ X371) @ X372))) & ! [X369 : term] : (($true != ((X366 @ id @ X369 @ id))) | ($true = ((X366 @ id @ (X368 @ id @ X369) @ id))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true) & ! [X318 : d_subst] : (d_id = X318) & (! [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true != ((X160 @ X162))) | (((X161 @ one)) = $true) | ? [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) != ((X161 @ X163)))) <=> (pushprop_lem1v2 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X137 : (term > $o),X136 : term] : (? [X140 : term] : (($true != ((X137 @ (lam @ X140)))) & ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ($true != ((X137 @ X141))))) | ? [X139 : term,X138 : term] : (($true = ((X137 @ X139))) & ($true != ((X137 @ (ap @ X139 @ X138)))) & ($true = ((X137 @ X138)))) | ($true = ((X137 @ X136))) | ? [X142 : term] : (($true != ((X137 @ X142))) & (((var @ X142)) = $true))) <=> (induction2 = $true)) & (termmset_gthm = $true) & ((laminj = $true) <=> ! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317))) & ((induction2lem = $true) <=> ! [X252 : subst,X251 : (term > $o),X253 : term] : (? [X254 : term] : (! [X255 : term] : (($true != ((X251 @ X255))) | (((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true)) & ($true != ((X251 @ (lam @ X254))))) | ? [X258 : term] : (($true != ((X251 @ (sub @ X258 @ X252)))) & (((var @ X258)) = $true)) | ? [X257 : term,X256 : term] : (($true != ((X251 @ (ap @ X256 @ X257)))) & ($true = ((X251 @ X256))) & (((X251 @ X257)) = $true)) | (((X251 @ (sub @ X253 @ X252))) = $true))) & (lamnotvar = $true) & (! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (? [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) != ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ? [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) != ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (($true != ((X335 @ id @ X334 @ id))) | ? [X336 : subst,X339 : term,X338 : subst,X337 : subst] : (($true != ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) & (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) = $true)) | ? [X341 : subst,X343 : subst,X340 : term,X342 : subst] : (($true = ((X335 @ X342 @ X340 @ (comp @ X341 @ X343)))) & (((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) != $true)) | ? [X345 : term,X344 : term] : ((((X335 @ id @ X344 @ id)) = $true) & (((X335 @ id @ X345 @ id)) = $true) & ($true != ((X335 @ id @ (ap @ (sub @ X344 @ id) @ X345) @ id)))) | (((X335 @ id @ X333 @ id)) != $true) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true))) & ((pushprop_lem0_lthm = $true) <=> ! [X505 : subst,X504 : (term > $o),X506 : term] : ? [X507 : (term > $o)] : ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (! [X30 : (subst > term > subst > $o),X29 : term] : (? [X31 : term] : (($true = ((X30 @ id @ X31 @ id))) & ($true != ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id)))) | ? [X33 : term,X32 : (subst > term > term)] : (! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) & ($true != ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id))) & ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) & ! [X37 : term] : (($true != ((X30 @ id @ X37 @ id))) | ($true = ((X30 @ id @ (X32 @ id @ X37) @ id))))) | ($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((substmonoid = $true) <=> (! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346))) & ((axscons = $true) <=> ! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X276 : term] : ? [X277 : (subst > term > term)] : ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278))))) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X195 : term,X196 : (subst > term > subst > $o)] : (? [X202 : term,X203 : term] : (($true = ((X196 @ id @ X203 @ id))) & (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) != $true) & ($true = ((X196 @ id @ X202 @ id)))) | ($true = ((X196 @ id @ X195 @ id))) | ? [X197 : (subst > term > term)] : (! [X198 : term] : (($true != ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id)))) & (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true) & ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X116 : term] : (((sub @ X116 @ id)) != X116) | ? [X110 : (term > $o),X109 : term] : (! [X115 : term] : (($true != ((var @ X115))) | ($true = ((X110 @ X115)))) & (((X110 @ X109)) != $true) & ! [X113 : term,X114 : term] : ((((X110 @ X114)) != $true) | ($true = ((X110 @ (ap @ X114 @ X113)))) | ($true != ((X110 @ X113)))) & ! [X111 : term] : (? [X112 : term] : (($true != ((X110 @ (sub @ X111 @ (push @ X112 @ id))))) & ($true = ((X110 @ X112)))) | ($true = ((X110 @ (lam @ X111)))))) | ? [X119 : (subst > term > subst > $o),X118 : (term > $o),X117 : term] : (($true != ((X118 @ (lam @ X117)))) & ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) & ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ($true != ((X118 @ X126)))) & ! [X120 : (subst > term > term)] : ((((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ? [X124 : term] : (($true = ((X119 @ id @ X124 @ id))) & ($true != ((X119 @ id @ (X120 @ id @ X124) @ id)))) | ? [X122 : subst,X121 : term,X123 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) != ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122)))))) | ? [X106 : (subst > term > subst > $o)] : ! [X107 : (term > $o)] : ? [X108 : term] : (((X106 @ id @ X108 @ id)) != ((X107 @ X108))) | ! [X128 : term,X127 : (subst > term > subst > $o)] : (? [X129 : term,X130 : term] : (($true = ((X127 @ id @ X129 @ id))) & ($true = ((X127 @ id @ X130 @ id))) & ($true != ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)))) | ? [X131 : (subst > term > term)] : (! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133)))) & ($true != ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) & ! [X132 : term] : (($true != ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id))))) | ($true = ((X127 @ id @ X128 @ id)))))) & ((hoasapinj1_lthm = $true) <=> (? [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 != X185) & (((ap @ X183 @ X186)) = ((ap @ X185 @ X184)))) | ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190)) | ? [X182 : term] : (((sub @ X182 @ id)) != X182))) & (hoaslamnotvar = $true) & (! [X268 : term,X269 : (subst > term > subst > $o)] : (? [X270 : (subst > term > term)] : (($true != ((X269 @ id @ (lam @ (X270 @ sh @ one)) @ id))) & ! [X273 : term,X274 : subst,X272 : subst] : (((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274))) = ((sub @ (X270 @ X272 @ X273) @ X274))) & ! [X271 : term] : (($true != ((X269 @ id @ X271 @ id))) | ($true = ((X269 @ id @ (X270 @ id @ X271) @ id))))) | ($true = ((X269 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id))) | ? [X275 : term] : ((((X269 @ id @ X275 @ id)) = $true) & (((X269 @ id @ (sub @ X268 @ (push @ X275 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa = $true)) & (! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X486 : term] : ? [X487 : (subst > term > term)] : ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489))))) & (axclos = $true) & ((induction2_lthm = $true) <=> (? [X470 : term] : (((sub @ X470 @ id)) != X470) | ! [X480 : (term > $o),X479 : term] : ((((X480 @ X479)) = $true) | ? [X482 : term,X483 : term] : ((((X480 @ X483)) = $true) & (((X480 @ (ap @ X483 @ X482))) != $true) & ($true = ((X480 @ X482)))) | ? [X481 : term] : ((((var @ X481)) = $true) & ($true != ((X480 @ X481)))) | ? [X484 : term] : ((((X480 @ (lam @ X484))) != $true) & ! [X485 : term] : (($true = ((X480 @ (sub @ X484 @ (push @ X485 @ id))))) | (((X480 @ X485)) != $true)))) | ? [X471 : subst,X472 : (term > $o),X473 : term] : (! [X474 : term] : (? [X475 : term] : ((((X472 @ (sub @ X474 @ (push @ X475 @ id)))) != $true) & (((X472 @ X475)) = $true)) | (((X472 @ (lam @ X474))) = $true)) & ! [X476 : term] : (($true = ((X472 @ (sub @ X476 @ X471)))) | (((var @ X476)) != $true)) & ! [X478 : term,X477 : term] : (($true != ((X472 @ X477))) | ($true = ((X472 @ (ap @ X477 @ X478)))) | (((X472 @ X478)) != $true)) & ($true != ((X472 @ (sub @ X473 @ X471))))))) & (ulamvarsh = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) != X324) | ! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true)) | ? [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) != X323))) & (axmap = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ? [X249 : (term > $o)] : ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) != ((d2subst @ X12))) | (X12 = X13)) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X511 : term,X510 : (subst > term > subst > $o),X509 : (term > $o)] : ((((X509 @ (lam @ X511))) = $true) | ? [X517 : term] : (((X509 @ X517)) != ((X510 @ id @ X517 @ id))) | ? [X518 : term] : (($true != ((X509 @ (sub @ X511 @ (push @ X518 @ id))))) & ($true = ((X509 @ X518)))) | ? [X512 : (subst > term > term)] : (! [X516 : subst,X514 : term,X515 : subst] : (((X512 @ (comp @ X516 @ X515) @ (sub @ X514 @ X515))) = ((sub @ (X512 @ X516 @ X514) @ X515))) & ($true != ((X510 @ id @ (lam @ (X512 @ sh @ one)) @ id))) & ! [X513 : term] : (($true = ((X510 @ id @ (X512 @ id @ X513) @ id))) | ($true != ((X510 @ id @ X513 @ id))))))) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280))))) & (pushprop_lem3v2_lthm = $true) & ! [X332 : d_term,X331 : d_term] : ((((d2term @ X331)) != ((d2term @ X332))) | (X331 = X332)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (? [X402 : term] : (((sub @ X402 @ id)) != X402) | ? [X404 : (subst > term > subst > $o),X403 : term] : (! [X405 : term] : (($true != ((X404 @ id @ X405 @ id))) | ($true = ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)))) & ($true != ((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id))) & ! [X406 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true) | ? [X407 : term] : (($true = ((X404 @ id @ X407 @ id))) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X409 : term,X410 : subst,X408 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) != ((sub @ (X406 @ X408 @ X409) @ X410))))) | ! [X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (lam @ X412) @ id))) | ? [X414 : subst,X415 : subst,X416 : term,X413 : subst] : (($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X416 @ X415) @ X413))) & ($true != ((X411 @ X414 @ X416 @ (comp @ X415 @ X413))))) | ? [X417 : (subst > term > term)] : (! [X418 : subst,X419 : subst,X420 : term] : (((X417 @ (comp @ X418 @ X419) @ (sub @ X420 @ X419))) = ((sub @ (X417 @ X418 @ X420) @ X419))) & ($true != ((X411 @ id @ (lam @ (X417 @ sh @ one)) @ id))) & ! [X421 : term] : (($true != ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (X417 @ id @ X421) @ id))))) | ? [X423 : subst,X424 : term,X425 : subst,X422 : subst] : ((((X411 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423) @ X422)) != $true) & ($true = ((X411 @ X425 @ X424 @ (comp @ X423 @ X422))))) | ? [X426 : term] : (($true = ((X411 @ id @ X426 @ id))) & ($true != ((X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))))))) & (hoasapnotvar_lthm = $true) & ((apinj1 = $true) <=> ! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265))) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & (! [X164 : (term > $o),X166 : (subst > term > subst > $o),X165 : term] : (? [X180 : term,X179 : subst,X178 : subst,X177 : subst] : (($true != ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179))) & ($true = ((X166 @ X178 @ X180 @ (comp @ X177 @ X179))))) | ? [X181 : term] : (((X164 @ X181)) != ((X166 @ id @ X181 @ id))) | ($true = ((X164 @ (lam @ X165)))) | ? [X167 : (subst > term > term)] : (! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) & ($true != ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))) & ! [X171 : term] : ((((X166 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X166 @ id @ X171 @ id)) != $true))) | ? [X174 : subst,X175 : subst,X173 : subst,X172 : term] : (($true != ((X166 @ X173 @ X172 @ (comp @ X175 @ X174)))) & ($true = ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174)))) | ? [X176 : term] : (($true != ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) & (((X164 @ X176)) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (! [X302 : term,X303 : term,X304 : (subst > term > subst > $o),X301 : (term > $o)] : (($true != ((X301 @ X302))) | ? [X306 : term,X305 : term] : (($true = ((X304 @ id @ X305 @ id))) & ($true = ((X304 @ id @ X306 @ id))) & (((X304 @ id @ (ap @ (sub @ X305 @ id) @ X306) @ id)) != $true)) | ($true != ((X301 @ X303))) | ? [X311 : term] : (((X301 @ X311)) != ((X304 @ id @ X311 @ id))) | ? [X315 : subst,X314 : subst,X313 : subst,X312 : term] : (($true = ((X304 @ X313 @ X312 @ (comp @ X314 @ X315)))) & (((X304 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314) @ X315)) != $true)) | ? [X310 : term,X307 : subst,X309 : subst,X308 : subst] : (($true != ((X304 @ X307 @ X310 @ (comp @ X308 @ X309)))) & (((X304 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309)) = $true)) | ($true = ((X301 @ (ap @ X302 @ X303))))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_gthm = $true) & ((? [X449 : term] : (((sub @ X449 @ id)) != X449) | ! [X450 : term] : (((sub @ X450 @ id)) = X450)) <=> (termmset_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98))) | ? [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) != ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))))) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X396 : subst,X395 : (term > $o),X394 : term] : (? [X399 : term] : ((((X395 @ (lam @ X399))) != $true) & ! [X400 : term] : (($true = ((X395 @ (sub @ X399 @ (push @ X400 @ id))))) | (((X395 @ X400)) != $true))) | ? [X398 : term,X397 : term] : (($true = ((X395 @ X397))) & ($true = ((X395 @ X398))) & (((X395 @ (ap @ X398 @ X397))) != $true)) | ? [X401 : term] : (($true = ((var @ X401))) & ($true != ((X395 @ (sub @ X401 @ X396))))) | ($true = ((X395 @ (sub @ X394 @ X396))))) | ? [X385 : term,X386 : subst] : (((comp @ sh @ (push @ X385 @ X386))) != X386) | ? [X388 : (term > $o),X389 : term] : (! [X391 : term] : (($true = ((X388 @ X391))) | ($true != ((var @ X391)))) & ! [X390 : term] : ((((X388 @ (lam @ X390))) = $true) | (((X388 @ X390)) != $true)) & (((X388 @ X389)) != $true) & ! [X393 : term,X392 : term] : ((((X388 @ X393)) != $true) | ($true != ((X388 @ X392))) | ($true = ((X388 @ (ap @ X392 @ X393)))))) | ? [X383 : subst,X384 : term] : (((sub @ one @ (push @ X384 @ X383))) != X384) | ? [X387 : subst] : (((comp @ X387 @ id)) != X387))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) <=> (axidr = $true)) & (one = ((d2term @ d_one))) & (((! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500)) <=> (substmonoid_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((? [X432 : term] : (((sub @ X432 @ id)) != X432) | ! [X441 : term,X442 : (subst > term > subst > $o)] : (? [X448 : term] : (($true = ((X442 @ id @ X448 @ id))) & ($true != ((X442 @ id @ (sub @ X441 @ (push @ X448 @ id)) @ id)))) | ? [X443 : (subst > term > term)] : (! [X447 : term] : (($true = ((X442 @ id @ (X443 @ id @ X447) @ id))) | (((X442 @ id @ X447 @ id)) != $true)) & ! [X444 : subst,X445 : subst,X446 : term] : (((sub @ (X443 @ X444 @ X446) @ X445)) = ((X443 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445)))) & ($true != ((X442 @ id @ (lam @ (X443 @ sh @ one)) @ id)))) | ($true = ((X442 @ id @ (lam @ X441) @ id)))) | ? [X433 : (subst > term > subst > $o),X434 : term] : (! [X440 : term] : ((((X433 @ id @ X440 @ id)) != $true) | ($true = ((X433 @ id @ (sub @ X434 @ (push @ X440 @ id)) @ id)))) & (((X433 @ id @ (lam @ (sub @ X434 @ (push @ one @ sh))) @ id)) != $true) & ! [X435 : (subst > term > term)] : (? [X439 : term,X438 : subst,X437 : subst] : (((sub @ (X435 @ X438 @ X439) @ X437)) != ((X435 @ (comp @ X438 @ X437) @ (sub @ X439 @ X437)))) | (((X433 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true) | ? [X436 : term] : ((((X433 @ id @ X436 @ id)) = $true) & ($true != ((X433 @ id @ (X435 @ id @ X436) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction = $true) <=> ! [X349 : (subst > term > subst > $o),X348 : term] : ((((X349 @ id @ X348 @ id)) = $true) | ? [X364 : subst,X363 : subst,X362 : subst,X365 : term] : ((((X349 @ (comp @ X364 @ X362) @ (sub @ X365 @ X362) @ X363)) != $true) & ($true = ((X349 @ X364 @ X365 @ (comp @ X362 @ X363))))) | ? [X350 : term,X351 : term] : (($true = ((X349 @ id @ X350 @ id))) & ($true = ((X349 @ id @ X351 @ id))) & ($true != ((X349 @ id @ (ap @ (sub @ X350 @ id) @ X351) @ id)))) | ? [X357 : term] : ((((X349 @ id @ X357 @ id)) != $true) & ($true = ((var @ (sub @ X357 @ id))))) | ? [X360 : subst,X359 : subst,X358 : subst,X361 : term] : ((((X349 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359) @ X358)) = $true) & ($true != ((X349 @ X360 @ X361 @ (comp @ X359 @ X358))))) | ? [X352 : (subst > term > term)] : (! [X355 : subst,X354 : term,X353 : subst] : (((X352 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X353 @ X354) @ X355))) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true) & ! [X356 : term] : ((((X349 @ id @ X356 @ id)) != $true) | ($true = ((X349 @ id @ (X352 @ id @ X356) @ id))))))) & ((axshiftcons = $true) <=> ! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520)) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & (axapp = $true) & ((hoasapinj2_lthm = $true) <=> (? [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 != X378) & (((ap @ X377 @ X378)) = ((ap @ X375 @ X376)))) | ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379))))))),
% 6.44/1.37 inference(flattening,[],[f11])).
