%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX164^1 : 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 : n017.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 5.86s 1.20s
% Output : Refutation 5.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX164^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:04:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.27 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
% 0.57/0.44 % (519211)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.57/0.44 % (519217)lrs+10_16_si=on:nwc=1.5:random_seed=2105768520:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.57/0.44 % (519217)Instruction limit reached!
% 0.57/0.44 % (519217)------------------------------
% 0.57/0.44 % (519217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (519217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (519217)CaDiCaL version: 2.1.3
% 0.57/0.44 % (519217)Termination reason: Instruction limit
% 0.57/0.44 % (519217)Termination phase: shuffling
% 0.57/0.44 % (519217)Time elapsed: 0.006 s
% 0.57/0.44 % (519217)Peak memory usage: 10 MB
% 0.57/0.44 % (519217)Instructions burned: 20 (million)
% 0.57/0.44 % (519218)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2126434971:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.57/0.44 % (519216)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=565427277:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.57/0.44 % (519219)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=546132624: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)
% 0.57/0.44 % (519222)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.57/0.44 % (519222)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
% 0.57/0.44 % (519218)Instruction limit reached!
% 0.57/0.44 % (519218)------------------------------
% 0.57/0.44 % (519218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (519218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (519218)CaDiCaL version: 2.1.3
% 0.57/0.44 % (519218)Termination reason: Instruction limit
% 0.57/0.44 % (519218)Termination phase: shuffling
% 0.57/0.44 % (519218)Time elapsed: 0.003 s
% 0.57/0.44 % (519218)Peak memory usage: 9 MB
% 0.57/0.44 % (519218)Instructions burned: 5 (million)
% 0.57/0.44 % (519221)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3932512756:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.57/0.44 % (519220)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1046959059:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.57/0.44 % (519222)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=3860377859:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.57/0.44 % (519226)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=766752894:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.44 % (519226)Instruction limit reached!
% 0.57/0.44 % (519226)------------------------------
% 0.57/0.44 % (519226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (519226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (519226)CaDiCaL version: 2.1.3
% 0.57/0.44 % (519226)Termination reason: Instruction limit
% 0.57/0.44 % (519226)Termination phase: shuffling
% 0.57/0.44 % (519226)Time elapsed: 0.0000 s
% 0.57/0.44 % (519226)Peak memory usage: 10 MB
% 0.57/0.44 % (519226)Instructions burned: 2 (million)
% 0.57/0.44 % (519229)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2724586303:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.57/0.44 % (519229)Instruction limit reached!
% 0.57/0.44 % (519229)------------------------------
% 0.57/0.44 % (519229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (519229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (519229)CaDiCaL version: 2.1.3
% 0.57/0.44 % (519229)Termination reason: Instruction limit
% 0.57/0.44 % (519229)Termination phase: shuffling
% 0.57/0.44 % (519229)Time elapsed: 0.003 s
% 0.57/0.44 % (519229)Peak memory usage: 10 MB
% 0.57/0.44 % (519229)Instructions burned: 5 (million)
% 0.57/0.44 % (519233)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.47 % (519220)Instruction limit reached!
% 0.57/0.47 % (519220)------------------------------
% 0.57/0.47 % (519220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.47 % (519220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.47 % (519220)CaDiCaL version: 2.1.3
% 0.57/0.47 % (519220)Termination reason: Instruction limit
% 0.57/0.47 % (519220)Termination phase: Property scanning
% 0.57/0.47 % (519220)Time elapsed: 0.021 s
% 0.57/0.47 % (519220)Peak memory usage: 10 MB
% 0.57/0.47 % (519220)Instructions burned: 25 (million)
% 0.57/0.47 % (519233)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1257749022:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.57/0.47 % (519233)Instruction limit reached!
% 0.57/0.47 % (519233)------------------------------
% 0.57/0.47 % (519233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.47 % (519233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.47 % (519233)CaDiCaL version: 2.1.3
% 0.57/0.47 % (519233)Termination reason: Instruction limit
% 0.57/0.47 % (519233)Termination phase: shuffling
% 0.57/0.47 % (519233)Time elapsed: 0.002 s
% 0.57/0.47 % (519233)Peak memory usage: 9 MB
% 0.57/0.47 % (519233)Instructions burned: 10 (million)
% 0.57/0.47 % (519216)Instruction limit reached!
% 0.57/0.47 % (519216)------------------------------
% 0.57/0.47 % (519216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.47 % (519216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.47 % (519216)CaDiCaL version: 2.1.3
% 0.57/0.47 % (519216)Termination reason: Instruction limit
% 0.57/0.47 % (519216)Termination phase: Preprocessing 3
% 0.57/0.47 % (519216)Time elapsed: 0.040 s
% 0.57/0.47 % (519216)Peak memory usage: 13 MB
% 0.57/0.47 % (519216)Instructions burned: 87 (million)
% 0.57/0.47 % (519238)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=1567403481:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.57/0.47 % (519235)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2755472583:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.57/0.47 % (519221)Instruction limit reached!
% 0.57/0.47 % (519221)------------------------------
% 0.57/0.47 % (519221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.47 % (519221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.47 % (519221)CaDiCaL version: 2.1.3
% 0.57/0.47 % (519221)Termination reason: Instruction limit
% 0.57/0.47 % (519221)Termination phase: Preprocessing 3
% 0.57/0.47 % (519221)Time elapsed: 0.043 s
% 0.57/0.47 % (519221)Peak memory usage: 12 MB
% 0.57/0.47 % (519221)Instructions burned: 75 (million)
% 0.57/0.47 % (519235)Instruction limit reached!
% 0.57/0.47 % (519235)------------------------------
% 0.57/0.47 % (519235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.47 % (519235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.47 % (519235)CaDiCaL version: 2.1.3
% 0.57/0.47 % (519235)Termination reason: Instruction limit
% 0.57/0.47 % (519235)Termination phase: shuffling
% 0.57/0.47 % (519235)Time elapsed: 0.006 s
% 0.57/0.47 % (519235)Peak memory usage: 10 MB
% 0.57/0.47 % (519235)Instructions burned: 14 (million)
% 0.57/0.47 % (519237)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
% 0.57/0.47 % (519237)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.47 % (519239)lrs+10_1_si=on:cs=on:random_seed=1594495271:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.57/0.47 % (519237)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3820489020:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.57/0.47 % (519238)Instruction limit reached!
% 0.57/0.47 % (519238)------------------------------
% 0.57/0.47 % (519238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (519238)CaDiCaL version: 2.1.3
% 1.37/0.51 % (519238)Termination reason: Instruction limit
% 1.37/0.51 % (519238)Termination phase: Saturation
% 1.37/0.51 % (519238)Time elapsed: 0.019 s
% 1.37/0.51 % (519238)Peak memory usage: 12 MB
% 1.37/0.51 % (519238)Instructions burned: 89 (million)
% 1.37/0.51 % (519242)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.37/0.51 % (519239)Instruction limit reached!
% 1.37/0.51 % (519239)------------------------------
% 1.37/0.51 % (519239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (519239)CaDiCaL version: 2.1.3
% 1.37/0.51 % (519239)Termination reason: Instruction limit
% 1.37/0.51 % (519239)Termination phase: shuffling
% 1.37/0.51 % (519239)Time elapsed: 0.005 s
% 1.37/0.51 % (519239)Peak memory usage: 10 MB
% 1.37/0.51 % (519239)Instructions burned: 10 (million)
% 1.37/0.51 % (519242)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=2656555685:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.37/0.51 % (519242)Instruction limit reached!
% 1.37/0.51 % (519242)------------------------------
% 1.37/0.51 % (519242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (519242)CaDiCaL version: 2.1.3
% 1.37/0.51 % (519242)Termination reason: Instruction limit
% 1.37/0.51 % (519242)Termination phase: shuffling
% 1.37/0.51 % (519242)Time elapsed: 0.001 s
% 1.37/0.51 % (519242)Peak memory usage: 9 MB
% 1.37/0.51 % (519242)Instructions burned: 2 (million)
% 1.37/0.51 % (519243)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2696095727:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.37/0.51 % (519246)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2844927987:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.37/0.51 % (519237)Instruction limit reached!
% 1.37/0.51 % (519237)------------------------------
% 1.37/0.51 % (519237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (519237)CaDiCaL version: 2.1.3
% 1.37/0.51 % (519237)Termination reason: Instruction limit
% 1.37/0.51 % (519237)Termination phase: shuffling
% 1.37/0.51 % (519237)Time elapsed: 0.012 s
% 1.37/0.51 % (519237)Peak memory usage: 10 MB
% 1.37/0.51 % (519237)Instructions burned: 28 (million)
% 1.37/0.51 % (519243)Instruction limit reached!
% 1.37/0.51 % (519243)------------------------------
% 1.37/0.51 % (519243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.51 % (519243)CaDiCaL version: 2.1.3
% 1.37/0.51 % (519243)Termination reason: Instruction limit
% 1.37/0.51 % (519243)Termination phase: Saturation
% 1.37/0.51 % (519243)Time elapsed: 0.017 s
% 1.37/0.51 % (519243)Peak memory usage: 11 MB
% 1.37/0.51 % (519243)Instructions burned: 38 (million)
% 1.37/0.51 % (519252)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1937548381:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.37/0.51 % (519247)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=85023017:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.37/0.51 % (519249)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1425075943:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.37/0.51 % (519253)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3603421753:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.37/0.51 % (519222)Instruction limit reached!
% 1.37/0.51 % (519222)------------------------------
% 1.37/0.51 % (519222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.51 % (519222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519222)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519222)Termination reason: Instruction limit
% 1.37/0.56 % (519222)Termination phase: Property scanning
% 1.37/0.56 % (519222)Time elapsed: 0.108 s
% 1.37/0.56 % (519222)Peak memory usage: 13 MB
% 1.37/0.56 % (519222)Instructions burned: 159 (million)
% 1.37/0.56 % (519253)Instruction limit reached!
% 1.37/0.56 % (519253)------------------------------
% 1.37/0.56 % (519253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519253)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519253)Termination reason: Instruction limit
% 1.37/0.56 % (519253)Termination phase: shuffling
% 1.37/0.56 % (519253)Time elapsed: 0.007 s
% 1.37/0.56 % (519253)Peak memory usage: 10 MB
% 1.37/0.56 % (519253)Instructions burned: 16 (million)
% 1.37/0.56 % (519247)Instruction limit reached!
% 1.37/0.56 % (519247)------------------------------
% 1.37/0.56 % (519247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519247)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519247)Termination reason: Instruction limit
% 1.37/0.56 % (519247)Termination phase: Property scanning
% 1.37/0.56 % (519247)Time elapsed: 0.019 s
% 1.37/0.56 % (519247)Peak memory usage: 10 MB
% 1.37/0.56 % (519247)Instructions burned: 28 (million)
% 1.37/0.56 % (519249)Instruction limit reached!
% 1.37/0.56 % (519249)------------------------------
% 1.37/0.56 % (519249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519249)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519249)Termination reason: Instruction limit
% 1.37/0.56 % (519249)Termination phase: shuffling
% 1.37/0.56 % (519249)Time elapsed: 0.011 s
% 1.37/0.56 % (519249)Peak memory usage: 10 MB
% 1.37/0.56 % (519249)Instructions burned: 16 (million)
% 1.37/0.56 % (519259)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=185777707:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.37/0.56 % (519260)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=126221768:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.37/0.56 % (519246)Instruction limit reached!
% 1.37/0.56 % (519246)------------------------------
% 1.37/0.56 % (519246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519246)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519246)Termination reason: Instruction limit
% 1.37/0.56 % (519246)Termination phase: Saturation
% 1.37/0.56 % (519246)Time elapsed: 0.062 s
% 1.37/0.56 % (519246)Peak memory usage: 15 MB
% 1.37/0.56 % (519246)Instructions burned: 249 (million)
% 1.37/0.56 % (519261)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1185404450:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.37/0.56 % (519264)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.37/0.56 % (519264)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.37/0.56 % (519259)Instruction limit reached!
% 1.37/0.56 % (519259)------------------------------
% 1.37/0.56 % (519259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519259)CaDiCaL version: 2.1.3
% 1.37/0.56 % (519259)Termination reason: Instruction limit
% 1.37/0.56 % (519259)Termination phase: shuffling
% 1.37/0.56 % (519259)Time elapsed: 0.012 s
% 1.37/0.56 % (519259)Peak memory usage: 10 MB
% 1.37/0.56 % (519259)Instructions burned: 27 (million)
% 1.37/0.56 % (519260)Instruction limit reached!
% 1.37/0.56 % (519260)------------------------------
% 1.37/0.56 % (519260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.37/0.56 % (519260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.37/0.56 % (519264)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=2572783679:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.93/0.60 % (519260)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519260)Termination reason: Instruction limit
% 1.93/0.60 % (519260)Termination phase: Property scanning
% 1.93/0.60 % (519260)Time elapsed: 0.011 s
% 1.93/0.60 % (519260)Peak memory usage: 10 MB
% 1.93/0.60 % (519260)Instructions burned: 25 (million)
% 1.93/0.60 % (519264)Instruction limit reached!
% 1.93/0.60 % (519264)------------------------------
% 1.93/0.60 % (519264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.60 % (519264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.60 % (519264)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519264)Termination reason: Instruction limit
% 1.93/0.60 % (519264)Termination phase: shuffling
% 1.93/0.60 % (519264)Time elapsed: 0.004 s
% 1.93/0.60 % (519264)Peak memory usage: 10 MB
% 1.93/0.60 % (519264)Instructions burned: 18 (million)
% 1.93/0.60 % (519258)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=397278876: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)
% 1.93/0.60 % (519258)Instruction limit reached!
% 1.93/0.60 % (519258)------------------------------
% 1.93/0.60 % (519258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.60 % (519258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.60 % (519258)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519258)Termination reason: Instruction limit
% 1.93/0.60 % (519258)Termination phase: shuffling
% 1.93/0.60 % (519258)Time elapsed: 0.005 s
% 1.93/0.60 % (519258)Peak memory usage: 10 MB
% 1.93/0.60 % (519258)Instructions burned: 2 (million)
% 1.93/0.60 % (519269)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=55603807:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.93/0.60 % (519267)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.93/0.60 % (519269)Instruction limit reached!
% 1.93/0.60 % (519269)------------------------------
% 1.93/0.60 % (519269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.60 % (519269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.60 % (519269)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519269)Termination reason: Instruction limit
% 1.93/0.60 % (519269)Termination phase: shuffling
% 1.93/0.60 % (519269)Time elapsed: 0.002 s
% 1.93/0.60 % (519269)Peak memory usage: 10 MB
% 1.93/0.60 % (519269)Instructions burned: 8 (million)
% 1.93/0.60 % (519267)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=3181247549:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.93/0.60 % (519267)Instruction limit reached!
% 1.93/0.60 % (519267)------------------------------
% 1.93/0.60 % (519267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.60 % (519267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.60 % (519267)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519267)Termination reason: Instruction limit
% 1.93/0.60 % (519267)Termination phase: shuffling
% 1.93/0.60 % (519267)Time elapsed: 0.004 s
% 1.93/0.60 % (519267)Peak memory usage: 10 MB
% 1.93/0.60 % (519267)Instructions burned: 9 (million)
% 1.93/0.60 % (519268)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=2689398673:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.93/0.60 % (519261)Instruction limit reached!
% 1.93/0.60 % (519261)------------------------------
% 1.93/0.60 % (519261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.60 % (519261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.60 % (519261)CaDiCaL version: 2.1.3
% 1.93/0.60 % (519261)Termination reason: Instruction limit
% 1.93/0.60 % (519261)Termination phase: Preprocessing 3
% 1.93/0.60 % (519261)Time elapsed: 0.034 s
% 1.93/0.60 % (519261)Peak memory usage: 11 MB
% 1.93/0.60 % (519261)Instructions burned: 62 (million)
% 1.93/0.60 % (519273)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1798571766:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.93/0.60 % (519273)Instruction limit reached!
% 1.93/0.60 % (519273)------------------------------
% 1.93/0.60 % (519273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519273)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519273)Termination reason: Instruction limit
% 2.18/0.69 % (519273)Termination phase: shuffling
% 2.18/0.69 % (519273)Time elapsed: 0.005 s
% 2.18/0.69 % (519273)Peak memory usage: 10 MB
% 2.18/0.69 % (519273)Instructions burned: 24 (million)
% 2.18/0.69 % (519271)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=540707982:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.18/0.69 % (519268)Instruction limit reached!
% 2.18/0.69 % (519268)------------------------------
% 2.18/0.69 % (519268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519268)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519268)Termination reason: Instruction limit
% 2.18/0.69 % (519268)Termination phase: Property scanning
% 2.18/0.69 % (519268)Time elapsed: 0.014 s
% 2.18/0.69 % (519268)Peak memory usage: 10 MB
% 2.18/0.69 % (519268)Instructions burned: 33 (million)
% 2.18/0.69 % (519275)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1675314955:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.18/0.69 % (519279)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2901522460:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.18/0.69 % (519278)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4207831116:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.18/0.69 % (519271)Instruction limit reached!
% 2.18/0.69 % (519271)------------------------------
% 2.18/0.69 % (519271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519271)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519271)Termination reason: Instruction limit
% 2.18/0.69 % (519271)Termination phase: shuffling
% 2.18/0.69 % (519271)Time elapsed: 0.010 s
% 2.18/0.69 % (519271)Peak memory usage: 10 MB
% 2.18/0.69 % (519271)Instructions burned: 24 (million)
% 2.18/0.69 % (519282)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=884881799:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.18/0.69 % (519285)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.18/0.69 % (519285)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2539932369:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.18/0.69 % (519285)Instruction limit reached!
% 2.18/0.69 % (519285)------------------------------
% 2.18/0.69 % (519285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519285)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519285)Termination reason: Instruction limit
% 2.18/0.69 % (519285)Termination phase: shuffling
% 2.18/0.69 % (519285)Time elapsed: 0.004 s
% 2.18/0.69 % (519285)Peak memory usage: 10 MB
% 2.18/0.69 % (519285)Instructions burned: 8 (million)
% 2.18/0.69 % (519282)Instruction limit reached!
% 2.18/0.69 % (519282)------------------------------
% 2.18/0.69 % (519282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519282)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519282)Termination reason: Instruction limit
% 2.18/0.69 % (519282)Termination phase: Naming
% 2.18/0.69 % (519282)Time elapsed: 0.020 s
% 2.18/0.69 % (519282)Peak memory usage: 11 MB
% 2.18/0.69 % (519282)Instructions burned: 46 (million)
% 2.18/0.69 % (519279)Instruction limit reached!
% 2.18/0.69 % (519279)------------------------------
% 2.18/0.69 % (519279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.69 % (519279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.69 % (519279)CaDiCaL version: 2.1.3
% 2.18/0.69 % (519279)Termination reason: Instruction limit
% 2.18/0.69 % (519279)Termination phase: Property scanning
% 2.18/0.69 % (519279)Time elapsed: 0.043 s
% 2.53/0.78 % (519279)Peak memory usage: 13 MB
% 2.53/0.78 % (519279)Instructions burned: 197 (million)
% 2.53/0.78 % (519288)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3685898392:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.53/0.78 % (519252)Instruction limit reached!
% 2.53/0.78 % (519252)------------------------------
% 2.53/0.78 % (519252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.78 % (519252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.78 % (519252)CaDiCaL version: 2.1.3
% 2.53/0.78 % (519252)Termination reason: Instruction limit
% 2.53/0.78 % (519252)Termination phase: Saturation
% 2.53/0.78 % (519252)Time elapsed: 0.148 s
% 2.53/0.78 % (519252)Peak memory usage: 16 MB
% 2.53/0.78 % (519252)Instructions burned: 328 (million)
% 2.53/0.78 % (519289)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=2192476896: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)
% 2.53/0.78 % (519291)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.53/0.78 % (519291)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2662855950:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.53/0.78 % (519291)Instruction limit reached!
% 2.53/0.78 % (519291)------------------------------
% 2.53/0.78 % (519291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.78 % (519291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.78 % (519291)CaDiCaL version: 2.1.3
% 2.53/0.78 % (519291)Termination reason: Instruction limit
% 2.53/0.78 % (519291)Termination phase: shuffling
% 2.53/0.78 % (519291)Time elapsed: 0.003 s
% 2.53/0.78 % (519291)Peak memory usage: 10 MB
% 2.53/0.78 % (519291)Instructions burned: 11 (million)
% 2.53/0.78 % (519292)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1341350382:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.53/0.78 % (519278)Instruction limit reached!
% 2.53/0.78 % (519278)------------------------------
% 2.53/0.78 % (519278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.78 % (519278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.78 % (519278)CaDiCaL version: 2.1.3
% 2.53/0.78 % (519278)Termination reason: Instruction limit
% 2.53/0.78 % (519278)Termination phase: Function definition elimination
% 2.53/0.78 % (519278)Time elapsed: 0.066 s
% 2.53/0.78 % (519278)Peak memory usage: 13 MB
% 2.53/0.78 % (519278)Instructions burned: 144 (million)
% 2.53/0.78 % (519295)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4087409286:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.53/0.78 % (519295)Instruction limit reached!
% 2.53/0.78 % (519295)------------------------------
% 2.53/0.78 % (519295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.78 % (519295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.78 % (519295)CaDiCaL version: 2.1.3
% 2.53/0.78 % (519295)Termination reason: Instruction limit
% 2.53/0.78 % (519295)Termination phase: shuffling
% 2.53/0.78 % (519295)Time elapsed: 0.005 s
% 2.53/0.78 % (519295)Peak memory usage: 10 MB
% 2.53/0.78 % (519295)Instructions burned: 22 (million)
% 2.53/0.78 % (519292)Instruction limit reached!
% 2.53/0.78 % (519292)------------------------------
% 2.53/0.78 % (519292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.53/0.78 % (519292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.78 % (519292)CaDiCaL version: 2.1.3
% 2.53/0.78 % (519292)Termination reason: Instruction limit
% 2.53/0.78 % (519292)Termination phase: shuffling
% 2.53/0.78 % (519292)Time elapsed: 0.009 s
% 2.53/0.78 % (519292)Peak memory usage: 10 MB
% 2.53/0.78 % (519292)Instructions burned: 22 (million)
% 2.53/0.78 % (519299)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=1308208173:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.04/0.87 % (519297)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=2467659230:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.04/0.87 % (519300)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=3875537455: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)
% 3.04/0.87 % (519300)Instruction limit reached!
% 3.04/0.87 % (519300)------------------------------
% 3.04/0.87 % (519300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.87 % (519300)CaDiCaL version: 2.1.3
% 3.04/0.87 % (519300)Termination reason: Instruction limit
% 3.04/0.87 % (519300)Termination phase: SInE selection
% 3.04/0.87 % (519300)Time elapsed: 0.019 s
% 3.04/0.87 % (519300)Peak memory usage: 10 MB
% 3.04/0.87 % (519300)Instructions burned: 45 (million)
% 3.04/0.87 % (519289)Instruction limit reached!
% 3.04/0.87 % (519289)------------------------------
% 3.04/0.87 % (519289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.87 % (519289)CaDiCaL version: 2.1.3
% 3.04/0.87 % (519289)Termination reason: Instruction limit
% 3.04/0.87 % (519289)Termination phase: Property scanning
% 3.04/0.87 % (519289)Time elapsed: 0.073 s
% 3.04/0.87 % (519289)Peak memory usage: 13 MB
% 3.04/0.87 % (519289)Instructions burned: 170 (million)
% 3.04/0.87 % (519288)Instruction limit reached!
% 3.04/0.87 % (519288)------------------------------
% 3.04/0.87 % (519288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.87 % (519288)CaDiCaL version: 2.1.3
% 3.04/0.87 % (519288)Termination reason: Instruction limit
% 3.04/0.87 % (519288)Termination phase: Saturation
% 3.04/0.87 % (519288)Time elapsed: 0.083 s
% 3.04/0.87 % (519288)Peak memory usage: 15 MB
% 3.04/0.87 % (519288)Instructions burned: 184 (million)
% 3.04/0.87 % (519304)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1838404536:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.04/0.87 % (519306)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.04/0.87 % (519219)Instruction limit reached!
% 3.04/0.87 % (519219)------------------------------
% 3.04/0.87 % (519219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.87 % (519219)CaDiCaL version: 2.1.3
% 3.04/0.87 % (519219)Termination reason: Instruction limit
% 3.04/0.87 % (519219)Termination phase: Saturation
% 3.04/0.87 % (519219)Time elapsed: 0.340 s
% 3.04/0.87 % (519219)Peak memory usage: 18 MB
% 3.04/0.87 % (519219)Instructions burned: 635 (million)
% 3.04/0.87 % (519305)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1581649563: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)
% 3.04/0.87 % (519306)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3026273329:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.04/0.87 % (519305)Instruction limit reached!
% 3.04/0.87 % (519305)------------------------------
% 3.04/0.87 % (519305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.87 % (519305)CaDiCaL version: 2.1.3
% 3.04/0.87 % (519305)Termination reason: Instruction limit
% 3.04/0.87 % (519305)Termination phase: shuffling
% 3.04/0.87 % (519305)Time elapsed: 0.010 s
% 3.04/0.87 % (519305)Peak memory usage: 10 MB
% 3.04/0.87 % (519305)Instructions burned: 23 (million)
% 3.04/0.87 % (519309)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3568707110:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.04/0.87 % (519309)Instruction limit reached!
% 3.04/0.87 % (519309)------------------------------
% 3.04/0.87 % (519309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.87 % (519309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519309)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519309)Termination reason: Instruction limit
% 5.14/1.07 % (519309)Termination phase: shuffling
% 5.14/1.07 % (519309)Time elapsed: 0.006 s
% 5.14/1.07 % (519309)Peak memory usage: 10 MB
% 5.14/1.07 % (519309)Instructions burned: 14 (million)
% 5.14/1.07 % (519311)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=2947789664:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.14/1.07 % (519313)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2662309862:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.14/1.07 % (519311)Instruction limit reached!
% 5.14/1.07 % (519311)------------------------------
% 5.14/1.07 % (519311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.14/1.07 % (519311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519311)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519311)Termination reason: Instruction limit
% 5.14/1.07 % (519311)Termination phase: SInE selection
% 5.14/1.07 % (519311)Time elapsed: 0.028 s
% 5.14/1.07 % (519311)Peak memory usage: 11 MB
% 5.14/1.07 % (519311)Instructions burned: 66 (million)
% 5.14/1.07 % (519313)Instruction limit reached!
% 5.14/1.07 % (519313)------------------------------
% 5.14/1.07 % (519313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.14/1.07 % (519313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519313)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519313)Termination reason: Instruction limit
% 5.14/1.07 % (519313)Termination phase: Preprocessing 3
% 5.14/1.07 % (519313)Time elapsed: 0.023 s
% 5.14/1.07 % (519313)Peak memory usage: 11 MB
% 5.14/1.07 % (519313)Instructions burned: 51 (million)
% 5.14/1.07 % (519316)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2771172127:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.14/1.07 % (519306)Instruction limit reached!
% 5.14/1.07 % (519306)------------------------------
% 5.14/1.07 % (519306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.14/1.07 % (519306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519306)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519306)Termination reason: Instruction limit
% 5.14/1.07 % (519306)Termination phase: Saturation
% 5.14/1.07 % (519306)Time elapsed: 0.086 s
% 5.14/1.07 % (519306)Peak memory usage: 14 MB
% 5.14/1.07 % (519306)Instructions burned: 202 (million)
% 5.14/1.07 % (519317)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2348126160:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.14/1.07 % (519316)Instruction limit reached!
% 5.14/1.07 % (519316)------------------------------
% 5.14/1.07 % (519316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.14/1.07 % (519316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519316)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519316)Termination reason: Instruction limit
% 5.14/1.07 % (519316)Termination phase: Property scanning
% 5.14/1.07 % (519316)Time elapsed: 0.014 s
% 5.14/1.07 % (519316)Peak memory usage: 10 MB
% 5.14/1.07 % (519316)Instructions burned: 31 (million)
% 5.14/1.07 % (519320)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=3059609750:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 5.14/1.07 % (519321)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=803854163:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.14/1.07 % (519304)Refutation not found, incomplete strategy
% 5.14/1.07 % (519304)------------------------------
% 5.14/1.07 % (519304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.14/1.07 % (519304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.07 % (519304)CaDiCaL version: 2.1.3
% 5.14/1.07 % (519304)Termination reason: Refutation not found, incomplete strategy
% 5.14/1.07 % (519304)Time elapsed: 0.124 s
% 5.14/1.07 % (519304)Peak memory usage: 16 MB
% 5.14/1.07 % (519304)Instructions burned: 271 (million)
% 5.14/1.07 % (519304)------------------------------
% 5.14/1.07 % (519304)------------------------------
% 5.80/1.17 % (519320)Instruction limit reached!
% 5.80/1.17 % (519320)------------------------------
% 5.80/1.17 % (519320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519320)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519320)Termination reason: Instruction limit
% 5.80/1.17 % (519320)Termination phase: Property scanning
% 5.80/1.17 % (519320)Time elapsed: 0.015 s
% 5.80/1.17 % (519320)Peak memory usage: 10 MB
% 5.80/1.17 % (519320)Instructions burned: 35 (million)
% 5.80/1.17 % (519324)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.80/1.17 % (519324)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3524513305:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 5.80/1.17 % (519321)Instruction limit reached!
% 5.80/1.17 % (519321)------------------------------
% 5.80/1.17 % (519321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519321)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519321)Termination reason: Instruction limit
% 5.80/1.17 % (519321)Termination phase: Preprocessing 3
% 5.80/1.17 % (519321)Time elapsed: 0.030 s
% 5.80/1.17 % (519321)Peak memory usage: 12 MB
% 5.80/1.17 % (519321)Instructions burned: 68 (million)
% 5.80/1.17 % (519325)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3142776773:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.80/1.17 % (519297)Instruction limit reached!
% 5.80/1.17 % (519297)------------------------------
% 5.80/1.17 % (519297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519297)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519297)Termination reason: Instruction limit
% 5.80/1.17 % (519297)Termination phase: Saturation
% 5.80/1.17 % (519297)Time elapsed: 0.203 s
% 5.80/1.17 % (519297)Peak memory usage: 15 MB
% 5.80/1.17 % (519297)Instructions burned: 317 (million)
% 5.80/1.17 % (519317)Instruction limit reached!
% 5.80/1.17 % (519317)------------------------------
% 5.80/1.17 % (519317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519317)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519317)Termination reason: Instruction limit
% 5.80/1.17 % (519317)Termination phase: Property scanning
% 5.80/1.17 % (519317)Time elapsed: 0.061 s
% 5.80/1.17 % (519317)Peak memory usage: 13 MB
% 5.80/1.17 % (519317)Instructions burned: 138 (million)
% 5.80/1.17 % (519327)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1625070706:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.80/1.17 % (519329)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=397231936:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.80/1.17 % (519330)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1574282342:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.80/1.17 % (519299)Instruction limit reached!
% 5.80/1.17 % (519299)------------------------------
% 5.80/1.17 % (519299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519299)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519299)Termination reason: Instruction limit
% 5.80/1.17 % (519299)Termination phase: Saturation
% 5.80/1.17 % (519299)Time elapsed: 0.250 s
% 5.80/1.17 % (519299)Peak memory usage: 19 MB
% 5.80/1.17 % (519299)Instructions burned: 855 (million)
% 5.80/1.17 % (519334)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3027902966:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.80/1.17 % (519327)Instruction limit reached!
% 5.80/1.17 % (519327)------------------------------
% 5.80/1.17 % (519327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.17 % (519327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.17 % (519327)CaDiCaL version: 2.1.3
% 5.80/1.17 % (519327)Termination reason: Instruction limit
% 5.80/1.17 % (519327)Termination phase: Property scanning
% 5.80/1.17 % (519327)Time elapsed: 0.043 s
% 5.86/1.20 % (519327)Peak memory usage: 13 MB
% 5.86/1.20 % (519327)Instructions burned: 97 (million)
% 5.86/1.20 % (519324)Instruction limit reached!
% 5.86/1.20 % (519324)------------------------------
% 5.86/1.20 % (519324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519324)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519324)Termination reason: Instruction limit
% 5.86/1.20 % (519324)Termination phase: Saturation
% 5.86/1.20 % (519324)Time elapsed: 0.074 s
% 5.86/1.20 % (519324)Peak memory usage: 12 MB
% 5.86/1.20 % (519324)Instructions burned: 182 (million)
% 5.86/1.20 % (519336)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1053981803:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.86/1.20 % (519337)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3643421881:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.86/1.20 % (519337)Instruction limit reached!
% 5.86/1.20 % (519337)------------------------------
% 5.86/1.20 % (519337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519337)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519337)Termination reason: Instruction limit
% 5.86/1.20 % (519337)Termination phase: Property scanning
% 5.86/1.20 % (519337)Time elapsed: 0.019 s
% 5.86/1.20 % (519337)Peak memory usage: 10 MB
% 5.86/1.20 % (519337)Instructions burned: 45 (million)
% 5.86/1.20 % (519325)Instruction limit reached!
% 5.86/1.20 % (519325)------------------------------
% 5.86/1.20 % (519325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519325)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519325)Termination reason: Instruction limit
% 5.86/1.20 % (519325)Termination phase: Saturation
% 5.86/1.20 % (519325)Time elapsed: 0.107 s
% 5.86/1.20 % (519325)Peak memory usage: 15 MB
% 5.86/1.20 % (519325)Instructions burned: 246 (million)
% 5.86/1.20 % (519340)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4028989335:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 5.86/1.20 % (519341)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1950112528:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 5.86/1.20 % (519336)Refutation not found, incomplete strategy
% 5.86/1.20 % (519336)------------------------------
% 5.86/1.20 % (519336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519336)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519336)Termination reason: Refutation not found, incomplete strategy
% 5.86/1.20 % (519336)Time elapsed: 0.057 s
% 5.86/1.20 % (519336)Peak memory usage: 13 MB
% 5.86/1.20 % (519336)Instructions burned: 120 (million)
% 5.86/1.20 % (519336)------------------------------
% 5.86/1.20 % (519336)------------------------------
% 5.86/1.20 % (519344)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1750316174:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.86/1.20 % (519344)Instruction limit reached!
% 5.86/1.20 % (519344)------------------------------
% 5.86/1.20 % (519344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519344)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519344)Termination reason: Instruction limit
% 5.86/1.20 % (519344)Termination phase: Property scanning
% 5.86/1.20 % (519344)Time elapsed: 0.047 s
% 5.86/1.20 % (519344)Peak memory usage: 13 MB
% 5.86/1.20 % (519344)Instructions burned: 96 (million)
% 5.86/1.20 % (519347)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=1159556911:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 5.86/1.20 % (519347)Instruction limit reached!
% 5.86/1.20 % (519347)------------------------------
% 5.86/1.20 % (519347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519347)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519347)Termination reason: Instruction limit
% 5.86/1.20 % (519347)Termination phase: Property scanning
% 5.86/1.20 % (519347)Time elapsed: 0.028 s
% 5.86/1.20 % (519347)Peak memory usage: 11 MB
% 5.86/1.20 % (519347)Instructions burned: 67 (million)
% 5.86/1.20 % (519334)Instruction limit reached!
% 5.86/1.20 % (519334)------------------------------
% 5.86/1.20 % (519334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519334)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519334)Termination reason: Instruction limit
% 5.86/1.20 % (519334)Termination phase: Saturation
% 5.86/1.20 % (519334)Time elapsed: 0.217 s
% 5.86/1.20 % (519334)Peak memory usage: 18 MB
% 5.86/1.20 % (519334)Instructions burned: 515 (million)
% 5.86/1.20 % (519350)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=1835144343: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_2992 on theBenchmark for (2992ds/105Mi)
% 5.86/1.20 % (519351)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=2744670509:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 5.86/1.20 % (519329)Instruction limit reached!
% 5.86/1.20 % (519329)------------------------------
% 5.86/1.20 % (519329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519329)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519329)Termination reason: Instruction limit
% 5.86/1.20 % (519329)Termination phase: Saturation
% 5.86/1.20 % (519329)Time elapsed: 0.291 s
% 5.86/1.20 % (519329)Peak memory usage: 18 MB
% 5.86/1.20 % (519329)Instructions burned: 427 (million)
% 5.86/1.20 % (519340)Refutation not found, incomplete strategy
% 5.86/1.20 % (519340)------------------------------
% 5.86/1.20 % (519340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519340)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519340)Termination reason: Refutation not found, incomplete strategy
% 5.86/1.20 % (519340)Time elapsed: 0.199 s
% 5.86/1.20 % (519340)Peak memory usage: 17 MB
% 5.86/1.20 % (519340)Instructions burned: 412 (million)
% 5.86/1.20 % (519340)------------------------------
% 5.86/1.20 % (519340)------------------------------
% 5.86/1.20 % (519350)Instruction limit reached!
% 5.86/1.20 % (519350)------------------------------
% 5.86/1.20 % (519350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519350)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519350)Termination reason: Instruction limit
% 5.86/1.20 % (519350)Termination phase: Saturation
% 5.86/1.20 % (519350)Time elapsed: 0.044 s
% 5.86/1.20 % (519350)Peak memory usage: 12 MB
% 5.86/1.20 % (519350)Instructions burned: 106 (million)
% 5.86/1.20 % (519341) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-519211-519341"...
% 5.86/1.20 % (519356)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=431543302:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 5.86/1.20 % (519355)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3683610188:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 5.86/1.20 % (519354)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2871306130:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 5.86/1.20 % (519356)Instruction limit reached!
% 5.86/1.20 % (519356)------------------------------
% 5.86/1.20 % (519356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.20 % (519356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.20 % (519356)CaDiCaL version: 2.1.3
% 5.86/1.20 % (519356)Termination reason: Instruction limit
% 5.86/1.20 % (519356)Termination phase: Property scanning
% 5.86/1.20 % (519356)Time elapsed: 0.015 s
% 5.86/1.20 % (519356)Peak memory usage: 10 MB
% 5.86/1.20 % (519356)Instructions burned: 36 (million)
% 5.86/1.20 % (519360)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2814738640:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/91Mi)
% 5.86/1.20 % (519341)...printing done.
% 5.86/1.20 % (519341)Refutation found. Thanks to Tanya!
% 5.86/1.20 % SZS status Theorem for theBenchmark
% 5.86/1.20 % SZS output start Proof for theBenchmark
% 5.86/1.20 thf(type_def_5, type, term: $tType).
% 5.86/1.20 thf(type_def_6, type, subst: $tType).
% 5.86/1.20 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 5.86/1.20 thf(type_def_8, type, d_term: $tType).
% 5.86/1.20 thf(type_def_9, type, d_subst: $tType).
% 5.86/1.20 thf(func_def_0, type, one: term).
% 5.86/1.20 thf(func_def_1, type, ap: (term > term > term)).
% 5.86/1.20 thf(func_def_2, type, lam: (term > term)).
% 5.86/1.20 thf(func_def_3, type, sub: (term > subst > term)).
% 5.86/1.20 thf(func_def_4, type, id: subst).
% 5.86/1.20 thf(func_def_5, type, sh: subst).
% 5.86/1.20 thf(func_def_6, type, push: (term > subst > subst)).
% 5.86/1.20 thf(func_def_7, type, comp: (subst > subst > subst)).
% 5.86/1.20 thf(func_def_8, type, var: (term > $o)).
% 5.86/1.20 thf(func_def_9, type, pushprop_lem1v2: $o).
% 5.86/1.20 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 5.86/1.20 thf(func_def_11, type, axmap: $o).
% 5.86/1.20 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 5.86/1.20 thf(func_def_13, type, shinj: $o).
% 5.86/1.20 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 5.86/1.20 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 5.86/1.20 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 5.86/1.20 thf(func_def_17, type, induction2lem: $o).
% 5.86/1.20 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 5.86/1.20 thf(func_def_19, type, axvarshift: $o).
% 5.86/1.20 thf(func_def_20, type, hoasapinj2: $o).
% 5.86/1.20 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 5.86/1.20 thf(func_def_22, type, hoasapinj1: $o).
% 5.86/1.20 thf(func_def_23, type, ulamvar1: $o).
% 5.86/1.20 thf(func_def_24, type, induction2lem_lthm: $o).
% 5.86/1.20 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 5.86/1.20 thf(func_def_26, type, apnotvar: $o).
% 5.86/1.20 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 5.86/1.20 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 5.86/1.20 thf(func_def_29, type, hoasinduction_lthm: $o).
% 5.86/1.20 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 5.86/1.20 thf(func_def_31, type, hoaslaminj: $o).
% 5.86/1.20 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 5.86/1.20 thf(func_def_33, type, induction2lem_gthm: $o).
% 5.86/1.20 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 5.86/1.20 thf(func_def_35, type, hoasinduction_lem3: $o).
% 5.86/1.20 thf(func_def_36, type, hoasinduction_lem2: $o).
% 5.86/1.20 thf(func_def_37, type, termmset_lthm: $o).
% 5.86/1.20 thf(func_def_38, type, hoasinduction_lem1: $o).
% 5.86/1.20 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 5.86/1.20 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 5.86/1.20 thf(func_def_41, type, hoasapnotvar: $o).
% 5.86/1.20 thf(func_def_42, type, hoasinduction_lem0: $o).
% 5.86/1.20 thf(func_def_43, type, hoasinduction: $o).
% 5.86/1.20 thf(func_def_44, type, hoasinduction_gthm: $o).
% 5.86/1.20 thf(func_def_45, type, axapp: $o).
% 5.86/1.20 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 5.86/1.20 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 5.86/1.20 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 5.86/1.20 thf(func_def_49, type, ulamvarind: $o).
% 5.86/1.20 thf(func_def_50, type, induction: $o).
% 5.86/1.20 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 5.86/1.20 thf(func_def_52, type, termmset_gthm: $o).
% 5.86/1.20 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 5.86/1.20 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 5.86/1.20 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 5.86/1.20 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 5.86/1.20 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 5.86/1.20 thf(func_def_58, type, pushprop_lem2v2: $o).
% 5.86/1.20 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 5.86/1.20 thf(func_def_60, type, axclos: $o).
% 5.86/1.20 thf(func_def_61, type, axassoc: $o).
% 5.86/1.20 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 5.86/1.20 thf(func_def_63, type, pushprop_lthm: $o).
% 5.86/1.20 thf(func_def_64, type, apinj2: $o).
% 5.86/1.20 thf(func_def_65, type, apinj1: $o).
% 5.86/1.20 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 5.86/1.20 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 5.86/1.20 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 5.86/1.20 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 5.86/1.20 thf(func_def_70, type, axvarcons: $o).
% 5.86/1.20 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 5.86/1.20 thf(func_def_72, type, axscons: $o).
% 5.86/1.20 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 5.86/1.20 thf(func_def_74, type, axidr: $o).
% 5.86/1.20 thf(func_def_75, type, pushprop_lem1: $o).
% 5.86/1.20 thf(func_def_76, type, laminj: $o).
% 5.86/1.20 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 5.86/1.20 thf(func_def_78, type, pushprop_lem0: $o).
% 5.86/1.20 thf(func_def_79, type, pushprop_gthm: $o).
% 5.86/1.20 thf(func_def_80, type, axabs: $o).
% 5.86/1.20 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 5.86/1.20 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 5.86/1.20 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 5.86/1.20 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 5.86/1.20 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 5.86/1.20 thf(func_def_86, type, lamnotap: $o).
% 5.86/1.20 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 5.86/1.20 thf(func_def_88, type, hoaslamnotvar: $o).
% 5.86/1.20 thf(func_def_89, type, axidl: $o).
% 5.86/1.20 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 5.86/1.20 thf(func_def_91, type, induction2_lthm: $o).
% 5.86/1.20 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 5.86/1.20 thf(func_def_93, type, substmonoid_lthm: $o).
% 5.86/1.20 thf(func_def_94, type, pushprop: $o).
% 5.86/1.20 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 5.86/1.20 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 5.86/1.20 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 5.86/1.20 thf(func_def_98, type, substmonoid: $o).
% 5.86/1.20 thf(func_def_99, type, lamnotvar: $o).
% 5.86/1.20 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 5.86/1.20 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 5.86/1.20 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 5.86/1.20 thf(func_def_103, type, induction2_gthm: $o).
% 5.86/1.20 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 5.86/1.20 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_106, type, hoaslamnotap: $o).
% 5.86/1.20 thf(func_def_107, type, substmonoid_gthm: $o).
% 5.86/1.20 thf(func_def_108, type, ulamvarsh: $o).
% 5.86/1.20 thf(func_def_109, type, induction2: $o).
% 5.86/1.20 thf(func_def_110, type, pushprop_lem3v2: $o).
% 5.86/1.20 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 5.86/1.20 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 5.86/1.20 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 5.86/1.20 thf(func_def_114, type, axshiftcons: $o).
% 5.86/1.20 thf(func_def_115, type, termmset: $o).
% 5.86/1.20 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 5.86/1.20 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 5.86/1.20 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 5.86/1.20 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 5.86/1.20 thf(func_def_120, type, axvarid: $o).
% 5.86/1.20 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 5.86/1.20 thf(func_def_122, type, d2term: (d_term > term)).
% 5.86/1.20 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 5.86/1.20 thf(func_def_124, type, d_one: d_term).
% 5.86/1.20 thf(func_def_125, type, d_id: d_subst).
% 5.86/1.20 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.86/1.20 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 5.86/1.20 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 5.86/1.20 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)).
% 5.86/1.20 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)).
% 5.86/1.20 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)).
% 5.86/1.20 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.86/1.20 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.86/1.20 thf(func_def_137, type, vIMP: ($o > $o > $o)).
% 5.86/1.20 thf(func_def_138, type, sP0: $o).
% 5.86/1.20 thf(func_def_139, type, sP1: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_140, type, sP2: $o).
% 5.86/1.20 thf(func_def_141, type, sP3: $o).
% 5.86/1.20 thf(func_def_142, type, sP4: $o).
% 5.86/1.20 thf(func_def_143, type, sP5: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_144, type, sP6: $o).
% 5.86/1.20 thf(func_def_145, type, sP7: $o).
% 5.86/1.20 thf(func_def_146, type, sP8: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_147, type, sP9: $o).
% 5.86/1.20 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_149, type, sP11: $o).
% 5.86/1.20 thf(func_def_150, type, sP12: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_151, type, sP13: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_152, type, sP14: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_153, type, sP15: $o).
% 5.86/1.20 thf(func_def_154, type, sP16: $o).
% 5.86/1.20 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_156, type, sP18: $o).
% 5.86/1.20 thf(func_def_157, type, sP19: $o).
% 5.86/1.20 thf(func_def_158, type, sP20: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_159, type, sP21: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_160, type, sP22: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_161, type, sP23: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_162, type, sP24: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_163, type, sP25: $o).
% 5.86/1.20 thf(func_def_164, type, sP26: $o).
% 5.86/1.20 thf(func_def_165, type, sP27: $o).
% 5.86/1.20 thf(func_def_166, type, sP28: $o).
% 5.86/1.20 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_168, type, sP30: $o).
% 5.86/1.20 thf(func_def_169, type, sP31: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_171, type, sP33: $o).
% 5.86/1.20 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_174, type, sP36: $o).
% 5.86/1.20 thf(func_def_175, type, sP37: $o).
% 5.86/1.20 thf(func_def_176, type, sP38: $o).
% 5.86/1.20 thf(func_def_177, type, sP39: $o).
% 5.86/1.20 thf(func_def_178, type, sP40: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_179, type, sP41: $o).
% 5.86/1.20 thf(func_def_180, type, sP42: $o).
% 5.86/1.20 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_182, type, sP44: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_183, type, sP45: $o).
% 5.86/1.20 thf(func_def_184, type, sP46: $o).
% 5.86/1.20 thf(func_def_185, type, sP47: $o).
% 5.86/1.20 thf(func_def_186, type, sP48: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_187, type, sP49: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 5.86/1.20 thf(func_def_189, type, sP51: $o).
% 5.86/1.20 thf(func_def_190, type, sP52: $o).
% 5.86/1.20 thf(func_def_191, type, sP53: $o).
% 5.86/1.20 thf(func_def_192, type, sP54: $o).
% 5.86/1.20 thf(func_def_193, type, sP55: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_194, type, sP56: ((term > $o) > $o)).
% 5.86/1.20 thf(func_def_195, type, sP57: $o).
% 5.86/1.20 thf(func_def_196, type, sP58: $o).
% 5.86/1.20 thf(func_def_197, type, sK59: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_198, type, sK60: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_199, type, sK61: term).
% 5.86/1.20 thf(func_def_200, type, sK62: subst).
% 5.86/1.20 thf(func_def_201, type, sK63: (term > $o)).
% 5.86/1.20 thf(func_def_202, type, sK64: term).
% 5.86/1.20 thf(func_def_203, type, sK65: term).
% 5.86/1.20 thf(func_def_204, type, sK66: subst).
% 5.86/1.20 thf(func_def_205, type, sK67: subst).
% 5.86/1.20 thf(func_def_206, type, sK68: subst).
% 5.86/1.20 thf(func_def_207, type, sK69: term).
% 5.86/1.20 thf(func_def_208, type, sK70: (term > $o)).
% 5.86/1.20 thf(func_def_209, type, sK71: (term > term)).
% 5.86/1.20 thf(func_def_210, type, sK72: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_211, type, sK73: ((term > $o) > subst > term)).
% 5.86/1.20 thf(func_def_212, type, sK74: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_213, type, sK75: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_214, type, sK76: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_215, type, sK77: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_216, type, sK78: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_217, type, sK79: term).
% 5.86/1.20 thf(func_def_218, type, sK80: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_219, type, sK81: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_220, type, sK82: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_221, type, sK83: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_223, type, sK85: (term > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > term > $o)).
% 5.86/1.20 thf(func_def_225, type, sK87: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_226, type, sK88: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_227, type, sK89: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_228, type, sK90: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_229, type, sK91: term).
% 5.86/1.20 thf(func_def_230, type, sK92: (term > $o)).
% 5.86/1.20 thf(func_def_231, type, sK93: (term > term)).
% 5.86/1.20 thf(func_def_232, type, sK94: term).
% 5.86/1.20 thf(func_def_233, type, sK95: term).
% 5.86/1.20 thf(func_def_234, type, sK96: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_235, type, sK97: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_236, type, sK98: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_237, type, sK99: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_238, type, sK100: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_240, type, sK102: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_241, type, sK103: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_242, type, sK104: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_243, type, sK105: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_244, type, sK106: ((term > $o) > term > term)).
% 5.86/1.20 thf(func_def_245, type, sK107: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_246, type, sK108: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_247, type, sK109: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_248, type, sK110: term).
% 5.86/1.20 thf(func_def_249, type, sK111: (term > $o)).
% 5.86/1.20 thf(func_def_250, type, sK112: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_251, type, sK113: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_252, type, sK114: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_253, type, sK115: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_254, type, sK116: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_255, type, sK117: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_256, type, sK118: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_257, type, sK119: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_258, type, sK120: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_259, type, sK121: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_261, type, sK123: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_262, type, sK124: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_263, type, sK125: term).
% 5.86/1.20 thf(func_def_264, type, sK126: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > term > $o)).
% 5.86/1.20 thf(func_def_266, type, sK128: term).
% 5.86/1.20 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_269, type, sK131: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_270, type, sK132: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_271, type, sK133: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_272, type, sK134: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_273, type, sK135: (term > $o)).
% 5.86/1.20 thf(func_def_274, type, sK136: term).
% 5.86/1.20 thf(func_def_275, type, sK137: (term > term)).
% 5.86/1.20 thf(func_def_276, type, sK138: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_277, type, sK139: (term > (term > $o) > term)).
% 5.86/1.20 thf(func_def_278, type, sK140: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_279, type, sK141: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_280, type, sK142: (term > $o)).
% 5.86/1.20 thf(func_def_281, type, sK143: term).
% 5.86/1.20 thf(func_def_282, type, sK144: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_283, type, sK145: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_284, type, sK146: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_285, type, sK147: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_286, type, sK148: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_287, type, sK149: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_288, type, sK150: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_290, type, sK152: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_291, type, sK153: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_293, type, sK155: term).
% 5.86/1.20 thf(func_def_294, type, sK156: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_295, type, sK157: ((subst > term > term) > term > subst)).
% 5.86/1.20 thf(func_def_296, type, sK158: ((subst > term > term) > term > subst)).
% 5.86/1.20 thf(func_def_297, type, sK159: ((subst > term > term) > term > term)).
% 5.86/1.20 thf(func_def_298, type, sK160: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_299, type, sK161: ((subst > term > term) > term > subst)).
% 5.86/1.20 thf(func_def_300, type, sK162: ((subst > term > term) > term > term)).
% 5.86/1.20 thf(func_def_301, type, sK163: ((subst > term > term) > term > subst)).
% 5.86/1.20 thf(func_def_302, type, sK164: ((subst > term > subst > $o) > term > term)).
% 5.86/1.20 thf(func_def_303, type, sK165: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_305, type, sK167: (term > $o)).
% 5.86/1.20 thf(func_def_306, type, sK168: term).
% 5.86/1.20 thf(func_def_307, type, sK169: (term > term)).
% 5.86/1.20 thf(func_def_308, type, sK170: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_309, type, sK171: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_310, type, sK172: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_311, type, sK173: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_312, type, sK174: (term > subst > term > term)).
% 5.86/1.20 thf(func_def_313, type, sK175: term).
% 5.86/1.20 thf(func_def_314, type, sK176: (term > $o)).
% 5.86/1.20 thf(func_def_315, type, sK177: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_316, type, sK178: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_317, type, sK179: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_318, type, sK180: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_319, type, sK181: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_320, type, sK182: term).
% 5.86/1.20 thf(func_def_321, type, sK183: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_322, type, sK184: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_323, type, sK185: term).