% 6.44/1.37 thf(f13,definition,(
% 6.44/1.37 ! [X349 : (subst > term > subst > $o)] : (($true = ((sP0 @ X349))) <=> ? [X352 : (subst > term > term)] : (! [X355 : subst,X354 : term,X353 : subst] : (((X352 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X353 @ X354) @ X355))) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true) & ! [X356 : term] : ((((X349 @ id @ X356 @ id)) != $true) | ($true = ((X349 @ id @ (X352 @ id @ X356) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f14,definition,(
% 6.44/1.37 ! [X349 : (subst > term > subst > $o)] : (($true = ((sP1 @ X349))) <=> ? [X350 : term,X351 : term] : (($true = ((X349 @ id @ X350 @ id))) & ($true = ((X349 @ id @ X351 @ id))) & ($true != ((X349 @ id @ (ap @ (sub @ X350 @ id) @ X351) @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f15,definition,(
% 6.44/1.37 (sP2 = $true) <=> ! [X349 : (subst > term > subst > $o),X348 : term] : ((((X349 @ id @ X348 @ id)) = $true) | ? [X364 : subst,X363 : subst,X362 : subst,X365 : term] : ((((X349 @ (comp @ X364 @ X362) @ (sub @ X365 @ X362) @ X363)) != $true) & ($true = ((X349 @ X364 @ X365 @ (comp @ X362 @ X363))))) | ($true = ((sP1 @ X349))) | ? [X357 : term] : ((((X349 @ id @ X357 @ id)) != $true) & ($true = ((var @ (sub @ X357 @ id))))) | ? [X360 : subst,X359 : subst,X358 : subst,X361 : term] : ((((X349 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359) @ X358)) = $true) & ($true != ((X349 @ X360 @ X361 @ (comp @ X359 @ X358))))) | ($true = ((sP0 @ X349))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f16,definition,(
% 6.44/1.37 ($true = sP3) <=> ? [X433 : (subst > term > subst > $o),X434 : term] : (! [X440 : term] : ((((X433 @ id @ X440 @ id)) != $true) | ($true = ((X433 @ id @ (sub @ X434 @ (push @ X440 @ id)) @ id)))) & (((X433 @ id @ (lam @ (sub @ X434 @ (push @ one @ sh))) @ id)) != $true) & ! [X435 : (subst > term > term)] : (? [X439 : term,X438 : subst,X437 : subst] : (((sub @ (X435 @ X438 @ X439) @ X437)) != ((X435 @ (comp @ X438 @ X437) @ (sub @ X439 @ X437)))) | (((X433 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true) | ? [X436 : term] : ((((X433 @ id @ X436 @ id)) = $true) & ($true != ((X433 @ id @ (X435 @ id @ X436) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f17,definition,(
% 6.44/1.37 ($true = sP4) <=> (? [X432 : term] : (((sub @ X432 @ id)) != X432) | ! [X441 : term,X442 : (subst > term > subst > $o)] : (? [X448 : term] : (($true = ((X442 @ id @ X448 @ id))) & ($true != ((X442 @ id @ (sub @ X441 @ (push @ X448 @ id)) @ id)))) | ? [X443 : (subst > term > term)] : (! [X447 : term] : (($true = ((X442 @ id @ (X443 @ id @ X447) @ id))) | (((X442 @ id @ X447 @ id)) != $true)) & ! [X444 : subst,X445 : subst,X446 : term] : (((sub @ (X443 @ X444 @ X446) @ X445)) = ((X443 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445)))) & ($true != ((X442 @ id @ (lam @ (X443 @ sh @ one)) @ id)))) | ($true = ((X442 @ id @ (lam @ X441) @ id)))) | ($true = sP3))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f18,definition,(
% 6.44/1.37 ! [X388 : (term > $o)] : (($true = ((sP5 @ X388))) <=> ! [X393 : term,X392 : term] : ((((X388 @ X393)) != $true) | ($true != ((X388 @ X392))) | ($true = ((X388 @ (ap @ X392 @ X393))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f19,definition,(
% 6.44/1.37 ! [X395 : (term > $o)] : ((((sP6 @ X395)) = $true) <=> ? [X398 : term,X397 : term] : (($true = ((X395 @ X397))) & ($true = ((X395 @ X398))) & (((X395 @ (ap @ X398 @ X397))) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f20,definition,(
% 6.44/1.37 ($true = sP7) <=> ! [X396 : subst,X395 : (term > $o),X394 : term] : (? [X399 : term] : ((((X395 @ (lam @ X399))) != $true) & ! [X400 : term] : (($true = ((X395 @ (sub @ X399 @ (push @ X400 @ id))))) | (((X395 @ X400)) != $true))) | (((sP6 @ X395)) = $true) | ? [X401 : term] : (($true = ((var @ X401))) & ($true != ((X395 @ (sub @ X401 @ X396))))) | ($true = ((X395 @ (sub @ X394 @ X396)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f21,definition,(
% 6.44/1.37 (sP8 = $true) <=> (($true = sP7) | ? [X385 : term,X386 : subst] : (((comp @ sh @ (push @ X385 @ X386))) != X386) | ? [X388 : (term > $o),X389 : term] : (! [X391 : term] : (($true = ((X388 @ X391))) | ($true != ((var @ X391)))) & ! [X390 : term] : ((((X388 @ (lam @ X390))) = $true) | (((X388 @ X390)) != $true)) & (((X388 @ X389)) != $true) & ($true = ((sP5 @ X388)))) | ? [X383 : subst,X384 : term] : (((sub @ one @ (push @ X384 @ X383))) != X384) | ? [X387 : subst] : (((comp @ X387 @ id)) != X387))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f22,definition,(
% 6.44/1.37 ! [X304 : (subst > term > subst > $o)] : (($true = ((sP9 @ X304))) <=> ? [X306 : term,X305 : term] : (($true = ((X304 @ id @ X305 @ id))) & ($true = ((X304 @ id @ X306 @ id))) & (((X304 @ id @ (ap @ (sub @ X305 @ id) @ X306) @ id)) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f23,definition,(
% 6.44/1.37 ($true = sP10) <=> ! [X302 : term,X303 : term,X304 : (subst > term > subst > $o),X301 : (term > $o)] : (($true != ((X301 @ X302))) | ($true = ((sP9 @ X304))) | ($true != ((X301 @ X303))) | ? [X311 : term] : (((X301 @ X311)) != ((X304 @ id @ X311 @ id))) | ? [X315 : subst,X314 : subst,X313 : subst,X312 : term] : (($true = ((X304 @ X313 @ X312 @ (comp @ X314 @ X315)))) & (((X304 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314) @ X315)) != $true)) | ? [X310 : term,X307 : subst,X309 : subst,X308 : subst] : (($true != ((X304 @ X307 @ X310 @ (comp @ X308 @ X309)))) & (((X304 @ (comp @ X307 @ X308) @ (sub @ X310 @ X308) @ X309)) = $true)) | ($true = ((X301 @ (ap @ X302 @ X303)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f24,definition,(
% 6.44/1.37 ! [X166 : (subst > term > subst > $o)] : (($true = ((sP11 @ X166))) <=> ? [X167 : (subst > term > term)] : (! [X170 : subst,X169 : term,X168 : subst] : (((X167 @ (comp @ X168 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (X167 @ X168 @ X169) @ X170))) & ($true != ((X166 @ id @ (lam @ (X167 @ sh @ one)) @ id))) & ! [X171 : term] : ((((X166 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X166 @ id @ X171 @ id)) != $true))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f25,definition,(
% 6.44/1.37 (sP12 = $true) <=> ! [X164 : (term > $o),X166 : (subst > term > subst > $o),X165 : term] : (? [X180 : term,X179 : subst,X178 : subst,X177 : subst] : (($true != ((X166 @ (comp @ X178 @ X177) @ (sub @ X180 @ X177) @ X179))) & ($true = ((X166 @ X178 @ X180 @ (comp @ X177 @ X179))))) | ? [X181 : term] : (((X164 @ X181)) != ((X166 @ id @ X181 @ id))) | ($true = ((X164 @ (lam @ X165)))) | ($true = ((sP11 @ X166))) | ? [X174 : subst,X175 : subst,X173 : subst,X172 : term] : (($true != ((X166 @ X173 @ X172 @ (comp @ X175 @ X174)))) & ($true = ((X166 @ (comp @ X173 @ X175) @ (sub @ X172 @ X175) @ X174)))) | ? [X176 : term] : (($true != ((X164 @ (sub @ X165 @ (push @ X176 @ id))))) & (((X164 @ X176)) = $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f26,definition,(
% 6.44/1.37 ! [X411 : (subst > term > subst > $o)] : ((((sP13 @ X411)) = $true) <=> ? [X417 : (subst > term > term)] : (! [X418 : subst,X419 : subst,X420 : term] : (((X417 @ (comp @ X418 @ X419) @ (sub @ X420 @ X419))) = ((sub @ (X417 @ X418 @ X420) @ X419))) & ($true != ((X411 @ id @ (lam @ (X417 @ sh @ one)) @ id))) & ! [X421 : term] : (($true != ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (X417 @ id @ X421) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f27,definition,(
% 6.44/1.37 (sP14 = $true) <=> ? [X404 : (subst > term > subst > $o),X403 : term] : (! [X405 : term] : (($true != ((X404 @ id @ X405 @ id))) | ($true = ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)))) & ($true != ((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id))) & ! [X406 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true) | ? [X407 : term] : (($true = ((X404 @ id @ X407 @ id))) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X409 : term,X410 : subst,X408 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) != ((sub @ (X406 @ X408 @ X409) @ X410)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f28,definition,(
% 6.44/1.37 (sP15 = $true) <=> (? [X402 : term] : (((sub @ X402 @ id)) != X402) | (sP14 = $true) | ! [X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (lam @ X412) @ id))) | ? [X414 : subst,X415 : subst,X416 : term,X413 : subst] : (($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X416 @ X415) @ X413))) & ($true != ((X411 @ X414 @ X416 @ (comp @ X415 @ X413))))) | (((sP13 @ X411)) = $true) | ? [X423 : subst,X424 : term,X425 : subst,X422 : subst] : ((((X411 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423) @ X422)) != $true) & ($true = ((X411 @ X425 @ X424 @ (comp @ X423 @ X422))))) | ? [X426 : term] : (($true = ((X411 @ id @ X426 @ id))) & ($true != ((X411 @ id @ (sub @ X412 @ (push @ X426 @ id)) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f29,definition,(
% 6.44/1.37 ($true = sP16) <=> ! [X511 : term,X510 : (subst > term > subst > $o),X509 : (term > $o)] : ((((X509 @ (lam @ X511))) = $true) | ? [X517 : term] : (((X509 @ X517)) != ((X510 @ id @ X517 @ id))) | ? [X518 : term] : (($true != ((X509 @ (sub @ X511 @ (push @ X518 @ id))))) & ($true = ((X509 @ X518)))) | ? [X512 : (subst > term > term)] : (! [X516 : subst,X514 : term,X515 : subst] : (((X512 @ (comp @ X516 @ X515) @ (sub @ X514 @ X515))) = ((sub @ (X512 @ X516 @ X514) @ X515))) & ($true != ((X510 @ id @ (lam @ (X512 @ sh @ one)) @ id))) & ! [X513 : term] : (($true = ((X510 @ id @ (X512 @ id @ X513) @ id))) | ($true != ((X510 @ id @ X513 @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f30,definition,(
% 6.44/1.37 ! [X472 : (term > $o)] : ((((sP17 @ X472)) = $true) <=> ! [X478 : term,X477 : term] : (($true != ((X472 @ X477))) | ($true = ((X472 @ (ap @ X477 @ X478)))) | (((X472 @ X478)) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f31,definition,(
% 6.44/1.37 ! [X480 : (term > $o)] : (($true = ((sP18 @ X480))) <=> ? [X482 : term,X483 : term] : ((((X480 @ X483)) = $true) & (((X480 @ (ap @ X483 @ X482))) != $true) & ($true = ((X480 @ X482)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f32,definition,(
% 6.44/1.37 (sP19 = $true) <=> ! [X480 : (term > $o),X479 : term] : ((((X480 @ X479)) = $true) | ($true = ((sP18 @ X480))) | ? [X481 : term] : ((((var @ X481)) = $true) & ($true != ((X480 @ X481)))) | ? [X484 : term] : ((((X480 @ (lam @ X484))) != $true) & ! [X485 : term] : (($true = ((X480 @ (sub @ X484 @ (push @ X485 @ id))))) | (((X480 @ X485)) != $true))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f33,definition,(
% 6.44/1.37 ($true = sP20) <=> (? [X470 : term] : (((sub @ X470 @ id)) != X470) | (sP19 = $true) | ? [X471 : subst,X472 : (term > $o),X473 : term] : (! [X474 : term] : (? [X475 : term] : ((((X472 @ (sub @ X474 @ (push @ X475 @ id)))) != $true) & (((X472 @ X475)) = $true)) | (((X472 @ (lam @ X474))) = $true)) & ! [X476 : term] : (($true = ((X472 @ (sub @ X476 @ X471)))) | (((var @ X476)) != $true)) & (((sP17 @ X472)) = $true) & ($true != ((X472 @ (sub @ X473 @ X471))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f34,definition,(
% 6.44/1.37 ($true = sP21) <=> ! [X268 : term,X269 : (subst > term > subst > $o)] : (? [X270 : (subst > term > term)] : (($true != ((X269 @ id @ (lam @ (X270 @ sh @ one)) @ id))) & ! [X273 : term,X274 : subst,X272 : subst] : (((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274))) = ((sub @ (X270 @ X272 @ X273) @ X274))) & ! [X271 : term] : (($true != ((X269 @ id @ X271 @ id))) | ($true = ((X269 @ id @ (X270 @ id @ X271) @ id))))) | ($true = ((X269 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id))) | ? [X275 : term] : ((((X269 @ id @ X275 @ id)) = $true) & (((X269 @ id @ (sub @ X268 @ (push @ X275 @ id)) @ id)) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f35,definition,(
% 6.44/1.37 ! [X127 : (subst > term > subst > $o)] : (($true = ((sP22 @ X127))) <=> ? [X131 : (subst > term > term)] : (! [X134 : term,X135 : subst,X133 : subst] : (((sub @ (X131 @ X135 @ X134) @ X133)) = ((X131 @ (comp @ X135 @ X133) @ (sub @ X134 @ X133)))) & ($true != ((X127 @ id @ (lam @ (X131 @ sh @ one)) @ id))) & ! [X132 : term] : (($true != ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (X131 @ id @ X132) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f36,definition,(
% 6.44/1.37 ! [X110 : (term > $o)] : (($true = ((sP23 @ X110))) <=> ! [X113 : term,X114 : term] : ((((X110 @ X114)) != $true) | ($true = ((X110 @ (ap @ X114 @ X113)))) | ($true != ((X110 @ X113)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f37,definition,(
% 6.44/1.37 (sP24 = $true) <=> ? [X119 : (subst > term > subst > $o),X118 : (term > $o),X117 : term] : (($true != ((X118 @ (lam @ X117)))) & ! [X125 : term] : (((X119 @ id @ X125 @ id)) = ((X118 @ X125))) & ! [X126 : term] : (($true = ((X118 @ (sub @ X117 @ (push @ X126 @ id))))) | ($true != ((X118 @ X126)))) & ! [X120 : (subst > term > term)] : ((((X119 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ? [X124 : term] : (($true = ((X119 @ id @ X124 @ id))) & ($true != ((X119 @ id @ (X120 @ id @ X124) @ id)))) | ? [X122 : subst,X121 : term,X123 : subst] : (((sub @ (X120 @ X123 @ X121) @ X122)) != ((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f38,definition,(
% 6.44/1.37 ($true = sP25) <=> ? [X110 : (term > $o),X109 : term] : (! [X115 : term] : (($true != ((var @ X115))) | ($true = ((X110 @ X115)))) & (((X110 @ X109)) != $true) & ($true = ((sP23 @ X110))) & ! [X111 : term] : (? [X112 : term] : (($true != ((X110 @ (sub @ X111 @ (push @ X112 @ id))))) & ($true = ((X110 @ X112)))) | ($true = ((X110 @ (lam @ X111))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f39,definition,(
% 6.44/1.37 (sP26 = $true) <=> (? [X116 : term] : (((sub @ X116 @ id)) != X116) | ($true = sP25) | (sP24 = $true) | ? [X106 : (subst > term > subst > $o)] : ! [X107 : (term > $o)] : ? [X108 : term] : (((X106 @ id @ X108 @ id)) != ((X107 @ X108))) | ! [X128 : term,X127 : (subst > term > subst > $o)] : (? [X129 : term,X130 : term] : (($true = ((X127 @ id @ X129 @ id))) & ($true = ((X127 @ id @ X130 @ id))) & ($true != ((X127 @ id @ (ap @ (sub @ X130 @ id) @ X129) @ id)))) | ($true = ((sP22 @ X127))) | ($true = ((X127 @ id @ X128 @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f40,definition,(
% 6.44/1.37 ! [X196 : (subst > term > subst > $o)] : (($true = ((sP27 @ X196))) <=> ? [X197 : (subst > term > term)] : (! [X198 : term] : (($true != ((X196 @ id @ X198 @ id))) | ($true = ((X196 @ id @ (X197 @ id @ X198) @ id)))) & (((X196 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true) & ! [X201 : subst,X199 : subst,X200 : term] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f41,definition,(
% 6.44/1.37 ($true = sP28) <=> ! [X30 : (subst > term > subst > $o),X29 : term] : (? [X31 : term] : (($true = ((X30 @ id @ X31 @ id))) & ($true != ((X30 @ id @ (sub @ X29 @ (push @ X31 @ id)) @ id)))) | ? [X33 : term,X32 : (subst > term > term)] : (! [X40 : subst,X38 : subst,X39 : term] : (((X32 @ (comp @ X38 @ X40) @ (sub @ X39 @ X40))) = ((sub @ X33 @ (push @ (sub @ X39 @ X40) @ (comp @ X38 @ X40))))) & ($true != ((X30 @ id @ (lam @ (X32 @ sh @ one)) @ id))) & ! [X36 : term,X35 : subst,X34 : subst] : (((sub @ (X32 @ X35 @ X36) @ X34)) = ((sub @ (sub @ X33 @ (push @ X36 @ X35)) @ X34))) & ! [X37 : term] : (($true != ((X30 @ id @ X37 @ id))) | ($true = ((X30 @ id @ (X32 @ id @ X37) @ id))))) | ($true = ((X30 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f42,definition,(
% 6.44/1.37 ! [X335 : (subst > term > subst > $o)] : ((((sP29 @ X335)) = $true) <=> ? [X345 : term,X344 : term] : ((((X335 @ id @ X344 @ id)) = $true) & (((X335 @ id @ X345 @ id)) = $true) & ($true != ((X335 @ id @ (ap @ (sub @ X344 @ id) @ X345) @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f43,definition,(
% 6.44/1.37 ($true = sP30) <=> ! [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (($true != ((X335 @ id @ X334 @ id))) | ? [X336 : subst,X339 : term,X338 : subst,X337 : subst] : (($true != ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) & (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) = $true)) | ? [X341 : subst,X343 : subst,X340 : term,X342 : subst] : (($true = ((X335 @ X342 @ X340 @ (comp @ X341 @ X343)))) & (((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) != $true)) | (((sP29 @ X335)) = $true) | (((X335 @ id @ X333 @ id)) != $true) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f44,definition,(
% 6.44/1.37 ! [X251 : (term > $o)] : (($true = ((sP31 @ X251))) <=> ? [X257 : term,X256 : term] : (($true != ((X251 @ (ap @ X256 @ X257)))) & ($true = ((X251 @ X256))) & (((X251 @ X257)) = $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f45,definition,(
% 6.44/1.37 (sP32 = $true) <=> ! [X252 : subst,X251 : (term > $o),X253 : term] : (? [X254 : term] : (! [X255 : term] : (($true != ((X251 @ X255))) | (((X251 @ (sub @ X254 @ (push @ X255 @ id)))) = $true)) & ($true != ((X251 @ (lam @ X254))))) | ? [X258 : term] : (($true != ((X251 @ (sub @ X258 @ X252)))) & (((var @ X258)) = $true)) | ($true = ((sP31 @ X251))) | (((X251 @ (sub @ X253 @ X252))) = $true))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f46,definition,(
% 6.44/1.37 ! [X137 : (term > $o)] : ((((sP33 @ X137)) = $true) <=> ? [X139 : term,X138 : term] : (($true = ((X137 @ X139))) & ($true != ((X137 @ (ap @ X139 @ X138)))) & ($true = ((X137 @ X138)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f47,definition,(
% 6.44/1.37 (sP34 = $true) <=> ! [X137 : (term > $o),X136 : term] : (? [X140 : term] : (($true != ((X137 @ (lam @ X140)))) & ! [X141 : term] : ((((X137 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ($true != ((X137 @ X141))))) | (((sP33 @ X137)) = $true) | ($true = ((X137 @ X136))) | ? [X142 : term] : (($true != ((X137 @ X142))) & (((var @ X142)) = $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f48,definition,(
% 6.44/1.37 (sP35 = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : (? [X373 : term] : (($true = ((X366 @ id @ X373 @ id))) & ($true != ((X366 @ id @ (sub @ X367 @ (push @ X373 @ id)) @ id)))) | (((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : (subst > term > term)] : (($true != ((X366 @ id @ (lam @ (X368 @ sh @ one)) @ id))) & ! [X371 : term,X370 : subst,X372 : subst] : (((X368 @ (comp @ X370 @ X372) @ (sub @ X371 @ X372))) = ((sub @ (X368 @ X370 @ X371) @ X372))) & ! [X369 : term] : (($true != ((X366 @ id @ X369 @ id))) | ($true = ((X366 @ id @ (X368 @ id @ X369) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f49,definition,(
% 6.44/1.37 ! [X529 : (term > $o)] : (($true = ((sP36 @ X529))) <=> ? [X533 : term,X532 : term] : (($true = ((X529 @ X533))) & (((X529 @ X532)) = $true) & ($true != ((X529 @ (ap @ X532 @ X533))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f50,definition,(
% 6.44/1.37 ! [X285 : (subst > term > subst > $o)] : ((((sP37 @ X285)) = $true) <=> ? [X291 : (subst > term > term)] : (($true != ((X285 @ id @ (lam @ (X291 @ sh @ one)) @ id))) & ! [X294 : term,X293 : subst,X292 : subst] : (((sub @ (X291 @ X292 @ X294) @ X293)) = ((X291 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) & ! [X295 : term] : (($true != ((X285 @ id @ X295 @ id))) | ($true = ((X285 @ id @ (X291 @ id @ X295) @ id))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f51,definition,(