% 5.86/1.20 thf(func_def_324, type, sK186: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_325, type, sK187: ((term > $o) > term > term)).
% 5.86/1.20 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.86/1.20 thf(func_def_327, type, sK189: term).
% 5.86/1.20 thf(func_def_328, type, sK190: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_329, type, sK191: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_330, type, sK192: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_331, type, sK193: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_332, type, sK194: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_333, type, sK195: term).
% 5.86/1.20 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_335, type, sK197: ((subst > term > subst > $o) > term > term)).
% 5.86/1.20 thf(func_def_336, type, sK198: (term > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_337, type, sK199: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_338, type, sK200: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_339, type, sK201: term).
% 5.86/1.20 thf(func_def_340, type, sK202: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_341, type, sK203: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_342, type, sK204: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_343, type, sK205: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_344, type, sK206: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_345, type, sK207: term).
% 5.86/1.20 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_348, type, sK210: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_349, type, sK211: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_350, type, sK212: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_351, type, sK213: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_352, type, sK214: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_353, type, sK215: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_354, type, sK216: (term > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_355, type, sK217: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_356, type, sK218: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_357, type, sK219: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_358, type, sK220: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_359, type, sK221: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_360, type, sK222: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_361, type, sK223: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_362, type, sK224: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_363, type, sK225: term).
% 5.86/1.20 thf(func_def_364, type, sK226: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_365, type, sK227: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_369, type, sK231: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_371, type, sK233: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_375, type, sK237: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_376, type, sK238: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_377, type, sK239: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_378, type, sK240: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_380, type, sK242: term).
% 5.86/1.20 thf(func_def_381, type, sK243: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_382, type, sK244: term).
% 5.86/1.20 thf(func_def_383, type, sK245: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_386, type, sK248: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_387, type, sK249: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_388, type, sK250: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_389, type, sK251: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_390, type, sK252: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_393, type, sK255: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_394, type, sK256: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_395, type, sK257: (term > $o)).
% 5.86/1.20 thf(func_def_396, type, sK258: term).
% 5.86/1.20 thf(func_def_397, type, sK259: (term > term)).
% 5.86/1.20 thf(func_def_398, type, sK260: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_399, type, sK261: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_400, type, sK262: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_404, type, sK266: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_406, type, sK268: term).
% 5.86/1.20 thf(func_def_407, type, sK269: term).
% 5.86/1.20 thf(func_def_408, type, sK270: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_409, type, sK271: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_410, type, sK272: term).
% 5.86/1.20 thf(func_def_411, type, sK273: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_412, type, sK274: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_413, type, sK275: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_414, type, sK276: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_415, type, sK277: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_417, type, sK279: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_418, type, sK280: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_419, type, sK281: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > term > term)).
% 5.86/1.20 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_422, type, sK284: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_423, type, sK285: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_425, type, sK287: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_427, type, sK289: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_428, type, sK290: ((subst > term > subst > $o) > subst)).
% 5.86/1.20 thf(func_def_429, type, sK291: term).
% 5.86/1.20 thf(func_def_430, type, sK292: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_431, type, sK293: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_432, type, sK294: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_433, type, sK295: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_434, type, sK296: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_438, type, sK300: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_439, type, sK301: ((term > $o) > term)).
% 5.86/1.20 thf(func_def_440, type, sK302: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.20 thf(func_def_443, type, sK305: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_444, type, sK306: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_445, type, sK307: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_446, type, sK308: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_447, type, sK309: (subst > term > term)).
% 5.86/1.20 thf(func_def_448, type, sK310: (subst > term > term)).
% 5.86/1.20 thf(func_def_449, type, sK311: term).
% 5.86/1.20 thf(func_def_450, type, sK312: subst).
% 5.86/1.20 thf(func_def_451, type, sK313: subst).
% 5.86/1.20 thf(func_def_452, type, sK314: term).
% 5.86/1.20 thf(func_def_453, type, sK315: term).
% 5.86/1.20 thf(func_def_454, type, sK316: subst).
% 5.86/1.20 thf(func_def_455, type, sK317: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_456, type, sK318: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_457, type, sK319: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_458, type, sK320: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_459, type, sK321: ((subst > term > term) > term)).
% 5.86/1.20 thf(func_def_460, type, sK322: ((subst > term > term) > subst)).
% 5.86/1.20 thf(func_def_461, type, sK323: term).
% 5.86/1.20 thf(func_def_462, type, sK324: term).
% 5.86/1.20 thf(func_def_463, type, sK325: term).
% 5.86/1.20 thf(func_def_464, type, sK326: term).
% 5.86/1.20 thf(func_def_465, type, sK327: (subst > term > subst > $o)).
% 5.86/1.20 thf(func_def_466, type, sK328: (term > $o)).
% 5.86/1.20 thf(func_def_467, type, sK329: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.86/1.20 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_469, type, sK331: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_471, type, sK333: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_473, type, sK335: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_474, type, sK336: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_475, type, sK337: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_477, type, sK339: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_478, type, sK340: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_479, type, sK341: ((term > $o) > subst > term)).
% 5.86/1.21 thf(func_def_480, type, sK342: term).
% 5.86/1.21 thf(func_def_481, type, sK343: subst).
% 5.86/1.21 thf(func_def_482, type, sK344: term).
% 5.86/1.21 thf(func_def_483, type, sK345: (term > $o)).
% 5.86/1.21 thf(func_def_484, type, sK346: (term > term)).
% 5.86/1.21 thf(func_def_485, type, sK347: term).
% 5.86/1.21 thf(func_def_486, type, sK348: (term > $o)).
% 5.86/1.21 thf(func_def_487, type, sK349: (term > term)).
% 5.86/1.21 thf(func_def_488, type, sK350: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_489, type, sK351: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_490, type, sK352: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_491, type, sK353: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_492, type, sK354: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_493, type, sK355: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_494, type, sK356: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_495, type, sK357: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_496, type, sK358: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_497, type, sK359: term).
% 5.86/1.21 thf(func_def_498, type, sK360: (term > $o)).
% 5.86/1.21 thf(func_def_499, type, sK361: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_500, type, sK362: ((term > $o) > term > term)).
% 5.86/1.21 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_503, type, sK365: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_509, type, sK371: term).
% 5.86/1.21 thf(func_def_510, type, sK372: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_511, type, sK373: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_512, type, sK374: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_513, type, sK375: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_515, type, sK377: term).
% 5.86/1.21 thf(func_def_516, type, sK378: subst).
% 5.86/1.21 thf(func_def_517, type, sK379: (term > $o)).
% 5.86/1.21 thf(func_def_518, type, sK380: (term > term)).
% 5.86/1.21 thf(func_def_519, type, sK381: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_520, type, sK382: ((term > $o) > subst > term)).
% 5.86/1.21 thf(func_def_521, type, sK383: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_522, type, sK384: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_523, type, sK385: (term > $o)).
% 5.86/1.21 thf(func_def_524, type, sK386: term).
% 5.86/1.21 thf(func_def_525, type, sK387: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_526, type, sK388: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_527, type, sK389: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_528, type, sK390: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_529, type, sK391: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.86/1.21 thf(func_def_532, type, sK394: (term > (term > $o) > term)).
% 5.86/1.21 thf(func_def_533, type, sK395: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_534, type, sK396: term).
% 5.86/1.21 thf(func_def_535, type, sK397: (term > $o)).
% 5.86/1.21 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_538, type, sK400: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_540, type, sK402: ((term > $o) > term > term)).
% 5.86/1.21 thf(func_def_541, type, sK403: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_544, type, sK406: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_546, type, sK408: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_547, type, sK409: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_548, type, sK410: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_549, type, sK411: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_551, type, sK413: term).
% 5.86/1.21 thf(func_def_552, type, sK414: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_553, type, sK415: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_554, type, sK416: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_555, type, sK417: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_556, type, sK418: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_557, type, sK419: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_558, type, sK420: ((subst > term > subst > $o) > term > term)).
% 5.86/1.21 thf(func_def_559, type, sK421: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_560, type, sK422: term).
% 5.86/1.21 thf(func_def_561, type, sK423: (term > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_563, type, sK425: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_564, type, sK426: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_569, type, sK431: ((subst > term > subst > $o) > subst)).
% 5.86/1.21 thf(func_def_570, type, sK432: term).
% 5.86/1.21 thf(func_def_571, type, sK433: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_572, type, sK434: (term > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_573, type, sK435: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_574, type, sK436: term).
% 5.86/1.21 thf(func_def_575, type, sK437: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_576, type, sK438: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_577, type, sK439: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_578, type, sK440: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_579, type, sK441: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.86/1.21 thf(func_def_580, type, sK442: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_581, type, sK443: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_582, type, sK444: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_584, type, sK446: term).
% 5.86/1.21 thf(func_def_585, type, sK447: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_586, type, sK448: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_587, type, sK449: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_588, type, sK450: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_589, type, sK451: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_590, type, sK452: ((subst > term > subst > $o) > term > term)).
% 5.86/1.21 thf(func_def_591, type, sK453: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_592, type, sK454: (term > d_term)).
% 5.86/1.21 thf(func_def_593, type, sK455: term).
% 5.86/1.21 thf(func_def_594, type, sK456: term).
% 5.86/1.21 thf(func_def_595, type, sK457: term).
% 5.86/1.21 thf(func_def_596, type, sK458: term).
% 5.86/1.21 thf(func_def_597, type, sK459: term).
% 5.86/1.21 thf(func_def_598, type, sK460: (subst > term > term)).
% 5.86/1.21 thf(func_def_599, type, sK461: term).
% 5.86/1.21 thf(func_def_600, type, sK462: subst).
% 5.86/1.21 thf(func_def_601, type, sK463: (subst > term > term)).
% 5.86/1.21 thf(func_def_602, type, sK464: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_603, type, sK465: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_604, type, sK466: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_605, type, sK467: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_606, type, sK468: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_607, type, sK469: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_608, type, sK470: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_609, type, sK471: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_610, type, sK472: ((subst > term > subst > $o) > term > $o)).
% 5.86/1.21 thf(func_def_611, type, sK473: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_612, type, sK474: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_613, type, sK475: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_614, type, sK476: term).
% 5.86/1.21 thf(func_def_615, type, sK477: (subst > term > term)).
% 5.86/1.21 thf(func_def_616, type, sK478: term).
% 5.86/1.21 thf(func_def_617, type, sK479: term).
% 5.86/1.21 thf(func_def_618, type, sK480: term).
% 5.86/1.21 thf(func_def_619, type, sK481: term).
% 5.86/1.21 thf(func_def_620, type, sK482: term).
% 5.86/1.21 thf(func_def_621, type, sK483: term).
% 5.86/1.21 thf(func_def_622, type, sK484: term).
% 5.86/1.21 thf(func_def_623, type, sK485: term).
% 5.86/1.21 thf(func_def_624, type, sK486: term).
% 5.86/1.21 thf(func_def_625, type, sK487: term).
% 5.86/1.21 thf(func_def_626, type, sK488: (term > $o)).
% 5.86/1.21 thf(func_def_627, type, sK489: (term > $o)).
% 5.86/1.21 thf(func_def_628, type, sK490: subst).
% 5.86/1.21 thf(func_def_629, type, sK491: term).
% 5.86/1.21 thf(func_def_630, type, sK492: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_631, type, sK493: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_632, type, sK494: term).
% 5.86/1.21 thf(func_def_633, type, sK495: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_634, type, sK496: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_635, type, sK497: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_636, type, sK498: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_637, type, sK499: term).
% 5.86/1.21 thf(func_def_638, type, sK500: (term > subst > term > term)).
% 5.86/1.21 thf(func_def_639, type, sK501: subst).
% 5.86/1.21 thf(func_def_640, type, sK502: term).
% 5.86/1.21 thf(func_def_641, type, sK503: (term > $o)).
% 5.86/1.21 thf(func_def_642, type, sK504: term).
% 5.86/1.21 thf(func_def_643, type, sK505: (term > $o)).
% 5.86/1.21 thf(func_def_644, type, sK506: term).
% 5.86/1.21 thf(func_def_645, type, sK507: subst).
% 5.86/1.21 thf(func_def_646, type, sK508: term).
% 5.86/1.21 thf(func_def_647, type, sK509: subst).
% 5.86/1.21 thf(func_def_648, type, sK510: term).
% 5.86/1.21 thf(func_def_649, type, sK511: term).
% 5.86/1.21 thf(func_def_650, type, sK512: subst).
% 5.86/1.21 thf(func_def_651, type, sK513: subst).
% 5.86/1.21 thf(func_def_652, type, sK514: term).
% 5.86/1.21 thf(func_def_653, type, sK515: term).
% 5.86/1.21 thf(func_def_654, type, sK516: term).
% 5.86/1.21 thf(func_def_655, type, sK517: term).
% 5.86/1.21 thf(func_def_656, type, sK518: (subst > d_subst)).
% 5.86/1.21 thf(func_def_657, type, sK519: term).
% 5.86/1.21 thf(func_def_658, type, sK520: subst).
% 5.86/1.21 thf(func_def_659, type, sK521: term).
% 5.86/1.21 thf(func_def_660, type, sK522: term).
% 5.86/1.21 thf(func_def_661, type, sK523: term).
% 5.86/1.21 thf(func_def_662, type, sK524: term).
% 5.86/1.21 thf(func_def_663, type, sK525: subst).
% 5.86/1.21 thf(func_def_664, type, sK526: subst).
% 5.86/1.21 thf(func_def_665, type, sK527: (term > $o)).
% 5.86/1.21 thf(func_def_666, type, sK528: term).
% 5.86/1.21 thf(func_def_667, type, sK529: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_668, type, sK530: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_669, type, sK531: subst).
% 5.86/1.21 thf(func_def_670, type, sK532: term).
% 5.86/1.21 thf(func_def_671, type, sK533: ((term > $o) > term > subst > (term > $o) > term)).
% 5.86/1.21 thf(func_def_672, type, sK534: (term > $o)).
% 5.86/1.21 thf(func_def_673, type, sK535: subst).
% 5.86/1.21 thf(func_def_674, type, sK536: term).
% 5.86/1.21 thf(func_def_675, type, sK537: (term > $o)).
% 5.86/1.21 thf(func_def_676, type, sK538: (term > (term > $o) > subst > (term > $o) > term)).
% 5.86/1.21 thf(func_def_677, type, sK539: (term > $o)).
% 5.86/1.21 thf(func_def_678, type, sK540: subst).
% 5.86/1.21 thf(func_def_679, type, sK541: (term > $o)).
% 5.86/1.21 thf(func_def_680, type, sK542: term).
% 5.86/1.21 thf(func_def_681, type, sK543: term).
% 5.86/1.21 thf(func_def_682, type, sK544: subst).
% 5.86/1.21 thf(func_def_683, type, sK545: (subst > term > (term > $o) > term > $o)).
% 5.86/1.21 thf(func_def_684, type, sK546: (term > $o)).
% 5.86/1.21 thf(func_def_685, type, sK547: term).
% 5.86/1.21 thf(func_def_686, type, sK548: subst).
% 5.86/1.21 thf(func_def_687, type, sK549: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_688, type, sK550: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_689, type, sK551: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_690, type, sK552: ((subst > term > subst > $o) > term > $o)).
% 5.86/1.21 thf(func_def_691, type, sK553: (term > subst > term > term)).
% 5.86/1.21 thf(func_def_692, type, sK554: term).
% 5.86/1.21 thf(func_def_693, type, sK555: term).
% 5.86/1.21 thf(func_def_694, type, sK556: term).
% 5.86/1.21 thf(func_def_695, type, sK557: term).
% 5.86/1.21 thf(func_def_696, type, sK558: term).
% 5.86/1.21 thf(func_def_697, type, sK559: subst).
% 5.86/1.21 thf(func_def_698, type, sK560: subst).
% 5.86/1.21 thf(func_def_699, type, sK561: subst).
% 5.86/1.21 thf(func_def_700, type, sK562: subst).
% 5.86/1.21 thf(func_def_701, type, sK563: (term > subst > term > term)).
% 5.86/1.21 thf(func_def_702, type, sK564: term).
% 5.86/1.21 thf(func_def_703, type, sK565: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_704, type, sK566: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_705, type, sK567: term).
% 5.86/1.21 thf(func_def_706, type, sK568: term).
% 5.86/1.21 thf(func_def_707, type, sK569: term).
% 5.86/1.21 thf(func_def_708, type, sK570: term).
% 5.86/1.21 thf(func_def_709, type, sK571: term).
% 5.86/1.21 thf(func_def_710, type, sK572: term).
% 5.86/1.21 thf(func_def_711, type, sK573: term).
% 5.86/1.21 thf(func_def_712, type, sK574: term).
% 5.86/1.21 thf(func_def_713, type, sK575: term).
% 5.86/1.21 thf(func_def_714, type, sK576: (term > subst > (term > $o) > term > $o)).
% 5.86/1.21 thf(func_def_715, type, sK577: (term > $o)).
% 5.86/1.21 thf(func_def_716, type, sK578: subst).
% 5.86/1.21 thf(func_def_717, type, sK579: term).
% 5.86/1.21 thf(func_def_718, type, sK580: ((term > $o) > term)).
% 5.86/1.21 thf(func_def_719, type, sK581: term).
% 5.86/1.21 thf(func_def_720, type, sK582: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_721, type, sK583: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_722, type, sK584: (term > subst > term > term)).
% 5.86/1.21 thf(func_def_723, type, sK585: term).
% 5.86/1.21 thf(func_def_724, type, sK586: term).
% 5.86/1.21 thf(func_def_725, type, sK587: term).
% 5.86/1.21 thf(func_def_726, type, sK588: term).
% 5.86/1.21 thf(func_def_727, type, sK589: term).
% 5.86/1.21 thf(func_def_728, type, sK590: subst).
% 5.86/1.21 thf(func_def_729, type, sF591: term).
% 5.86/1.21 thf(func_def_730, type, sF592: $o).
% 5.86/1.21 thf(func_def_731, type, sK593: ((subst > term > subst > $o) > subst > term > term)).
% 5.86/1.21 thf(func_def_732, type, sK594: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.86/1.21 thf(func_def_733, type, sK595: (term > (term > $o) > term)).
% 5.86/1.21 thf(func_def_734, type, sK596: (term > (term > $o) > term)).
% 5.86/1.21 thf(func_def_735, type, sK597: (term > (term > $o) > term)).
% 5.86/1.21 thf(func_def_736, type, sK598: (term > (term > $o) > term)).
% 5.86/1.21 thf(func_def_737, type, sK599: (subst > term > subst > $o)).
% 5.86/1.21 thf(func_def_738, type, sK600: (term > $o)).
% 5.86/1.21 thf(func_def_739, type, sK601: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_740, type, sK602: ((subst > term > term) > term)).
% 5.86/1.21 thf(func_def_741, type, sK603: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_742, type, sK604: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_743, type, sK605: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_744, type, sK606: ((subst > term > term) > subst)).
% 5.86/1.21 thf(func_def_745, type, sK607: term).
% 5.86/1.21 thf(f1,axiom,(
% 5.86/1.21 (! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ! [X5 : d_subst] : (X5 = d_id) & (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem1v2_gthm & lamnotvar & (sh = ((d2subst @ d_id))) & hoasinduction_lem1 & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & induction2_gthm & pushprop_lem2v2_lthm & (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3aa_lthm) & axabs & (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id)) <=> hoasinduction_lem2) & hoaslamnotvar & hoasapinj1_gthm & pushprop_lem2v2_gthm & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X32 : subst,X18 : (subst > term > term),X33 : term,X31 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))))) <=> hoaslaminj_lthm) & hoasinduction_lem1_lthm & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3b_gthm & ~ulamvar1 & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & pushprop_lem2v2 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ulamvarind & pushprop_lem3v2 & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & hoasinduction_lem1v2 & termmset_gthm & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)))))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) & hoasinduction_lem1v2_gthm & (id = ((d2subst @ d_id))) & axapp & pushprop_lem1_gthm & pushprop & (hoaslamnotap <=> ! [X18 : (subst > term > term),X47 : term,X46 : term] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))))) & (! [X45 : term,X44 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X44) | ~(X11 @ X45)) <=> hoasinduction_lem2v2) & hoasinduction_lem3a_gthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (hoaslaminj <=> ! [X18 : (subst > term > term),X32 : subst,X31 : (subst > term > term),X33 : term] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (induction2 <=> ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))) & pushprop_lem0_gthm & (induction2lem <=> ! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)))) & hoasinduction_lem3_gthm & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & apnotvar & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & hoasinduction_lem1_gthm & (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & hoasapnotvar & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))))) & induction2lem_gthm & pushprop_lthm_orig & hoasinduction_lem2v2_gthm & (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) <=> induction) & (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ 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,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))) <=> hoasinduction_lem3v2a) & (hoasapinj2 <=> ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X30 @ id))) & (hoasapinj2_lthm <=> (! [X20 : term,X13 : term,X15 : term,X19 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & hoasapnotvar_lthm & (! [X14 : subst,X13 : term,X10 : (term > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13)) <=> pushprop_lem1v2) & (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X11 : (term > $o),X14 : subst,X10 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one)))) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X15 : term,X13 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & ulamvarsh & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ! [X1 : d_term] : (X1 = d_one) & pushprop_lthm & hoasinduction_lem2_gthm & (! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) <=> hoasinduction_lem3v2) & ((! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : (~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id)) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [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))))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X28 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) <=> hoasinduction_lthm) & (one = ((d2term @ d_one))) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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))) | (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)] : (~ ! [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))))) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))))) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) <=> substmonoid) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (pushprop_lem0_lthm <=> ! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X10 : (term > $o),X14 : subst,X13 : term,X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & hoaslaminj_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axvarshift & ~(var @ (d2term @ d_one)) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & hoaslamnotap_lthm & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) => ! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))))))))) & hoasinduction_lem3v2_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)))))))) & hoasapinj2_gthm & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & (hoasinduction_lem3a <=> ! [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)] : ((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))))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) <=> laminj) & substmonoid_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [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))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X37 : term,X36 : subst,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X39 : subst,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)))) & hoaslamnotvar_gthm & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & ~lamnotap & axassoc & (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X48 : term,X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) <=> hoasinduction_lem3v2_lthm) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) <=> apinj2) & (pushprop_lem1 <=> ! [X10 : (term > $o),X13 : term,X26 : (term > $o),X15 : term,X14 : subst] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & hoasinduction_lem2_lthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & axmap & hoaslamnotap_gthm & (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ 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))) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction_lem3) & hoasinduction_gthm & pushprop_gthm & hoasapnotvar_gthm & axclos & (((lam @ (d2term @ d_one))) = ((d2term @ d_one)))),
% 5.86/1.21 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 5.86/1.21 thf(f2,conjecture,(
% 5.86/1.21 (! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (! [X2 : (subst > term > term)] : (! [X5 : subst,X3 : subst,X4 : term] : (((sub @ (X2 @ X3 @ X4) @ X5)) = ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X2 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X2 @ X3 @ X4)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X4 : term] : (! [X6 : term] : ((X1 @ X6) => (X1 @ (sub @ X4 @ (push @ X6 @ id)))) => (X1 @ (lam @ X4))))) = hoasinduction_lem3v2a)),
% 5.86/1.21 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a)).
% 5.86/1.21 thf(f3,negated_conjecture,(
% 5.86/1.21 ~ (! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (! [X2 : (subst > term > term)] : (! [X5 : subst,X3 : subst,X4 : term] : (((sub @ (X2 @ X3 @ X4) @ X5)) = ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X2 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X2 @ X3 @ X4)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X4 : term] : (! [X6 : term] : ((X1 @ X6) => (X1 @ (sub @ X4 @ (push @ X6 @ id)))) => (X1 @ (lam @ X4))))) = hoasinduction_lem3v2a)),
% 5.86/1.21 inference(negated_conjecture,[status(cth)],[f2])).