% 6.44/1.37 ($true = sP38) <=> ! [X284 : term,X285 : (subst > term > subst > $o)] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & ($true = ((X285 @ id @ X286 @ id)))) | ? [X290 : term,X288 : subst,X289 : subst,X287 : subst] : ((((X285 @ X287 @ X290 @ (comp @ X289 @ X288))) != $true) & ($true = ((X285 @ (comp @ X287 @ X289) @ (sub @ X290 @ X289) @ X288)))) | ? [X298 : term,X299 : subst,X297 : subst,X296 : subst] : ((((X285 @ (comp @ X297 @ X299) @ (sub @ X298 @ X299) @ X296)) != $true) & ($true = ((X285 @ X297 @ X298 @ (comp @ X299 @ X296))))) | (((sP37 @ X285)) = $true))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f52,definition,(
% 6.44/1.37 ! [X43 : (term > $o)] : (($true = ((sP39 @ X43))) <=> ! [X47 : term,X46 : term] : ((((X43 @ X46)) != $true) | ($true != ((X43 @ X47))) | ($true = ((X43 @ (ap @ X47 @ X46))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f53,definition,(
% 6.44/1.37 ! [X63 : (subst > term > subst > $o)] : (($true = ((sP40 @ X63))) <=> ! [X70 : (subst > term > term)] : (($true = ((X63 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ? [X71 : term] : (($true = ((X63 @ id @ X71 @ id))) & (((X63 @ id @ (X70 @ id @ X71) @ id)) != $true)) | ? [X73 : subst,X74 : subst,X72 : term] : (((X70 @ (comp @ X74 @ X73) @ (sub @ X72 @ X73))) != ((sub @ (X70 @ X74 @ X72) @ X73)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f54,definition,(
% 6.44/1.37 ! [X79 : (subst > term > subst > $o)] : (($true = ((sP41 @ X79))) <=> ? [X87 : term,X88 : term] : ((((X79 @ id @ X88 @ id)) = $true) & ($true = ((X79 @ id @ X87 @ id))) & ($true != ((X79 @ id @ (ap @ (sub @ X88 @ id) @ X87) @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f55,definition,(
% 6.44/1.37 ! [X79 : (subst > term > subst > $o)] : (($true = ((sP42 @ X79))) <=> ? [X82 : (subst > term > term)] : (! [X86 : term] : (($true = ((X79 @ id @ (X82 @ id @ X86) @ id))) | (((X79 @ id @ X86 @ id)) != $true)) & ($true != ((X79 @ id @ (lam @ (X82 @ sh @ one)) @ id))) & ! [X85 : term,X84 : subst,X83 : subst] : (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83))) = ((sub @ (X82 @ X84 @ X85) @ X83)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f56,definition,(
% 6.44/1.37 ! [X50 : (subst > term > subst > $o)] : (($true = ((sP43 @ X50))) <=> ! [X53 : term,X54 : term] : ((((X50 @ id @ (ap @ (sub @ X54 @ id) @ X53) @ id)) = $true) | ($true != ((X50 @ id @ X54 @ id))) | ($true != ((X50 @ id @ X53 @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f57,definition,(
% 6.44/1.37 (sP44 = $true) <=> ? [X63 : (subst > term > subst > $o),X64 : term] : (! [X66 : subst,X67 : term,X65 : subst,X68 : subst] : ((((X63 @ X66 @ X67 @ (comp @ X65 @ X68))) = $true) | (((X63 @ (comp @ X66 @ X65) @ (sub @ X67 @ X65) @ X68)) != $true)) & ($true != ((X63 @ id @ (lam @ X64) @ id))) & ($true = ((sP40 @ X63))) & ! [X69 : term] : (($true = ((X63 @ id @ (sub @ X64 @ (push @ X69 @ id)) @ id))) | (((X63 @ id @ X69 @ id)) != $true)) & ! [X75 : term,X77 : subst,X78 : subst,X76 : subst] : ((((X63 @ (comp @ X78 @ X76) @ (sub @ X75 @ X76) @ X77)) = $true) | ($true != ((X63 @ X78 @ X75 @ (comp @ X76 @ X77))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f58,definition,(
% 6.44/1.37 (sP45 = $true) <=> ! [X80 : term,X79 : (subst > term > subst > $o)] : (($true = ((sP42 @ X79))) | ($true = ((X79 @ id @ X80 @ id))) | ? [X81 : term] : ((((var @ (sub @ X81 @ id))) = $true) & ($true != ((X79 @ id @ X81 @ id)))) | ? [X96 : subst,X94 : subst,X93 : subst,X95 : term] : (($true = ((X79 @ X94 @ X95 @ (comp @ X93 @ X96)))) & ($true != ((X79 @ (comp @ X94 @ X93) @ (sub @ X95 @ X93) @ X96)))) | ($true = ((sP41 @ X79))) | ? [X90 : subst,X91 : term,X92 : subst,X89 : subst] : ((((X79 @ (comp @ X90 @ X92) @ (sub @ X91 @ X92) @ X89)) = $true) & (((X79 @ X90 @ X91 @ (comp @ X92 @ X89))) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f59,definition,(
% 6.44/1.37 ($true = sP46) <=> ? [X43 : (term > $o),X44 : term] : ((((X43 @ X44)) != $true) & ! [X48 : term] : (? [X49 : term] : (($true != ((X43 @ (sub @ X48 @ (push @ X49 @ id))))) & (((X43 @ X49)) = $true)) | (((X43 @ (lam @ X48))) = $true)) & ! [X45 : term] : (($true = ((X43 @ X45))) | (((var @ X45)) != $true)) & ($true = ((sP39 @ X43))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f60,definition,(
% 6.44/1.37 ($true = sP47) <=> (? [X52 : term,X50 : (subst > term > subst > $o),X51 : term] : (! [X62 : subst,X59 : subst,X61 : term,X60 : subst] : (($true = ((X50 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60) @ X59))) | ($true != ((X50 @ X62 @ X61 @ (comp @ X60 @ X59))))) & ! [X56 : subst,X55 : subst,X57 : subst,X58 : term] : (($true = ((X50 @ X56 @ X58 @ (comp @ X55 @ X57)))) | ($true != ((X50 @ (comp @ X56 @ X55) @ (sub @ X58 @ X55) @ X57)))) & ($true != ((X50 @ id @ (ap @ X51 @ X52) @ id))) & ($true = ((X50 @ id @ X52 @ id))) & ($true = ((sP43 @ X50))) & ($true = ((X50 @ id @ X51 @ id)))) | (sP45 = $true) | (sP44 = $true) | ($true = sP46))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f61,definition,(
% 6.44/1.37 ($true = sP48) <=> ! [X492 : term,X493 : (subst > term > subst > $o)] : (? [X494 : term] : (($true != ((X493 @ id @ (sub @ X492 @ (push @ X494 @ id)) @ id))) & (((X493 @ id @ X494 @ id)) = $true)) | ? [X495 : (subst > term > term)] : ((((X493 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X499 : term] : ((((X493 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X493 @ id @ X499 @ id)) != $true)) & ! [X496 : subst,X497 : term,X498 : subst] : (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X495 @ X496 @ X497) @ X498)))) | ($true = ((X493 @ id @ (lam @ X492) @ id))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f62,definition,(
% 6.44/1.37 ! [X227 : (subst > term > subst > $o)] : (($true = ((sP49 @ X227))) <=> ? [X235 : (subst > term > term)] : (! [X239 : subst,X238 : term,X237 : subst] : (((X235 @ (comp @ X239 @ X237) @ (sub @ X238 @ X237))) = ((sub @ (X235 @ X239 @ X238) @ X237))) & ! [X236 : term] : ((((X227 @ id @ X236 @ id)) != $true) | ($true = ((X227 @ id @ (X235 @ id @ X236) @ id)))) & (((X227 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f63,definition,(
% 6.44/1.37 ! [X227 : (subst > term > subst > $o)] : (($true = ((sP50 @ X227))) <=> ? [X234 : term,X233 : term] : ((((X227 @ id @ (ap @ (sub @ X233 @ id) @ X234) @ id)) != $true) & ($true = ((X227 @ id @ X234 @ id))) & ($true = ((X227 @ id @ X233 @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f64,definition,(
% 6.44/1.37 ! [X209 : (term > $o)] : (($true = ((sP51 @ X209))) <=> ! [X213 : term,X214 : term] : (($true != ((X209 @ X213))) | ($true = ((X209 @ (ap @ X214 @ X213)))) | ($true != ((X209 @ X214)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f65,definition,(
% 6.44/1.37 ($true = sP52) <=> ? [X218 : (subst > term > subst > $o),X217 : term,X216 : (term > $o)] : (($true != ((X216 @ (lam @ X217)))) & ! [X220 : term] : (($true = ((X216 @ (sub @ X217 @ (push @ X220 @ id))))) | ($true != ((X216 @ X220)))) & ! [X219 : term] : (((X218 @ id @ X219 @ id)) = ((X216 @ X219))) & ! [X221 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ? [X223 : subst,X225 : term,X224 : subst] : (((X221 @ (comp @ X223 @ X224) @ (sub @ X225 @ X224))) != ((sub @ (X221 @ X223 @ X225) @ X224))) | ? [X222 : term] : ((((X218 @ id @ X222 @ id)) = $true) & (((X218 @ id @ (X221 @ id @ X222) @ id)) != $true))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f66,definition,(
% 6.44/1.37 (sP53 = $true) <=> ! [X226 : term,X227 : (subst > term > subst > $o)] : (($true = ((sP50 @ X227))) | ($true = ((sP49 @ X227))) | ? [X243 : subst,X242 : subst,X241 : term,X240 : subst] : ((((X227 @ X240 @ X241 @ (comp @ X243 @ X242))) = $true) & ($true != ((X227 @ (comp @ X240 @ X243) @ (sub @ X241 @ X243) @ X242)))) | ? [X229 : subst,X231 : term,X228 : subst,X230 : subst] : ((((X227 @ (comp @ X228 @ X229) @ (sub @ X231 @ X229) @ X230)) = $true) & ($true != ((X227 @ X228 @ X231 @ (comp @ X229 @ X230))))) | (((X227 @ id @ X226 @ id)) = $true) | ? [X232 : term] : (($true = ((var @ (sub @ X232 @ id)))) & ($true != ((X227 @ id @ X232 @ id)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f67,definition,(
% 6.44/1.37 ($true = sP54) <=> (? [X205 : (subst > term > subst > $o)] : ! [X206 : (term > $o)] : ? [X207 : term] : (((X205 @ id @ X207 @ id)) != ((X206 @ X207))) | ? [X208 : term,X209 : (term > $o)] : (($true = ((sP51 @ X209))) & ! [X210 : term] : (($true != ((var @ X210))) | ($true = ((X209 @ X210)))) & ! [X211 : term] : (($true = ((X209 @ (lam @ X211)))) | ? [X212 : term] : (($true = ((X209 @ X212))) & ($true != ((X209 @ (sub @ X211 @ (push @ X212 @ id))))))) & ($true != ((X209 @ X208)))) | (sP53 = $true) | ($true = sP52) | ? [X215 : term] : (((sub @ X215 @ id)) != X215))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f68,definition,(
% 6.44/1.37 ($true = sP55) <=> (? [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) != X144) | ? [X146 : subst,X145 : term] : (((comp @ sh @ (push @ X145 @ X146))) != X146) | ! [X149 : term,X152 : (subst > term > term),X150 : subst,X151 : (subst > term > term)] : ((((X151 @ X150 @ X149)) = ((X152 @ X150 @ X149))) | ? [X157 : term,X156 : subst,X158 : subst] : (((X152 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) != ((sub @ (X152 @ X156 @ X157) @ X158))) | (((lam @ (X152 @ sh @ one))) != ((lam @ (X151 @ sh @ one)))) | ? [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X151 @ X154 @ X155) @ X153)) != ((X151 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153))))) | ? [X147 : term,X148 : term] : ((((lam @ X147)) = ((lam @ X148))) & (X147 != X148)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f69,definition,(
% 6.44/1.37 (sP56 = $true) <=> (? [X14 : term] : ! [X15 : (subst > term > term)] : ? [X16 : subst,X17 : term] : (((X15 @ X16 @ X17)) != ((sub @ X14 @ (push @ X17 @ X16)))) | ! [X19 : (subst > term > subst > $o),X20 : (term > $o),X21 : term] : (? [X22 : term] : (((X19 @ id @ X22 @ id)) != ((X20 @ X22))) | ($true = ((X20 @ (lam @ X21)))) | ? [X24 : (subst > term > term)] : (! [X27 : subst,X25 : subst,X26 : term] : (((X24 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X24 @ X27 @ X26) @ X25))) & ($true != ((X19 @ id @ (lam @ (X24 @ sh @ one)) @ id))) & ! [X28 : term] : (($true = ((X19 @ id @ (X24 @ id @ X28) @ id))) | ($true != ((X19 @ id @ X28 @ id))))) | ? [X23 : term] : (($true != ((X20 @ (sub @ X21 @ (push @ X23 @ id))))) & (((X20 @ X23)) = $true))) | ? [X18 : term] : (((sub @ X18 @ id)) != X18))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f70,definition,(
% 6.44/1.37 ! [X453 : (subst > term > subst > $o)] : (($true = ((sP57 @ X453))) <=> ? [X463 : (subst > term > term)] : (($true != ((X453 @ id @ (lam @ (X463 @ sh @ one)) @ id))) & ! [X467 : term] : ((((X453 @ id @ X467 @ id)) != $true) | (((X453 @ id @ (X463 @ id @ X467) @ id)) = $true)) & ! [X465 : term,X464 : subst,X466 : subst] : (((X463 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X463 @ X466 @ X465) @ X464)))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f71,definition,(
% 6.44/1.37 (sP58 = $true) <=> (? [X451 : term] : (((sub @ X451 @ id)) != X451) | ! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (($true = ((X454 @ (lam @ X452)))) | ($true = ((sP57 @ X453))) | ? [X468 : term] : (($true = ((X454 @ X468))) & (((X454 @ (sub @ X452 @ (push @ X468 @ id)))) != $true)) | ? [X460 : term,X462 : subst,X459 : subst,X461 : subst] : (($true != ((X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461) @ X462))) & (((X453 @ X459 @ X460 @ (comp @ X461 @ X462))) = $true)) | ? [X469 : term] : (((X454 @ X469)) != ((X453 @ id @ X469 @ id))) | ? [X457 : subst,X458 : subst,X456 : term,X455 : subst] : ((((X453 @ X457 @ X456 @ (comp @ X455 @ X458))) != $true) & ($true = ((X453 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455) @ X458))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.44/1.37 thf(f72,plain,(
% 6.44/1.37 (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) <=> (axvarcons = $true)) & ((sP58 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X319 : (subst > term > subst > $o)] : ? [X320 : (term > $o)] : ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X490 : term] : ? [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) = ((X491 @ sh @ one)))) & ((sP56 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (? [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) != ((X525 @ X527))) | (((X526 @ X523)) != $true) | (((X525 @ one)) = $true)) | ? [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) != X521)) <=> (pushprop_lem1v2_lthm = $true)) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & ((hoasinduction_lem3b = $true) <=> ! [X246 : term] : ? [X247 : (subst > term > term)] : (((X247 @ sh @ one)) = ((sub @ X246 @ (push @ one @ sh))))) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & ((hoaslaminj_lthm = $true) <=> ($true = sP55)) & ! [X267 : d_term] : (d_one = X267) & (hoasapinj2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ($true = sP54)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) <=> (termmset = $true)) & (pushprop_lthm = $true) & (($true = sP48) <=> (hoasinduction_lem3a = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP47) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ($true = sP38)) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & ((apinj2 = $true) <=> ! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192))) & (axabs = $true) & ((axvarid = $true) <=> ! [X204 : term] : (((sub @ X204 @ id)) = X204)) & (axvarshift = $true) & ((induction = $true) <=> ! [X528 : term,X529 : (term > $o)] : (($true = ((sP36 @ X529))) | ? [X530 : term] : ((((X529 @ X530)) != $true) & ($true = ((var @ X530)))) | ? [X531 : term] : ((((X529 @ X531)) = $true) & ($true != ((X529 @ (lam @ X531))))) | (((X529 @ X528)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP35 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true) & ! [X318 : d_subst] : (d_id = X318) & (! [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true != ((X160 @ X162))) | (((X161 @ one)) = $true) | ? [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) != ((X161 @ X163)))) <=> (pushprop_lem1v2 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((sP34 = $true) <=> (induction2 = $true)) & (termmset_gthm = $true) & ((laminj = $true) <=> ! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317))) & ((induction2lem = $true) <=> (sP32 = $true)) & (lamnotvar = $true) & (! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (? [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) != ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ? [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) != ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem2 = $true) <=> ($true = sP30)) & ((pushprop_lem0_lthm = $true) <=> ! [X505 : subst,X504 : (term > $o),X506 : term] : ? [X507 : (term > $o)] : ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (($true = sP28) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((substmonoid = $true) <=> (! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346))) & ((axscons = $true) <=> ! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X276 : term] : ? [X277 : (subst > term > term)] : ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278))))) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X195 : term,X196 : (subst > term > subst > $o)] : (? [X202 : term,X203 : term] : (($true = ((X196 @ id @ X203 @ id))) & (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) != $true) & ($true = ((X196 @ id @ X202 @ id)))) | ($true = ((X196 @ id @ X195 @ id))) | ($true = ((sP27 @ X196))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (sP26 = $true)) & ((hoasapinj1_lthm = $true) <=> (? [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 != X185) & (((ap @ X183 @ X186)) = ((ap @ X185 @ X184)))) | ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190)) | ? [X182 : term] : (((sub @ X182 @ id)) != X182))) & (hoaslamnotvar = $true) & (($true = sP21) <=> (hoasinduction_lem3aa = $true)) & (! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X486 : term] : ? [X487 : (subst > term > term)] : ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489))))) & (axclos = $true) & ((induction2_lthm = $true) <=> ($true = sP20)) & (ulamvarsh = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) != X324) | ! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true)) | ? [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) != X323))) & (axmap = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) <=> ! [X248 : (subst > term > subst > $o)] : ? [X249 : (term > $o)] : ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id)))) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) != ((d2subst @ X12))) | (X12 = X13)) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP16)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280))))) & (pushprop_lem3v2_lthm = $true) & ! [X332 : d_term,X331 : d_term] : ((((d2term @ X331)) != ((d2term @ X332))) | (X331 = X332)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (sP15 = $true)) & (hoasapnotvar_lthm = $true) & ((apinj1 = $true) <=> ! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265))) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & ((sP12 = $true) <=> (hoasinduction_lem3v2 = $true)) & (($true = sP10) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_gthm = $true) & ((? [X449 : term] : (((sub @ X449 @ id)) != X449) | ! [X450 : term] : (((sub @ X450 @ id)) = X450)) <=> (termmset_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98))) | ? [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) != ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))))) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (sP8 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) <=> (axidr = $true)) & (one = ((d2term @ d_one))) & (((! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500)) <=> (substmonoid_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (($true = sP4) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction = $true) <=> (sP2 = $true)) & ((axshiftcons = $true) <=> ! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520)) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) <=> (shinj = $true)) & (axapp = $true) & ((hoasapinj2_lthm = $true) <=> (? [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 != X378) & (((ap @ X377 @ X378)) = ((ap @ X375 @ X376)))) | ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379))))))),
% 6.44/1.37 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 6.44/1.37 thf(f162,plain,(
% 6.44/1.37 (($true = sP30) | ? [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (($true = ((X335 @ id @ X334 @ id))) & ! [X336 : subst,X339 : term,X338 : subst,X337 : subst] : (($true = ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) | (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) != $true)) & ! [X341 : subst,X343 : subst,X340 : term,X342 : subst] : (($true != ((X335 @ X342 @ X340 @ (comp @ X341 @ X343)))) | (((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) = $true)) & (((sP29 @ X335)) != $true) & (((X335 @ id @ X333 @ id)) = $true) & (((X335 @ id @ (ap @ X334 @ X333) @ id)) != $true))) & (! [X333 : term,X334 : term,X335 : (subst > term > subst > $o)] : (($true != ((X335 @ id @ X334 @ id))) | ? [X336 : subst,X339 : term,X338 : subst,X337 : subst] : (($true != ((X335 @ X338 @ X339 @ (comp @ X337 @ X336)))) & (((X335 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) = $true)) | ? [X341 : subst,X343 : subst,X340 : term,X342 : subst] : (($true = ((X335 @ X342 @ X340 @ (comp @ X341 @ X343)))) & (((X335 @ (comp @ X342 @ X341) @ (sub @ X340 @ X341) @ X343)) != $true)) | (((sP29 @ X335)) = $true) | (((X335 @ id @ X333 @ id)) != $true) | (((X335 @ id @ (ap @ X334 @ X333) @ id)) = $true)) | ($true != sP30))),
% 6.44/1.37 inference(nnf_transformation,[],[f43])).
% 6.44/1.37 thf(f163,plain,(
% 6.44/1.37 (($true = sP30) | ? [X0 : term,X1 : term,X2 : (subst > term > subst > $o)] : ((((X2 @ id @ X1 @ id)) = $true) & ! [X3 : subst,X4 : term,X5 : subst,X6 : subst] : (($true = ((X2 @ X5 @ X4 @ (comp @ X6 @ X3)))) | (((X2 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3)) != $true)) & ! [X7 : subst,X8 : subst,X9 : term,X10 : subst] : ((((X2 @ X10 @ X9 @ (comp @ X7 @ X8))) != $true) | ($true = ((X2 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)))) & (((sP29 @ X2)) != $true) & ($true = ((X2 @ id @ X0 @ id))) & ($true != ((X2 @ id @ (ap @ X1 @ X0) @ id))))) & (! [X11 : term,X12 : term,X13 : (subst > term > subst > $o)] : ((((X13 @ id @ X12 @ id)) != $true) | ? [X14 : subst,X15 : term,X16 : subst,X17 : subst] : ((((X13 @ X16 @ X15 @ (comp @ X17 @ X14))) != $true) & (((X13 @ (comp @ X16 @ X17) @ (sub @ X15 @ X17) @ X14)) = $true)) | ? [X18 : subst,X19 : subst,X20 : term,X21 : subst] : (($true = ((X13 @ X21 @ X20 @ (comp @ X18 @ X19)))) & (((X13 @ (comp @ X21 @ X18) @ (sub @ X20 @ X18) @ X19)) != $true)) | ($true = ((sP29 @ X13))) | ($true != ((X13 @ id @ X11 @ id))) | ($true = ((X13 @ id @ (ap @ X12 @ X11) @ id)))) | ($true != sP30))),
% 6.44/1.37 inference(rectify,[],[f162])).
% 6.44/1.37 thf(f164,plain,(
% 6.44/1.37 (($true = sP30) | (($true = ((sK253 @ id @ sK252 @ id))) & ! [X3 : subst,X4 : term,X5 : subst,X6 : subst] : ((((sK253 @ X5 @ X4 @ (comp @ X6 @ X3))) = $true) | ($true != ((sK253 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3)))) & ! [X7 : subst,X8 : subst,X9 : term,X10 : subst] : ((((sK253 @ X10 @ X9 @ (comp @ X7 @ X8))) != $true) | (((sK253 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)) = $true)) & ($true != ((sP29 @ sK253))) & ($true = ((sK253 @ id @ sK251 @ id))) & ($true != ((sK253 @ id @ (ap @ sK252 @ sK251) @ id))))) & (! [X11 : term,X12 : term,X13 : (subst > term > subst > $o)] : ((((X13 @ id @ X12 @ id)) != $true) | (($true != ((X13 @ (sK256 @ X13) @ (sK255 @ X13) @ (comp @ (sK257 @ X13) @ (sK254 @ X13))))) & ($true = ((X13 @ (comp @ (sK256 @ X13) @ (sK257 @ X13)) @ (sub @ (sK255 @ X13) @ (sK257 @ X13)) @ (sK254 @ X13))))) | (($true = ((X13 @ (sK261 @ X13) @ (sK260 @ X13) @ (comp @ (sK258 @ X13) @ (sK259 @ X13))))) & ($true != ((X13 @ (comp @ (sK261 @ X13) @ (sK258 @ X13)) @ (sub @ (sK260 @ X13) @ (sK258 @ X13)) @ (sK259 @ X13))))) | ($true = ((sP29 @ X13))) | ($true != ((X13 @ id @ X11 @ id))) | ($true = ((X13 @ id @ (ap @ X12 @ X11) @ id)))) | ($true != sP30))),
% 6.44/1.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK251,sK252,sK253,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK251),skolemize(X1,sK252),skolemize(X2,sK253),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16)],[f163])).
% 6.44/1.37 thf(f260,plain,(
% 6.44/1.37 ((! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) != X42))) & (((sP58 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP58 != $true))) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X319 : (subst > term > subst > $o)] : ? [X320 : (term > $o)] : ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X319 : (subst > term > subst > $o)] : ! [X320 : (term > $o)] : ? [X321 : term] : (((X320 @ X321)) != ((X319 @ id @ X321 @ id))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X490 : term] : ! [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) != ((X491 @ sh @ one)))) & (! [X490 : term] : ? [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) = ((X491 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((sP56 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP56 != $true))) & (((! [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (? [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) != ((X525 @ X527))) | (((X526 @ X523)) != $true) | (((X525 @ one)) = $true)) | ? [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) != X521)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (! [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) = ((X525 @ X527))) & (((X526 @ X523)) = $true) & (((X525 @ one)) != $true)) & ! [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) = X521)))) & ((! [X536 : subst,X535 : term,X534 : (term > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X536 : subst,X535 : term,X534 : (term > $o)] : ! [X537 : (term > $o)] : ? [X538 : term] : (((X537 @ X538)) != ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & (((hoasinduction_lem3b = $true) | ? [X246 : term] : ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh))))) & (! [X246 : term] : ? [X247 : (subst > term > term)] : (((X247 @ sh @ one)) = ((sub @ X246 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((hoaslaminj_lthm = $true) | ($true != sP55)) & (($true = sP55) | (hoaslaminj_lthm != $true))) & ! [X267 : d_term] : (d_one = X267) & (hoasapinj2_gthm = $true) & (((hoasinduction_lthm_3 = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lthm_3 != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X300 : term] : (((sub @ X300 @ id)) = X300) | (termmset != $true)) & ((termmset = $true) | ? [X300 : term] : (((sub @ X300 @ id)) != X300))) & (pushprop_lthm = $true) & ((($true = sP48) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP48))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((($true = sP47) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP47))) & (((hoasinduction_lem3 = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3 != $true))) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & (((apinj2 = $true) | ? [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) = ((ap @ X193 @ X191))) & (X191 != X192))) & (! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192)) | (apinj2 != $true))) & (axabs = $true) & (((axvarid = $true) | ? [X204 : term] : (((sub @ X204 @ id)) != X204)) & (! [X204 : term] : (((sub @ X204 @ id)) = X204) | (axvarid != $true))) & (axvarshift = $true) & (((induction = $true) | ? [X528 : term,X529 : (term > $o)] : (($true != ((sP36 @ X529))) & ! [X530 : term] : ((((X529 @ X530)) = $true) | ($true != ((var @ X530)))) & ! [X531 : term] : ((((X529 @ X531)) != $true) | ($true = ((X529 @ (lam @ X531))))) & (((X529 @ X528)) != $true))) & (! [X528 : term,X529 : (term > $o)] : (($true = ((sP36 @ X529))) | ? [X530 : term] : ((((X529 @ X530)) != $true) & ($true = ((var @ X530)))) | ? [X531 : term] : ((((X529 @ X531)) = $true) & ($true != ((X529 @ (lam @ X531))))) | (((X529 @ X528)) = $true)) | (induction != $true))) & (((hoasinduction_lem3aa_lthm = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X103 : subst] : (((comp @ id @ X103)) = X103) | (axidl != $true)) & ((axidl = $true) | ? [X103 : subst] : (((comp @ id @ X103)) != X103))) & (hoaslamnotap_gthm = $true) & ! [X318 : d_subst] : (d_id = X318) & ((! [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true != ((X160 @ X162))) | (((X161 @ one)) = $true) | ? [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) != ((X161 @ X163)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true = ((X160 @ X162))) & (((X161 @ one)) != $true) & ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((sP34 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP34 != $true))) & (termmset_gthm = $true) & (((laminj = $true) | ? [X316 : term,X317 : term] : ((((lam @ X317)) = ((lam @ X316))) & (X316 != X317))) & (! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317)) | (laminj != $true))) & (((induction2lem = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem != $true))) & (lamnotvar = $true) & ((! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (? [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) != ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ? [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) != ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (! [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) & (((lam @ (X4 @ sh @ one))) = ((lam @ (X5 @ sh @ one)))) & (((X4 @ X2 @ X3)) != ((X5 @ X2 @ X3))) & ! [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))))) & (((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true))) & (((pushprop_lem0_lthm = $true) | ? [X505 : subst,X504 : (term > $o),X506 : term] : ! [X507 : (term > $o)] : ? [X508 : term] : (((X507 @ X508)) != ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (! [X505 : subst,X504 : (term > $o),X506 : term] : ? [X507 : (term > $o)] : ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505))))) | (pushprop_lem0_lthm != $true))) & ((($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & (((substmonoid = $true) | (? [X347 : subst] : (((comp @ X347 @ id)) != X347) | ? [X346 : subst] : (((comp @ id @ X346)) != X346))) & ((! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346)) | (substmonoid != $true))) & (((axscons = $true) | ? [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) != X374)) & (! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374) | (axscons != $true))) & (((hoasinduction_lem3v2_f = $true) | ? [X276 : term] : ! [X277 : (subst > term > term)] : ? [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) != ((sub @ X276 @ (push @ X279 @ X278))))) & (! [X276 : term] : ? [X277 : (subst > term > term)] : ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278)))) | (hoasinduction_lem3v2_f != $true))) & (hoasinduction_lem2_gthm = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X195 : term,X196 : (subst > term > subst > $o)] : (! [X202 : term,X203 : term] : (($true != ((X196 @ id @ X203 @ id))) | (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) = $true) | ($true != ((X196 @ id @ X202 @ id)))) & ($true != ((X196 @ id @ X195 @ id))) & ($true != ((sP27 @ X196))))) & (! [X195 : term,X196 : (subst > term > subst > $o)] : (? [X202 : term,X203 : term] : (($true = ((X196 @ id @ X203 @ id))) & (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) != $true) & ($true = ((X196 @ id @ X202 @ id)))) | ($true = ((X196 @ id @ X195 @ id))) | ($true = ((sP27 @ X196)))) | (hoasinduction_no_psi_cond != $true))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_no_psi_cond_lthm != $true))) & (((hoasapinj1_lthm = $true) | (! [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 = X185) | (((ap @ X183 @ X186)) != ((ap @ X185 @ X184)))) & ? [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) = ((ap @ (sub @ X190 @ id) @ X188))) & (X189 != X190)) & ! [X182 : term] : (((sub @ X182 @ id)) = X182))) & ((? [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 != X185) & (((ap @ X183 @ X186)) = ((ap @ X185 @ X184)))) | ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190)) | ? [X182 : term] : (((sub @ X182 @ id)) != X182)) | (hoasapinj1_lthm != $true))) & (hoaslamnotvar = $true) & ((($true = sP21) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP21))) & ((! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true = ((X430 @ X429))) & ($true != ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))))) & (hoasinduction_lem1v2 = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X486 : term] : ! [X487 : (subst > term > term)] : ? [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) != ((sub @ X486 @ (push @ X488 @ X489))))) & (! [X486 : term] : ? [X487 : (subst > term > term)] : ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (axclos = $true) & (((induction2_lthm = $true) | ($true != sP20)) & (($true = sP20) | (induction2_lthm != $true))) & (ulamvarsh = $true) & (((pushprop_lem1_lthm = $true) | (! [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) = X324) & ? [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true != ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) & (((X328 @ X329)) = $true)) & ! [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) = X323))) & ((? [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) != X324) | ! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true)) | ? [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) != X323)) | (pushprop_lem1_lthm != $true))) & (axmap = $true) & (((d2subst @ d_id)) = sh) & (((hoasinduction_lem0 = $true) | ? [X248 : (subst > term > subst > $o)] : ! [X249 : (term > $o)] : ? [X250 : term] : (((X249 @ X250)) != ((X248 @ id @ X250 @ id)))) & (! [X248 : (subst > term > subst > $o)] : ? [X249 : (term > $o)] : ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id))) | (hoasinduction_lem0 != $true))) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) != ((d2subst @ X12))) | (X12 = X13)) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoasinduction_lem1 = $true) & (((hoasinduction_lem3v2a = $true) | ($true != sP16)) & (($true = sP16) | (hoasinduction_lem3v2a != $true))) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((hoasapinj1 = $true) | ? [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 != X283) & (((ap @ (sub @ X283 @ id) @ X282)) = ((ap @ (sub @ X281 @ id) @ X280))))) & (! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280)))) | (hoasapinj1 != $true))) & (pushprop_lem3v2_lthm = $true) & ! [X332 : d_term,X331 : d_term] : ((((d2term @ X331)) != ((d2term @ X332))) | (X331 = X332)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & (((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true))) & (hoasapnotvar_lthm = $true) & (((apinj1 = $true) | ? [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) = ((ap @ X264 @ X266))) & (X264 != X265))) & (! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265)) | (apinj1 != $true))) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & (((sP12 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP12 != $true))) & ((($true = sP10) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP10))) & (hoasapnotvar_gthm = $true) & (((? [X449 : term] : (((sub @ X449 @ id)) != X449) | ! [X450 : term] : (((sub @ X450 @ id)) = X450)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X449 : term] : (((sub @ X449 @ id)) = X449) & ? [X450 : term] : (((sub @ X450 @ id)) != X450)))) & (((hoaslamnotap = $true) | ? [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) = ((ap @ (sub @ X97 @ id) @ X98))) & ! [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))))) & (! [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98))) | ? [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) != ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102))))) | (hoaslamnotap != $true))) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & (((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X539 : subst] : (((comp @ X539 @ id)) = X539) | (axidr != $true)) & ((axidr = $true) | ? [X539 : subst] : (((comp @ X539 @ id)) != X539))) & (one = ((d2term @ d_one))) & ((((! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X503 : subst] : (((comp @ id @ X503)) != X503) | ? [X502 : subst] : (((comp @ X502 @ id)) != X502)) & ! [X501 : subst] : (((comp @ X501 @ id)) = X501) & ! [X500 : subst] : (((comp @ id @ X500)) = X500)))) & (hoaslamnotvar_lthm = $true) & ((($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4))) & (((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true))) & (((axshiftcons = $true) | ? [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) != X520)) & (! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520) | (axshiftcons != $true))) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (((hoasapinj2 = $true) | ? [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 != X262) & (((ap @ (sub @ X260 @ id) @ X262)) = ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261)))) | (hoasapinj2 != $true))) & ((! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) | (shinj != $true)) & ((shinj = $true) | ? [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) = ((sub @ X1 @ sh))) & (X0 != X1)))) & (axapp = $true) & (((hoasapinj2_lthm = $true) | (! [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 = X378) | (((ap @ X377 @ X378)) != ((ap @ X375 @ X376)))) & ? [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 != X382) & (((ap @ (sub @ X381 @ id) @ X382)) = ((ap @ (sub @ X380 @ id) @ X379)))))) & ((? [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 != X378) & (((ap @ X377 @ X378)) = ((ap @ X375 @ X376)))) | ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379))))) | (hoasapinj2_lthm != $true)))),
% 6.44/1.37 inference(nnf_transformation,[],[f72])).