% 5.86/1.21 thf(f4,plain,(
% 5.86/1.21 (! [X0 : subst,X1 : (term > $o),X2 : term] : ~ ! [X3 : (term > $o)] : ~ ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> pushprop_lem0) & ! [X5 : d_subst] : (X5 = d_id) & (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X8 = X9) | (((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6)))) <=> hoasapinj1) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction2_lthm <=> (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (term > $o),X12 : subst,X13 : term] : ((X11 @ (sub @ X13 @ X12)) | ~ ! [X14 : term] : ((X11 @ (lam @ X14)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X14 @ (push @ X15 @ id))))) | ~ ! [X16 : term] : (~(var @ X16) | (X11 @ (sub @ X16 @ X12))) | ~ ! [X17 : term,X18 : term] : ((X11 @ (ap @ X18 @ X17)) | ~(X11 @ X18) | ~(X11 @ X17))) => ! [X19 : term,X20 : (term > $o)] : (~ ! [X21 : term] : ((X20 @ X21) | ~(var @ X21)) | ~ ! [X22 : term,X23 : term] : ((X20 @ (ap @ X22 @ X23)) | ~(X20 @ X23) | ~(X20 @ X22)) | (X20 @ X19) | ~ ! [X24 : term] : (~ ! [X25 : term] : ((X20 @ (sub @ X24 @ (push @ X25 @ id))) | ~(X20 @ X25)) | (X20 @ (lam @ X24))))))) & (termmset <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & (hoaslam = (^[X27 : subst, X28 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem1v2_gthm & lamnotvar & (sh = ((d2subst @ d_id))) & hoasinduction_lem1 & (axscons <=> ! [X29 : subst] : (((push @ (sub @ one @ X29) @ (comp @ sh @ X29))) = X29)) & induction2_gthm & pushprop_lem2v2_lthm & (! [X30 : subst,X31 : term] : (((comp @ sh @ (push @ X31 @ X30))) = X30) <=> axshiftcons) & (! [X32 : term,X33 : (subst > term > subst > $o)] : ((X33 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id) | ~ ! [X34 : term] : ((X33 @ id @ (sub @ X32 @ (push @ X34 @ id)) @ id) | ~(X33 @ id @ X34 @ id)) | ~ ! [X35 : (subst > term > term)] : ((X33 @ id @ (lam @ (X35 @ sh @ one)) @ id) | ~ ! [X36 : term] : (~(X33 @ id @ X36 @ id) | (X33 @ id @ (X35 @ id @ X36) @ id)) | ~ ! [X37 : subst,X38 : subst,X39 : term] : (((X35 @ (comp @ X37 @ X38) @ (sub @ X39 @ X38))) = ((sub @ (X35 @ X37 @ X39) @ X38))))) <=> hoasinduction_lem3aa_lthm) & axabs & (! [X40 : term,X41 : term,X42 : (subst > term > subst > $o)] : (~ ! [X43 : subst,X44 : subst,X45 : term,X46 : subst] : ((X42 @ (comp @ X44 @ X46) @ (sub @ X45 @ X46) @ X43) | ~(X42 @ X44 @ X45 @ (comp @ X46 @ X43))) | ~ ! [X47 : term,X48 : term] : (~(X42 @ id @ X47 @ id) | ~(X42 @ id @ X48 @ id) | (X42 @ id @ (ap @ (sub @ X48 @ id) @ X47) @ id)) | (X42 @ id @ (ap @ X40 @ X41) @ id) | ~(X42 @ id @ X41 @ id) | ~ ! [X49 : subst,X50 : subst,X51 : term,X52 : subst] : ((X42 @ X49 @ X51 @ (comp @ X52 @ X50)) | ~(X42 @ (comp @ X49 @ X52) @ (sub @ X51 @ X52) @ X50)) | ~(X42 @ id @ X40 @ id)) <=> hoasinduction_lem2) & hoaslamnotvar & hoasapinj1_gthm & pushprop_lem2v2_gthm & ((! [X53 : term,X54 : subst] : (((sub @ one @ (push @ X53 @ X54))) = X53) => (! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56) => (! [X57 : term,X58 : term] : ((((lam @ X58)) != ((lam @ X57))) | (X57 = X58)) => ! [X59 : subst,X60 : (subst > term > term),X61 : term,X62 : (subst > term > term)] : (~ ! [X63 : subst,X64 : subst,X65 : term] : (((X62 @ (comp @ X64 @ X63) @ (sub @ X65 @ X63))) = ((sub @ (X62 @ X64 @ X65) @ X63))) | ~ ! [X66 : term,X67 : subst,X68 : subst] : (((X60 @ (comp @ X67 @ X68) @ (sub @ X66 @ X68))) = ((sub @ (X60 @ X67 @ X66) @ X68))) | (((X60 @ X59 @ X61)) = ((X62 @ X59 @ X61))) | (((lam @ (X62 @ sh @ one))) != ((lam @ (X60 @ sh @ one)))))))) <=> hoaslaminj_lthm) & hoasinduction_lem1_lthm & (hoasinduction_lem3v2_f_lthm <=> ! [X69 : term] : ~ ! [X70 : (subst > term > term)] : ~ ! [X71 : subst,X72 : term] : (((sub @ X69 @ (push @ X72 @ X71))) = ((X70 @ X71 @ X72)))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3b_gthm & ~ulamvar1 & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> axidr) & pushprop_lem2v2 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ulamvarind & pushprop_lem3v2 & (axidl <=> ! [X74 : subst] : (((comp @ id @ X74)) = X74)) & hoasinduction_lem1v2 & termmset_gthm & (hoasinduction_lem3_lthm <=> (! [X75 : term] : (((sub @ X75 @ id)) = X75) => (! [X76 : term,X77 : (subst > term > subst > $o)] : ((X77 @ id @ (lam @ (sub @ X76 @ (push @ one @ sh))) @ id) | ~ ! [X78 : term] : (~(X77 @ id @ X78 @ id) | (X77 @ id @ (sub @ X76 @ (push @ X78 @ id)) @ id)) | ~ ! [X79 : (subst > term > term)] : (~ ! [X80 : term] : (~(X77 @ id @ X80 @ id) | (X77 @ id @ (X79 @ id @ X80) @ id)) | (X77 @ id @ (lam @ (X79 @ sh @ one)) @ id) | ~ ! [X81 : subst,X82 : term,X83 : subst] : (((sub @ (X79 @ X81 @ X82) @ X83)) = ((X79 @ (comp @ X81 @ X83) @ (sub @ X82 @ X83)))))) => ! [X84 : (subst > term > subst > $o),X85 : term] : (~ ! [X86 : (subst > term > term)] : (~ ! [X87 : subst,X88 : subst,X89 : term] : (((X86 @ (comp @ X88 @ X87) @ (sub @ X89 @ X87))) = ((sub @ (X86 @ X88 @ X89) @ X87))) | (X84 @ id @ (lam @ (X86 @ sh @ one)) @ id) | ~ ! [X90 : term] : ((X84 @ id @ (X86 @ id @ X90) @ id) | ~(X84 @ id @ X90 @ id))) | ~ ! [X91 : term] : (~(X84 @ id @ X91 @ id) | (X84 @ id @ (sub @ X85 @ (push @ X91 @ id)) @ id)) | (X84 @ id @ (lam @ X85) @ id) | ~ ! [X92 : subst,X93 : subst,X94 : term,X95 : subst] : (~(X84 @ (comp @ X95 @ X92) @ (sub @ X94 @ X92) @ X93) | (X84 @ X95 @ X94 @ (comp @ X92 @ X93))) | ~ ! [X96 : subst,X97 : subst,X98 : term,X99 : subst] : (~(X84 @ X96 @ X98 @ (comp @ X97 @ X99)) | (X84 @ (comp @ X96 @ X97) @ (sub @ X98 @ X97) @ X99)))))) & hoasinduction_lem1v2_gthm & (id = ((d2subst @ d_id))) & axapp & pushprop_lem1_gthm & pushprop & (hoaslamnotap <=> ! [X100 : (subst > term > term),X101 : term,X102 : term] : (~ ! [X103 : subst,X104 : term,X105 : subst] : (((sub @ (X100 @ X105 @ X104) @ X103)) = ((X100 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103)))) | (((lam @ (X100 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X101))))) & (! [X106 : term,X107 : term,X108 : (term > $o),X109 : (subst > term > subst > $o)] : (~ ! [X110 : term,X111 : term] : (~(X109 @ id @ X111 @ id) | ~(X109 @ id @ X110 @ id) | (X109 @ id @ (ap @ (sub @ X111 @ id) @ X110) @ id)) | ~ ! [X112 : term] : (((X108 @ X112)) = ((X109 @ id @ X112 @ id))) | ~ ! [X113 : subst,X114 : subst,X115 : term,X116 : subst] : ((X109 @ (comp @ X116 @ X113) @ (sub @ X115 @ X113) @ X114) | ~(X109 @ X116 @ X115 @ (comp @ X113 @ X114))) | (X108 @ (ap @ X107 @ X106)) | ~ ! [X117 : subst,X118 : term,X119 : subst,X120 : subst] : ((X109 @ X117 @ X118 @ (comp @ X120 @ X119)) | ~(X109 @ (comp @ X117 @ X120) @ (sub @ X118 @ X120) @ X119)) | ~(X108 @ X107) | ~(X108 @ X106)) <=> hoasinduction_lem2v2) & hoasinduction_lem3a_gthm & ! [X121 : subst] : ? [X122 : d_subst] : (((d2subst @ X122)) = X121) & (hoaslaminj <=> ! [X123 : (subst > term > term),X124 : subst,X125 : (subst > term > term),X126 : term] : (~ ! [X127 : subst,X128 : term,X129 : subst] : (((X123 @ (comp @ X127 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X123 @ X127 @ X128) @ X129))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X125 @ sh @ one)))) | (((X123 @ X124 @ X126)) = ((X125 @ X124 @ X126))) | ~ ! [X130 : subst,X131 : term,X132 : subst] : (((sub @ (X125 @ X130 @ X131) @ X132)) = ((X125 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132)))))) & (induction2 <=> ! [X133 : (term > $o),X134 : term] : ((X133 @ X134) | ~ ! [X135 : term,X136 : term] : (~(X133 @ X135) | ~(X133 @ X136) | (X133 @ (ap @ X136 @ X135))) | ~ ! [X137 : term] : ((X133 @ (lam @ X137)) | ~ ! [X138 : term] : ((X133 @ (sub @ X137 @ (push @ X138 @ id))) | ~(X133 @ X138))) | ~ ! [X139 : term] : (~(var @ X139) | (X133 @ X139)))) & pushprop_lem0_gthm & (induction2lem <=> ! [X140 : (term > $o),X141 : term,X142 : subst] : (~ ! [X143 : term] : ((X140 @ (lam @ X143)) | ~ ! [X144 : term] : (~(X140 @ X144) | (X140 @ (sub @ X143 @ (push @ X144 @ id))))) | ~ ! [X145 : term,X146 : term] : (~(X140 @ X145) | ~(X140 @ X146) | (X140 @ (ap @ X146 @ X145))) | ~ ! [X147 : term] : ((X140 @ (sub @ X147 @ X142)) | ~(var @ X147)) | (X140 @ (sub @ X141 @ X142)))) & hoasinduction_lem3_gthm & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & apnotvar & (hoasinduction_p_and_p_prime = (^[X148 : (subst > term > subst > $o), X149 : (term > $o)] : (! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))))) & hoasinduction_lem1_gthm & (! [X151 : term,X152 : term,X153 : term,X154 : term] : ((((ap @ X151 @ X154)) != ((ap @ X152 @ X153))) | (X151 = X152)) <=> apinj1) & hoasapnotvar & (hoasinduction_lem3v2a_lthm <=> (! [X155 : term] : ~ ! [X156 : (subst > term > term)] : ~ ! [X157 : term,X158 : subst] : (((sub @ X155 @ (push @ X157 @ X158))) = ((X156 @ X158 @ X157))) => (! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (subst > term > subst > $o),X162 : (term > $o)] : (~ ! [X163 : (subst > term > term)] : (~ ! [X164 : term] : (~(X161 @ id @ X164 @ id) | (X161 @ id @ (X163 @ id @ X164) @ id)) | ~ ! [X165 : subst,X166 : subst,X167 : term] : (((sub @ (X163 @ X165 @ X167) @ X166)) = ((X163 @ (comp @ X165 @ X166) @ (sub @ X167 @ X166)))) | (X161 @ id @ (lam @ (X163 @ sh @ one)) @ id)) | (X162 @ (lam @ X160)) | ~ ! [X168 : term] : ((X162 @ (sub @ X160 @ (push @ X168 @ id))) | ~(X162 @ X168)) | ~ ! [X169 : term] : (((X162 @ X169)) = ((X161 @ id @ X169 @ id))))))) & induction2lem_gthm & pushprop_lthm_orig & hoasinduction_lem2v2_gthm & (! [X170 : (term > $o),X171 : term] : ((X170 @ X171) | ~ ! [X172 : term] : ((X170 @ X172) | ~(var @ X172)) | ~ ! [X173 : term] : (~(X170 @ X173) | (X170 @ (lam @ X173))) | ~ ! [X174 : term,X175 : term] : (~(X170 @ X175) | ~(X170 @ X174) | (X170 @ (ap @ X175 @ X174)))) <=> induction) & (! [X176 : term,X177 : (term > $o),X178 : (subst > term > subst > $o)] : (~ ! [X179 : term] : (((X177 @ X179)) = ((X178 @ id @ X179 @ id))) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term] : (~(X178 @ id @ X181 @ id) | (X178 @ id @ (X180 @ id @ X181) @ id)) | (X178 @ id @ (lam @ (X180 @ sh @ one)) @ id) | ~ ! [X182 : subst,X183 : subst,X184 : term] : (((X180 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182))) = ((sub @ (X180 @ X183 @ X184) @ X182)))) | ~ ! [X185 : term] : (~(X177 @ X185) | (X177 @ (sub @ X176 @ (push @ X185 @ id)))) | (X177 @ (lam @ X176))) <=> hoasinduction_lem3v2a) & (hoasapinj2 <=> ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X187 = X188) | (((ap @ (sub @ X186 @ id) @ X187)) != ((ap @ (sub @ X189 @ id) @ X188))))) & (! [X190 : term,X191 : term] : ((X190 = X191) | (((sub @ X191 @ sh)) != ((sub @ X190 @ sh)))) <=> shinj) & (hoasinduction_no_psi_cond <=> ! [X192 : term,X193 : (subst > term > subst > $o)] : (~ ! [X194 : term,X195 : term] : (~(X193 @ id @ X195 @ id) | (X193 @ id @ (ap @ (sub @ X195 @ id) @ X194) @ id) | ~(X193 @ id @ X194 @ id)) | ~ ! [X196 : (subst > term > term)] : (~ ! [X197 : term] : ((X193 @ id @ (X196 @ id @ X197) @ id) | ~(X193 @ id @ X197 @ id)) | (X193 @ id @ (lam @ (X196 @ sh @ one)) @ id) | ~ ! [X198 : term,X199 : subst,X200 : subst] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))) | (X193 @ id @ X192 @ id))) & (hoasapinj2_lthm <=> (! [X201 : term,X202 : term,X203 : term,X204 : term] : ((X201 = X204) | (((ap @ X203 @ X201)) != ((ap @ X202 @ X204)))) => ! [X205 : term,X206 : term,X207 : term,X208 : term] : ((X206 = X207) | (((ap @ (sub @ X208 @ id) @ X206)) != ((ap @ (sub @ X205 @ id) @ X207)))))) & hoasapnotvar_lthm & (! [X209 : subst,X210 : term,X211 : (term > $o),X212 : (term > $o)] : (~ ! [X213 : term] : (((X211 @ (sub @ X213 @ (push @ X210 @ X209)))) = ((X212 @ X213))) | (X212 @ one) | ~(X211 @ X210)) <=> pushprop_lem1v2) & (pushprop_lem1v2_lthm <=> (! [X214 : subst,X215 : term] : (((sub @ one @ (push @ X215 @ X214))) = X215) => ! [X216 : term,X217 : (term > $o),X218 : subst,X219 : (term > $o)] : (~ ! [X220 : term] : (((X219 @ (sub @ X220 @ (push @ X216 @ X218)))) = ((X217 @ X220))) | ~(X219 @ X216) | (X217 @ one)))) & (hoasapinj1_lthm <=> (! [X221 : term] : (((sub @ X221 @ id)) = X221) => (! [X222 : term,X223 : term,X224 : term,X225 : term] : ((X223 = X224) | (((ap @ X224 @ X222)) != ((ap @ X223 @ X225)))) => ! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ (sub @ X228 @ id) @ X226)) != ((ap @ (sub @ X229 @ id) @ X227))) | (X228 = X229))))) & (hoasinduction <=> ! [X230 : (subst > term > subst > $o),X231 : term] : (~ ! [X232 : subst,X233 : term,X234 : subst,X235 : subst] : (~(X230 @ X232 @ X233 @ (comp @ X234 @ X235)) | (X230 @ (comp @ X232 @ X234) @ (sub @ X233 @ X234) @ X235)) | ~ ! [X236 : term] : (~(var @ (sub @ X236 @ id)) | (X230 @ id @ X236 @ id)) | (X230 @ id @ X231 @ id) | ~ ! [X237 : term,X238 : term] : (~(X230 @ id @ X237 @ id) | ~(X230 @ id @ X238 @ id) | (X230 @ id @ (ap @ (sub @ X238 @ id) @ X237) @ id)) | ~ ! [X239 : (subst > term > term)] : ((X230 @ id @ (lam @ (X239 @ sh @ one)) @ id) | ~ ! [X240 : subst,X241 : subst,X242 : term] : (((sub @ (X239 @ X241 @ X242) @ X240)) = ((X239 @ (comp @ X241 @ X240) @ (sub @ X242 @ X240)))) | ~ ! [X243 : term] : (~(X230 @ id @ X243 @ id) | (X230 @ id @ (X239 @ id @ X243) @ id))) | ~ ! [X244 : term,X245 : subst,X246 : subst,X247 : subst] : ((X230 @ X245 @ X244 @ (comp @ X247 @ X246)) | ~(X230 @ (comp @ X245 @ X247) @ (sub @ X244 @ X247) @ X246)))) & (hoasinduction_lem3b_lthm <=> ! [X248 : term] : ~ ! [X249 : (subst > term > term)] : (((X249 @ sh @ one)) != ((sub @ X248 @ (push @ one @ sh))))) & ulamvarsh & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ! [X250 : d_term] : (d_one = X250) & pushprop_lthm & hoasinduction_lem2_gthm & (! [X251 : term,X252 : (term > $o),X253 : (subst > term > subst > $o)] : ((X252 @ (lam @ X251)) | ~ ! [X254 : term] : (((X253 @ id @ X254 @ id)) = ((X252 @ X254))) | ~ ! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (~(X253 @ X255 @ X256 @ (comp @ X258 @ X257)) | (X253 @ (comp @ X255 @ X258) @ (sub @ X256 @ X258) @ X257)) | ~ ! [X259 : subst,X260 : term,X261 : subst,X262 : subst] : ((X253 @ X259 @ X260 @ (comp @ X261 @ X262)) | ~(X253 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) | ~ ! [X263 : term] : (~(X252 @ X263) | (X252 @ (sub @ X251 @ (push @ X263 @ id)))) | ~ ! [X264 : (subst > term > term)] : ((X253 @ id @ (lam @ (X264 @ sh @ one)) @ id) | ~ ! [X265 : term,X266 : subst,X267 : subst] : (((sub @ (X264 @ X266 @ X265) @ X267)) = ((X264 @ (comp @ X266 @ X267) @ (sub @ X265 @ X267)))) | ~ ! [X268 : term] : (~(X253 @ id @ X268 @ id) | (X253 @ id @ (X264 @ id @ X268) @ id)))) <=> hoasinduction_lem3v2) & ((! [X269 : (term > $o),X270 : term] : (~ ! [X271 : term] : ((X269 @ (lam @ X271)) | ~ ! [X272 : term] : ((X269 @ (sub @ X271 @ (push @ X272 @ id))) | ~(X269 @ X272))) | ~ ! [X273 : term,X274 : term] : (~(X269 @ X274) | (X269 @ (ap @ X274 @ X273)) | ~(X269 @ X273)) | (X269 @ X270) | ~ ! [X275 : term] : ((X269 @ X275) | ~(var @ X275))) => (! [X276 : term,X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term,X280 : subst,X281 : subst,X282 : subst] : (~(X277 @ (comp @ X280 @ X282) @ (sub @ X279 @ X282) @ X281) | (X277 @ X280 @ X279 @ (comp @ X282 @ X281))) | ~ ! [X283 : term,X284 : term] : (~(X277 @ id @ X284 @ id) | ~(X277 @ id @ X283 @ id) | (X277 @ id @ (ap @ (sub @ X284 @ id) @ X283) @ id)) | ~(X277 @ id @ X276 @ id) | ~(X277 @ id @ X278 @ id) | ~ ! [X285 : subst,X286 : subst,X287 : term,X288 : subst] : (~(X277 @ X288 @ X287 @ (comp @ X286 @ X285)) | (X277 @ (comp @ X288 @ X286) @ (sub @ X287 @ X286) @ X285)) | (X277 @ id @ (ap @ X278 @ X276) @ id)) => (! [X289 : (subst > term > subst > $o),X290 : term] : (~ ! [X291 : (subst > term > term)] : (~ ! [X292 : term] : ((X289 @ id @ (X291 @ id @ X292) @ id) | ~(X289 @ id @ X292 @ id)) | (X289 @ id @ (lam @ (X291 @ sh @ one)) @ id) | ~ ! [X293 : subst,X294 : term,X295 : subst] : (((X291 @ (comp @ X295 @ X293) @ (sub @ X294 @ X293))) = ((sub @ (X291 @ X295 @ X294) @ X293)))) | ~ ! [X296 : subst,X297 : term,X298 : subst,X299 : subst] : (~(X289 @ X298 @ X297 @ (comp @ X296 @ X299)) | (X289 @ (comp @ X298 @ X296) @ (sub @ X297 @ X296) @ X299)) | (X289 @ id @ (lam @ X290) @ id) | ~ ! [X300 : subst,X301 : subst,X302 : subst,X303 : term] : (~(X289 @ (comp @ X302 @ X300) @ (sub @ X303 @ X300) @ X301) | (X289 @ X302 @ X303 @ (comp @ X300 @ X301))) | ~ ! [X304 : term] : (~(X289 @ id @ X304 @ id) | (X289 @ id @ (sub @ X290 @ (push @ X304 @ id)) @ id))) => ! [X305 : term,X306 : (subst > term > subst > $o)] : ((X306 @ id @ X305 @ id) | ~ ! [X307 : term,X308 : term] : ((X306 @ id @ (ap @ (sub @ X307 @ id) @ X308) @ id) | ~(X306 @ id @ X308 @ id) | ~(X306 @ id @ X307 @ id)) | ~ ! [X309 : subst,X310 : term,X311 : subst,X312 : subst] : ((X306 @ X311 @ X310 @ (comp @ X312 @ X309)) | ~(X306 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312) @ X309)) | ~ ! [X313 : (subst > term > term)] : ((X306 @ id @ (lam @ (X313 @ sh @ one)) @ id) | ~ ! [X314 : term] : ((X306 @ id @ (X313 @ id @ X314) @ id) | ~(X306 @ id @ X314 @ id)) | ~ ! [X315 : term,X316 : subst,X317 : subst] : (((sub @ (X313 @ X316 @ X315) @ X317)) = ((X313 @ (comp @ X316 @ X317) @ (sub @ X315 @ X317))))) | ~ ! [X318 : term] : (~(var @ (sub @ X318 @ id)) | (X306 @ id @ X318 @ id)) | ~ ! [X319 : subst,X320 : subst,X321 : subst,X322 : term] : (~(X306 @ X321 @ X322 @ (comp @ X319 @ X320)) | (X306 @ (comp @ X321 @ X319) @ (sub @ X322 @ X319) @ X320)))))) <=> hoasinduction_lthm) & (one = ((d2term @ d_one))) & (hoasinduction_lem3a_lthm <=> (! [X323 : term] : (((sub @ X323 @ id)) = X323) => (! [X324 : term,X325 : (subst > term > subst > $o)] : (~ ! [X326 : (subst > term > term)] : (~ ! [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X326 @ X329 @ X328) @ X327)) = ((X326 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327)))) | (X325 @ id @ (lam @ (X326 @ sh @ one)) @ id) | ~ ! [X330 : term] : ((X325 @ id @ (X326 @ id @ X330) @ id) | ~(X325 @ id @ X330 @ id))) | (X325 @ id @ (lam @ (sub @ X324 @ (push @ one @ sh))) @ id) | ~ ! [X331 : term] : ((X325 @ id @ (sub @ X324 @ (push @ X331 @ id)) @ id) | ~(X325 @ id @ X331 @ id))) => ! [X332 : term,X333 : (subst > term > subst > $o)] : (~ ! [X334 : (subst > term > term)] : (~ ! [X335 : term] : (~(X333 @ id @ X335 @ id) | (X333 @ id @ (X334 @ id @ X335) @ id)) | (X333 @ id @ (lam @ (X334 @ sh @ one)) @ id) | ~ ! [X336 : subst,X337 : subst,X338 : term] : (((sub @ (X334 @ X336 @ X338) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X338 @ X337))))) | (X333 @ id @ (lam @ X332) @ id) | ~ ! [X339 : term] : (~(X333 @ id @ X339 @ id) | (X333 @ id @ (sub @ X332 @ (push @ X339 @ id)) @ id)))))) & ((! [X340 : subst] : (((comp @ id @ X340)) = X340) & ! [X341 : subst] : (((comp @ X341 @ id)) = X341)) <=> substmonoid) & ((! [X342 : (subst > term > subst > $o)] : ~ ! [X343 : (term > $o)] : ~ ! [X344 : term] : (((X343 @ X344)) = ((X342 @ id @ X344 @ id))) => (! [X345 : (term > $o),X346 : term] : (~ ! [X347 : term,X348 : term] : (~(X345 @ X347) | ~(X345 @ X348) | (X345 @ (ap @ X347 @ X348))) | (X345 @ X346) | ~ ! [X349 : term] : (~(var @ X349) | (X345 @ X349)) | ~ ! [X350 : term] : ((X345 @ (lam @ X350)) | ~ ! [X351 : term] : (~(X345 @ X351) | (X345 @ (sub @ X350 @ (push @ X351 @ id)))))) => (! [X352 : term] : (((sub @ X352 @ id)) = X352) => (! [X353 : term,X354 : (term > $o),X355 : (subst > term > subst > $o)] : (~ ! [X356 : (subst > term > term)] : ((X355 @ id @ (lam @ (X356 @ sh @ one)) @ id) | ~ ! [X357 : subst,X358 : term,X359 : subst] : (((X356 @ (comp @ X359 @ X357) @ (sub @ X358 @ X357))) = ((sub @ (X356 @ X359 @ X358) @ X357))) | ~ ! [X360 : term] : (~(X355 @ id @ X360 @ id) | (X355 @ id @ (X356 @ id @ X360) @ id))) | (X354 @ (lam @ X353)) | ~ ! [X361 : term] : ((X354 @ (sub @ X353 @ (push @ X361 @ id))) | ~(X354 @ X361)) | ~ ! [X362 : term] : (((X355 @ id @ X362 @ id)) = ((X354 @ X362)))) => ! [X363 : term,X364 : (subst > term > subst > $o)] : (~ ! [X365 : (subst > term > term)] : ((X364 @ id @ (lam @ (X365 @ sh @ one)) @ id) | ~ ! [X366 : term,X367 : subst,X368 : subst] : (((X365 @ (comp @ X368 @ X367) @ (sub @ X366 @ X367))) = ((sub @ (X365 @ X368 @ X366) @ X367))) | ~ ! [X369 : term] : ((X364 @ id @ (X365 @ id @ X369) @ id) | ~(X364 @ id @ X369 @ id))) | (X364 @ id @ X363 @ id) | ~ ! [X370 : term,X371 : term] : (~(X364 @ id @ X370 @ id) | (X364 @ id @ (ap @ (sub @ X370 @ id) @ X371) @ id) | ~(X364 @ id @ X371 @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (pushprop_lem0_lthm <=> ! [X372 : subst,X373 : (term > $o),X374 : term] : ~ ! [X375 : (term > $o)] : ~ ! [X376 : term] : (((X373 @ (sub @ X376 @ (push @ X374 @ X372)))) = ((X375 @ X376)))) & (pushprop_lem1_lthm <=> (! [X377 : subst,X378 : term] : (((sub @ one @ (push @ X378 @ X377))) = X378) => (! [X379 : term,X380 : subst] : (((comp @ sh @ (push @ X379 @ X380))) = X380) => ! [X381 : term,X382 : (term > $o),X383 : subst,X384 : term,X385 : (term > $o)] : (~(X382 @ X384) | (X385 @ (sub @ X384 @ (push @ X381 @ X383))))))) & hoaslaminj_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axvarshift & ~(var @ (d2term @ d_one)) & (! [X386 : term] : (((sub @ X386 @ id)) = X386) <=> axvarid) & hoaslamnotap_lthm & (induction2lem_lthm <=> (! [X387 : subst,X388 : term] : (((sub @ one @ (push @ X388 @ X387))) = X388) => (! [X389 : subst,X390 : term] : (((comp @ sh @ (push @ X390 @ X389))) = X389) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : (term > $o),X393 : term] : (~ ! [X394 : term] : ((X392 @ X394) | ~(var @ X394)) | ~ ! [X395 : term] : (~(X392 @ X395) | (X392 @ (lam @ X395))) | (X392 @ X393) | ~ ! [X396 : term,X397 : term] : (~(X392 @ X396) | ~(X392 @ X397) | (X392 @ (ap @ X397 @ X396)))) => ! [X398 : term,X399 : (term > $o),X400 : subst] : (~ ! [X401 : term,X402 : term] : (~(X399 @ X401) | ~(X399 @ X402) | (X399 @ (ap @ X401 @ X402))) | (X399 @ (sub @ X398 @ X400)) | ~ ! [X403 : term] : ((X399 @ (sub @ X403 @ X400)) | ~(var @ X403)) | ~ ! [X404 : term] : ((X399 @ (lam @ X404)) | ~ ! [X405 : term] : ((X399 @ (sub @ X404 @ (push @ X405 @ id))) | ~(X399 @ X405))))))))) & hoasinduction_lem3v2_gthm & (pushprop_p_and_p_prime = (^[X406 : term, X407 : subst, X408 : (term > $o), X409 : (term > $o)] : (! [X410 : term] : (((X409 @ X410)) = ((X408 @ (sub @ X410 @ (push @ X406 @ X407)))))))) & hoasapinj2_gthm & ! [X411 : d_term,X412 : d_term] : ((((d2term @ X412)) = ((d2term @ X411))) => (X411 = X412)) & (substmonoid_lthm <=> (! [X413 : subst] : (((comp @ id @ X413)) = X413) => (! [X414 : subst] : (((comp @ X414 @ id)) = X414) => (! [X415 : subst] : (((comp @ X415 @ id)) = X415) & ! [X416 : subst] : (((comp @ id @ X416)) = X416))))) & (! [X417 : subst,X418 : term] : (((sub @ one @ (push @ X418 @ X417))) = X418) <=> axvarcons) & (hoasinduction_lem3a <=> ! [X419 : term,X420 : (subst > term > subst > $o)] : ((X420 @ id @ (lam @ X419) @ id) | ~ ! [X421 : term] : (~(X420 @ id @ X421 @ id) | (X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id)) | ~ ! [X422 : (subst > term > term)] : ((X420 @ id @ (lam @ (X422 @ sh @ one)) @ id) | ~ ! [X423 : subst,X424 : subst,X425 : term] : (((X422 @ (comp @ X423 @ X424) @ (sub @ X425 @ X424))) = ((sub @ (X422 @ X423 @ X425) @ X424))) | ~ ! [X426 : term] : (~(X420 @ id @ X426 @ id) | (X420 @ id @ (X422 @ id @ X426) @ id))))) & ! [X427 : term] : ? [X428 : d_term] : (((d2term @ X428)) = X427) & ((! [X429 : term] : (((sub @ X429 @ id)) = X429) => ! [X430 : term] : (((sub @ X430 @ id)) = X430)) <=> termmset_lthm) & (! [X431 : term,X432 : term] : ((X431 = X432) | (((lam @ X432)) != ((lam @ X431)))) <=> laminj) & substmonoid_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X433 : (subst > term > subst > $o)] : ~ ! [X434 : (term > $o)] : ~ ! [X435 : term] : (((X434 @ X435)) = ((X433 @ id @ X435 @ id))) => (! [X436 : (term > $o),X437 : term] : (~ ! [X438 : term,X439 : term] : (~(X436 @ X439) | (X436 @ (ap @ X439 @ X438)) | ~(X436 @ X438)) | (X436 @ X437) | ~ ! [X440 : term] : (~(var @ X440) | (X436 @ X440)) | ~ ! [X441 : term] : (~ ! [X442 : term] : (~(X436 @ X442) | (X436 @ (sub @ X441 @ (push @ X442 @ id)))) | (X436 @ (lam @ X441)))) => (! [X443 : term] : (((sub @ X443 @ id)) = X443) => (! [X444 : (term > $o),X445 : (subst > term > subst > $o),X446 : term] : (~ ! [X447 : term] : ((X444 @ (sub @ X446 @ (push @ X447 @ id))) | ~(X444 @ X447)) | ~ ! [X448 : (subst > term > term)] : ((X445 @ id @ (lam @ (X448 @ sh @ one)) @ id) | ~ ! [X449 : subst,X450 : term,X451 : subst] : (((sub @ (X448 @ X449 @ X450) @ X451)) = ((X448 @ (comp @ X449 @ X451) @ (sub @ X450 @ X451)))) | ~ ! [X452 : term] : (~(X445 @ id @ X452 @ id) | (X445 @ id @ (X448 @ id @ X452) @ id))) | (X444 @ (lam @ X446)) | ~ ! [X453 : term] : (((X445 @ id @ X453 @ id)) = ((X444 @ X453)))) => ! [X454 : term,X455 : (subst > term > subst > $o)] : (~ ! [X456 : (subst > term > term)] : (~ ! [X457 : subst,X458 : term,X459 : subst] : (((sub @ (X456 @ X457 @ X458) @ X459)) = ((X456 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))) | ~ ! [X460 : term] : ((X455 @ id @ (X456 @ id @ X460) @ id) | ~(X455 @ id @ X460 @ id)) | (X455 @ id @ (lam @ (X456 @ sh @ one)) @ id)) | ~ ! [X461 : term,X462 : subst,X463 : subst,X464 : subst] : ((X455 @ (comp @ X463 @ X464) @ (sub @ X461 @ X464) @ X462) | ~(X455 @ X463 @ X461 @ (comp @ X464 @ X462))) | ~ ! [X465 : term] : ((X455 @ id @ X465 @ id) | ~(var @ (sub @ X465 @ id))) | (X455 @ id @ X454 @ id) | ~ ! [X466 : term,X467 : term] : (~(X455 @ id @ X466 @ id) | (X455 @ id @ (ap @ (sub @ X467 @ id) @ X466) @ id) | ~(X455 @ id @ X467 @ id)) | ~ ! [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (~(X455 @ (comp @ X471 @ X469) @ (sub @ X468 @ X469) @ X470) | (X455 @ X471 @ X468 @ (comp @ X469 @ X470)))))))) <=> hoasinduction_lthm_3) & (hoasinduction_lem3aaa <=> ! [X472 : (subst > term > subst > $o),X473 : term] : (~ ! [X474 : term] : ((X472 @ id @ (sub @ X473 @ (push @ X474 @ id)) @ id) | ~(X472 @ id @ X474 @ id)) | (X472 @ id @ (lam @ (sub @ X473 @ (push @ one @ sh))) @ id) | ~ ! [X475 : (subst > term > term),X476 : term] : (~ ! [X477 : term,X478 : subst,X479 : subst] : (((sub @ (sub @ X476 @ (push @ X477 @ X478)) @ X479)) = ((sub @ (X475 @ X478 @ X477) @ X479))) | ~ ! [X480 : term] : (~(X472 @ id @ X480 @ id) | (X472 @ id @ (X475 @ id @ X480) @ id)) | ~ ! [X481 : subst,X482 : term,X483 : subst] : (((X475 @ (comp @ X481 @ X483) @ (sub @ X482 @ X483))) = ((sub @ X476 @ (push @ (sub @ X482 @ X483) @ (comp @ X481 @ X483))))) | (X472 @ id @ (lam @ (X475 @ sh @ one)) @ id)))) & hoaslamnotvar_gthm & (hoasinduction_lem0_lthm <=> ! [X484 : (subst > term > subst > $o)] : ~ ! [X485 : (term > $o)] : ~ ! [X486 : term] : (((X485 @ X486)) = ((X484 @ id @ X486 @ id)))) & ~lamnotap & axassoc & (! [X487 : (subst > term > subst > $o),X488 : term] : (~ ! [X489 : term] : (~(X487 @ id @ X489 @ id) | (X487 @ id @ (sub @ X488 @ (push @ X489 @ id)) @ id)) | ~ ! [X490 : (subst > term > term)] : (~ ! [X491 : term] : ((X487 @ id @ (X490 @ id @ X491) @ id) | ~(X487 @ id @ X491 @ id)) | (X487 @ id @ (lam @ (X490 @ sh @ one)) @ id) | ~ ! [X492 : term,X493 : subst,X494 : subst] : (((X490 @ (comp @ X493 @ X494) @ (sub @ X492 @ X494))) = ((sub @ (X490 @ X493 @ X492) @ X494)))) | (X487 @ id @ (lam @ (sub @ X488 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (hoasinduction_lem3b <=> ! [X495 : term] : ~ ! [X496 : (subst > term > term)] : (((sub @ X495 @ (push @ one @ sh))) != ((X496 @ sh @ one)))) & ((! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X498 : (term > $o),X499 : term,X500 : (subst > term > subst > $o)] : ((X498 @ (lam @ X499)) | ~ ! [X501 : term] : (((X500 @ id @ X501 @ id)) = ((X498 @ X501))) | ~ ! [X502 : (subst > term > term)] : ((X500 @ id @ (lam @ (X502 @ sh @ one)) @ id) | ~ ! [X503 : term] : (~(X500 @ id @ X503 @ id) | (X500 @ id @ (X502 @ id @ X503) @ id)) | ~ ! [X504 : term,X505 : subst,X506 : subst] : (((X502 @ (comp @ X506 @ X505) @ (sub @ X504 @ X505))) = ((sub @ (X502 @ X506 @ X504) @ X505)))) | ~ ! [X507 : term] : (~(X498 @ X507) | (X498 @ (sub @ X499 @ (push @ X507 @ id)))) | ~ ! [X508 : subst,X509 : subst,X510 : subst,X511 : term] : ((X500 @ (comp @ X508 @ X510) @ (sub @ X511 @ X510) @ X509) | ~(X500 @ X508 @ X511 @ (comp @ X510 @ X509))) | ~ ! [X512 : term,X513 : subst,X514 : subst,X515 : subst] : ((X500 @ X513 @ X512 @ (comp @ X514 @ X515)) | ~(X500 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515)))) <=> hoasinduction_lem3v2_lthm) & ! [X516 : d_subst,X517 : d_subst] : ((((d2subst @ X516)) = ((d2subst @ X517))) => (X516 = X517)) & (! [X518 : term,X519 : term,X520 : term,X521 : term] : ((((ap @ X520 @ X518)) != ((ap @ X521 @ X519))) | (X518 = X519)) <=> apinj2) & (pushprop_lem1 <=> ! [X522 : (term > $o),X523 : term,X524 : (term > $o),X525 : term,X526 : subst] : (~(X522 @ X523) | (X524 @ (sub @ X523 @ (push @ X525 @ X526))))) & hoasinduction_lem2_lthm & (! [X527 : (subst > term > subst > $o)] : ~ ! [X528 : (term > $o)] : ~ ! [X529 : term] : (((X527 @ id @ X529 @ id)) = ((X528 @ X529))) <=> hoasinduction_lem0) & (! [X530 : term] : ~ ! [X531 : (subst > term > term)] : ~ ! [X532 : subst,X533 : term] : (((sub @ X530 @ (push @ X533 @ X532))) = ((X531 @ X532 @ X533))) <=> hoasinduction_lem3v2_f) & axmap & hoaslamnotap_gthm & (! [X534 : (subst > term > subst > $o),X535 : term] : (~ ! [X536 : term] : (~(X534 @ id @ X536 @ id) | (X534 @ id @ (sub @ X535 @ (push @ X536 @ id)) @ id)) | (X534 @ id @ (lam @ X535) @ id) | ~ ! [X537 : (subst > term > term)] : (~ ! [X538 : subst,X539 : term,X540 : subst] : (((X537 @ (comp @ X538 @ X540) @ (sub @ X539 @ X540))) = ((sub @ (X537 @ X538 @ X539) @ X540))) | (X534 @ id @ (lam @ (X537 @ sh @ one)) @ id) | ~ ! [X541 : term] : (~(X534 @ id @ X541 @ id) | (X534 @ id @ (X537 @ id @ X541) @ id))) | ~ ! [X542 : subst,X543 : subst,X544 : term,X545 : subst] : (~(X534 @ (comp @ X543 @ X542) @ (sub @ X544 @ X542) @ X545) | (X534 @ X543 @ X544 @ (comp @ X542 @ X545))) | ~ ! [X546 : subst,X547 : term,X548 : subst,X549 : subst] : ((X534 @ (comp @ X546 @ X549) @ (sub @ X547 @ X549) @ X548) | ~(X534 @ X546 @ X547 @ (comp @ X549 @ X548)))) <=> hoasinduction_lem3) & hoasinduction_gthm & pushprop_gthm & hoasapnotvar_gthm & axclos & (((lam @ (d2term @ d_one))) = ((d2term @ d_one)))),
% 5.86/1.21 inference(rectify,[],[f1])).
% 5.86/1.21 thf(f5,plain,(
% 5.86/1.21 (! [X1 : (term > $o),X0 : subst,X2 : term] : ~ ! [X3 : (term > $o)] : ~ ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & ! [X5 : d_subst] : (d_id = X5) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((induction2_lthm = $true) <=> (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (term > $o),X12 : subst,X13 : term] : (($true = ((X11 @ (sub @ X13 @ X12)))) | ~ ! [X14 : term] : (($true = ((X11 @ (lam @ X14)))) | ~ ! [X15 : term] : (~ (((X11 @ X15)) = $true) | ($true = ((X11 @ (sub @ X14 @ (push @ X15 @ id))))))) | ~ ! [X16 : term] : (~ ($true = ((var @ X16))) | ($true = ((X11 @ (sub @ X16 @ X12))))) | ~ ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ~ ($true = ((X11 @ X18))) | ~ (((X11 @ X17)) = $true))) => ! [X19 : term,X20 : (term > $o)] : (~ ! [X21 : term] : (($true = ((X20 @ X21))) | ~ ($true = ((var @ X21)))) | ~ ! [X22 : term,X23 : term] : ((((X20 @ (ap @ X22 @ X23))) = $true) | ~ ($true = ((X20 @ X23))) | ~ ($true = ((X20 @ X22)))) | ($true = ((X20 @ X19))) | ~ ! [X24 : term] : (~ ! [X25 : term] : (($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id))))) | ~ ($true = ((X20 @ X25)))) | ($true = ((X20 @ (lam @ X24))))))))) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & (lamnotvar = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem1 = $true) & ((axscons = $true) <=> ! [X29 : subst] : (((push @ (sub @ one @ X29) @ (comp @ sh @ X29))) = X29)) & (induction2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X30 : subst,X31 : term] : (((comp @ sh @ (push @ X31 @ X30))) = X30) <=> (axshiftcons = $true)) & (! [X32 : term,X33 : (subst > term > subst > $o)] : (($true = ((X33 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id))) | ~ ! [X34 : term] : (($true = ((X33 @ id @ (sub @ X32 @ (push @ X34 @ id)) @ id))) | ~ (((X33 @ id @ X34 @ id)) = $true)) | ~ ! [X35 : (subst > term > term)] : (($true = ((X33 @ id @ (lam @ (X35 @ sh @ one)) @ id))) | ~ ! [X36 : term] : (~ ($true = ((X33 @ id @ X36 @ id))) | ($true = ((X33 @ id @ (X35 @ id @ X36) @ id)))) | ~ ! [X37 : subst,X38 : subst,X39 : term] : (((X35 @ (comp @ X37 @ X38) @ (sub @ X39 @ X38))) = ((sub @ (X35 @ X37 @ X39) @ X38))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (axabs = $true) & (! [X40 : term,X41 : term,X42 : (subst > term > subst > $o)] : (~ ! [X43 : subst,X44 : subst,X45 : term,X46 : subst] : (($true = ((X42 @ (comp @ X44 @ X46) @ (sub @ X45 @ X46) @ X43))) | ~ ($true = ((X42 @ X44 @ X45 @ (comp @ X46 @ X43))))) | ~ ! [X47 : term,X48 : term] : (~ ($true = ((X42 @ id @ X47 @ id))) | ~ ($true = ((X42 @ id @ X48 @ id))) | (((X42 @ id @ (ap @ (sub @ X48 @ id) @ X47) @ id)) = $true)) | ($true = ((X42 @ id @ (ap @ X40 @ X41) @ id))) | ~ (((X42 @ id @ X41 @ id)) = $true) | ~ ! [X49 : subst,X50 : subst,X51 : term,X52 : subst] : (($true = ((X42 @ X49 @ X51 @ (comp @ X52 @ X50)))) | ~ ($true = ((X42 @ (comp @ X49 @ X52) @ (sub @ X51 @ X52) @ X50)))) | ~ ($true = ((X42 @ id @ X40 @ id)))) <=> (hoasinduction_lem2 = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X53 : term,X54 : subst] : (((sub @ one @ (push @ X53 @ X54))) = X53) => (! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56) => (! [X57 : term,X58 : term] : ((((lam @ X58)) != ((lam @ X57))) | (X57 = X58)) => ! [X59 : subst,X60 : (subst > term > term),X61 : term,X62 : (subst > term > term)] : (~ ! [X63 : subst,X64 : subst,X65 : term] : (((X62 @ (comp @ X64 @ X63) @ (sub @ X65 @ X63))) = ((sub @ (X62 @ X64 @ X65) @ X63))) | ~ ! [X66 : term,X67 : subst,X68 : subst] : (((X60 @ (comp @ X67 @ X68) @ (sub @ X66 @ X68))) = ((sub @ (X60 @ X67 @ X66) @ X68))) | (((X60 @ X59 @ X61)) = ((X62 @ X59 @ X61))) | (((lam @ (X62 @ sh @ one))) != ((lam @ (X60 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X69 : term] : ~ ! [X70 : (subst > term > term)] : ~ ! [X71 : subst,X72 : term] : (((sub @ X69 @ (push @ X72 @ X71))) = ((X70 @ X71 @ X72)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (pushprop_lem2v2 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (ulamvarind = $true) & (pushprop_lem3v2 = $true) & ((axidl = $true) <=> ! [X74 : subst] : (((comp @ id @ X74)) = X74)) & (hoasinduction_lem1v2 = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X75 : term] : (((sub @ X75 @ id)) = X75) => (! [X76 : term,X77 : (subst > term > subst > $o)] : (($true = ((X77 @ id @ (lam @ (sub @ X76 @ (push @ one @ sh))) @ id))) | ~ ! [X78 : term] : (~ ($true = ((X77 @ id @ X78 @ id))) | ($true = ((X77 @ id @ (sub @ X76 @ (push @ X78 @ id)) @ id)))) | ~ ! [X79 : (subst > term > term)] : (~ ! [X80 : term] : (~ ($true = ((X77 @ id @ X80 @ id))) | ($true = ((X77 @ id @ (X79 @ id @ X80) @ id)))) | ($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ~ ! [X81 : subst,X82 : term,X83 : subst] : (((sub @ (X79 @ X81 @ X82) @ X83)) = ((X79 @ (comp @ X81 @ X83) @ (sub @ X82 @ X83)))))) => ! [X84 : (subst > term > subst > $o),X85 : term] : (~ ! [X86 : (subst > term > term)] : (~ ! [X87 : subst,X88 : subst,X89 : term] : (((X86 @ (comp @ X88 @ X87) @ (sub @ X89 @ X87))) = ((sub @ (X86 @ X88 @ X89) @ X87))) | ($true = ((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id))) | ~ ! [X90 : term] : (($true = ((X84 @ id @ (X86 @ id @ X90) @ id))) | ~ ($true = ((X84 @ id @ X90 @ id))))) | ~ ! [X91 : term] : (~ ($true = ((X84 @ id @ X91 @ id))) | ($true = ((X84 @ id @ (sub @ X85 @ (push @ X91 @ id)) @ id)))) | ($true = ((X84 @ id @ (lam @ X85) @ id))) | ~ ! [X92 : subst,X93 : subst,X94 : term,X95 : subst] : (~ ($true = ((X84 @ (comp @ X95 @ X92) @ (sub @ X94 @ X92) @ X93))) | (((X84 @ X95 @ X94 @ (comp @ X92 @ X93))) = $true)) | ~ ! [X96 : subst,X97 : subst,X98 : term,X99 : subst] : (~ ($true = ((X84 @ X96 @ X98 @ (comp @ X97 @ X99)))) | ($true = ((X84 @ (comp @ X96 @ X97) @ (sub @ X98 @ X97) @ X99)))))))) & (hoasinduction_lem1v2_gthm = $true) & (((d2subst @ d_id)) = id) & (axapp = $true) & (pushprop_lem1_gthm = $true) & (pushprop = $true) & ((hoaslamnotap = $true) <=> ! [X100 : (subst > term > term),X101 : term,X102 : term] : (~ ! [X103 : subst,X104 : term,X105 : subst] : (((sub @ (X100 @ X105 @ X104) @ X103)) = ((X100 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103)))) | (((lam @ (X100 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X101))))) & (! [X106 : term,X107 : term,X108 : (term > $o),X109 : (subst > term > subst > $o)] : (~ ! [X110 : term,X111 : term] : (~ ($true = ((X109 @ id @ X111 @ id))) | ~ (((X109 @ id @ X110 @ id)) = $true) | ($true = ((X109 @ id @ (ap @ (sub @ X111 @ id) @ X110) @ id)))) | ~ ! [X112 : term] : (((X108 @ X112)) = ((X109 @ id @ X112 @ id))) | ~ ! [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (($true = ((X109 @ (comp @ X116 @ X113) @ (sub @ X115 @ X113) @ X114))) | ~ (((X109 @ X116 @ X115 @ (comp @ X113 @ X114))) = $true)) | ($true = ((X108 @ (ap @ X107 @ X106)))) | ~ ! [X117 : subst,X118 : term,X119 : subst,X120 : subst] : (($true = ((X109 @ X117 @ X118 @ (comp @ X120 @ X119)))) | ~ ($true = ((X109 @ (comp @ X117 @ X120) @ (sub @ X118 @ X120) @ X119)))) | ~ ($true = ((X108 @ X107))) | ~ ($true = ((X108 @ X106)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X121 : subst] : ? [X122 : d_subst] : (((d2subst @ X122)) = X121) & ((hoaslaminj = $true) <=> ! [X123 : (subst > term > term),X124 : subst,X125 : (subst > term > term),X126 : term] : (~ ! [X127 : subst,X128 : term,X129 : subst] : (((X123 @ (comp @ X127 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X123 @ X127 @ X128) @ X129))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X125 @ sh @ one)))) | (((X123 @ X124 @ X126)) = ((X125 @ X124 @ X126))) | ~ ! [X130 : subst,X131 : term,X132 : subst] : (((sub @ (X125 @ X130 @ X131) @ X132)) = ((X125 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132)))))) & ((induction2 = $true) <=> ! [X133 : (term > $o),X134 : term] : ((((X133 @ X134)) = $true) | ~ ! [X135 : term,X136 : term] : (~ (((X133 @ X135)) = $true) | ~ ($true = ((X133 @ X136))) | (((X133 @ (ap @ X136 @ X135))) = $true)) | ~ ! [X137 : term] : (($true = ((X133 @ (lam @ X137)))) | ~ ! [X138 : term] : (($true = ((X133 @ (sub @ X137 @ (push @ X138 @ id))))) | ~ ($true = ((X133 @ X138))))) | ~ ! [X139 : term] : (~ ($true = ((var @ X139))) | ($true = ((X133 @ X139)))))) & (pushprop_lem0_gthm = $true) & ((induction2lem = $true) <=> ! [X140 : (term > $o),X141 : term,X142 : subst] : (~ ! [X143 : term] : (($true = ((X140 @ (lam @ X143)))) | ~ ! [X144 : term] : (~ ($true = ((X140 @ X144))) | ($true = ((X140 @ (sub @ X143 @ (push @ X144 @ id))))))) | ~ ! [X145 : term,X146 : term] : (~ (((X140 @ X145)) = $true) | ~ ($true = ((X140 @ X146))) | (((X140 @ (ap @ X146 @ X145))) = $true)) | ~ ! [X147 : term] : (($true = ((X140 @ (sub @ X147 @ X142)))) | ~ ($true = ((var @ X147)))) | ($true = ((X140 @ (sub @ X141 @ X142)))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (apnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem1_gthm = $true) & (! [X151 : term,X152 : term,X153 : term,X154 : term] : ((((ap @ X151 @ X154)) != ((ap @ X152 @ X153))) | (X151 = X152)) <=> (apinj1 = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X155 : term] : ~ ! [X156 : (subst > term > term)] : ~ ! [X157 : term,X158 : subst] : (((sub @ X155 @ (push @ X157 @ X158))) = ((X156 @ X158 @ X157))) => (! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (subst > term > subst > $o),X162 : (term > $o)] : (~ ! [X163 : (subst > term > term)] : (~ ! [X164 : term] : (~ ($true = ((X161 @ id @ X164 @ id))) | ($true = ((X161 @ id @ (X163 @ id @ X164) @ id)))) | ~ ! [X165 : subst,X166 : subst,X167 : term] : (((sub @ (X163 @ X165 @ X167) @ X166)) = ((X163 @ (comp @ X165 @ X166) @ (sub @ X167 @ X166)))) | ($true = ((X161 @ id @ (lam @ (X163 @ sh @ one)) @ id)))) | ($true = ((X162 @ (lam @ X160)))) | ~ ! [X168 : term] : (($true = ((X162 @ (sub @ X160 @ (push @ X168 @ id))))) | ~ ($true = ((X162 @ X168)))) | ~ ! [X169 : term] : (((X162 @ X169)) = ((X161 @ id @ X169 @ id))))))) & (induction2lem_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X170 : (term > $o),X171 : term] : (($true = ((X170 @ X171))) | ~ ! [X172 : term] : ((((X170 @ X172)) = $true) | ~ ($true = ((var @ X172)))) | ~ ! [X173 : term] : (~ ($true = ((X170 @ X173))) | ($true = ((X170 @ (lam @ X173))))) | ~ ! [X174 : term,X175 : term] : (~ (((X170 @ X175)) = $true) | ~ ($true = ((X170 @ X174))) | ($true = ((X170 @ (ap @ X175 @ X174)))))) <=> (induction = $true)) & (! [X176 : term,X177 : (term > $o),X178 : (subst > term > subst > $o)] : (~ ! [X179 : term] : (((X177 @ X179)) = ((X178 @ id @ X179 @ id))) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term] : (~ ($true = ((X178 @ id @ X181 @ id))) | ($true = ((X178 @ id @ (X180 @ id @ X181) @ id)))) | ($true = ((X178 @ id @ (lam @ (X180 @ sh @ one)) @ id))) | ~ ! [X182 : subst,X183 : subst,X184 : term] : (((X180 @ (comp @ X183 @ X182) @ (sub @ X184 @ X182))) = ((sub @ (X180 @ X183 @ X184) @ X182)))) | ~ ! [X185 : term] : (~ ($true = ((X177 @ X185))) | ($true = ((X177 @ (sub @ X176 @ (push @ X185 @ id)))))) | ($true = ((X177 @ (lam @ X176))))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj2 = $true) <=> ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X187 = X188) | (((ap @ (sub @ X186 @ id) @ X187)) != ((ap @ (sub @ X189 @ id) @ X188))))) & (! [X190 : term,X191 : term] : ((X190 = X191) | (((sub @ X191 @ sh)) != ((sub @ X190 @ sh)))) <=> (shinj = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X192 : term,X193 : (subst > term > subst > $o)] : (~ ! [X194 : term,X195 : term] : (~ ($true = ((X193 @ id @ X195 @ id))) | ($true = ((X193 @ id @ (ap @ (sub @ X195 @ id) @ X194) @ id))) | ~ ($true = ((X193 @ id @ X194 @ id)))) | ~ ! [X196 : (subst > term > term)] : (~ ! [X197 : term] : ((((X193 @ id @ (X196 @ id @ X197) @ id)) = $true) | ~ ($true = ((X193 @ id @ X197 @ id)))) | ($true = ((X193 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ~ ! [X198 : term,X199 : subst,X200 : subst] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))) | ($true = ((X193 @ id @ X192 @ id))))) & ((hoasapinj2_lthm = $true) <=> (! [X201 : term,X202 : term,X203 : term,X204 : term] : ((X201 = X204) | (((ap @ X203 @ X201)) != ((ap @ X202 @ X204)))) => ! [X205 : term,X206 : term,X207 : term,X208 : term] : ((X206 = X207) | (((ap @ (sub @ X208 @ id) @ X206)) != ((ap @ (sub @ X205 @ id) @ X207)))))) & (hoasapnotvar_lthm = $true) & (! [X209 : subst,X210 : term,X211 : (term > $o),X212 : (term > $o)] : (~ ! [X213 : term] : (((X211 @ (sub @ X213 @ (push @ X210 @ X209)))) = ((X212 @ X213))) | (((X212 @ one)) = $true) | ~ ($true = ((X211 @ X210)))) <=> (pushprop_lem1v2 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X214 : subst,X215 : term] : (((sub @ one @ (push @ X215 @ X214))) = X215) => ! [X216 : term,X217 : (term > $o),X218 : subst,X219 : (term > $o)] : (~ ! [X220 : term] : (((X219 @ (sub @ X220 @ (push @ X216 @ X218)))) = ((X217 @ X220))) | ~ ($true = ((X219 @ X216))) | ($true = ((X217 @ one)))))) & ((hoasapinj1_lthm = $true) <=> (! [X221 : term] : (((sub @ X221 @ id)) = X221) => (! [X222 : term,X223 : term,X224 : term,X225 : term] : ((X223 = X224) | (((ap @ X224 @ X222)) != ((ap @ X223 @ X225)))) => ! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ (sub @ X228 @ id) @ X226)) != ((ap @ (sub @ X229 @ id) @ X227))) | (X228 = X229))))) & ((hoasinduction = $true) <=> ! [X230 : (subst > term > subst > $o),X231 : term] : (~ ! [X232 : subst,X233 : term,X234 : subst,X235 : subst] : (~ (((X230 @ X232 @ X233 @ (comp @ X234 @ X235))) = $true) | ($true = ((X230 @ (comp @ X232 @ X234) @ (sub @ X233 @ X234) @ X235)))) | ~ ! [X236 : term] : (~ (((var @ (sub @ X236 @ id))) = $true) | ($true = ((X230 @ id @ X236 @ id)))) | ($true = ((X230 @ id @ X231 @ id))) | ~ ! [X237 : term,X238 : term] : (~ ($true = ((X230 @ id @ X237 @ id))) | ~ (((X230 @ id @ X238 @ id)) = $true) | ($true = ((X230 @ id @ (ap @ (sub @ X238 @ id) @ X237) @ id)))) | ~ ! [X239 : (subst > term > term)] : (($true = ((X230 @ id @ (lam @ (X239 @ sh @ one)) @ id))) | ~ ! [X240 : subst,X241 : subst,X242 : term] : (((sub @ (X239 @ X241 @ X242) @ X240)) = ((X239 @ (comp @ X241 @ X240) @ (sub @ X242 @ X240)))) | ~ ! [X243 : term] : (~ (((X230 @ id @ X243 @ id)) = $true) | ($true = ((X230 @ id @ (X239 @ id @ X243) @ id))))) | ~ ! [X244 : term,X245 : subst,X246 : subst,X247 : subst] : (($true = ((X230 @ X245 @ X244 @ (comp @ X247 @ X246)))) | ~ ($true = ((X230 @ (comp @ X245 @ X247) @ (sub @ X244 @ X247) @ X246)))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X248 : term] : ~ ! [X249 : (subst > term > term)] : (((X249 @ sh @ one)) != ((sub @ X248 @ (push @ one @ sh))))) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X250 : d_term] : (d_one = X250) & (pushprop_lthm = $true) & (hoasinduction_lem2_gthm = $true) & (! [X251 : term,X252 : (term > $o),X253 : (subst > term > subst > $o)] : (($true = ((X252 @ (lam @ X251)))) | ~ ! [X254 : term] : (((X253 @ id @ X254 @ id)) = ((X252 @ X254))) | ~ ! [X255 : subst,X256 : term,X257 : subst,X258 : subst] : (~ ($true = ((X253 @ X255 @ X256 @ (comp @ X258 @ X257)))) | ($true = ((X253 @ (comp @ X255 @ X258) @ (sub @ X256 @ X258) @ X257)))) | ~ ! [X259 : subst,X260 : term,X261 : subst,X262 : subst] : (($true = ((X253 @ X259 @ X260 @ (comp @ X261 @ X262)))) | ~ ($true = ((X253 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)))) | ~ ! [X263 : term] : (~ ($true = ((X252 @ X263))) | ($true = ((X252 @ (sub @ X251 @ (push @ X263 @ id)))))) | ~ ! [X264 : (subst > term > term)] : (($true = ((X253 @ id @ (lam @ (X264 @ sh @ one)) @ id))) | ~ ! [X265 : term,X266 : subst,X267 : subst] : (((sub @ (X264 @ X266 @ X265) @ X267)) = ((X264 @ (comp @ X266 @ X267) @ (sub @ X265 @ X267)))) | ~ ! [X268 : term] : (~ ($true = ((X253 @ id @ X268 @ id))) | ($true = ((X253 @ id @ (X264 @ id @ X268) @ id)))))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X269 : (term > $o),X270 : term] : (~ ! [X271 : term] : (($true = ((X269 @ (lam @ X271)))) | ~ ! [X272 : term] : (($true = ((X269 @ (sub @ X271 @ (push @ X272 @ id))))) | ~ ($true = ((X269 @ X272))))) | ~ ! [X273 : term,X274 : term] : (~ ($true = ((X269 @ X274))) | ($true = ((X269 @ (ap @ X274 @ X273)))) | ~ ($true = ((X269 @ X273)))) | ($true = ((X269 @ X270))) | ~ ! [X275 : term] : (($true = ((X269 @ X275))) | ~ ($true = ((var @ X275))))) => (! [X276 : term,X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term,X280 : subst,X281 : subst,X282 : subst] : (~ ($true = ((X277 @ (comp @ X280 @ X282) @ (sub @ X279 @ X282) @ X281))) | ($true = ((X277 @ X280 @ X279 @ (comp @ X282 @ X281))))) | ~ ! [X283 : term,X284 : term] : (~ ($true = ((X277 @ id @ X284 @ id))) | ~ ($true = ((X277 @ id @ X283 @ id))) | ($true = ((X277 @ id @ (ap @ (sub @ X284 @ id) @ X283) @ id)))) | ~ ($true = ((X277 @ id @ X276 @ id))) | ~ ($true = ((X277 @ id @ X278 @ id))) | ~ ! [X285 : subst,X286 : subst,X287 : term,X288 : subst] : (~ ($true = ((X277 @ X288 @ X287 @ (comp @ X286 @ X285)))) | ($true = ((X277 @ (comp @ X288 @ X286) @ (sub @ X287 @ X286) @ X285)))) | (((X277 @ id @ (ap @ X278 @ X276) @ id)) = $true)) => (! [X289 : (subst > term > subst > $o),X290 : term] : (~ ! [X291 : (subst > term > term)] : (~ ! [X292 : term] : (($true = ((X289 @ id @ (X291 @ id @ X292) @ id))) | ~ (((X289 @ id @ X292 @ id)) = $true)) | ($true = ((X289 @ id @ (lam @ (X291 @ sh @ one)) @ id))) | ~ ! [X293 : subst,X294 : term,X295 : subst] : (((X291 @ (comp @ X295 @ X293) @ (sub @ X294 @ X293))) = ((sub @ (X291 @ X295 @ X294) @ X293)))) | ~ ! [X296 : subst,X297 : term,X298 : subst,X299 : subst] : (~ ($true = ((X289 @ X298 @ X297 @ (comp @ X296 @ X299)))) | (((X289 @ (comp @ X298 @ X296) @ (sub @ X297 @ X296) @ X299)) = $true)) | ($true = ((X289 @ id @ (lam @ X290) @ id))) | ~ ! [X300 : subst,X301 : subst,X302 : subst,X303 : term] : (~ ($true = ((X289 @ (comp @ X302 @ X300) @ (sub @ X303 @ X300) @ X301))) | ($true = ((X289 @ X302 @ X303 @ (comp @ X300 @ X301))))) | ~ ! [X304 : term] : (~ ($true = ((X289 @ id @ X304 @ id))) | ($true = ((X289 @ id @ (sub @ X290 @ (push @ X304 @ id)) @ id))))) => ! [X305 : term,X306 : (subst > term > subst > $o)] : (($true = ((X306 @ id @ X305 @ id))) | ~ ! [X307 : term,X308 : term] : (($true = ((X306 @ id @ (ap @ (sub @ X307 @ id) @ X308) @ id))) | ~ ($true = ((X306 @ id @ X308 @ id))) | ~ ($true = ((X306 @ id @ X307 @ id)))) | ~ ! [X309 : subst,X310 : term,X311 : subst,X312 : subst] : (($true = ((X306 @ X311 @ X310 @ (comp @ X312 @ X309)))) | ~ ($true = ((X306 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312) @ X309)))) | ~ ! [X313 : (subst > term > term)] : ((((X306 @ id @ (lam @ (X313 @ sh @ one)) @ id)) = $true) | ~ ! [X314 : term] : (($true = ((X306 @ id @ (X313 @ id @ X314) @ id))) | ~ ($true = ((X306 @ id @ X314 @ id)))) | ~ ! [X315 : term,X316 : subst,X317 : subst] : (((sub @ (X313 @ X316 @ X315) @ X317)) = ((X313 @ (comp @ X316 @ X317) @ (sub @ X315 @ X317))))) | ~ ! [X318 : term] : (~ ($true = ((var @ (sub @ X318 @ id)))) | ($true = ((X306 @ id @ X318 @ id)))) | ~ ! [X319 : subst,X320 : subst,X321 : subst,X322 : term] : (~ ($true = ((X306 @ X321 @ X322 @ (comp @ X319 @ X320)))) | (((X306 @ (comp @ X321 @ X319) @ (sub @ X322 @ X319) @ X320)) = $true)))))) <=> (hoasinduction_lthm = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X323 : term] : (((sub @ X323 @ id)) = X323) => (! [X324 : term,X325 : (subst > term > subst > $o)] : (~ ! [X326 : (subst > term > term)] : (~ ! [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X326 @ X329 @ X328) @ X327)) = ((X326 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327)))) | ($true = ((X325 @ id @ (lam @ (X326 @ sh @ one)) @ id))) | ~ ! [X330 : term] : (($true = ((X325 @ id @ (X326 @ id @ X330) @ id))) | ~ ($true = ((X325 @ id @ X330 @ id))))) | ($true = ((X325 @ id @ (lam @ (sub @ X324 @ (push @ one @ sh))) @ id))) | ~ ! [X331 : term] : (($true = ((X325 @ id @ (sub @ X324 @ (push @ X331 @ id)) @ id))) | ~ ($true = ((X325 @ id @ X331 @ id))))) => ! [X332 : term,X333 : (subst > term > subst > $o)] : (~ ! [X334 : (subst > term > term)] : (~ ! [X335 : term] : (~ ($true = ((X333 @ id @ X335 @ id))) | ($true = ((X333 @ id @ (X334 @ id @ X335) @ id)))) | (((X333 @ id @ (lam @ (X334 @ sh @ one)) @ id)) = $true) | ~ ! [X336 : subst,X337 : subst,X338 : term] : (((sub @ (X334 @ X336 @ X338) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X338 @ X337))))) | (((X333 @ id @ (lam @ X332) @ id)) = $true) | ~ ! [X339 : term] : (~ ($true = ((X333 @ id @ X339 @ id))) | ($true = ((X333 @ id @ (sub @ X332 @ (push @ X339 @ id)) @ id)))))))) & ((! [X340 : subst] : (((comp @ id @ X340)) = X340) & ! [X341 : subst] : (((comp @ X341 @ id)) = X341)) <=> (substmonoid = $true)) & ((! [X342 : (subst > term > subst > $o)] : ~ ! [X343 : (term > $o)] : ~ ! [X344 : term] : (((X343 @ X344)) = ((X342 @ id @ X344 @ id))) => (! [X345 : (term > $o),X346 : term] : (~ ! [X347 : term,X348 : term] : (~ (((X345 @ X347)) = $true) | ~ ($true = ((X345 @ X348))) | ($true = ((X345 @ (ap @ X347 @ X348))))) | ($true = ((X345 @ X346))) | ~ ! [X349 : term] : (~ ($true = ((var @ X349))) | ($true = ((X345 @ X349)))) | ~ ! [X350 : term] : (($true = ((X345 @ (lam @ X350)))) | ~ ! [X351 : term] : (~ (((X345 @ X351)) = $true) | ($true = ((X345 @ (sub @ X350 @ (push @ X351 @ id)))))))) => (! [X352 : term] : (((sub @ X352 @ id)) = X352) => (! [X353 : term,X354 : (term > $o),X355 : (subst > term > subst > $o)] : (~ ! [X356 : (subst > term > term)] : (($true = ((X355 @ id @ (lam @ (X356 @ sh @ one)) @ id))) | ~ ! [X357 : subst,X358 : term,X359 : subst] : (((X356 @ (comp @ X359 @ X357) @ (sub @ X358 @ X357))) = ((sub @ (X356 @ X359 @ X358) @ X357))) | ~ ! [X360 : term] : (~ ($true = ((X355 @ id @ X360 @ id))) | ($true = ((X355 @ id @ (X356 @ id @ X360) @ id))))) | (((X354 @ (lam @ X353))) = $true) | ~ ! [X361 : term] : (($true = ((X354 @ (sub @ X353 @ (push @ X361 @ id))))) | ~ ($true = ((X354 @ X361)))) | ~ ! [X362 : term] : (((X355 @ id @ X362 @ id)) = ((X354 @ X362)))) => ! [X363 : term,X364 : (subst > term > subst > $o)] : (~ ! [X365 : (subst > term > term)] : ((((X364 @ id @ (lam @ (X365 @ sh @ one)) @ id)) = $true) | ~ ! [X366 : term,X367 : subst,X368 : subst] : (((X365 @ (comp @ X368 @ X367) @ (sub @ X366 @ X367))) = ((sub @ (X365 @ X368 @ X366) @ X367))) | ~ ! [X369 : term] : (($true = ((X364 @ id @ (X365 @ id @ X369) @ id))) | ~ ($true = ((X364 @ id @ X369 @ id))))) | ($true = ((X364 @ id @ X363 @ id))) | ~ ! [X370 : term,X371 : term] : (~ ($true = ((X364 @ id @ X370 @ id))) | ($true = ((X364 @ id @ (ap @ (sub @ X370 @ id) @ X371) @ id))) | ~ (((X364 @ id @ X371 @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X372 : subst,X373 : (term > $o),X374 : term] : ~ ! [X375 : (term > $o)] : ~ ! [X376 : term] : (((X373 @ (sub @ X376 @ (push @ X374 @ X372)))) = ((X375 @ X376)))) & ((pushprop_lem1_lthm = $true) <=> (! [X377 : subst,X378 : term] : (((sub @ one @ (push @ X378 @ X377))) = X378) => (! [X379 : term,X380 : subst] : (((comp @ sh @ (push @ X379 @ X380))) = X380) => ! [X381 : term,X382 : (term > $o),X383 : subst,X384 : term,X385 : (term > $o)] : (~ ($true = ((X382 @ X384))) | ($true = ((X385 @ (sub @ X384 @ (push @ X381 @ X383))))))))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axvarshift = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X386 : term] : (((sub @ X386 @ id)) = X386) <=> (axvarid = $true)) & (hoaslamnotap_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X387 : subst,X388 : term] : (((sub @ one @ (push @ X388 @ X387))) = X388) => (! [X389 : subst,X390 : term] : (((comp @ sh @ (push @ X390 @ X389))) = X389) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : (term > $o),X393 : term] : (~ ! [X394 : term] : (($true = ((X392 @ X394))) | ~ ($true = ((var @ X394)))) | ~ ! [X395 : term] : (~ ($true = ((X392 @ X395))) | ($true = ((X392 @ (lam @ X395))))) | ($true = ((X392 @ X393))) | ~ ! [X396 : term,X397 : term] : (~ ($true = ((X392 @ X396))) | ~ ($true = ((X392 @ X397))) | ($true = ((X392 @ (ap @ X397 @ X396)))))) => ! [X398 : term,X399 : (term > $o),X400 : subst] : (~ ! [X401 : term,X402 : term] : (~ ($true = ((X399 @ X401))) | ~ ($true = ((X399 @ X402))) | ($true = ((X399 @ (ap @ X401 @ X402))))) | ($true = ((X399 @ (sub @ X398 @ X400)))) | ~ ! [X403 : term] : (($true = ((X399 @ (sub @ X403 @ X400)))) | ~ ($true = ((var @ X403)))) | ~ ! [X404 : term] : (($true = ((X399 @ (lam @ X404)))) | ~ ! [X405 : term] : (($true = ((X399 @ (sub @ X404 @ (push @ X405 @ id))))) | ~ ($true = ((X399 @ X405))))))))))) & (hoasinduction_lem3v2_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)))))))))))))) & (hoasapinj2_gthm = $true) & ! [X411 : d_term,X412 : d_term] : ((((d2term @ X412)) = ((d2term @ X411))) => (X411 = X412)) & ((substmonoid_lthm = $true) <=> (! [X413 : subst] : (((comp @ id @ X413)) = X413) => (! [X414 : subst] : (((comp @ X414 @ id)) = X414) => (! [X415 : subst] : (((comp @ X415 @ id)) = X415) & ! [X416 : subst] : (((comp @ id @ X416)) = X416))))) & (! [X417 : subst,X418 : term] : (((sub @ one @ (push @ X418 @ X417))) = X418) <=> (axvarcons = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X419 : term,X420 : (subst > term > subst > $o)] : (($true = ((X420 @ id @ (lam @ X419) @ id))) | ~ ! [X421 : term] : (~ ($true = ((X420 @ id @ X421 @ id))) | ($true = ((X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id)))) | ~ ! [X422 : (subst > term > term)] : ((((X420 @ id @ (lam @ (X422 @ sh @ one)) @ id)) = $true) | ~ ! [X423 : subst,X424 : subst,X425 : term] : (((X422 @ (comp @ X423 @ X424) @ (sub @ X425 @ X424))) = ((sub @ (X422 @ X423 @ X425) @ X424))) | ~ ! [X426 : term] : (~ ($true = ((X420 @ id @ X426 @ id))) | ($true = ((X420 @ id @ (X422 @ id @ X426) @ id))))))) & ! [X427 : term] : ? [X428 : d_term] : (((d2term @ X428)) = X427) & ((! [X429 : term] : (((sub @ X429 @ id)) = X429) => ! [X430 : term] : (((sub @ X430 @ id)) = X430)) <=> (termmset_lthm = $true)) & (! [X431 : term,X432 : term] : ((X431 = X432) | (((lam @ X432)) != ((lam @ X431)))) <=> (laminj = $true)) & (substmonoid_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X433 : (subst > term > subst > $o)] : ~ ! [X434 : (term > $o)] : ~ ! [X435 : term] : (((X434 @ X435)) = ((X433 @ id @ X435 @ id))) => (! [X436 : (term > $o),X437 : term] : (~ ! [X438 : term,X439 : term] : (~ ($true = ((X436 @ X439))) | ($true = ((X436 @ (ap @ X439 @ X438)))) | ~ ($true = ((X436 @ X438)))) | (((X436 @ X437)) = $true) | ~ ! [X440 : term] : (~ ($true = ((var @ X440))) | ($true = ((X436 @ X440)))) | ~ ! [X441 : term] : (~ ! [X442 : term] : (~ ($true = ((X436 @ X442))) | ($true = ((X436 @ (sub @ X441 @ (push @ X442 @ id)))))) | ($true = ((X436 @ (lam @ X441)))))) => (! [X443 : term] : (((sub @ X443 @ id)) = X443) => (! [X444 : (term > $o),X445 : (subst > term > subst > $o),X446 : term] : (~ ! [X447 : term] : (($true = ((X444 @ (sub @ X446 @ (push @ X447 @ id))))) | ~ ($true = ((X444 @ X447)))) | ~ ! [X448 : (subst > term > term)] : ((((X445 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X449 : subst,X450 : term,X451 : subst] : (((sub @ (X448 @ X449 @ X450) @ X451)) = ((X448 @ (comp @ X449 @ X451) @ (sub @ X450 @ X451)))) | ~ ! [X452 : term] : (~ ($true = ((X445 @ id @ X452 @ id))) | (((X445 @ id @ (X448 @ id @ X452) @ id)) = $true))) | ($true = ((X444 @ (lam @ X446)))) | ~ ! [X453 : term] : (((X445 @ id @ X453 @ id)) = ((X444 @ X453)))) => ! [X454 : term,X455 : (subst > term > subst > $o)] : (~ ! [X456 : (subst > term > term)] : (~ ! [X457 : subst,X458 : term,X459 : subst] : (((sub @ (X456 @ X457 @ X458) @ X459)) = ((X456 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))) | ~ ! [X460 : term] : ((((X455 @ id @ (X456 @ id @ X460) @ id)) = $true) | ~ ($true = ((X455 @ id @ X460 @ id)))) | ($true = ((X455 @ id @ (lam @ (X456 @ sh @ one)) @ id)))) | ~ ! [X461 : term,X462 : subst,X463 : subst,X464 : subst] : (($true = ((X455 @ (comp @ X463 @ X464) @ (sub @ X461 @ X464) @ X462))) | ~ (((X455 @ X463 @ X461 @ (comp @ X464 @ X462))) = $true)) | ~ ! [X465 : term] : (($true = ((X455 @ id @ X465 @ id))) | ~ ($true = ((var @ (sub @ X465 @ id))))) | ($true = ((X455 @ id @ X454 @ id))) | ~ ! [X466 : term,X467 : term] : (~ ($true = ((X455 @ id @ X466 @ id))) | (((X455 @ id @ (ap @ (sub @ X467 @ id) @ X466) @ id)) = $true) | ~ ($true = ((X455 @ id @ X467 @ id)))) | ~ ! [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (~ ($true = ((X455 @ (comp @ X471 @ X469) @ (sub @ X468 @ X469) @ X470))) | ($true = ((X455 @ X471 @ X468 @ (comp @ X469 @ X470)))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X472 : (subst > term > subst > $o),X473 : term] : (~ ! [X474 : term] : ((((X472 @ id @ (sub @ X473 @ (push @ X474 @ id)) @ id)) = $true) | ~ ($true = ((X472 @ id @ X474 @ id)))) | ($true = ((X472 @ id @ (lam @ (sub @ X473 @ (push @ one @ sh))) @ id))) | ~ ! [X475 : (subst > term > term),X476 : term] : (~ ! [X477 : term,X478 : subst,X479 : subst] : (((sub @ (sub @ X476 @ (push @ X477 @ X478)) @ X479)) = ((sub @ (X475 @ X478 @ X477) @ X479))) | ~ ! [X480 : term] : (~ ($true = ((X472 @ id @ X480 @ id))) | ($true = ((X472 @ id @ (X475 @ id @ X480) @ id)))) | ~ ! [X481 : subst,X482 : term,X483 : subst] : (((X475 @ (comp @ X481 @ X483) @ (sub @ X482 @ X483))) = ((sub @ X476 @ (push @ (sub @ X482 @ X483) @ (comp @ X481 @ X483))))) | ($true = ((X472 @ id @ (lam @ (X475 @ sh @ one)) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X484 : (subst > term > subst > $o)] : ~ ! [X485 : (term > $o)] : ~ ! [X486 : term] : (((X485 @ X486)) = ((X484 @ id @ X486 @ id)))) & ~ (lamnotap = $true) & (axassoc = $true) & (! [X487 : (subst > term > subst > $o),X488 : term] : (~ ! [X489 : term] : (~ ($true = ((X487 @ id @ X489 @ id))) | ($true = ((X487 @ id @ (sub @ X488 @ (push @ X489 @ id)) @ id)))) | ~ ! [X490 : (subst > term > term)] : (~ ! [X491 : term] : (($true = ((X487 @ id @ (X490 @ id @ X491) @ id))) | ~ ($true = ((X487 @ id @ X491 @ id)))) | ($true = ((X487 @ id @ (lam @ (X490 @ sh @ one)) @ id))) | ~ ! [X492 : term,X493 : subst,X494 : subst] : (((X490 @ (comp @ X493 @ X494) @ (sub @ X492 @ X494))) = ((sub @ (X490 @ X493 @ X492) @ X494)))) | ($true = ((X487 @ id @ (lam @ (sub @ X488 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X495 : term] : ~ ! [X496 : (subst > term > term)] : (((sub @ X495 @ (push @ one @ sh))) != ((X496 @ sh @ one)))) & ((! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X498 : (term > $o),X499 : term,X500 : (subst > term > subst > $o)] : (($true = ((X498 @ (lam @ X499)))) | ~ ! [X501 : term] : (((X500 @ id @ X501 @ id)) = ((X498 @ X501))) | ~ ! [X502 : (subst > term > term)] : (($true = ((X500 @ id @ (lam @ (X502 @ sh @ one)) @ id))) | ~ ! [X503 : term] : (~ ($true = ((X500 @ id @ X503 @ id))) | (((X500 @ id @ (X502 @ id @ X503) @ id)) = $true)) | ~ ! [X504 : term,X505 : subst,X506 : subst] : (((X502 @ (comp @ X506 @ X505) @ (sub @ X504 @ X505))) = ((sub @ (X502 @ X506 @ X504) @ X505)))) | ~ ! [X507 : term] : (~ ($true = ((X498 @ X507))) | (((X498 @ (sub @ X499 @ (push @ X507 @ id)))) = $true)) | ~ ! [X508 : subst,X509 : subst,X510 : subst,X511 : term] : ((((X500 @ (comp @ X508 @ X510) @ (sub @ X511 @ X510) @ X509)) = $true) | ~ ($true = ((X500 @ X508 @ X511 @ (comp @ X510 @ X509))))) | ~ ! [X512 : term,X513 : subst,X514 : subst,X515 : subst] : (($true = ((X500 @ X513 @ X512 @ (comp @ X514 @ X515)))) | ~ ($true = ((X500 @ (comp @ X513 @ X514) @ (sub @ X512 @ X514) @ X515)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X516 : d_subst,X517 : d_subst] : ((((d2subst @ X516)) = ((d2subst @ X517))) => (X516 = X517)) & (! [X518 : term,X519 : term,X520 : term,X521 : term] : ((((ap @ X520 @ X518)) != ((ap @ X521 @ X519))) | (X518 = X519)) <=> (apinj2 = $true)) & ((pushprop_lem1 = $true) <=> ! [X522 : (term > $o),X523 : term,X524 : (term > $o),X525 : term,X526 : subst] : (~ ($true = ((X522 @ X523))) | ($true = ((X524 @ (sub @ X523 @ (push @ X525 @ X526))))))) & (hoasinduction_lem2_lthm = $true) & (! [X527 : (subst > term > subst > $o)] : ~ ! [X528 : (term > $o)] : ~ ! [X529 : term] : (((X527 @ id @ X529 @ id)) = ((X528 @ X529))) <=> (hoasinduction_lem0 = $true)) & (! [X530 : term] : ~ ! [X531 : (subst > term > term)] : ~ ! [X532 : subst,X533 : term] : (((sub @ X530 @ (push @ X533 @ X532))) = ((X531 @ X532 @ X533))) <=> (hoasinduction_lem3v2_f = $true)) & (axmap = $true) & (hoaslamnotap_gthm = $true) & (! [X534 : (subst > term > subst > $o),X535 : term] : (~ ! [X536 : term] : (~ ($true = ((X534 @ id @ X536 @ id))) | ($true = ((X534 @ id @ (sub @ X535 @ (push @ X536 @ id)) @ id)))) | ($true = ((X534 @ id @ (lam @ X535) @ id))) | ~ ! [X537 : (subst > term > term)] : (~ ! [X538 : subst,X539 : term,X540 : subst] : (((X537 @ (comp @ X538 @ X540) @ (sub @ X539 @ X540))) = ((sub @ (X537 @ X538 @ X539) @ X540))) | ($true = ((X534 @ id @ (lam @ (X537 @ sh @ one)) @ id))) | ~ ! [X541 : term] : (~ ($true = ((X534 @ id @ X541 @ id))) | ($true = ((X534 @ id @ (X537 @ id @ X541) @ id))))) | ~ ! [X542 : subst,X543 : subst,X544 : term,X545 : subst] : (~ (((X534 @ (comp @ X543 @ X542) @ (sub @ X544 @ X542) @ X545)) = $true) | ($true = ((X534 @ X543 @ X544 @ (comp @ X542 @ X545))))) | ~ ! [X546 : subst,X547 : term,X548 : subst,X549 : subst] : ((((X534 @ (comp @ X546 @ X549) @ (sub @ X547 @ X549) @ X548)) = $true) | ~ (((X534 @ X546 @ X547 @ (comp @ X549 @ X548))) = $true))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (hoasapnotvar_gthm = $true) & (axclos = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one))))),
% 5.86/1.21 inference(fool_elimination,[],[f4])).