% 6.44/1.37 thf(f261,plain,(
% 6.44/1.37 (! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) != X42)) & ((sP58 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP58 != $true)) & ! [X244 : subst] : ? [X245 : d_subst] : (((d2subst @ X245)) = X244) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X319 : (subst > term > subst > $o)] : ? [X320 : (term > $o)] : ! [X321 : term] : (((X320 @ X321)) = ((X319 @ id @ X321 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X319 : (subst > term > subst > $o)] : ! [X320 : (term > $o)] : ? [X321 : term] : (((X320 @ X321)) != ((X319 @ id @ X321 @ id)))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X490 : term] : ! [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) != ((X491 @ sh @ one)))) & (! [X490 : term] : ? [X491 : (subst > term > term)] : (((sub @ X490 @ (push @ one @ sh))) = ((X491 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP56 != $true)) & (! [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (? [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) != ((X525 @ X527))) | (((X526 @ X523)) != $true) | (((X525 @ one)) = $true)) | ? [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) != X521) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X525 : (term > $o),X524 : subst,X523 : term,X526 : (term > $o)] : (! [X527 : term] : (((X526 @ (sub @ X527 @ (push @ X523 @ X524)))) = ((X525 @ X527))) & (((X526 @ X523)) = $true) & (((X525 @ one)) != $true)) & ! [X522 : subst,X521 : term] : (((sub @ one @ (push @ X521 @ X522))) = X521))) & (! [X536 : subst,X535 : term,X534 : (term > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X537 @ X538)) = ((X534 @ (sub @ X538 @ (push @ X535 @ X536))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X536 : subst,X535 : term,X534 : (term > $o)] : ! [X537 : (term > $o)] : ? [X538 : term] : (((X537 @ X538)) != ((X534 @ (sub @ X538 @ (push @ X535 @ X536)))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & ((hoasinduction_lem3b = $true) | ? [X246 : term] : ! [X247 : (subst > term > term)] : (((X247 @ sh @ one)) != ((sub @ X246 @ (push @ one @ sh))))) & (! [X246 : term] : ? [X247 : (subst > term > term)] : (((X247 @ sh @ one)) = ((sub @ X246 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & ((hoaslaminj_lthm = $true) | ($true != sP55)) & (($true = sP55) | (hoaslaminj_lthm != $true)) & ! [X267 : d_term] : (d_one = X267) & (hoasapinj2_gthm = $true) & ((hoasinduction_lthm_3 = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lthm_3 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X300 : term] : (((sub @ X300 @ id)) = X300) | (termmset != $true)) & ((termmset = $true) | ? [X300 : term] : (((sub @ X300 @ id)) != X300)) & (pushprop_lthm = $true) & (($true = sP48) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP48)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP47) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP47)) & ((hoasinduction_lem3 = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & ((apinj2 = $true) | ? [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) = ((ap @ X193 @ X191))) & (X191 != X192))) & (! [X192 : term,X194 : term,X191 : term,X193 : term] : ((((ap @ X194 @ X192)) != ((ap @ X193 @ X191))) | (X191 = X192)) | (apinj2 != $true)) & (axabs = $true) & ((axvarid = $true) | ? [X204 : term] : (((sub @ X204 @ id)) != X204)) & (! [X204 : term] : (((sub @ X204 @ id)) = X204) | (axvarid != $true)) & (axvarshift = $true) & ((induction = $true) | ? [X528 : term,X529 : (term > $o)] : (($true != ((sP36 @ X529))) & ! [X530 : term] : ((((X529 @ X530)) = $true) | ($true != ((var @ X530)))) & ! [X531 : term] : ((((X529 @ X531)) != $true) | ($true = ((X529 @ (lam @ X531))))) & (((X529 @ X528)) != $true))) & (! [X528 : term,X529 : (term > $o)] : (($true = ((sP36 @ X529))) | ? [X530 : term] : ((((X529 @ X530)) != $true) & ($true = ((var @ X530)))) | ? [X531 : term] : ((((X529 @ X531)) = $true) & ($true != ((X529 @ (lam @ X531))))) | (((X529 @ X528)) = $true)) | (induction != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X103 : subst] : (((comp @ id @ X103)) = X103) | (axidl != $true)) & ((axidl = $true) | ? [X103 : subst] : (((comp @ id @ X103)) != X103)) & (hoaslamnotap_gthm = $true) & ! [X318 : d_subst] : (d_id = X318) & (! [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true != ((X160 @ X162))) | (((X161 @ one)) = $true) | ? [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) != ((X161 @ X163)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X160 : (term > $o),X161 : (term > $o),X162 : term,X159 : subst] : (($true = ((X160 @ X162))) & (((X161 @ one)) != $true) & ! [X163 : term] : (((X160 @ (sub @ X163 @ (push @ X162 @ X159)))) = ((X161 @ X163))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((sP34 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP34 != $true)) & (termmset_gthm = $true) & ((laminj = $true) | ? [X316 : term,X317 : term] : ((((lam @ X317)) = ((lam @ X316))) & (X316 != X317))) & (! [X316 : term,X317 : term] : ((((lam @ X317)) != ((lam @ X316))) | (X316 = X317)) | (laminj != $true)) & ((induction2lem = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem != $true)) & (lamnotvar = $true) & (! [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (? [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) != ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) | (((lam @ (X4 @ sh @ one))) != ((lam @ (X5 @ sh @ one)))) | (((X4 @ X2 @ X3)) = ((X5 @ X2 @ X3))) | ? [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) != ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X5 : (subst > term > term),X4 : (subst > term > term),X2 : subst,X3 : term] : (! [X10 : subst,X9 : term,X11 : subst] : (((sub @ (X5 @ X10 @ X9) @ X11)) = ((X5 @ (comp @ X10 @ X11) @ (sub @ X9 @ X11)))) & (((lam @ (X4 @ sh @ one))) = ((lam @ (X5 @ sh @ one)))) & (((X4 @ X2 @ X3)) != ((X5 @ X2 @ X3))) & ! [X7 : term,X6 : subst,X8 : subst] : (((sub @ (X4 @ X8 @ X7) @ X6)) = ((X4 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6)))))) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X505 : subst,X504 : (term > $o),X506 : term] : ! [X507 : (term > $o)] : ? [X508 : term] : (((X507 @ X508)) != ((X504 @ (sub @ X508 @ (push @ X506 @ X505)))))) & (! [X505 : subst,X504 : (term > $o),X506 : term] : ? [X507 : (term > $o)] : ! [X508 : term] : (((X507 @ X508)) = ((X504 @ (sub @ X508 @ (push @ X506 @ X505))))) | (pushprop_lem0_lthm != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((substmonoid = $true) | ? [X347 : subst] : (((comp @ X347 @ id)) != X347) | ? [X346 : subst] : (((comp @ id @ X346)) != X346)) & ((! [X347 : subst] : (((comp @ X347 @ id)) = X347) & ! [X346 : subst] : (((comp @ id @ X346)) = X346)) | (substmonoid != $true)) & ((axscons = $true) | ? [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) != X374)) & (! [X374 : subst] : (((push @ (sub @ one @ X374) @ (comp @ sh @ X374))) = X374) | (axscons != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X276 : term] : ! [X277 : (subst > term > term)] : ? [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) != ((sub @ X276 @ (push @ X279 @ X278))))) & (! [X276 : term] : ? [X277 : (subst > term > term)] : ! [X279 : term,X278 : subst] : (((X277 @ X278 @ X279)) = ((sub @ X276 @ (push @ X279 @ X278)))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X195 : term,X196 : (subst > term > subst > $o)] : (! [X202 : term,X203 : term] : (($true != ((X196 @ id @ X203 @ id))) | (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) = $true) | ($true != ((X196 @ id @ X202 @ id)))) & ($true != ((X196 @ id @ X195 @ id))) & ($true != ((sP27 @ X196))))) & (! [X195 : term,X196 : (subst > term > subst > $o)] : (? [X202 : term,X203 : term] : (($true = ((X196 @ id @ X203 @ id))) & (((X196 @ id @ (ap @ (sub @ X203 @ id) @ X202) @ id)) != $true) & ($true = ((X196 @ id @ X202 @ id)))) | ($true = ((X196 @ id @ X195 @ id))) | ($true = ((sP27 @ X196)))) | (hoasinduction_no_psi_cond != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 = X185) | (((ap @ X183 @ X186)) != ((ap @ X185 @ X184)))) & ? [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) = ((ap @ (sub @ X190 @ id) @ X188))) & (X189 != X190)) & ! [X182 : term] : (((sub @ X182 @ id)) = X182))) & (? [X184 : term,X186 : term,X185 : term,X183 : term] : ((X183 != X185) & (((ap @ X183 @ X186)) = ((ap @ X185 @ X184)))) | ! [X189 : term,X188 : term,X190 : term,X187 : term] : ((((ap @ (sub @ X189 @ id) @ X187)) != ((ap @ (sub @ X190 @ id) @ X188))) | (X189 = X190)) | ? [X182 : term] : (((sub @ X182 @ id)) != X182) | (hoasapinj1_lthm != $true)) & (hoaslamnotvar = $true) & (($true = sP21) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP21)) & (! [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true != ((X430 @ X429))) | ($true = ((X427 @ (sub @ X429 @ (push @ X428 @ X431)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X427 : (term > $o),X430 : (term > $o),X431 : subst,X429 : term,X428 : term] : (($true = ((X430 @ X429))) & ($true != ((X427 @ (sub @ X429 @ (push @ X428 @ X431))))))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X486 : term] : ! [X487 : (subst > term > term)] : ? [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) != ((sub @ X486 @ (push @ X488 @ X489))))) & (! [X486 : term] : ? [X487 : (subst > term > term)] : ! [X489 : subst,X488 : term] : (((X487 @ X489 @ X488)) = ((sub @ X486 @ (push @ X488 @ X489)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (axclos = $true) & ((induction2_lthm = $true) | ($true != sP20)) & (($true = sP20) | (induction2_lthm != $true)) & (ulamvarsh = $true) & ((pushprop_lem1_lthm = $true) | (! [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) = X324) & ? [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true != ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) & (((X328 @ X329)) = $true)) & ! [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) = X323))) & (? [X325 : term,X324 : subst] : (((comp @ sh @ (push @ X325 @ X324))) != X324) | ! [X327 : (term > $o),X326 : subst,X329 : term,X328 : (term > $o),X330 : term] : (($true = ((X327 @ (sub @ X329 @ (push @ X330 @ X326))))) | (((X328 @ X329)) != $true)) | ? [X323 : term,X322 : subst] : (((sub @ one @ (push @ X323 @ X322))) != X323) | (pushprop_lem1_lthm != $true)) & (axmap = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) | ? [X248 : (subst > term > subst > $o)] : ! [X249 : (term > $o)] : ? [X250 : term] : (((X249 @ X250)) != ((X248 @ id @ X250 @ id)))) & (! [X248 : (subst > term > subst > $o)] : ? [X249 : (term > $o)] : ! [X250 : term] : (((X249 @ X250)) = ((X248 @ id @ X250 @ id))) | (hoasinduction_lem0 != $true)) & ! [X13 : d_subst,X12 : d_subst] : ((((d2subst @ X13)) != ((d2subst @ X12))) | (X12 = X13)) & ! [X104 : term] : ? [X105 : d_term] : (((d2term @ X105)) = X104) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP16)) & (($true = sP16) | (hoasinduction_lem3v2a != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) | ? [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 != X283) & (((ap @ (sub @ X283 @ id) @ X282)) = ((ap @ (sub @ X281 @ id) @ X280))))) & (! [X283 : term,X282 : term,X280 : term,X281 : term] : ((X281 = X283) | (((ap @ (sub @ X283 @ id) @ X282)) != ((ap @ (sub @ X281 @ id) @ X280)))) | (hoasapinj1 != $true)) & (pushprop_lem3v2_lthm = $true) & ! [X332 : d_term,X331 : d_term] : ((((d2term @ X331)) != ((d2term @ X332))) | (X331 = X332)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((apinj1 = $true) | ? [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) = ((ap @ X264 @ X266))) & (X264 != X265))) & (! [X266 : term,X265 : term,X263 : term,X264 : term] : ((((ap @ X265 @ X263)) != ((ap @ X264 @ X266))) | (X264 = X265)) | (apinj1 != $true)) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & ((sP12 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP12 != $true)) & (($true = sP10) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP10)) & (hoasapnotvar_gthm = $true) & (? [X449 : term] : (((sub @ X449 @ id)) != X449) | ! [X450 : term] : (((sub @ X450 @ id)) = X450) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X449 : term] : (((sub @ X449 @ id)) = X449) & ? [X450 : term] : (((sub @ X450 @ id)) != X450))) & ((hoaslamnotap = $true) | ? [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) = ((ap @ (sub @ X97 @ id) @ X98))) & ! [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) = ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102)))))) & (! [X99 : (subst > term > term),X98 : term,X97 : term] : ((((lam @ (X99 @ sh @ one))) != ((ap @ (sub @ X97 @ id) @ X98))) | ? [X100 : term,X101 : subst,X102 : subst] : (((sub @ (X99 @ X101 @ X100) @ X102)) != ((X99 @ (comp @ X101 @ X102) @ (sub @ X100 @ X102))))) | (hoaslamnotap != $true)) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) | (axidr != $true)) & ((axidr = $true) | ? [X539 : subst] : (((comp @ X539 @ id)) != X539)) & (one = ((d2term @ d_one))) & ((! [X503 : subst] : (((comp @ id @ X503)) = X503) & ! [X502 : subst] : (((comp @ X502 @ id)) = X502)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X503 : subst] : (((comp @ id @ X503)) != X503) | ? [X502 : subst] : (((comp @ X502 @ id)) != X502)) & ! [X501 : subst] : (((comp @ X501 @ id)) = X501) & ! [X500 : subst] : (((comp @ id @ X500)) = X500))) & (hoaslamnotvar_lthm = $true) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) != X520)) & (! [X519 : term,X520 : subst] : (((comp @ sh @ (push @ X519 @ X520))) = X520) | (axshiftcons != $true)) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ? [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 != X262) & (((ap @ (sub @ X260 @ id) @ X262)) = ((ap @ (sub @ X259 @ id) @ X261))))) & (! [X260 : term,X261 : term,X262 : term,X259 : term] : ((X261 = X262) | (((ap @ (sub @ X260 @ id) @ X262)) != ((ap @ (sub @ X259 @ id) @ X261)))) | (hoasapinj2 != $true)) & (! [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) != ((sub @ X1 @ sh))) | (X0 = X1)) | (shinj != $true)) & ((shinj = $true) | ? [X0 : term,X1 : term] : ((((sub @ X0 @ sh)) = ((sub @ X1 @ sh))) & (X0 != X1))) & (axapp = $true) & ((hoasapinj2_lthm = $true) | (! [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 = X378) | (((ap @ X377 @ X378)) != ((ap @ X375 @ X376)))) & ? [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 != X382) & (((ap @ (sub @ X381 @ id) @ X382)) = ((ap @ (sub @ X380 @ id) @ X379)))))) & (? [X378 : term,X377 : term,X376 : term,X375 : term] : ((X376 != X378) & (((ap @ X377 @ X378)) = ((ap @ X375 @ X376)))) | ! [X380 : term,X381 : term,X382 : term,X379 : term] : ((X379 = X382) | (((ap @ (sub @ X381 @ id) @ X382)) != ((ap @ (sub @ X380 @ id) @ X379)))) | (hoasapinj2_lthm != $true))),
% 6.44/1.37 inference(flattening,[],[f260])).
% 6.44/1.37 thf(f262,plain,(
% 6.44/1.37 (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) != X3)) & ((sP58 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP58 != $true)) & ! [X4 : subst] : ? [X5 : d_subst] : (((d2subst @ X5)) = X4) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X6 : (subst > term > subst > $o)] : ? [X7 : (term > $o)] : ! [X8 : term] : (((X6 @ id @ X8 @ id)) = ((X7 @ X8))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X9 : (subst > term > subst > $o)] : ! [X10 : (term > $o)] : ? [X11 : term] : (((X9 @ id @ X11 @ id)) != ((X10 @ X11)))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X12 : term] : ! [X13 : (subst > term > term)] : (((sub @ X12 @ (push @ one @ sh))) != ((X13 @ sh @ one)))) & (! [X14 : term] : ? [X15 : (subst > term > term)] : (((X15 @ sh @ one)) = ((sub @ X14 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP56 != $true)) & (! [X16 : (term > $o),X17 : subst,X18 : term,X19 : (term > $o)] : (? [X20 : term] : (((X16 @ X20)) != ((X19 @ (sub @ X20 @ (push @ X18 @ X17))))) | (((X19 @ X18)) != $true) | (((X16 @ one)) = $true)) | ? [X21 : subst,X22 : term] : (((sub @ one @ (push @ X22 @ X21))) != X22) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X23 : (term > $o),X24 : subst,X25 : term,X26 : (term > $o)] : (! [X27 : term] : (((X23 @ X27)) = ((X26 @ (sub @ X27 @ (push @ X25 @ X24))))) & ($true = ((X26 @ X25))) & ($true != ((X23 @ one)))) & ! [X28 : subst,X29 : term] : (((sub @ one @ (push @ X29 @ X28))) = X29))) & (! [X30 : subst,X31 : term,X32 : (term > $o)] : ? [X33 : (term > $o)] : ! [X34 : term] : (((X33 @ X34)) = ((X32 @ (sub @ X34 @ (push @ X31 @ X30))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X35 : subst,X36 : term,X37 : (term > $o)] : ! [X38 : (term > $o)] : ? [X39 : term] : (((X38 @ X39)) != ((X37 @ (sub @ X39 @ (push @ X36 @ X35)))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & ((hoasinduction_lem3b = $true) | ? [X40 : term] : ! [X41 : (subst > term > term)] : (((X41 @ sh @ one)) != ((sub @ X40 @ (push @ one @ sh))))) & (! [X42 : term] : ? [X43 : (subst > term > term)] : (((sub @ X42 @ (push @ one @ sh))) = ((X43 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & ((hoaslaminj_lthm = $true) | ($true != sP55)) & (($true = sP55) | (hoaslaminj_lthm != $true)) & ! [X44 : d_term] : (d_one = X44) & (hoasapinj2_gthm = $true) & ((hoasinduction_lthm_3 = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lthm_3 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X45 : term] : (((sub @ X45 @ id)) = X45) | (termmset != $true)) & ((termmset = $true) | ? [X46 : term] : (((sub @ X46 @ id)) != X46)) & (pushprop_lthm = $true) & (($true = sP48) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP48)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP47) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP47)) & ((hoasinduction_lem3 = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & ((apinj2 = $true) | ? [X47 : term,X48 : term,X49 : term,X50 : term] : ((((ap @ X50 @ X49)) = ((ap @ X48 @ X47))) & (X47 != X49))) & (! [X51 : term,X52 : term,X53 : term,X54 : term] : ((((ap @ X52 @ X51)) != ((ap @ X54 @ X53))) | (X51 = X53)) | (apinj2 != $true)) & (axabs = $true) & ((axvarid = $true) | ? [X55 : term] : (((sub @ X55 @ id)) != X55)) & (! [X56 : term] : (((sub @ X56 @ id)) = X56) | (axvarid != $true)) & (axvarshift = $true) & ((induction = $true) | ? [X57 : term,X58 : (term > $o)] : (($true != ((sP36 @ X58))) & ! [X59 : term] : (($true = ((X58 @ X59))) | ($true != ((var @ X59)))) & ! [X60 : term] : ((((X58 @ X60)) != $true) | ($true = ((X58 @ (lam @ X60))))) & ($true != ((X58 @ X57))))) & (! [X61 : term,X62 : (term > $o)] : ((((sP36 @ X62)) = $true) | ? [X63 : term] : ((((X62 @ X63)) != $true) & ($true = ((var @ X63)))) | ? [X64 : term] : (($true = ((X62 @ X64))) & (((X62 @ (lam @ X64))) != $true)) | (((X62 @ X61)) = $true)) | (induction != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X65 : subst] : (((comp @ id @ X65)) = X65) | (axidl != $true)) & ((axidl = $true) | ? [X66 : subst] : (((comp @ id @ X66)) != X66)) & (hoaslamnotap_gthm = $true) & ! [X67 : d_subst] : (d_id = X67) & (! [X68 : (term > $o),X69 : (term > $o),X70 : term,X71 : subst] : ((((X68 @ X70)) != $true) | (((X69 @ one)) = $true) | ? [X72 : term] : (((X69 @ X72)) != ((X68 @ (sub @ X72 @ (push @ X70 @ X71)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X73 : (term > $o),X74 : (term > $o),X75 : term,X76 : subst] : ((((X73 @ X75)) = $true) & (((X74 @ one)) != $true) & ! [X77 : term] : (((X73 @ (sub @ X77 @ (push @ X75 @ X76)))) = ((X74 @ X77))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((sP34 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP34 != $true)) & (termmset_gthm = $true) & ((laminj = $true) | ? [X78 : term,X79 : term] : ((((lam @ X79)) = ((lam @ X78))) & (X78 != X79))) & (! [X80 : term,X81 : term] : ((((lam @ X80)) != ((lam @ X81))) | (X80 = X81)) | (laminj != $true)) & ((induction2lem = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem != $true)) & (lamnotvar = $true) & (! [X82 : (subst > term > term),X83 : (subst > term > term),X84 : subst,X85 : term] : (? [X86 : subst,X87 : term,X88 : subst] : (((sub @ (X82 @ X86 @ X87) @ X88)) != ((X82 @ (comp @ X86 @ X88) @ (sub @ X87 @ X88)))) | (((lam @ (X82 @ sh @ one))) != ((lam @ (X83 @ sh @ one)))) | (((X82 @ X84 @ X85)) = ((X83 @ X84 @ X85))) | ? [X89 : term,X90 : subst,X91 : subst] : (((sub @ (X83 @ X91 @ X89) @ X90)) != ((X83 @ (comp @ X91 @ X90) @ (sub @ X89 @ X90))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X92 : (subst > term > term),X93 : (subst > term > term),X94 : subst,X95 : term] : (! [X96 : subst,X97 : term,X98 : subst] : (((X92 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X92 @ X96 @ X97) @ X98))) & (((lam @ (X92 @ sh @ one))) = ((lam @ (X93 @ sh @ one)))) & (((X93 @ X94 @ X95)) != ((X92 @ X94 @ X95))) & ! [X99 : term,X100 : subst,X101 : subst] : (((sub @ (X93 @ X101 @ X99) @ X100)) = ((X93 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)))))) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X102 : subst,X103 : (term > $o),X104 : term] : ! [X105 : (term > $o)] : ? [X106 : term] : (((X105 @ X106)) != ((X103 @ (sub @ X106 @ (push @ X104 @ X102)))))) & (! [X107 : subst,X108 : (term > $o),X109 : term] : ? [X110 : (term > $o)] : ! [X111 : term] : (((X110 @ X111)) = ((X108 @ (sub @ X111 @ (push @ X109 @ X107))))) | (pushprop_lem0_lthm != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((substmonoid = $true) | ? [X112 : subst] : (((comp @ X112 @ id)) != X112) | ? [X113 : subst] : (((comp @ id @ X113)) != X113)) & ((! [X114 : subst] : (((comp @ X114 @ id)) = X114) & ! [X115 : subst] : (((comp @ id @ X115)) = X115)) | (substmonoid != $true)) & ((axscons = $true) | ? [X116 : subst] : (((push @ (sub @ one @ X116) @ (comp @ sh @ X116))) != X116)) & (! [X117 : subst] : (((push @ (sub @ one @ X117) @ (comp @ sh @ X117))) = X117) | (axscons != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X118 : term] : ! [X119 : (subst > term > term)] : ? [X120 : term,X121 : subst] : (((sub @ X118 @ (push @ X120 @ X121))) != ((X119 @ X121 @ X120)))) & (! [X122 : term] : ? [X123 : (subst > term > term)] : ! [X124 : term,X125 : subst] : (((X123 @ X125 @ X124)) = ((sub @ X122 @ (push @ X124 @ X125)))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X126 : term,X127 : (subst > term > subst > $o)] : (! [X128 : term,X129 : term] : (($true != ((X127 @ id @ X129 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X129 @ id) @ X128) @ id))) | ($true != ((X127 @ id @ X128 @ id)))) & ($true != ((X127 @ id @ X126 @ id))) & ($true != ((sP27 @ X127))))) & (! [X130 : term,X131 : (subst > term > subst > $o)] : (? [X132 : term,X133 : term] : (($true = ((X131 @ id @ X133 @ id))) & (((X131 @ id @ (ap @ (sub @ X133 @ id) @ X132) @ id)) != $true) & ($true = ((X131 @ id @ X132 @ id)))) | ($true = ((X131 @ id @ X130 @ id))) | ($true = ((sP27 @ X131)))) | (hoasinduction_no_psi_cond != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X134 : term,X135 : term,X136 : term,X137 : term] : ((X136 = X137) | (((ap @ X137 @ X135)) != ((ap @ X136 @ X134)))) & ? [X138 : term,X139 : term,X140 : term,X141 : term] : ((((ap @ (sub @ X140 @ id) @ X139)) = ((ap @ (sub @ X138 @ id) @ X141))) & (X138 != X140)) & ! [X142 : term] : (((sub @ X142 @ id)) = X142))) & (? [X143 : term,X144 : term,X145 : term,X146 : term] : ((X145 != X146) & (((ap @ X145 @ X143)) = ((ap @ X146 @ X144)))) | ! [X147 : term,X148 : term,X149 : term,X150 : term] : ((((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X147 @ id) @ X150))) | (X147 = X149)) | ? [X151 : term] : (((sub @ X151 @ id)) != X151) | (hoasapinj1_lthm != $true)) & (hoaslamnotvar = $true) & (($true = sP21) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP21)) & (! [X152 : (term > $o),X153 : (term > $o),X154 : subst,X155 : term,X156 : term] : (($true != ((X153 @ X155))) | ($true = ((X152 @ (sub @ X155 @ (push @ X156 @ X154)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X157 : (term > $o),X158 : (term > $o),X159 : subst,X160 : term,X161 : term] : (($true = ((X158 @ X160))) & ($true != ((X157 @ (sub @ X160 @ (push @ X161 @ X159))))))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X162 : term] : ! [X163 : (subst > term > term)] : ? [X164 : subst,X165 : term] : (((X163 @ X164 @ X165)) != ((sub @ X162 @ (push @ X165 @ X164))))) & (! [X166 : term] : ? [X167 : (subst > term > term)] : ! [X168 : subst,X169 : term] : (((sub @ X166 @ (push @ X169 @ X168))) = ((X167 @ X168 @ X169))) | (hoasinduction_lem3v2_f_lthm != $true)) & (axclos = $true) & ((induction2_lthm = $true) | ($true != sP20)) & (($true = sP20) | (induction2_lthm != $true)) & (ulamvarsh = $true) & ((pushprop_lem1_lthm = $true) | (! [X170 : term,X171 : subst] : (((comp @ sh @ (push @ X170 @ X171))) = X171) & ? [X172 : (term > $o),X173 : subst,X174 : term,X175 : (term > $o),X176 : term] : ((((X172 @ (sub @ X174 @ (push @ X176 @ X173)))) != $true) & ($true = ((X175 @ X174)))) & ! [X177 : term,X178 : subst] : (((sub @ one @ (push @ X177 @ X178))) = X177))) & (? [X179 : term,X180 : subst] : (((comp @ sh @ (push @ X179 @ X180))) != X180) | ! [X181 : (term > $o),X182 : subst,X183 : term,X184 : (term > $o),X185 : term] : (($true = ((X181 @ (sub @ X183 @ (push @ X185 @ X182))))) | (((X184 @ X183)) != $true)) | ? [X186 : term,X187 : subst] : (((sub @ one @ (push @ X186 @ X187))) != X186) | (pushprop_lem1_lthm != $true)) & (axmap = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) | ? [X188 : (subst > term > subst > $o)] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X188 @ id @ X190 @ id)) != ((X189 @ X190)))) & (! [X191 : (subst > term > subst > $o)] : ? [X192 : (term > $o)] : ! [X193 : term] : (((X191 @ id @ X193 @ id)) = ((X192 @ X193))) | (hoasinduction_lem0 != $true)) & ! [X194 : d_subst,X195 : d_subst] : ((((d2subst @ X194)) != ((d2subst @ X195))) | (X194 = X195)) & ! [X196 : term] : ? [X197 : d_term] : (((d2term @ X197)) = X196) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP16)) & (($true = sP16) | (hoasinduction_lem3v2a != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) | ? [X198 : term,X199 : term,X200 : term,X201 : term] : ((X198 != X201) & (((ap @ (sub @ X201 @ id) @ X200)) = ((ap @ (sub @ X198 @ id) @ X199))))) & (! [X202 : term,X203 : term,X204 : term,X205 : term] : ((X202 = X205) | (((ap @ (sub @ X205 @ id) @ X204)) != ((ap @ (sub @ X202 @ id) @ X203)))) | (hoasapinj1 != $true)) & (pushprop_lem3v2_lthm = $true) & ! [X206 : d_term,X207 : d_term] : ((((d2term @ X206)) != ((d2term @ X207))) | (X206 = X207)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((apinj1 = $true) | ? [X208 : term,X209 : term,X210 : term,X211 : term] : ((((ap @ X211 @ X208)) = ((ap @ X209 @ X210))) & (X209 != X211))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((((ap @ X213 @ X214)) != ((ap @ X215 @ X212))) | (X213 = X215)) | (apinj1 != $true)) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & ((sP12 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP12 != $true)) & (($true = sP10) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP10)) & (hoasapnotvar_gthm = $true) & (? [X216 : term] : (((sub @ X216 @ id)) != X216) | ! [X217 : term] : (((sub @ X217 @ id)) = X217) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X218 : term] : (((sub @ X218 @ id)) = X218) & ? [X219 : term] : (((sub @ X219 @ id)) != X219))) & ((hoaslamnotap = $true) | ? [X220 : (subst > term > term),X221 : term,X222 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) = ((lam @ (X220 @ sh @ one)))) & ! [X223 : term,X224 : subst,X225 : subst] : (((X220 @ (comp @ X224 @ X225) @ (sub @ X223 @ X225))) = ((sub @ (X220 @ X224 @ X223) @ X225))))) & (! [X226 : (subst > term > term),X227 : term,X228 : term] : ((((ap @ (sub @ X228 @ id) @ X227)) != ((lam @ (X226 @ sh @ one)))) | ? [X229 : term,X230 : subst,X231 : subst] : (((sub @ (X226 @ X230 @ X229) @ X231)) != ((X226 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231))))) | (hoaslamnotap != $true)) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X232 : subst] : (((comp @ X232 @ id)) = X232) | (axidr != $true)) & ((axidr = $true) | ? [X233 : subst] : (((comp @ X233 @ id)) != X233)) & (one = ((d2term @ d_one))) & ((! [X234 : subst] : (((comp @ id @ X234)) = X234) & ! [X235 : subst] : (((comp @ X235 @ id)) = X235)) | ? [X236 : subst] : (((comp @ X236 @ id)) != X236) | ? [X237 : subst] : (((comp @ id @ X237)) != X237) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X238 : subst] : (((comp @ id @ X238)) != X238) | ? [X239 : subst] : (((comp @ X239 @ id)) != X239)) & ! [X240 : subst] : (((comp @ X240 @ id)) = X240) & ! [X241 : subst] : (((comp @ id @ X241)) = X241))) & (hoaslamnotvar_lthm = $true) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | ? [X242 : term,X243 : subst] : (((comp @ sh @ (push @ X242 @ X243))) != X243)) & (! [X244 : term,X245 : subst] : (((comp @ sh @ (push @ X244 @ X245))) = X245) | (axshiftcons != $true)) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ? [X246 : term,X247 : term,X248 : term,X249 : term] : ((X247 != X248) & (((ap @ (sub @ X249 @ id) @ X247)) = ((ap @ (sub @ X246 @ id) @ X248))))) & (! [X250 : term,X251 : term,X252 : term,X253 : term] : ((X251 = X252) | (((ap @ (sub @ X250 @ id) @ X252)) != ((ap @ (sub @ X253 @ id) @ X251)))) | (hoasapinj2 != $true)) & (! [X254 : term,X255 : term] : ((((sub @ X254 @ sh)) != ((sub @ X255 @ sh))) | (X254 = X255)) | (shinj != $true)) & ((shinj = $true) | ? [X256 : term,X257 : term] : ((((sub @ X257 @ sh)) = ((sub @ X256 @ sh))) & (X256 != X257))) & (axapp = $true) & ((hoasapinj2_lthm = $true) | (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((X258 = X260) | (((ap @ X261 @ X260)) != ((ap @ X259 @ X258)))) & ? [X262 : term,X263 : term,X264 : term,X265 : term] : ((X264 != X265) & (((ap @ (sub @ X263 @ id) @ X264)) = ((ap @ (sub @ X262 @ id) @ X265)))))) & (? [X266 : term,X267 : term,X268 : term,X269 : term] : ((X266 != X268) & (((ap @ X267 @ X266)) = ((ap @ X269 @ X268)))) | ! [X270 : term,X271 : term,X272 : term,X273 : term] : ((X272 = X273) | (((ap @ (sub @ X270 @ id) @ X273)) != ((ap @ (sub @ X271 @ id) @ X272)))) | (hoasapinj2_lthm != $true))),
% 6.44/1.37 inference(rectify,[],[f261])).
% 6.44/1.37 thf(f263,plain,(
% 6.44/1.37 (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) | (axvarcons != $true)) & ((axvarcons = $true) | (sK458 != ((sub @ one @ (push @ sK458 @ sK457))))) & ((sP58 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP58 != $true)) & ! [X4 : subst] : (((d2subst @ (sK459 @ X4))) = X4) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X6 : (subst > term > subst > $o)] : ! [X8 : term] : (((sK460 @ X6 @ X8)) = ((X6 @ id @ X8 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X10 : (term > $o)] : (((sK461 @ id @ (sK462 @ X10) @ id)) != ((X10 @ (sK462 @ X10))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X13 : (subst > term > term)] : (((sub @ sK463 @ (push @ one @ sh))) != ((X13 @ sh @ one)))) & (! [X14 : term] : (((sK464 @ X14 @ sh @ one)) = ((sub @ X14 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((sP56 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP56 != $true)) & (! [X16 : (term > $o),X17 : subst,X18 : term,X19 : (term > $o)] : ((((X19 @ (sub @ (sK465 @ X19 @ X18 @ X17 @ X16) @ (push @ X18 @ X17)))) != ((X16 @ (sK465 @ X19 @ X18 @ X17 @ X16)))) | (((X19 @ X18)) != $true) | (((X16 @ one)) = $true)) | (sK467 != ((sub @ one @ (push @ sK467 @ sK466)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((! [X27 : term] : (((sK468 @ X27)) = ((sK471 @ (sub @ X27 @ (push @ sK470 @ sK469))))) & ($true = ((sK471 @ sK470))) & ($true != ((sK468 @ one)))) & ! [X28 : subst,X29 : term] : (((sub @ one @ (push @ X29 @ X28))) = X29))) & (! [X30 : subst,X31 : term,X32 : (term > $o)] : ! [X34 : term] : (((X32 @ (sub @ X34 @ (push @ X31 @ X30)))) = ((sK472 @ X32 @ X31 @ X30 @ X34))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X38 : (term > $o)] : (((X38 @ (sK476 @ X38))) != ((sK475 @ (sub @ (sK476 @ X38) @ (push @ sK474 @ sK473)))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (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)))))))))))))) & ((hoasinduction_lem3b = $true) | ! [X41 : (subst > term > term)] : (((X41 @ sh @ one)) != ((sub @ sK477 @ (push @ one @ sh))))) & (! [X42 : term] : (((sub @ X42 @ (push @ one @ sh))) = ((sK478 @ X42 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & ((hoaslaminj_lthm = $true) | ($true != sP55)) & (($true = sP55) | (hoaslaminj_lthm != $true)) & ! [X44 : d_term] : (d_one = X44) & (hoasapinj2_gthm = $true) & ((hoasinduction_lthm_3 = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lthm_3 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X45 : term] : (((sub @ X45 @ id)) = X45) | (termmset != $true)) & ((termmset = $true) | (sK479 != ((sub @ sK479 @ id)))) & (pushprop_lthm = $true) & (($true = sP48) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP48)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP47) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP47)) & ((hoasinduction_lem3 = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotap_lthm = $true) & ((apinj2 = $true) | ((((ap @ sK483 @ sK482)) = ((ap @ sK481 @ sK480))) & (sK480 != sK482))) & (! [X51 : term,X52 : term,X53 : term,X54 : term] : ((((ap @ X52 @ X51)) != ((ap @ X54 @ X53))) | (X51 = X53)) | (apinj2 != $true)) & (axabs = $true) & ((axvarid = $true) | (sK484 != ((sub @ sK484 @ id)))) & (! [X56 : term] : (((sub @ X56 @ id)) = X56) | (axvarid != $true)) & (axvarshift = $true) & ((induction = $true) | (($true != ((sP36 @ sK486))) & ! [X59 : term] : ((((sK486 @ X59)) = $true) | ($true != ((var @ X59)))) & ! [X60 : term] : (($true != ((sK486 @ X60))) | ($true = ((sK486 @ (lam @ X60))))) & ($true != ((sK486 @ sK485))))) & (! [X61 : term,X62 : (term > $o)] : ((((sP36 @ X62)) = $true) | (($true != ((X62 @ (sK487 @ X62)))) & (((var @ (sK487 @ X62))) = $true)) | ((((X62 @ (sK488 @ X62))) = $true) & ($true != ((X62 @ (lam @ (sK488 @ X62)))))) | (((X62 @ X61)) = $true)) | (induction != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X65 : subst] : (((comp @ id @ X65)) = X65) | (axidl != $true)) & ((axidl = $true) | (((comp @ id @ sK489)) != sK489)) & (hoaslamnotap_gthm = $true) & ! [X67 : d_subst] : (d_id = X67) & (! [X68 : (term > $o),X69 : (term > $o),X70 : term,X71 : subst] : ((((X68 @ X70)) != $true) | (((X69 @ one)) = $true) | (((X69 @ (sK490 @ X71 @ X70 @ X69 @ X68))) != ((X68 @ (sub @ (sK490 @ X71 @ X70 @ X69 @ X68) @ (push @ X70 @ X71)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true = ((sK491 @ sK493))) & ($true != ((sK492 @ one))) & ! [X77 : term] : (((sK492 @ X77)) = ((sK491 @ (sub @ X77 @ (push @ sK493 @ sK494))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((sP34 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP34 != $true)) & (termmset_gthm = $true) & ((laminj = $true) | ((((lam @ sK495)) = ((lam @ sK496))) & (sK496 != sK495))) & (! [X80 : term,X81 : term] : ((((lam @ X80)) != ((lam @ X81))) | (X80 = X81)) | (laminj != $true)) & ((induction2lem = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem != $true)) & (lamnotvar = $true) & (! [X82 : (subst > term > term),X83 : (subst > term > term),X84 : subst,X85 : term] : ((((X82 @ (comp @ (sK497 @ X82) @ (sK499 @ X82)) @ (sub @ (sK498 @ X82) @ (sK499 @ X82)))) != ((sub @ (X82 @ (sK497 @ X82) @ (sK498 @ X82)) @ (sK499 @ X82)))) | (((lam @ (X82 @ sh @ one))) != ((lam @ (X83 @ sh @ one)))) | (((X82 @ X84 @ X85)) = ((X83 @ X84 @ X85))) | (((sub @ (X83 @ (sK502 @ X83) @ (sK500 @ X83)) @ (sK501 @ X83))) != ((X83 @ (comp @ (sK502 @ X83) @ (sK501 @ X83)) @ (sub @ (sK500 @ X83) @ (sK501 @ X83)))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X96 : subst,X97 : term,X98 : subst] : (((sub @ (sK503 @ X96 @ X97) @ X98)) = ((sK503 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) & (((lam @ (sK503 @ sh @ one))) = ((lam @ (sK504 @ sh @ one)))) & (((sK503 @ sK505 @ sK506)) != ((sK504 @ sK505 @ sK506))) & ! [X99 : term,X100 : subst,X101 : subst] : (((sub @ (sK504 @ X101 @ X99) @ X100)) = ((sK504 @ (comp @ X101 @ X100) @ (sub @ X99 @ X100)))))) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & ((pushprop_lem0_lthm = $true) | ! [X105 : (term > $o)] : (((X105 @ (sK510 @ X105))) != ((sK508 @ (sub @ (sK510 @ X105) @ (push @ sK509 @ sK507)))))) & (! [X107 : subst,X108 : (term > $o),X109 : term] : ! [X111 : term] : (((sK511 @ X109 @ X108 @ X107 @ X111)) = ((X108 @ (sub @ X111 @ (push @ X109 @ X107))))) | (pushprop_lem0_lthm != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((substmonoid = $true) | (sK512 != ((comp @ sK512 @ id))) | (sK513 != ((comp @ id @ sK513)))) & ((! [X114 : subst] : (((comp @ X114 @ id)) = X114) & ! [X115 : subst] : (((comp @ id @ X115)) = X115)) | (substmonoid != $true)) & ((axscons = $true) | (sK514 != ((push @ (sub @ one @ sK514) @ (comp @ sh @ sK514))))) & (! [X117 : subst] : (((push @ (sub @ one @ X117) @ (comp @ sh @ X117))) = X117) | (axscons != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X119 : (subst > term > term)] : (((sub @ sK515 @ (push @ (sK516 @ X119) @ (sK517 @ X119)))) != ((X119 @ (sK517 @ X119) @ (sK516 @ X119))))) & (! [X122 : term] : ! [X124 : term,X125 : subst] : (((sub @ X122 @ (push @ X124 @ X125))) = ((sK518 @ X122 @ X125 @ X124))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | (! [X128 : term,X129 : term] : ((((sK520 @ id @ X129 @ id)) != $true) | ($true = ((sK520 @ id @ (ap @ (sub @ X129 @ id) @ X128) @ id))) | (((sK520 @ id @ X128 @ id)) != $true)) & ($true != ((sK520 @ id @ sK519 @ id))) & (((sP27 @ sK520)) != $true))) & (! [X130 : term,X131 : (subst > term > subst > $o)] : ((($true = ((X131 @ id @ (sK522 @ X131) @ id))) & ($true != ((X131 @ id @ (ap @ (sub @ (sK522 @ X131) @ id) @ (sK521 @ X131)) @ id))) & ($true = ((X131 @ id @ (sK521 @ X131) @ id)))) | ($true = ((X131 @ id @ X130 @ id))) | ($true = ((sP27 @ X131)))) | (hoasinduction_no_psi_cond != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X134 : term,X135 : term,X136 : term,X137 : term] : ((X136 = X137) | (((ap @ X137 @ X135)) != ((ap @ X136 @ X134)))) & ((((ap @ (sub @ sK525 @ id) @ sK524)) = ((ap @ (sub @ sK523 @ id) @ sK526))) & (sK523 != sK525)) & ! [X142 : term] : (((sub @ X142 @ id)) = X142))) & (((sK529 != sK530) & (((ap @ sK530 @ sK528)) = ((ap @ sK529 @ sK527)))) | ! [X147 : term,X148 : term,X149 : term,X150 : term] : ((((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X147 @ id) @ X150))) | (X147 = X149)) | (sK531 != ((sub @ sK531 @ id))) | (hoasapinj1_lthm != $true)) & (hoaslamnotvar = $true) & (($true = sP21) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP21)) & (! [X152 : (term > $o),X153 : (term > $o),X154 : subst,X155 : term,X156 : term] : (($true != ((X153 @ X155))) | ($true = ((X152 @ (sub @ X155 @ (push @ X156 @ X154)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true = ((sK533 @ sK535))) & ($true != ((sK532 @ (sub @ sK535 @ (push @ sK536 @ sK534))))))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X163 : (subst > term > term)] : (((sub @ sK537 @ (push @ (sK539 @ X163) @ (sK538 @ X163)))) != ((X163 @ (sK538 @ X163) @ (sK539 @ X163))))) & (! [X166 : term] : ! [X168 : subst,X169 : term] : (((sub @ X166 @ (push @ X169 @ X168))) = ((sK540 @ X166 @ X168 @ X169))) | (hoasinduction_lem3v2_f_lthm != $true)) & (axclos = $true) & ((induction2_lthm = $true) | ($true != sP20)) & (($true = sP20) | (induction2_lthm != $true)) & (ulamvarsh = $true) & ((pushprop_lem1_lthm = $true) | (! [X170 : term,X171 : subst] : (((comp @ sh @ (push @ X170 @ X171))) = X171) & ((((sK541 @ (sub @ sK543 @ (push @ sK545 @ sK542)))) != $true) & (((sK544 @ sK543)) = $true)) & ! [X177 : term,X178 : subst] : (((sub @ one @ (push @ X177 @ X178))) = X177))) & ((((comp @ sh @ (push @ sK546 @ sK547))) != sK547) | ! [X181 : (term > $o),X182 : subst,X183 : term,X184 : (term > $o),X185 : term] : (($true = ((X181 @ (sub @ X183 @ (push @ X185 @ X182))))) | (((X184 @ X183)) != $true)) | (sK548 != ((sub @ one @ (push @ sK548 @ sK549)))) | (pushprop_lem1_lthm != $true)) & (axmap = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) | ! [X189 : (term > $o)] : (((X189 @ (sK551 @ X189))) != ((sK550 @ id @ (sK551 @ X189) @ id)))) & (! [X191 : (subst > term > subst > $o)] : ! [X193 : term] : (((X191 @ id @ X193 @ id)) = ((sK552 @ X191 @ X193))) | (hoasinduction_lem0 != $true)) & ! [X194 : d_subst,X195 : d_subst] : ((((d2subst @ X194)) != ((d2subst @ X195))) | (X194 = X195)) & ! [X196 : term] : (((d2term @ (sK553 @ X196))) = X196) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP16)) & (($true = sP16) | (hoasinduction_lem3v2a != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) | ((sK557 != sK554) & (((ap @ (sub @ sK557 @ id) @ sK556)) = ((ap @ (sub @ sK554 @ id) @ sK555))))) & (! [X202 : term,X203 : term,X204 : term,X205 : term] : ((X202 = X205) | (((ap @ (sub @ X205 @ id) @ X204)) != ((ap @ (sub @ X202 @ id) @ X203)))) | (hoasapinj1 != $true)) & (pushprop_lem3v2_lthm = $true) & ! [X206 : d_term,X207 : d_term] : ((((d2term @ X206)) != ((d2term @ X207))) | (X206 = X207)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((apinj1 = $true) | ((((ap @ sK559 @ sK560)) = ((ap @ sK561 @ sK558))) & (sK561 != sK559))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((((ap @ X213 @ X214)) != ((ap @ X215 @ X212))) | (X213 = X215)) | (apinj1 != $true)) & (ulamvar1 != $true) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & ((sP12 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP12 != $true)) & (($true = sP10) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP10)) & (hoasapnotvar_gthm = $true) & ((((sub @ sK562 @ id)) != sK562) | ! [X217 : term] : (((sub @ X217 @ id)) = X217) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X218 : term] : (((sub @ X218 @ id)) = X218) & (((sub @ sK563 @ id)) != sK563))) & ((hoaslamnotap = $true) | ((((lam @ (sK564 @ sh @ one))) = ((ap @ (sub @ sK566 @ id) @ sK565))) & ! [X223 : term,X224 : subst,X225 : subst] : (((sK564 @ (comp @ X224 @ X225) @ (sub @ X223 @ X225))) = ((sub @ (sK564 @ X224 @ X223) @ X225))))) & (! [X226 : (subst > term > term),X227 : term,X228 : term] : ((((ap @ (sub @ X228 @ id) @ X227)) != ((lam @ (X226 @ sh @ one)))) | (((sub @ (X226 @ (sK568 @ X226) @ (sK567 @ X226)) @ (sK569 @ X226))) != ((X226 @ (comp @ (sK568 @ X226) @ (sK569 @ X226)) @ (sub @ (sK567 @ X226) @ (sK569 @ X226)))))) | (hoaslamnotap != $true)) & (ulamvarind = $true) & (hoaslamnotvar_gthm = $true) & (axassoc = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X232 : subst] : (((comp @ X232 @ id)) = X232) | (axidr != $true)) & ((axidr = $true) | (sK570 != ((comp @ sK570 @ id)))) & (one = ((d2term @ d_one))) & ((! [X234 : subst] : (((comp @ id @ X234)) = X234) & ! [X235 : subst] : (((comp @ X235 @ id)) = X235)) | (sK571 != ((comp @ sK571 @ id))) | (sK572 != ((comp @ id @ sK572))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (((((comp @ id @ sK573)) != sK573) | (sK574 != ((comp @ sK574 @ id)))) & ! [X240 : subst] : (((comp @ X240 @ id)) = X240) & ! [X241 : subst] : (((comp @ id @ X241)) = X241))) & (hoaslamnotvar_lthm = $true) & (($true = sP4) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP4)) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & ((axshiftcons = $true) | (sK576 != ((comp @ sh @ (push @ sK575 @ sK576))))) & (! [X244 : term,X245 : subst] : (((comp @ sh @ (push @ X244 @ X245))) = X245) | (axshiftcons != $true)) & (hoasinduction_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ((sK579 != sK578) & (((ap @ (sub @ sK577 @ id) @ sK579)) = ((ap @ (sub @ sK580 @ id) @ sK578))))) & (! [X250 : term,X251 : term,X252 : term,X253 : term] : ((X251 = X252) | (((ap @ (sub @ X250 @ id) @ X252)) != ((ap @ (sub @ X253 @ id) @ X251)))) | (hoasapinj2 != $true)) & (! [X254 : term,X255 : term] : ((((sub @ X254 @ sh)) != ((sub @ X255 @ sh))) | (X254 = X255)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK582 @ sh)) = ((sub @ sK581 @ sh))) & (sK582 != sK581))) & (axapp = $true) & ((hoasapinj2_lthm = $true) | (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((X258 = X260) | (((ap @ X261 @ X260)) != ((ap @ X259 @ X258)))) & ((sK586 != sK585) & (((ap @ (sub @ sK584 @ id) @ sK585)) = ((ap @ (sub @ sK583 @ id) @ sK586)))))) & (((sK589 != sK587) & (((ap @ sK588 @ sK587)) = ((ap @ sK590 @ sK589)))) | ! [X270 : term,X271 : term,X272 : term,X273 : term] : ((X272 = X273) | (((ap @ (sub @ X270 @ id) @ X273)) != ((ap @ (sub @ X271 @ id) @ X272)))) | (hoasapinj2_lthm != $true))),
% 6.44/1.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,vAPP,vAPP,sK461,vAPP,sK463,vAPP,vAPP,sK466,sK467,sK468,sK469,sK470,sK471,vAPP,sK473,sK474,sK475,vAPP,sK477,vAPP,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,vAPP,vAPP,sK489,vAPP,sK491,sK492,sK493,sK494,sK495,sK496,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK503,sK504,sK505,sK506,sK507,sK508,sK509,vAPP,vAPP,sK512,sK513,sK514,sK515,vAPP,vAPP,vAPP,sK519,sK520,vAPP,vAPP,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,vAPP,vAPP,vAPP,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,vAPP,vAPP,vAPP,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,vAPP,vAPP,vAPP,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590]),skolemize(X2,sK457),skolemize(X3,sK458),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X9,sK461),skolemize(X27,sK72 @ X16),skolemize(X12,sK463),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X21,sK466),skolemize(X22,sK467),skolemize(X23,sK468),skolemize(X24,sK469),skolemize(X25,sK470),skolemize(X26,sK471),skolemize(X27,sK72 @ X16),skolemize(X35,sK473),skolemize(X36,sK474),skolemize(X37,sK475),skolemize(X27,sK72 @ X16),skolemize(X40,sK477),skolemize(X27,sK72 @ X16),skolemize(X46,sK479),skolemize(X47,sK480),skolemize(X48,sK481),skolemize(X49,sK482),skolemize(X50,sK483),skolemize(X55,sK484),skolemize(X57,sK485),skolemize(X58,sK486),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X66,sK489),skolemize(X27,sK72 @ X16),skolemize(X73,sK491),skolemize(X74,sK492),skolemize(X75,sK493),skolemize(X76,sK494),skolemize(X78,sK495),skolemize(X79,sK496),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X92,sK503),skolemize(X93,sK504),skolemize(X94,sK505),skolemize(X95,sK506),skolemize(X102,sK507),skolemize(X103,sK508),skolemize(X104,sK509),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X112,sK512),skolemize(X113,sK513),skolemize(X116,sK514),skolemize(X118,sK515),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X126,sK519),skolemize(X127,sK520),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X138,sK523),skolemize(X139,sK524),skolemize(X140,sK525),skolemize(X141,sK526),skolemize(X143,sK527),skolemize(X144,sK528),skolemize(X145,sK529),skolemize(X146,sK530),skolemize(X151,sK531),skolemize(X157,sK532),skolemize(X158,sK533),skolemize(X159,sK534),skolemize(X160,sK535),skolemize(X161,sK536),skolemize(X162,sK537),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X172,sK541),skolemize(X173,sK542),skolemize(X174,sK543),skolemize(X175,sK544),skolemize(X176,sK545),skolemize(X179,sK546),skolemize(X180,sK547),skolemize(X186,sK548),skolemize(X187,sK549),skolemize(X188,sK550),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X198,sK554),skolemize(X199,sK555),skolemize(X200,sK556),skolemize(X201,sK557),skolemize(X208,sK558),skolemize(X209,sK559),skolemize(X210,sK560),skolemize(X211,sK561),skolemize(X216,sK562),skolemize(X219,sK563),skolemize(X220,sK564),skolemize(X221,sK565),skolemize(X222,sK566),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X27,sK72 @ X16),skolemize(X233,sK570),skolemize(X236,sK571),skolemize(X237,sK572),skolemize(X238,sK573),skolemize(X239,sK574),skolemize(X242,sK575),skolemize(X243,sK576),skolemize(X246,sK577),skolemize(X247,sK578),skolemize(X248,sK579),skolemize(X249,sK580),skolemize(X256,sK581),skolemize(X257,sK582),skolemize(X262,sK583),skolemize(X263,sK584),skolemize(X264,sK585),skolemize(X265,sK586),skolemize(X266,sK587),skolemize(X267,sK588),skolemize(X268,sK589),skolemize(X269,sK590)],[f262])).
% 6.44/1.37 thf(f500,plain,(
% 6.44/1.37 ($true = sP30) | ($true != ((sK253 @ id @ (ap @ sK252 @ sK251) @ id)))),
% 6.44/1.37 inference(cnf_transformation,[],[f164])).
% 6.44/1.37 thf(f501,plain,(
% 6.44/1.37 ($true = sP30) | ($true = ((sK253 @ id @ sK251 @ id)))),
% 6.44/1.37 inference(cnf_transformation,[],[f164])).
% 6.44/1.37 thf(f503,plain,(
% 6.44/1.37 ( ! [X10 : subst,X8 : subst,X9 : term,X7 : subst] : ((((sK253 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)) = $true) | ($true = sP30) | (((sK253 @ X10 @ X9 @ (comp @ X7 @ X8))) != $true)) )),
% 6.44/1.37 inference(cnf_transformation,[],[f164])).
% 6.44/1.37 thf(f504,plain,(
% 6.44/1.37 ( ! [X3 : subst,X6 : subst,X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ (comp @ X6 @ X3))) = $true) | ($true = sP30) | ($true != ((sK253 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3)))) )),
% 6.44/1.37 inference(cnf_transformation,[],[f164])).
% 6.44/1.37 thf(f781,plain,(
% 6.44/1.37 (one = ((d2term @ d_one)))),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f827,plain,(
% 6.44/1.37 ( ! [X196 : term] : ((((d2term @ (sK553 @ X196))) = X196)) )),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f831,plain,(
% 6.44/1.37 (((d2subst @ d_id)) = sh)),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f885,plain,(
% 6.44/1.37 (hoasinduction_lem2 = $true) | ($true != sP30)),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f905,plain,(
% 6.44/1.37 ( ! [X67 : d_subst] : ((d_id = X67)) )),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f943,plain,(
% 6.44/1.37 ( ! [X44 : d_term] : ((d_one = X44)) )),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f973,plain,(
% 6.44/1.37 ( ! [X4 : subst] : ((((d2subst @ (sK459 @ X4))) = X4)) )),
% 6.44/1.37 inference(cnf_transformation,[],[f263])).
% 6.44/1.37 thf(f978,plain,(
% 6.44/1.37 (hoasinduction_lem2 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))))),
% 6.44/1.37 inference(cnf_transformation,[],[f10])).
% 6.44/1.37 thf(f981,definition,(
% 6.44/1.37 (sF591 = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[sF591])],[function_definition])).
% 6.44/1.37 thf(f982,plain,(
% 6.44/1.37 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))) = sF591)),
% 6.44/1.37 inference(reorient_equations,[],[f981])).
% 6.44/1.37 thf(f983,plain,(
% 6.44/1.37 (hoasinduction_lem2 != sF591)),
% 6.44/1.37 inference(definition_folding,[],[f978,f982])).
% 6.44/1.37 thf(f1017,plain,(
% 6.44/1.37 ($true = sF591) | (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))))) = $false)),
% 6.44/1.37 inference(iff_proxy_clausification,[],[f982])).
% 6.44/1.37 thf(f1018,plain,(
% 6.44/1.37 ($false = (((^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y1 @ (comp @ Y3 @ Y2)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y1 @ Y3) @ Y2)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2) @ Y4) => (Y0 @ Y1 @ Y3 @ (comp @ Y2 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => (!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (ap @ Y2 @ Y1) @ id))))))))))) @ sK592))) | ($true = sF591)),
% 6.44/1.37 inference(sigma_proxy_clausification,[],[f1017])).
% 6.44/1.37 thf(f1019,plain,(
% 6.44/1.37 ($true = sF591) | ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ Y3 @ Y0 @ (comp @ Y2 @ Y1)) => (sK592 @ (comp @ Y3 @ Y2) @ (sub @ Y0 @ Y2) @ Y1)))))))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1) @ Y3) => (sK592 @ Y0 @ Y2 @ (comp @ Y1 @ Y3))))))))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (ap @ Y1 @ Y0) @ id))))))))))) = $false)),
% 6.44/1.37 inference(beta-eta_normalization,[],[f1018])).
% 6.44/1.37 thf(f1020,plain,(
% 6.44/1.37 ($true = sF591) | ($false = (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sK592 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1) @ Y3) => (sK592 @ Y0 @ Y2 @ (comp @ Y1 @ Y3))))))))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (ap @ Y1 @ Y0) @ id)))))))))))),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1019])).
% 6.44/1.37 thf(f1031,plain,(
% 6.44/1.37 ((((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (ap @ Y1 @ Y0) @ id))))))))) = $false) | ($true = sF591)),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1020])).
% 6.44/1.37 thf(f1042,plain,(
% 6.44/1.37 ($true = sF591) | (((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (ap @ Y1 @ Y0) @ id)))))))) = $false)),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1031])).
% 6.44/1.37 thf(f1050,plain,(
% 6.44/1.37 ((((^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (ap @ Y1 @ Y0) @ id)))))) @ sK593)) = $false) | ($true = sF591)),
% 6.44/1.37 inference(sigma_proxy_clausification,[],[f1042])).
% 6.44/1.37 thf(f1051,plain,(
% 6.44/1.37 ($true = sF591) | (((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => ((sK592 @ id @ sK593 @ id) => (sK592 @ id @ (ap @ Y0 @ sK593) @ id)))))) = $false)),
% 6.44/1.37 inference(beta-eta_normalization,[],[f1050])).
% 6.44/1.37 thf(f1052,plain,(
% 6.44/1.37 ((((^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => ((sK592 @ id @ sK593 @ id) => (sK592 @ id @ (ap @ Y0 @ sK593) @ id)))) @ sK594)) = $false) | ($true = sF591)),
% 6.44/1.37 inference(sigma_proxy_clausification,[],[f1051])).
% 6.44/1.37 thf(f1053,plain,(
% 6.44/1.37 ((((sK592 @ id @ sK594 @ id) => ((sK592 @ id @ sK593 @ id) => (sK592 @ id @ (ap @ sK594 @ sK593) @ id)))) = $false) | ($true = sF591)),
% 6.44/1.37 inference(beta-eta_normalization,[],[f1052])).
% 6.44/1.37 thf(f1054,plain,(
% 6.44/1.37 ((((sK592 @ id @ sK593 @ id) => (sK592 @ id @ (ap @ sK594 @ sK593) @ id))) = $false) | ($true = sF591)),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1053])).
% 6.44/1.37 thf(f1055,plain,(
% 6.44/1.37 ($true = ((sK592 @ id @ sK594 @ id))) | ($true = sF591)),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1053])).
% 6.44/1.37 thf(f1056,plain,(
% 6.44/1.37 (((sK592 @ id @ (ap @ sK594 @ sK593) @ id)) = $false) | ($true = sF591)),
% 6.44/1.37 inference(imp_proxy_clausification,[],[f1054])).
% 6.44/1.37 thf(f1185,plain,(
% 6.44/1.37 (hoasinduction_lem2 = $false) | (sF591 = $false)),
% 6.44/1.37 inference(xor_proxy_clausification,[],[f983])).
% 6.44/1.37 thf(f1502,definition,(
% 6.44/1.37 spl610_66 <=> ($true = sP30)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_66])],[avatar_definition])).
% 6.44/1.37 thf(f1889,definition,(
% 6.44/1.37 spl610_159 <=> ($true = sF591)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_159])],[avatar_definition])).
% 6.44/1.37 thf(f1891,plain,(
% 6.44/1.37 ($true = sF591) | ~spl610_159),
% 6.44/1.37 inference(avatar_component_clause,[],[f1889])).
% 6.44/1.37 thf(f1902,definition,(
% 6.44/1.37 spl610_162 <=> ($true = ((sK592 @ id @ sK594 @ id)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_162])],[avatar_definition])).
% 6.44/1.37 thf(f1904,plain,(
% 6.44/1.37 ($true = ((sK592 @ id @ sK594 @ id))) | ~spl610_162),
% 6.44/1.37 inference(avatar_component_clause,[],[f1902])).
% 6.44/1.37 thf(f1905,plain,(
% 6.44/1.37 spl610_159 | spl610_162),
% 6.44/1.37 inference(avatar_split_clause,[],[f1055,f1902,f1889])).
% 6.44/1.37 thf(f1912,definition,(
% 6.44/1.37 spl610_164 <=> (((sK592 @ id @ (ap @ sK594 @ sK593) @ id)) = $false)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_164])],[avatar_definition])).
% 6.44/1.37 thf(f1914,plain,(
% 6.44/1.37 (((sK592 @ id @ (ap @ sK594 @ sK593) @ id)) = $false) | ~spl610_164),
% 6.44/1.37 inference(avatar_component_clause,[],[f1912])).
% 6.44/1.37 thf(f1915,plain,(
% 6.44/1.37 spl610_159 | spl610_164),
% 6.44/1.37 inference(avatar_split_clause,[],[f1056,f1912,f1889])).
% 6.44/1.37 thf(f1917,definition,(
% 6.44/1.37 spl610_165 <=> (sF591 = $false)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_165])],[avatar_definition])).
% 6.44/1.37 thf(f1919,plain,(
% 6.44/1.37 (sF591 = $false) | ~spl610_165),
% 6.44/1.37 inference(avatar_component_clause,[],[f1917])).
% 6.44/1.37 thf(f2480,definition,(
% 6.44/1.37 spl610_296 <=> (hoasinduction_lem2 = $true)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_296])],[avatar_definition])).
% 6.44/1.37 thf(f2481,plain,(
% 6.44/1.37 (hoasinduction_lem2 = $true) | ~spl610_296),
% 6.44/1.37 inference(avatar_component_clause,[],[f2480])).
% 6.44/1.37 thf(f3217,definition,(
% 6.44/1.37 spl610_465 <=> (hoasinduction_lem2 = $false)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_465])],[avatar_definition])).
% 6.44/1.37 thf(f3219,plain,(
% 6.44/1.37 (hoasinduction_lem2 = $false) | ~spl610_465),
% 6.44/1.37 inference(avatar_component_clause,[],[f3217])).
% 6.44/1.37 thf(f3220,plain,(
% 6.44/1.37 spl610_465 | spl610_165),
% 6.44/1.37 inference(avatar_split_clause,[],[f1185,f1917,f3217])).
% 6.44/1.37 thf(f3351,definition,(
% 6.44/1.37 spl610_495 <=> ($true = ((sK253 @ id @ sK251 @ id)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_495])],[avatar_definition])).
% 6.44/1.37 thf(f3353,plain,(
% 6.44/1.37 ($true = ((sK253 @ id @ sK251 @ id))) | ~spl610_495),
% 6.44/1.37 inference(avatar_component_clause,[],[f3351])).
% 6.44/1.37 thf(f3354,plain,(
% 6.44/1.37 spl610_66 | spl610_495),
% 6.44/1.37 inference(avatar_split_clause,[],[f501,f3351,f1502])).
% 6.44/1.37 thf(f3454,plain,(
% 6.44/1.37 ~spl610_66 | spl610_296),
% 6.44/1.37 inference(avatar_split_clause,[],[f885,f2480,f1502])).
% 6.44/1.37 thf(f3645,definition,(
% 6.44/1.37 spl610_563 <=> ! [X10 : subst,X7 : subst,X9 : term,X8 : subst] : ((((sK253 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)) = $true) | (((sK253 @ X10 @ X9 @ (comp @ X7 @ X8))) != $true))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_563])],[avatar_definition])).
% 6.44/1.37 thf(f3646,plain,(
% 6.44/1.37 ( ! [X10 : subst,X8 : subst,X9 : term,X7 : subst] : ((((sK253 @ X10 @ X9 @ (comp @ X7 @ X8))) != $true) | (((sK253 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)) = $true)) ) | ~spl610_563),
% 6.44/1.37 inference(avatar_component_clause,[],[f3645])).
% 6.44/1.37 thf(f3647,plain,(
% 6.44/1.37 spl610_563 | spl610_66),
% 6.44/1.37 inference(avatar_split_clause,[],[f503,f1502,f3645])).
% 6.44/1.37 thf(f3925,definition,(
% 6.44/1.37 spl610_627 <=> ($true = ((sK253 @ id @ (ap @ sK252 @ sK251) @ id)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_627])],[avatar_definition])).
% 6.44/1.37 thf(f3927,plain,(
% 6.44/1.37 ($true != ((sK253 @ id @ (ap @ sK252 @ sK251) @ id))) | spl610_627),
% 6.44/1.37 inference(avatar_component_clause,[],[f3925])).
% 6.44/1.37 thf(f3928,plain,(
% 6.44/1.37 ~spl610_627 | spl610_66),
% 6.44/1.37 inference(avatar_split_clause,[],[f500,f1502,f3925])).
% 6.44/1.37 thf(f3951,definition,(
% 6.44/1.37 spl610_633 <=> ! [X5 : subst,X4 : term,X6 : subst,X3 : subst] : ((((sK253 @ X5 @ X4 @ (comp @ X6 @ X3))) = $true) | ($true != ((sK253 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3))))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_633])],[avatar_definition])).
% 6.44/1.37 thf(f3952,plain,(
% 6.44/1.37 ( ! [X3 : subst,X6 : subst,X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ (comp @ X6 @ X3))) = $true) | ($true != ((sK253 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3)))) ) | ~spl610_633),
% 6.44/1.37 inference(avatar_component_clause,[],[f3951])).
% 6.44/1.37 thf(f3953,plain,(
% 6.44/1.37 spl610_633 | spl610_66),
% 6.44/1.37 inference(avatar_split_clause,[],[f504,f1502,f3951])).
% 6.44/1.37 thf(f4020,plain,(
% 6.44/1.37 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 6.44/1.37 inference(superposition,[],[f781,f943])).
% 6.44/1.37 thf(f4021,plain,(
% 6.44/1.37 ( ! [X0 : d_subst] : ((sh = ((d2subst @ X0)))) )),
% 6.44/1.37 inference(superposition,[],[f831,f905])).
% 6.44/1.37 thf(f4030,plain,(
% 6.44/1.37 ($true = $false) | (~spl610_159 | ~spl610_165)),
% 6.44/1.37 inference(superposition,[],[f1919,f1891])).
% 6.44/1.37 thf(f4034,plain,(
% 6.44/1.37 $false | (~spl610_159 | ~spl610_165)),
% 6.44/1.37 inference(trivial_inequality_removal,[],[f4030])).
% 6.44/1.37 thf(f4035,plain,(
% 6.44/1.37 ~spl610_159 | ~spl610_165),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f4034])).
% 6.44/1.37 thf(f4039,plain,(
% 6.44/1.37 ( ! [X196 : term] : ((one = X196)) )),
% 6.44/1.37 inference(forward_demodulation,[],[f827,f4020])).
% 6.44/1.37 thf(f4042,plain,(
% 6.44/1.37 ( ! [X4 : subst] : ((sh = X4)) )),
% 6.44/1.37 inference(forward_demodulation,[],[f973,f4021])).
% 6.44/1.37 thf(f4601,plain,(
% 6.44/1.37 ($true = ((sK592 @ sh @ sK594 @ sh))) | ~spl610_162),
% 6.44/1.37 inference(forward_demodulation,[],[f1904,f4042])).
% 6.44/1.37 thf(f4602,plain,(
% 6.44/1.37 ($true = ((sK592 @ sh @ one @ sh))) | ~spl610_162),
% 6.44/1.37 inference(forward_demodulation,[],[f4601,f4039])).
% 6.44/1.37 thf(f4603,plain,(
% 6.44/1.37 ( ! [X0 : term] : ((((sK592 @ sh @ X0 @ sh)) = $true)) ) | ~spl610_162),
% 6.44/1.37 inference(superposition,[],[f4602,f4039])).
% 6.44/1.37 thf(f4611,plain,(
% 6.44/1.37 ( ! [X0 : subst,X1 : term] : (($true = ((sK592 @ X0 @ X1 @ X0)))) ) | ~spl610_162),
% 6.44/1.37 inference(superposition,[],[f4603,f4042])).
% 6.44/1.37 thf(f5019,plain,(
% 6.44/1.37 ($true = $false) | (~spl610_162 | ~spl610_164)),
% 6.44/1.37 inference(forward_demodulation,[],[f1914,f4611])).
% 6.44/1.37 thf(f5020,plain,(
% 6.44/1.37 $false | (~spl610_162 | ~spl610_164)),
% 6.44/1.37 inference(trivial_inequality_removal,[],[f5019])).
% 6.44/1.37 thf(f5021,plain,(
% 6.44/1.37 ~spl610_162 | ~spl610_164),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f5020])).
% 6.44/1.37 thf(f5153,plain,(
% 6.44/1.37 ($true = $false) | (~spl610_296 | ~spl610_465)),
% 6.44/1.37 inference(superposition,[],[f2481,f3219])).
% 6.44/1.37 thf(f5156,plain,(
% 6.44/1.37 $false | (~spl610_296 | ~spl610_465)),
% 6.44/1.37 inference(trivial_inequality_removal,[],[f5153])).
% 6.44/1.37 thf(f5157,plain,(
% 6.44/1.37 ~spl610_296 | ~spl610_465),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f5156])).
% 6.44/1.37 thf(f5158,plain,(
% 6.44/1.37 ($true != ((sK253 @ sh @ (ap @ sK252 @ sK251) @ sh))) | spl610_627),
% 6.44/1.37 inference(forward_demodulation,[],[f3927,f4042])).
% 6.44/1.37 thf(f5161,plain,(
% 6.44/1.37 ( ! [X3 : subst,X6 : subst,X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ sh)) = $true) | ($true != ((sK253 @ (comp @ X5 @ X6) @ (sub @ X4 @ X6) @ X3)))) ) | ~spl610_633),
% 6.44/1.37 inference(forward_demodulation,[],[f3952,f4042])).
% 6.44/1.37 thf(f5162,plain,(
% 6.44/1.37 ($true = ((sK253 @ sh @ sK251 @ sh))) | ~spl610_495),
% 6.44/1.37 inference(forward_demodulation,[],[f3353,f4042])).
% 6.44/1.37 thf(f5163,plain,(
% 6.44/1.37 ( ! [X10 : subst,X8 : subst,X9 : term,X7 : subst] : ((((sK253 @ X10 @ X9 @ sh)) != $true) | (((sK253 @ (comp @ X10 @ X7) @ (sub @ X9 @ X7) @ X8)) = $true)) ) | ~spl610_563),
% 6.44/1.37 inference(forward_demodulation,[],[f3646,f4042])).
% 6.44/1.37 thf(f5164,plain,(
% 6.44/1.37 ($true != ((sK253 @ sh @ one @ sh))) | spl610_627),
% 6.44/1.37 inference(forward_demodulation,[],[f5158,f4039])).
% 6.44/1.37 thf(f5165,plain,(
% 6.44/1.37 ( ! [X3 : subst,X6 : subst,X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ sh)) = $true) | ($true != ((sK253 @ sh @ (sub @ X4 @ X6) @ X3)))) ) | ~spl610_633),
% 6.44/1.37 inference(forward_demodulation,[],[f5161,f4042])).
% 6.44/1.37 thf(f5166,plain,(
% 6.44/1.37 ( ! [X10 : subst,X8 : subst,X9 : term,X7 : subst] : ((((sK253 @ X10 @ X9 @ sh)) != $true) | (((sK253 @ sh @ (sub @ X9 @ X7) @ X8)) = $true)) ) | ~spl610_563),
% 6.44/1.37 inference(forward_demodulation,[],[f5163,f4042])).
% 6.44/1.37 thf(f5167,plain,(
% 6.44/1.37 ( ! [X3 : subst,X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ sh)) = $true) | ($true != ((sK253 @ sh @ one @ X3)))) ) | ~spl610_633),
% 6.44/1.37 inference(forward_demodulation,[],[f5165,f4039])).
% 6.44/1.37 thf(f5168,plain,(
% 6.44/1.37 ( ! [X10 : subst,X8 : subst,X9 : term] : ((((sK253 @ sh @ one @ X8)) = $true) | (((sK253 @ X10 @ X9 @ sh)) != $true)) ) | ~spl610_563),
% 6.44/1.37 inference(forward_demodulation,[],[f5166,f4039])).
% 6.44/1.37 thf(f5170,definition,(
% 6.44/1.37 spl610_663 <=> ! [X3 : subst] : ($true != ((sK253 @ sh @ one @ X3)))),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_663])],[avatar_definition])).
% 6.44/1.37 thf(f5171,plain,(
% 6.44/1.37 ( ! [X3 : subst] : (($true != ((sK253 @ sh @ one @ X3)))) ) | ~spl610_663),
% 6.44/1.37 inference(avatar_component_clause,[],[f5170])).
% 6.44/1.37 thf(f5173,definition,(
% 6.44/1.37 spl610_664 <=> ! [X4 : term,X5 : subst] : (((sK253 @ X5 @ X4 @ sh)) = $true)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_664])],[avatar_definition])).
% 6.44/1.37 thf(f5174,plain,(
% 6.44/1.37 ( ! [X4 : term,X5 : subst] : ((((sK253 @ X5 @ X4 @ sh)) = $true)) ) | ~spl610_664),
% 6.44/1.37 inference(avatar_component_clause,[],[f5173])).
% 6.44/1.37 thf(f5175,plain,(
% 6.44/1.37 spl610_663 | spl610_664 | ~spl610_633),
% 6.44/1.37 inference(avatar_split_clause,[],[f5167,f3951,f5173,f5170])).
% 6.44/1.37 thf(f5177,definition,(
% 6.44/1.37 spl610_665 <=> ! [X9 : term,X10 : subst] : (((sK253 @ X10 @ X9 @ sh)) != $true)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_665])],[avatar_definition])).
% 6.44/1.37 thf(f5178,plain,(
% 6.44/1.37 ( ! [X10 : subst,X9 : term] : ((((sK253 @ X10 @ X9 @ sh)) != $true)) ) | ~spl610_665),
% 6.44/1.37 inference(avatar_component_clause,[],[f5177])).
% 6.44/1.37 thf(f5180,definition,(
% 6.44/1.37 spl610_666 <=> ! [X8 : subst] : (((sK253 @ sh @ one @ X8)) = $true)),
% 6.44/1.37 introduced(definition,[new_symbols(definition,[spl610_666])],[avatar_definition])).
% 6.44/1.37 thf(f5181,plain,(
% 6.44/1.37 ( ! [X8 : subst] : ((((sK253 @ sh @ one @ X8)) = $true)) ) | ~spl610_666),
% 6.44/1.37 inference(avatar_component_clause,[],[f5180])).
% 6.44/1.37 thf(f5182,plain,(
% 6.44/1.37 spl610_665 | spl610_666 | ~spl610_563),
% 6.44/1.37 inference(avatar_split_clause,[],[f5168,f3645,f5180,f5177])).
% 6.44/1.37 thf(f5206,plain,(
% 6.44/1.37 $false | (~spl610_663 | ~spl610_666)),
% 6.44/1.37 inference(forward_subsumption_resolution,[],[f5181,f5171])).
% 6.44/1.37 thf(f5207,plain,(
% 6.44/1.37 ~spl610_663 | ~spl610_666),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f5206])).
% 6.44/1.37 thf(f5211,plain,(
% 6.44/1.37 ($true != $true) | (spl610_627 | ~spl610_664)),
% 6.44/1.37 inference(superposition,[],[f5164,f5174])).
% 6.44/1.37 thf(f5212,plain,(
% 6.44/1.37 $false | (spl610_627 | ~spl610_664)),
% 6.44/1.37 inference(trivial_inequality_removal,[],[f5211])).
% 6.44/1.37 thf(f5213,plain,(
% 6.44/1.37 spl610_627 | ~spl610_664),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f5212])).
% 6.44/1.37 thf(f5224,plain,(
% 6.44/1.37 ($true != $true) | (~spl610_495 | ~spl610_665)),
% 6.44/1.37 inference(superposition,[],[f5178,f5162])).
% 6.44/1.37 thf(f5225,plain,(
% 6.44/1.37 $false | (~spl610_495 | ~spl610_665)),
% 6.44/1.37 inference(trivial_inequality_removal,[],[f5224])).
% 6.44/1.37 thf(f5226,plain,(
% 6.44/1.37 ~spl610_495 | ~spl610_665),
% 6.44/1.37 inference(avatar_contradiction_clause,[],[f5225])).
% 6.44/1.37 cnf(s106, plain, spl610_159 | spl610_162, inference(sat_conversion,[],[f1905])).
% 6.44/1.37 cnf(s108, plain, spl610_159 | spl610_164, inference(sat_conversion,[],[f1915])).
% 6.44/1.37 cnf(s409, plain, spl610_165 | spl610_465, inference(sat_conversion,[],[f3220])).
% 6.44/1.37 cnf(s445, plain, spl610_66 | spl610_495, inference(sat_conversion,[],[f3354])).
% 6.44/1.37 cnf(s472, plain, ~spl610_66 | spl610_296, inference(sat_conversion,[],[f3454])).
% 6.44/1.37 cnf(s523, plain, spl610_66 | spl610_563, inference(sat_conversion,[],[f3647])).
% 6.44/1.37 cnf(s598, plain, spl610_66 | ~spl610_627, inference(sat_conversion,[],[f3928])).
% 6.44/1.37 cnf(s604, plain, spl610_66 | spl610_633, inference(sat_conversion,[],[f3953])).
% 6.44/1.37 cnf(s623, plain, ~spl610_159 | ~spl610_165, inference(sat_conversion,[],[f4035])).
% 6.44/1.37 cnf(s724, plain, ~spl610_162 | ~spl610_164, inference(sat_conversion,[],[f5021])).
% 6.44/1.37 cnf(s726, plain, ~spl610_296 | ~spl610_465, inference(sat_conversion,[],[f5157])).
% 6.44/1.37 cnf(s727, plain, ~spl610_633 | spl610_663 | spl610_664, inference(sat_conversion,[],[f5175])).
% 6.44/1.37 cnf(s728, plain, ~spl610_563 | spl610_665 | spl610_666, inference(sat_conversion,[],[f5182])).
% 6.44/1.37 cnf(s729, plain, ~spl610_663 | ~spl610_666, inference(sat_conversion,[],[f5207])).
% 6.44/1.37 cnf(s730, plain, spl610_627 | ~spl610_664, inference(sat_conversion,[],[f5213])).
% 6.44/1.37 cnf(s731, plain, ~spl610_495 | ~spl610_665, inference(sat_conversion,[],[f5226])).
% 6.44/1.37 cnf(s827, plain, spl610_66, inference(rat,[],[s729,s728,s727,s731,s730,s445,s523,s598,s604])).
% 6.44/1.37 cnf(s829, plain, spl610_296, inference(rat,[],[s472,s827])).
% 6.44/1.37 cnf(s833, plain, ~spl610_465, inference(rat,[],[s726,s829])).
% 6.44/1.37 cnf(s834, plain, spl610_165, inference(rat,[],[s409,s833])).
% 6.44/1.37 cnf(s835, plain, ~spl610_159, inference(rat,[],[s623,s834])).
% 6.44/1.37 cnf(s836, plain, spl610_164, inference(rat,[],[s108,s835])).
% 6.44/1.37 cnf(s838, plain, spl610_162, inference(rat,[],[s106,s835])).
% 6.44/1.37 cnf(s842, plain, $false, inference(rat,[],[s724,s836,s838])).
% 6.44/1.37 thf(f5229,plain,(
% 6.44/1.37 $false),
% 6.44/1.37 inference(avatar_sat_refutation,[],[s842])).
% 6.44/1.37 % SZS output end Proof for theBenchmark
% 6.44/1.37 % (3054554)------------------------------
% 6.44/1.37 % (3054554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.44/1.37 % (3054554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.37 % (3054554)CaDiCaL version: 2.1.3
% 6.44/1.37 % (3054554)Termination reason: Refutation
% 6.44/1.37 % (3054554)Time elapsed: 0.438 s
% 6.44/1.37 % (3054554)Peak memory usage: 17 MB
% 6.44/1.37 % (3054554)Instructions burned: 528 (million)
% 6.44/1.37 % (3054299)Success in time 1.091 s
% 6.44/1.37 % Vampire exiting
%------------------------------------------------------------------------------