% 5.86/1.21 thf(f6,plain,(
% 5.86/1.21 ~ (! [X0 : (term > $o),X1 : (subst > term > subst > $o)] : (! [X2 : (subst > term > term)] : (! [X3 : subst,X4 : subst,X5 : term] : (((sub @ (X2 @ X4 @ X5) @ X3)) = ((X2 @ (comp @ X4 @ X3) @ (sub @ X5 @ X3)))) => (! [X6 : term] : ((X1 @ id @ X6 @ id) => (X1 @ id @ (X2 @ id @ X6) @ id)) => (X1 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : ((X2 @ X7 @ X8)))) @ id))) => ((hoasinduction_p_and_p_prime @ X1 @ X0) => ! [X9 : term] : (! [X10 : term] : ((X0 @ X10) => (X0 @ (sub @ X9 @ (push @ X10 @ id)))) => (X0 @ (lam @ X9))))) = hoasinduction_lem3v2a)),
% 5.86/1.21 inference(rectify,[],[f3])).
% 5.86/1.21 thf(f7,plain,(
% 5.86/1.21 ~ (hoasinduction_lem3v2a = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))))),
% 5.86/1.21 inference(fool_elimination,[],[f6])).
% 5.86/1.21 thf(f8,plain,(
% 5.86/1.21 (! [X1 : (term > $o),X0 : subst,X2 : term] : ~ ! [X3 : (term > $o)] : ~ ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & ! [X5 : d_subst] : (d_id = X5) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((induction2_lthm = $true) <=> (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (term > $o),X12 : subst,X13 : term] : (($true = ((X11 @ (sub @ X13 @ X12)))) | ~ ! [X14 : term] : (($true = ((X11 @ (lam @ X14)))) | ~ ! [X15 : term] : (~ (((X11 @ X15)) = $true) | ($true = ((X11 @ (sub @ X14 @ (push @ X15 @ id))))))) | ~ ! [X16 : term] : (~ ($true = ((var @ X16))) | ($true = ((X11 @ (sub @ X16 @ X12))))) | ~ ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ~ ($true = ((X11 @ X18))) | ~ (((X11 @ X17)) = $true))) => ! [X19 : term,X20 : (term > $o)] : (~ ! [X21 : term] : (($true = ((X20 @ X21))) | ~ ($true = ((var @ X21)))) | ~ ! [X22 : term,X23 : term] : ((((X20 @ (ap @ X22 @ X23))) = $true) | ~ ($true = ((X20 @ X23))) | ~ ($true = ((X20 @ X22)))) | ($true = ((X20 @ X19))) | ~ ! [X24 : term] : (~ ! [X25 : term] : (($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id))))) | ~ ($true = ((X20 @ X25)))) | ($true = ((X20 @ (lam @ X24))))))))) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & (lamnotvar = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem1 = $true) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) <=> (axscons = $true)) & (induction2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) <=> (axshiftcons = $true)) & (! [X30 : term,X31 : (subst > term > subst > $o)] : (($true = ((X31 @ id @ (lam @ (sub @ X30 @ (push @ one @ sh))) @ id))) | ~ ! [X32 : term] : (($true = ((X31 @ id @ (sub @ X30 @ (push @ X32 @ id)) @ id))) | ~ ($true = ((X31 @ id @ X32 @ id)))) | ~ ! [X33 : (subst > term > term)] : (($true = ((X31 @ id @ (lam @ (X33 @ sh @ one)) @ id))) | ~ ! [X34 : term] : (~ ($true = ((X31 @ id @ X34 @ id))) | ($true = ((X31 @ id @ (X33 @ id @ X34) @ id)))) | ~ ! [X36 : subst,X37 : term,X35 : subst] : (((X33 @ (comp @ X35 @ X36) @ (sub @ X37 @ X36))) = ((sub @ (X33 @ X35 @ X37) @ X36))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (axabs = $true) & (! [X38 : term,X39 : term,X40 : (subst > term > subst > $o)] : (~ ! [X41 : subst,X42 : subst,X43 : term,X44 : subst] : (($true = ((X40 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) | ~ ($true = ((X40 @ X42 @ X43 @ (comp @ X44 @ X41))))) | ~ ! [X45 : term,X46 : term] : (~ ($true = ((X40 @ id @ X45 @ id))) | ~ ($true = ((X40 @ id @ X46 @ id))) | ($true = ((X40 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id)))) | ($true = ((X40 @ id @ (ap @ X38 @ X39) @ id))) | ~ ($true = ((X40 @ id @ X39 @ id))) | ~ ! [X47 : subst,X48 : subst,X49 : term,X50 : subst] : ((((X40 @ X47 @ X49 @ (comp @ X50 @ X48))) = $true) | ~ ($true = ((X40 @ (comp @ X47 @ X50) @ (sub @ X49 @ X50) @ X48)))) | ~ ($true = ((X40 @ id @ X38 @ id)))) <=> (hoasinduction_lem2 = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X51 : term,X52 : subst] : (((sub @ one @ (push @ X51 @ X52))) = X51) => (! [X54 : subst,X53 : term] : (((comp @ sh @ (push @ X53 @ X54))) = X54) => (! [X56 : term,X55 : term] : ((X55 = X56) | (((lam @ X55)) != ((lam @ X56)))) => ! [X59 : term,X60 : (subst > term > term),X58 : (subst > term > term),X57 : subst] : ((((lam @ (X58 @ sh @ one))) != ((lam @ (X60 @ sh @ one)))) | ~ ! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X58 @ X65 @ X64) @ X66)) = ((X58 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | ~ ! [X63 : term,X61 : subst,X62 : subst] : (((sub @ (X60 @ X62 @ X63) @ X61)) = ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | (((X58 @ X57 @ X59)) = ((X60 @ X57 @ X59))))))) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X67 : term] : ~ ! [X68 : (subst > term > term)] : ~ ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & ((axidr = $true) <=> ! [X71 : subst] : (((comp @ X71 @ id)) = X71)) & (pushprop_lem2v2 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (ulamvarind = $true) & (pushprop_lem3v2 = $true) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (hoasinduction_lem1v2 = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X73 : term] : (((sub @ X73 @ id)) = X73) => (! [X74 : term,X75 : (subst > term > subst > $o)] : (($true = ((X75 @ id @ (lam @ (sub @ X74 @ (push @ one @ sh))) @ id))) | ~ ! [X76 : term] : (~ ($true = ((X75 @ id @ X76 @ id))) | ($true = ((X75 @ id @ (sub @ X74 @ (push @ X76 @ id)) @ id)))) | ~ ! [X77 : (subst > term > term)] : (~ ! [X78 : term] : (~ ($true = ((X75 @ id @ X78 @ id))) | ($true = ((X75 @ id @ (X77 @ id @ X78) @ id)))) | (((X75 @ id @ (lam @ (X77 @ sh @ one)) @ id)) = $true) | ~ ! [X80 : term,X79 : subst,X81 : subst] : (((sub @ (X77 @ X79 @ X80) @ X81)) = ((X77 @ (comp @ X79 @ X81) @ (sub @ X80 @ X81)))))) => ! [X82 : (subst > term > subst > $o),X83 : term] : (~ ! [X84 : (subst > term > term)] : (~ ! [X85 : subst,X86 : subst,X87 : term] : (((X84 @ (comp @ X86 @ X85) @ (sub @ X87 @ X85))) = ((sub @ (X84 @ X86 @ X87) @ X85))) | ($true = ((X82 @ id @ (lam @ (X84 @ sh @ one)) @ id))) | ~ ! [X88 : term] : (($true = ((X82 @ id @ (X84 @ id @ X88) @ id))) | ~ ($true = ((X82 @ id @ X88 @ id))))) | ~ ! [X89 : term] : (~ ($true = ((X82 @ id @ X89 @ id))) | ($true = ((X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)))) | ($true = ((X82 @ id @ (lam @ X83) @ id))) | ~ ! [X90 : subst,X91 : subst,X92 : term,X93 : subst] : (~ ($true = ((X82 @ (comp @ X93 @ X90) @ (sub @ X92 @ X90) @ X91))) | ($true = ((X82 @ X93 @ X92 @ (comp @ X90 @ X91))))) | ~ ! [X94 : subst,X95 : subst,X96 : term,X97 : subst] : (~ (((X82 @ X94 @ X96 @ (comp @ X95 @ X97))) = $true) | ($true = ((X82 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95) @ X97)))))))) & (hoasinduction_lem1v2_gthm = $true) & (((d2subst @ d_id)) = id) & (axapp = $true) & (pushprop_lem1_gthm = $true) & (pushprop = $true) & (! [X98 : (subst > term > term),X100 : term,X99 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ~ ! [X103 : subst,X102 : term,X101 : subst] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) = ((sub @ (X98 @ X103 @ X102) @ X101)))) <=> (hoaslamnotap = $true)) & (! [X104 : term,X105 : term,X106 : (term > $o),X107 : (subst > term > subst > $o)] : (~ ! [X108 : term,X109 : term] : (~ ($true = ((X107 @ id @ X109 @ id))) | ~ ($true = ((X107 @ id @ X108 @ id))) | ($true = ((X107 @ id @ (ap @ (sub @ X109 @ id) @ X108) @ id)))) | ~ ! [X110 : term] : (((X107 @ id @ X110 @ id)) = ((X106 @ X110))) | ~ ! [X111 : subst,X112 : subst,X113 : term,X114 : subst] : (($true = ((X107 @ (comp @ X114 @ X111) @ (sub @ X113 @ X111) @ X112))) | ~ ($true = ((X107 @ X114 @ X113 @ (comp @ X111 @ X112))))) | (((X106 @ (ap @ X105 @ X104))) = $true) | ~ ! [X115 : subst,X116 : term,X117 : subst,X118 : subst] : (($true = ((X107 @ X115 @ X116 @ (comp @ X118 @ X117)))) | ~ ($true = ((X107 @ (comp @ X115 @ X118) @ (sub @ X116 @ X118) @ X117)))) | ~ ($true = ((X106 @ X105))) | ~ ($true = ((X106 @ X104)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & (! [X121 : (subst > term > term),X122 : subst,X123 : (subst > term > term),X124 : term] : (~ ! [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) = ((sub @ (X123 @ X128 @ X129) @ X130))) | ~ ! [X127 : subst,X126 : term,X125 : subst] : (((sub @ (X121 @ X125 @ X126) @ X127)) = ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one))))) <=> (hoaslaminj = $true)) & ((induction2 = $true) <=> ! [X131 : (term > $o),X132 : term] : (($true = ((X131 @ X132))) | ~ ! [X133 : term,X134 : term] : (~ ($true = ((X131 @ X133))) | ~ ($true = ((X131 @ X134))) | ($true = ((X131 @ (ap @ X134 @ X133))))) | ~ ! [X135 : term] : (($true = ((X131 @ (lam @ X135)))) | ~ ! [X136 : term] : (($true = ((X131 @ (sub @ X135 @ (push @ X136 @ id))))) | ~ ($true = ((X131 @ X136))))) | ~ ! [X137 : term] : (~ ($true = ((var @ X137))) | ($true = ((X131 @ X137)))))) & (pushprop_lem0_gthm = $true) & ((induction2lem = $true) <=> ! [X138 : (term > $o),X139 : term,X140 : subst] : (~ ! [X141 : term] : (($true = ((X138 @ (lam @ X141)))) | ~ ! [X142 : term] : (~ ($true = ((X138 @ X142))) | (((X138 @ (sub @ X141 @ (push @ X142 @ id)))) = $true))) | ~ ! [X143 : term,X144 : term] : (~ ($true = ((X138 @ X143))) | ~ ($true = ((X138 @ X144))) | ($true = ((X138 @ (ap @ X144 @ X143))))) | ~ ! [X145 : term] : (($true = ((X138 @ (sub @ X145 @ X140)))) | ~ ($true = ((var @ X145)))) | ($true = ((X138 @ (sub @ X139 @ X140)))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (apnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasinduction_lem1_gthm = $true) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) <=> (apinj1 = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X153 : subst,X152 : term] : (((X151 @ X153 @ X152)) = ((sub @ X150 @ (push @ X152 @ X153)))) => (! [X154 : term] : (((sub @ X154 @ id)) = X154) => ! [X155 : term,X156 : (subst > term > subst > $o),X157 : (term > $o)] : (~ ! [X158 : (subst > term > term)] : (~ ! [X159 : term] : (~ ($true = ((X156 @ id @ X159 @ id))) | ($true = ((X156 @ id @ (X158 @ id @ X159) @ id)))) | ~ ! [X161 : subst,X162 : term,X160 : subst] : (((X158 @ (comp @ X160 @ X161) @ (sub @ X162 @ X161))) = ((sub @ (X158 @ X160 @ X162) @ X161))) | ($true = ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ($true = ((X157 @ (lam @ X155)))) | ~ ! [X163 : term] : ((((X157 @ (sub @ X155 @ (push @ X163 @ id)))) = $true) | ~ ($true = ((X157 @ X163)))) | ~ ! [X164 : term] : (((X156 @ id @ X164 @ id)) = ((X157 @ X164))))))) & (induction2lem_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X165 : (term > $o),X166 : term] : (($true = ((X165 @ X166))) | ~ ! [X167 : term] : (($true = ((X165 @ X167))) | ~ ($true = ((var @ X167)))) | ~ ! [X168 : term] : (~ ($true = ((X165 @ X168))) | ($true = ((X165 @ (lam @ X168))))) | ~ ! [X169 : term,X170 : term] : (~ ($true = ((X165 @ X170))) | ~ ($true = ((X165 @ X169))) | ($true = ((X165 @ (ap @ X170 @ X169)))))) <=> (induction = $true)) & (! [X171 : term,X172 : (term > $o),X173 : (subst > term > subst > $o)] : (~ ! [X174 : term] : (((X173 @ id @ X174 @ id)) = ((X172 @ X174))) | ~ ! [X175 : (subst > term > term)] : (~ ! [X176 : term] : (~ ($true = ((X173 @ id @ X176 @ id))) | ($true = ((X173 @ id @ (X175 @ id @ X176) @ id)))) | ($true = ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) | ~ ! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177))))) | ~ ! [X180 : term] : (~ ($true = ((X172 @ X180))) | ($true = ((X172 @ (sub @ X171 @ (push @ X180 @ id)))))) | ($true = ((X172 @ (lam @ X171))))) <=> (hoasinduction_lem3v2a = $true)) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) <=> (hoasapinj2 = $true)) & ((shinj = $true) <=> ! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X187 : term,X188 : (subst > term > subst > $o)] : (~ ! [X189 : term,X190 : term] : (~ ($true = ((X188 @ id @ X190 @ id))) | ($true = ((X188 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id))) | ~ ($true = ((X188 @ id @ X189 @ id)))) | ~ ! [X191 : (subst > term > term)] : (~ ! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | ~ (((X188 @ id @ X192 @ id)) = $true)) | ($true = ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) | ~ ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))))) & ((hoasapinj2_lthm = $true) <=> (! [X196 : term,X197 : term,X198 : term,X199 : term] : ((X196 = X199) | (((ap @ X198 @ X196)) != ((ap @ X197 @ X199)))) => ! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))))) & (hoasapnotvar_lthm = $true) & (! [X204 : subst,X205 : term,X206 : (term > $o),X207 : (term > $o)] : (~ ! [X208 : term] : (((X207 @ X208)) = ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | (((X207 @ one)) = $true) | ~ ($true = ((X206 @ X205)))) <=> (pushprop_lem1v2 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) = X210) => ! [X211 : term,X212 : (term > $o),X213 : subst,X214 : (term > $o)] : (~ ! [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) = ((X212 @ X215))) | ~ ($true = ((X214 @ X211))) | (((X212 @ one)) = $true)))) & ((hoasapinj1_lthm = $true) <=> (! [X216 : term] : (((sub @ X216 @ id)) = X216) => (! [X219 : term,X217 : term,X220 : term,X218 : term] : ((((ap @ X218 @ X220)) != ((ap @ X219 @ X217))) | (X218 = X219)) => ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224))))) & ((hoasinduction = $true) <=> ! [X225 : (subst > term > subst > $o),X226 : term] : (~ ! [X227 : subst,X228 : term,X229 : subst,X230 : subst] : (~ ($true = ((X225 @ X227 @ X228 @ (comp @ X229 @ X230)))) | ($true = ((X225 @ (comp @ X227 @ X229) @ (sub @ X228 @ X229) @ X230)))) | ~ ! [X231 : term] : (~ ($true = ((var @ (sub @ X231 @ id)))) | ($true = ((X225 @ id @ X231 @ id)))) | ($true = ((X225 @ id @ X226 @ id))) | ~ ! [X232 : term,X233 : term] : (~ ($true = ((X225 @ id @ X232 @ id))) | ~ ($true = ((X225 @ id @ X233 @ id))) | ($true = ((X225 @ id @ (ap @ (sub @ X233 @ id) @ X232) @ id)))) | ~ ! [X234 : (subst > term > term)] : (($true = ((X225 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X235 : subst,X236 : subst,X237 : term] : (((X234 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))) = ((sub @ (X234 @ X236 @ X237) @ X235))) | ~ ! [X238 : term] : (~ ($true = ((X225 @ id @ X238 @ id))) | ($true = ((X225 @ id @ (X234 @ id @ X238) @ id))))) | ~ ! [X239 : term,X240 : subst,X241 : subst,X242 : subst] : ((((X225 @ X240 @ X239 @ (comp @ X242 @ X241))) = $true) | ~ ($true = ((X225 @ (comp @ X240 @ X242) @ (sub @ X239 @ X242) @ X241)))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X243 : term] : ~ ! [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) != ((X244 @ sh @ one)))) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X245 : d_term] : (d_one = X245) & (pushprop_lthm = $true) & (hoasinduction_lem2_gthm = $true) & (! [X246 : term,X247 : (term > $o),X248 : (subst > term > subst > $o)] : (($true = ((X247 @ (lam @ X246)))) | ~ ! [X249 : term] : (((X248 @ id @ X249 @ id)) = ((X247 @ X249))) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~ ($true = ((X248 @ X250 @ X251 @ (comp @ X253 @ X252)))) | ($true = ((X248 @ (comp @ X250 @ X253) @ (sub @ X251 @ X253) @ X252)))) | ~ ! [X254 : subst,X255 : term,X256 : subst,X257 : subst] : (($true = ((X248 @ X254 @ X255 @ (comp @ X256 @ X257)))) | ~ ($true = ((X248 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257)))) | ~ ! [X258 : term] : (~ ($true = ((X247 @ X258))) | ($true = ((X247 @ (sub @ X246 @ (push @ X258 @ id)))))) | ~ ! [X259 : (subst > term > term)] : (($true = ((X248 @ id @ (lam @ (X259 @ sh @ one)) @ id))) | ~ ! [X260 : term,X262 : subst,X261 : subst] : (((sub @ (X259 @ X261 @ X260) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X260 @ X262)))) | ~ ! [X263 : term] : (~ ($true = ((X248 @ id @ X263 @ id))) | ($true = ((X248 @ id @ (X259 @ id @ X263) @ id)))))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X264 : (term > $o),X265 : term] : (~ ! [X266 : term] : (($true = ((X264 @ (lam @ X266)))) | ~ ! [X267 : term] : (($true = ((X264 @ (sub @ X266 @ (push @ X267 @ id))))) | ~ ($true = ((X264 @ X267))))) | ~ ! [X268 : term,X269 : term] : (~ ($true = ((X264 @ X269))) | ($true = ((X264 @ (ap @ X269 @ X268)))) | ~ ($true = ((X264 @ X268)))) | ($true = ((X264 @ X265))) | ~ ! [X270 : term] : ((((X264 @ X270)) = $true) | ~ ($true = ((var @ X270))))) => (! [X271 : term,X272 : (subst > term > subst > $o),X273 : term] : (~ ! [X274 : term,X275 : subst,X276 : subst,X277 : subst] : (~ ($true = ((X272 @ (comp @ X275 @ X277) @ (sub @ X274 @ X277) @ X276))) | ($true = ((X272 @ X275 @ X274 @ (comp @ X277 @ X276))))) | ~ ! [X278 : term,X279 : term] : (~ ($true = ((X272 @ id @ X279 @ id))) | ~ ($true = ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (ap @ (sub @ X279 @ id) @ X278) @ id)))) | ~ ($true = ((X272 @ id @ X271 @ id))) | ~ ($true = ((X272 @ id @ X273 @ id))) | ~ ! [X280 : subst,X281 : subst,X282 : term,X283 : subst] : (~ ($true = ((X272 @ X283 @ X282 @ (comp @ X281 @ X280)))) | ($true = ((X272 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281) @ X280)))) | ($true = ((X272 @ id @ (ap @ X273 @ X271) @ id)))) => (! [X284 : (subst > term > subst > $o),X285 : term] : (~ ! [X286 : (subst > term > term)] : (~ ! [X287 : term] : (($true = ((X284 @ id @ (X286 @ id @ X287) @ id))) | ~ ($true = ((X284 @ id @ X287 @ id)))) | ($true = ((X284 @ id @ (lam @ (X286 @ sh @ one)) @ id))) | ~ ! [X289 : term,X288 : subst,X290 : subst] : (((sub @ (X286 @ X290 @ X289) @ X288)) = ((X286 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))))) | ~ ! [X291 : subst,X292 : term,X293 : subst,X294 : subst] : (~ (((X284 @ X293 @ X292 @ (comp @ X291 @ X294))) = $true) | (((X284 @ (comp @ X293 @ X291) @ (sub @ X292 @ X291) @ X294)) = $true)) | ($true = ((X284 @ id @ (lam @ X285) @ id))) | ~ ! [X295 : subst,X296 : subst,X297 : subst,X298 : term] : (~ ($true = ((X284 @ (comp @ X297 @ X295) @ (sub @ X298 @ X295) @ X296))) | ($true = ((X284 @ X297 @ X298 @ (comp @ X295 @ X296))))) | ~ ! [X299 : term] : (~ ($true = ((X284 @ id @ X299 @ id))) | ($true = ((X284 @ id @ (sub @ X285 @ (push @ X299 @ id)) @ id))))) => ! [X300 : term,X301 : (subst > term > subst > $o)] : (($true = ((X301 @ id @ X300 @ id))) | ~ ! [X302 : term,X303 : term] : (($true = ((X301 @ id @ (ap @ (sub @ X302 @ id) @ X303) @ id))) | ~ ($true = ((X301 @ id @ X303 @ id))) | ~ ($true = ((X301 @ id @ X302 @ id)))) | ~ ! [X304 : subst,X305 : term,X306 : subst,X307 : subst] : (($true = ((X301 @ X306 @ X305 @ (comp @ X307 @ X304)))) | ~ ($true = ((X301 @ (comp @ X306 @ X307) @ (sub @ X305 @ X307) @ X304)))) | ~ ! [X308 : (subst > term > term)] : (($true = ((X301 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X309 : term] : (($true = ((X301 @ id @ (X308 @ id @ X309) @ id))) | ~ ($true = ((X301 @ id @ X309 @ id)))) | ~ ! [X311 : subst,X312 : subst,X310 : term] : (((sub @ (X308 @ X311 @ X310) @ X312)) = ((X308 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312))))) | ~ ! [X313 : term] : (~ ($true = ((var @ (sub @ X313 @ id)))) | ($true = ((X301 @ id @ X313 @ id)))) | ~ ! [X314 : subst,X315 : subst,X316 : subst,X317 : term] : (~ ($true = ((X301 @ X316 @ X317 @ (comp @ X314 @ X315)))) | ($true = ((X301 @ (comp @ X316 @ X314) @ (sub @ X317 @ X314) @ X315)))))))) <=> (hoasinduction_lthm = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X318 : term] : (((sub @ X318 @ id)) = X318) => (! [X319 : term,X320 : (subst > term > subst > $o)] : (~ ! [X321 : (subst > term > term)] : (~ ! [X322 : subst,X323 : term,X324 : subst] : (((X321 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))) = ((sub @ (X321 @ X324 @ X323) @ X322))) | ($true = ((X320 @ id @ (lam @ (X321 @ sh @ one)) @ id))) | ~ ! [X325 : term] : (($true = ((X320 @ id @ (X321 @ id @ X325) @ id))) | ~ ($true = ((X320 @ id @ X325 @ id))))) | ($true = ((X320 @ id @ (lam @ (sub @ X319 @ (push @ one @ sh))) @ id))) | ~ ! [X326 : term] : ((((X320 @ id @ (sub @ X319 @ (push @ X326 @ id)) @ id)) = $true) | ~ (((X320 @ id @ X326 @ id)) = $true))) => ! [X327 : term,X328 : (subst > term > subst > $o)] : (~ ! [X329 : (subst > term > term)] : (~ ! [X330 : term] : (~ ($true = ((X328 @ id @ X330 @ id))) | ($true = ((X328 @ id @ (X329 @ id @ X330) @ id)))) | ($true = ((X328 @ id @ (lam @ (X329 @ sh @ one)) @ id))) | ~ ! [X333 : term,X331 : subst,X332 : subst] : (((sub @ (X329 @ X331 @ X333) @ X332)) = ((X329 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))))) | ($true = ((X328 @ id @ (lam @ X327) @ id))) | ~ ! [X334 : term] : (~ ($true = ((X328 @ id @ X334 @ id))) | ($true = ((X328 @ id @ (sub @ X327 @ (push @ X334 @ id)) @ id)))))))) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) <=> (substmonoid = $true)) & ((! [X337 : (subst > term > subst > $o)] : ~ ! [X338 : (term > $o)] : ~ ! [X339 : term] : (((X337 @ id @ X339 @ id)) = ((X338 @ X339))) => (! [X340 : (term > $o),X341 : term] : (~ ! [X342 : term,X343 : term] : (~ (((X340 @ X342)) = $true) | ~ ($true = ((X340 @ X343))) | (((X340 @ (ap @ X342 @ X343))) = $true)) | ($true = ((X340 @ X341))) | ~ ! [X344 : term] : (~ ($true = ((var @ X344))) | ($true = ((X340 @ X344)))) | ~ ! [X345 : term] : ((((X340 @ (lam @ X345))) = $true) | ~ ! [X346 : term] : (~ (((X340 @ X346)) = $true) | ($true = ((X340 @ (sub @ X345 @ (push @ X346 @ id)))))))) => (! [X347 : term] : (((sub @ X347 @ id)) = X347) => (! [X348 : term,X349 : (term > $o),X350 : (subst > term > subst > $o)] : (~ ! [X351 : (subst > term > term)] : (($true = ((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id))) | ~ ! [X352 : subst,X354 : subst,X353 : term] : (((X351 @ (comp @ X354 @ X352) @ (sub @ X353 @ X352))) = ((sub @ (X351 @ X354 @ X353) @ X352))) | ~ ! [X355 : term] : (~ (((X350 @ id @ X355 @ id)) = $true) | ($true = ((X350 @ id @ (X351 @ id @ X355) @ id))))) | ($true = ((X349 @ (lam @ X348)))) | ~ ! [X356 : term] : (($true = ((X349 @ (sub @ X348 @ (push @ X356 @ id))))) | ~ ($true = ((X349 @ X356)))) | ~ ! [X357 : term] : (((X349 @ X357)) = ((X350 @ id @ X357 @ id)))) => ! [X358 : term,X359 : (subst > term > subst > $o)] : (~ ! [X360 : (subst > term > term)] : (($true = ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id))) | ~ ! [X362 : subst,X361 : term,X363 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) | ~ ! [X364 : term] : (($true = ((X359 @ id @ (X360 @ id @ X364) @ id))) | ~ ($true = ((X359 @ id @ X364 @ id))))) | ($true = ((X359 @ id @ X358 @ id))) | ~ ! [X365 : term,X366 : term] : (~ ($true = ((X359 @ id @ X365 @ id))) | ($true = ((X359 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id))) | ~ ($true = ((X359 @ id @ X366 @ id))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X369 : term,X367 : subst,X368 : (term > $o)] : ~ ! [X370 : (term > $o)] : ~ ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) <=> (pushprop_lem0_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) = X373) => (! [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) = X375) => ! [X376 : term,X377 : (term > $o),X378 : subst,X379 : term,X380 : (term > $o)] : (~ ($true = ((X377 @ X379))) | ($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))))))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axvarshift = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((axvarid = $true) <=> ! [X381 : term] : (((sub @ X381 @ id)) = X381)) & (hoaslamnotap_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X382 : subst,X383 : term] : (((sub @ one @ (push @ X383 @ X382))) = X383) => (! [X384 : subst,X385 : term] : (((comp @ sh @ (push @ X385 @ X384))) = X384) => (! [X386 : subst] : (((comp @ X386 @ id)) = X386) => (! [X387 : (term > $o),X388 : term] : (~ ! [X389 : term] : (($true = ((X387 @ X389))) | ~ (((var @ X389)) = $true)) | ~ ! [X390 : term] : (~ ($true = ((X387 @ X390))) | ($true = ((X387 @ (lam @ X390))))) | ($true = ((X387 @ X388))) | ~ ! [X391 : term,X392 : term] : (~ ($true = ((X387 @ X391))) | ~ (((X387 @ X392)) = $true) | ($true = ((X387 @ (ap @ X392 @ X391)))))) => ! [X393 : term,X394 : (term > $o),X395 : subst] : (~ ! [X396 : term,X397 : term] : (~ ($true = ((X394 @ X396))) | ~ ($true = ((X394 @ X397))) | (((X394 @ (ap @ X396 @ X397))) = $true)) | ($true = ((X394 @ (sub @ X393 @ X395)))) | ~ ! [X398 : term] : ((((X394 @ (sub @ X398 @ X395))) = $true) | ~ ($true = ((var @ X398)))) | ~ ! [X399 : term] : (($true = ((X394 @ (lam @ X399)))) | ~ ! [X400 : term] : (($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id))))) | ~ ($true = ((X394 @ X400))))))))))) & (hoasinduction_lem3v2_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)))))))))))))) & (hoasapinj2_gthm = $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) = ((d2term @ X401))) => (X401 = X402)) & ((! [X403 : subst] : (((comp @ id @ X403)) = X403) => (! [X404 : subst] : (((comp @ X404 @ id)) = X404) => (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)))) <=> (substmonoid_lthm = $true)) & ((axvarcons = $true) <=> ! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408)) & ((hoasinduction_lem3a = $true) <=> ! [X409 : term,X410 : (subst > term > subst > $o)] : (($true = ((X410 @ id @ (lam @ X409) @ id))) | ~ ! [X411 : term] : (~ ($true = ((X410 @ id @ X411 @ id))) | (((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id)) = $true)) | ~ ! [X412 : (subst > term > term)] : (($true = ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) | ~ ! [X413 : subst,X414 : subst,X415 : term] : (((sub @ (X412 @ X413 @ X415) @ X414)) = ((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414)))) | ~ ! [X416 : term] : (~ ($true = ((X410 @ id @ X416 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X416) @ id))))))) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & ((! [X419 : term] : (((sub @ X419 @ id)) = X419) => ! [X420 : term] : (((sub @ X420 @ id)) = X420)) <=> (termmset_lthm = $true)) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) <=> (laminj = $true)) & (substmonoid_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X423 : (subst > term > subst > $o)] : ~ ! [X424 : (term > $o)] : ~ ! [X425 : term] : (((X423 @ id @ X425 @ id)) = ((X424 @ X425))) => (! [X426 : (term > $o),X427 : term] : (~ ! [X428 : term,X429 : term] : (~ ($true = ((X426 @ X429))) | ($true = ((X426 @ (ap @ X429 @ X428)))) | ~ ($true = ((X426 @ X428)))) | ($true = ((X426 @ X427))) | ~ ! [X430 : term] : (~ (((var @ X430)) = $true) | ($true = ((X426 @ X430)))) | ~ ! [X431 : term] : (~ ! [X432 : term] : (~ ($true = ((X426 @ X432))) | ($true = ((X426 @ (sub @ X431 @ (push @ X432 @ id)))))) | ($true = ((X426 @ (lam @ X431)))))) => (! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X434 : (term > $o),X435 : (subst > term > subst > $o),X436 : term] : (~ ! [X437 : term] : (($true = ((X434 @ (sub @ X436 @ (push @ X437 @ id))))) | ~ (((X434 @ X437)) = $true)) | ~ ! [X438 : (subst > term > term)] : (($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id))) | ~ ! [X440 : term,X439 : subst,X441 : subst] : (((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441))) = ((sub @ (X438 @ X439 @ X440) @ X441))) | ~ ! [X442 : term] : (~ ($true = ((X435 @ id @ X442 @ id))) | ($true = ((X435 @ id @ (X438 @ id @ X442) @ id))))) | ($true = ((X434 @ (lam @ X436)))) | ~ ! [X443 : term] : (((X434 @ X443)) = ((X435 @ id @ X443 @ id)))) => ! [X444 : term,X445 : (subst > term > subst > $o)] : (~ ! [X446 : (subst > term > term)] : (~ ! [X448 : term,X449 : subst,X447 : subst] : (((sub @ (X446 @ X447 @ X448) @ X449)) = ((X446 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) | ~ ! [X450 : term] : (($true = ((X445 @ id @ (X446 @ id @ X450) @ id))) | ~ ($true = ((X445 @ id @ X450 @ id)))) | ($true = ((X445 @ id @ (lam @ (X446 @ sh @ one)) @ id)))) | ~ ! [X451 : term,X452 : subst,X453 : subst,X454 : subst] : (($true = ((X445 @ (comp @ X453 @ X454) @ (sub @ X451 @ X454) @ X452))) | ~ (((X445 @ X453 @ X451 @ (comp @ X454 @ X452))) = $true)) | ~ ! [X455 : term] : (($true = ((X445 @ id @ X455 @ id))) | ~ ($true = ((var @ (sub @ X455 @ id))))) | ($true = ((X445 @ id @ X444 @ id))) | ~ ! [X456 : term,X457 : term] : (~ ($true = ((X445 @ id @ X456 @ id))) | ($true = ((X445 @ id @ (ap @ (sub @ X457 @ id) @ X456) @ id))) | ~ ($true = ((X445 @ id @ X457 @ id)))) | ~ ! [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (~ ($true = ((X445 @ (comp @ X461 @ X459) @ (sub @ X458 @ X459) @ X460))) | ($true = ((X445 @ X461 @ X458 @ (comp @ X459 @ X460)))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X462 : (subst > term > subst > $o),X463 : term] : (~ ! [X464 : term] : (($true = ((X462 @ id @ (sub @ X463 @ (push @ X464 @ id)) @ id))) | ~ ($true = ((X462 @ id @ X464 @ id)))) | ($true = ((X462 @ id @ (lam @ (sub @ X463 @ (push @ one @ sh))) @ id))) | ~ ! [X465 : (subst > term > term),X466 : term] : (~ ! [X468 : subst,X467 : term,X469 : subst] : (((sub @ (X465 @ X468 @ X467) @ X469)) = ((sub @ (sub @ X466 @ (push @ X467 @ X468)) @ X469))) | ~ ! [X470 : term] : (~ ($true = ((X462 @ id @ X470 @ id))) | ($true = ((X462 @ id @ (X465 @ id @ X470) @ id)))) | ~ ! [X471 : subst,X473 : subst,X472 : term] : (((X465 @ (comp @ X471 @ X473) @ (sub @ X472 @ X473))) = ((sub @ X466 @ (push @ (sub @ X472 @ X473) @ (comp @ X471 @ X473))))) | ($true = ((X462 @ id @ (lam @ (X465 @ sh @ one)) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X474 : (subst > term > subst > $o)] : ~ ! [X475 : (term > $o)] : ~ ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id)))) & ~ (lamnotap = $true) & (axassoc = $true) & (! [X477 : (subst > term > subst > $o),X478 : term] : (~ ! [X479 : term] : (~ ($true = ((X477 @ id @ X479 @ id))) | ($true = ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id)))) | ~ ! [X480 : (subst > term > term)] : (~ ! [X481 : term] : (($true = ((X477 @ id @ (X480 @ id @ X481) @ id))) | ~ ($true = ((X477 @ id @ X481 @ id)))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ~ ! [X482 : term,X484 : subst,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (! [X485 : term] : ~ ! [X486 : (subst > term > term)] : (((X486 @ sh @ one)) != ((sub @ X485 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((! [X487 : term] : (((sub @ X487 @ id)) = X487) => ! [X488 : (term > $o),X489 : term,X490 : (subst > term > subst > $o)] : (($true = ((X488 @ (lam @ X489)))) | ~ ! [X491 : term] : (((X488 @ X491)) = ((X490 @ id @ X491 @ id))) | ~ ! [X492 : (subst > term > term)] : (($true = ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) | ~ ! [X493 : term] : (~ (((X490 @ id @ X493 @ id)) = $true) | ($true = ((X490 @ id @ (X492 @ id @ X493) @ id)))) | ~ ! [X496 : subst,X494 : term,X495 : subst] : (((sub @ (X492 @ X496 @ X494) @ X495)) = ((X492 @ (comp @ X496 @ X495) @ (sub @ X494 @ X495))))) | ~ ! [X497 : term] : (~ ($true = ((X488 @ X497))) | ($true = ((X488 @ (sub @ X489 @ (push @ X497 @ id)))))) | ~ ! [X498 : subst,X499 : subst,X500 : subst,X501 : term] : (($true = ((X490 @ (comp @ X498 @ X500) @ (sub @ X501 @ X500) @ X499))) | ~ ($true = ((X490 @ X498 @ X501 @ (comp @ X500 @ X499))))) | ~ ! [X502 : term,X503 : subst,X504 : subst,X505 : subst] : (($true = ((X490 @ X503 @ X502 @ (comp @ X504 @ X505)))) | ~ ($true = ((X490 @ (comp @ X503 @ X504) @ (sub @ X502 @ X504) @ X505)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ! [X506 : d_subst,X507 : d_subst] : ((((d2subst @ X507)) = ((d2subst @ X506))) => (X506 = X507)) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) <=> (apinj2 = $true)) & ((pushprop_lem1 = $true) <=> ! [X512 : (term > $o),X513 : term,X514 : (term > $o),X515 : term,X516 : subst] : (~ ($true = ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X517 : (subst > term > subst > $o)] : ~ ! [X518 : (term > $o)] : ~ ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id)))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X520 : term] : ~ ! [X521 : (subst > term > term)] : ~ ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522))))) & (axmap = $true) & (hoaslamnotap_gthm = $true) & (! [X524 : (subst > term > subst > $o),X525 : term] : (~ ! [X526 : term] : (~ ($true = ((X524 @ id @ X526 @ id))) | ($true = ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id)))) | ($true = ((X524 @ id @ (lam @ X525) @ id))) | ~ ! [X527 : (subst > term > term)] : (~ ! [X528 : subst,X530 : subst,X529 : term] : (((sub @ (X527 @ X528 @ X529) @ X530)) = ((X527 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530)))) | ($true = ((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id))) | ~ ! [X531 : term] : (~ ($true = ((X524 @ id @ X531 @ id))) | ($true = ((X524 @ id @ (X527 @ id @ X531) @ id))))) | ~ ! [X532 : subst,X533 : subst,X534 : term,X535 : subst] : (~ ($true = ((X524 @ (comp @ X533 @ X532) @ (sub @ X534 @ X532) @ X535))) | ($true = ((X524 @ X533 @ X534 @ (comp @ X532 @ X535))))) | ~ ! [X536 : subst,X537 : term,X538 : subst,X539 : subst] : (($true = ((X524 @ (comp @ X536 @ X539) @ (sub @ X537 @ X539) @ X538))) | ~ ($true = ((X524 @ X536 @ X537 @ (comp @ X539 @ X538)))))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (hoasapnotvar_gthm = $true) & (axclos = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one))))),
% 5.86/1.21 inference(rectify,[],[f5])).
% 5.86/1.21 thf(f9,plain,(
% 5.86/1.21 (hoaslamnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) = X210) => ! [X214 : (term > $o),X213 : subst,X212 : (term > $o),X211 : term] : (~ ! [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) = ((X212 @ X215))) | ($true != ((X214 @ X211))) | (((X212 @ one)) = $true)))) & (! [X410 : (subst > term > subst > $o),X409 : term] : (~ ! [X412 : (subst > term > term)] : (($true = ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) | ~ ! [X416 : term] : (($true != ((X410 @ id @ X416 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X416) @ id)))) | ~ ! [X413 : subst,X414 : subst,X415 : term] : (((sub @ (X412 @ X413 @ X415) @ X414)) = ((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))))) | ($true = ((X410 @ id @ (lam @ X409) @ id))) | ~ ! [X411 : term] : (($true != ((X410 @ id @ X411 @ id))) | (((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3a = $true)) & (axapp = $true) & ((! [X337 : (subst > term > subst > $o)] : ~ ! [X338 : (term > $o)] : ~ ! [X339 : term] : (((X337 @ id @ X339 @ id)) = ((X338 @ X339))) => (! [X341 : term,X340 : (term > $o)] : (~ ! [X345 : term] : (~ ! [X346 : term] : ((((X340 @ X346)) != $true) | ($true = ((X340 @ (sub @ X345 @ (push @ X346 @ id)))))) | (((X340 @ (lam @ X345))) = $true)) | ~ ! [X342 : term,X343 : term] : ((((X340 @ X342)) != $true) | (((X340 @ (ap @ X342 @ X343))) = $true) | ($true != ((X340 @ X343)))) | ~ ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344)))) | ($true = ((X340 @ X341)))) => (! [X347 : term] : (((sub @ X347 @ id)) = X347) => (! [X349 : (term > $o),X348 : term,X350 : (subst > term > subst > $o)] : (~ ! [X351 : (subst > term > term)] : (~ ! [X355 : term] : (($true = ((X350 @ id @ (X351 @ id @ X355) @ id))) | (((X350 @ id @ X355 @ id)) != $true)) | ($true = ((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id))) | ~ ! [X352 : subst,X354 : subst,X353 : term] : (((X351 @ (comp @ X354 @ X352) @ (sub @ X353 @ X352))) = ((sub @ (X351 @ X354 @ X353) @ X352)))) | ~ ! [X357 : term] : (((X349 @ X357)) = ((X350 @ id @ X357 @ id))) | ~ ! [X356 : term] : (($true = ((X349 @ (sub @ X348 @ (push @ X356 @ id))))) | ($true != ((X349 @ X356)))) | ($true = ((X349 @ (lam @ X348))))) => ! [X358 : term,X359 : (subst > term > subst > $o)] : (($true = ((X359 @ id @ X358 @ id))) | ~ ! [X360 : (subst > term > term)] : (~ ! [X362 : subst,X361 : term,X363 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) | ~ ! [X364 : term] : (($true = ((X359 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X359 @ id @ X364 @ id)))) | ($true = ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id)))) | ~ ! [X365 : term,X366 : term] : (($true != ((X359 @ id @ X366 @ id))) | ($true = ((X359 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id))) | ($true != ((X359 @ id @ X365 @ id))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (substmonoid_gthm = $true) & ((induction2 = $true) <=> ! [X132 : term,X131 : (term > $o)] : (~ ! [X135 : term] : (($true = ((X131 @ (lam @ X135)))) | ~ ! [X136 : term] : (($true != ((X131 @ X136))) | ($true = ((X131 @ (sub @ X135 @ (push @ X136 @ id))))))) | ~ ! [X134 : term,X133 : term] : (($true != ((X131 @ X134))) | ($true != ((X131 @ X133))) | ($true = ((X131 @ (ap @ X134 @ X133))))) | ~ ! [X137 : term] : (($true = ((X131 @ X137))) | ($true != ((var @ X137)))) | ($true = ((X131 @ X132))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X243 : term] : ~ ! [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) != ((X244 @ sh @ one)))) & (pushprop_lthm_orig = $true) & ((! [X318 : term] : (((sub @ X318 @ id)) = X318) => (! [X319 : term,X320 : (subst > term > subst > $o)] : (($true = ((X320 @ id @ (lam @ (sub @ X319 @ (push @ one @ sh))) @ id))) | ~ ! [X326 : term] : ((((X320 @ id @ X326 @ id)) != $true) | (((X320 @ id @ (sub @ X319 @ (push @ X326 @ id)) @ id)) = $true)) | ~ ! [X321 : (subst > term > term)] : (~ ! [X322 : subst,X323 : term,X324 : subst] : (((X321 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))) = ((sub @ (X321 @ X324 @ X323) @ X322))) | ($true = ((X320 @ id @ (lam @ (X321 @ sh @ one)) @ id))) | ~ ! [X325 : term] : (($true != ((X320 @ id @ X325 @ id))) | ($true = ((X320 @ id @ (X321 @ id @ X325) @ id)))))) => ! [X327 : term,X328 : (subst > term > subst > $o)] : (($true = ((X328 @ id @ (lam @ X327) @ id))) | ~ ! [X334 : term] : (($true != ((X328 @ id @ X334 @ id))) | ($true = ((X328 @ id @ (sub @ X327 @ (push @ X334 @ id)) @ id)))) | ~ ! [X329 : (subst > term > term)] : (~ ! [X333 : term,X331 : subst,X332 : subst] : (((sub @ (X329 @ X331 @ X333) @ X332)) = ((X329 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)))) | ($true = ((X328 @ id @ (lam @ (X329 @ sh @ one)) @ id))) | ~ ! [X330 : term] : (($true = ((X328 @ id @ (X329 @ id @ X330) @ id))) | ($true != ((X328 @ id @ X330 @ id)))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasapnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) <=> (apinj1 = $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X171 : term,X172 : (term > $o),X173 : (subst > term > subst > $o)] : (($true = ((X172 @ (lam @ X171)))) | ~ ! [X180 : term] : (($true != ((X172 @ X180))) | ($true = ((X172 @ (sub @ X171 @ (push @ X180 @ id)))))) | ~ ! [X174 : term] : (((X173 @ id @ X174 @ id)) = ((X172 @ X174))) | ~ ! [X175 : (subst > term > term)] : (($true = ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) | ~ ! [X176 : term] : (($true = ((X173 @ id @ (X175 @ id @ X176) @ id))) | ($true != ((X173 @ id @ X176 @ id)))) | ~ ! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177))))))) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ! [X245 : d_term] : (d_one = X245) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axvarshift = $true) & ((! [X382 : subst,X383 : term] : (((sub @ one @ (push @ X383 @ X382))) = X383) => (! [X384 : subst,X385 : term] : (((comp @ sh @ (push @ X385 @ X384))) = X384) => (! [X386 : subst] : (((comp @ X386 @ id)) = X386) => (! [X387 : (term > $o),X388 : term] : (~ ! [X392 : term,X391 : term] : ((((X387 @ X392)) != $true) | ($true = ((X387 @ (ap @ X392 @ X391)))) | ($true != ((X387 @ X391)))) | ~ ! [X390 : term] : (($true != ((X387 @ X390))) | ($true = ((X387 @ (lam @ X390))))) | ($true = ((X387 @ X388))) | ~ ! [X389 : term] : (($true = ((X387 @ X389))) | (((var @ X389)) != $true))) => ! [X393 : term,X394 : (term > $o),X395 : subst] : (($true = ((X394 @ (sub @ X393 @ X395)))) | ~ ! [X396 : term,X397 : term] : (($true != ((X394 @ X396))) | (((X394 @ (ap @ X396 @ X397))) = $true) | ($true != ((X394 @ X397)))) | ~ ! [X399 : term] : (($true = ((X394 @ (lam @ X399)))) | ~ ! [X400 : term] : (($true != ((X394 @ X400))) | ($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id))))))) | ~ ! [X398 : term] : ((((X394 @ (sub @ X398 @ X395))) = $true) | ($true != ((var @ X398))))))))) <=> (induction2lem_lthm = $true)) & (ulamvarind = $true) & ((hoasapinj2_lthm = $true) <=> (! [X196 : term,X197 : term,X198 : term,X199 : term] : ((X196 = X199) | (((ap @ X198 @ X196)) != ((ap @ X197 @ X199)))) => ! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))))) & (induction2_gthm = $true) & (hoasapnotvar = $true) & (! [X477 : (subst > term > subst > $o),X478 : term] : (($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id))) | ~ ! [X479 : term] : (($true != ((X477 @ id @ X479 @ id))) | ($true = ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id)))) | ~ ! [X480 : (subst > term > term)] : (~ ! [X481 : term] : (($true != ((X477 @ id @ X481 @ id))) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id)))) | ~ ! [X482 : term,X484 : subst,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484)))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & (ulamvar1 != $true) & ((hoasinduction_lthm = $true) <=> (! [X265 : term,X264 : (term > $o)] : (($true = ((X264 @ X265))) | ~ ! [X269 : term,X268 : term] : (($true = ((X264 @ (ap @ X269 @ X268)))) | ($true != ((X264 @ X268))) | ($true != ((X264 @ X269)))) | ~ ! [X266 : term] : (($true = ((X264 @ (lam @ X266)))) | ~ ! [X267 : term] : (($true = ((X264 @ (sub @ X266 @ (push @ X267 @ id))))) | ($true != ((X264 @ X267))))) | ~ ! [X270 : term] : ((((X264 @ X270)) = $true) | ($true != ((var @ X270))))) => (! [X271 : term,X273 : term,X272 : (subst > term > subst > $o)] : (($true = ((X272 @ id @ (ap @ X273 @ X271) @ id))) | ($true != ((X272 @ id @ X273 @ id))) | ($true != ((X272 @ id @ X271 @ id))) | ~ ! [X277 : subst,X276 : subst,X275 : subst,X274 : term] : (($true != ((X272 @ (comp @ X275 @ X277) @ (sub @ X274 @ X277) @ X276))) | ($true = ((X272 @ X275 @ X274 @ (comp @ X277 @ X276))))) | ~ ! [X282 : term,X280 : subst,X281 : subst,X283 : subst] : (($true = ((X272 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281) @ X280))) | ($true != ((X272 @ X283 @ X282 @ (comp @ X281 @ X280))))) | ~ ! [X278 : term,X279 : term] : (($true != ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (ap @ (sub @ X279 @ id) @ X278) @ id))) | ($true != ((X272 @ id @ X279 @ id))))) => (! [X285 : term,X284 : (subst > term > subst > $o)] : (~ ! [X299 : term] : (($true != ((X284 @ id @ X299 @ id))) | ($true = ((X284 @ id @ (sub @ X285 @ (push @ X299 @ id)) @ id)))) | ($true = ((X284 @ id @ (lam @ X285) @ id))) | ~ ! [X296 : subst,X295 : subst,X298 : term,X297 : subst] : (($true != ((X284 @ (comp @ X297 @ X295) @ (sub @ X298 @ X295) @ X296))) | ($true = ((X284 @ X297 @ X298 @ (comp @ X295 @ X296))))) | ~ ! [X286 : (subst > term > term)] : (($true = ((X284 @ id @ (lam @ (X286 @ sh @ one)) @ id))) | ~ ! [X289 : term,X288 : subst,X290 : subst] : (((sub @ (X286 @ X290 @ X289) @ X288)) = ((X286 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288)))) | ~ ! [X287 : term] : (($true = ((X284 @ id @ (X286 @ id @ X287) @ id))) | ($true != ((X284 @ id @ X287 @ id))))) | ~ ! [X291 : subst,X294 : subst,X292 : term,X293 : subst] : ((((X284 @ (comp @ X293 @ X291) @ (sub @ X292 @ X291) @ X294)) = $true) | (((X284 @ X293 @ X292 @ (comp @ X291 @ X294))) != $true))) => ! [X301 : (subst > term > subst > $o),X300 : term] : (~ ! [X314 : subst,X316 : subst,X315 : subst,X317 : term] : (($true != ((X301 @ X316 @ X317 @ (comp @ X314 @ X315)))) | ($true = ((X301 @ (comp @ X316 @ X314) @ (sub @ X317 @ X314) @ X315)))) | ~ ! [X306 : subst,X307 : subst,X304 : subst,X305 : term] : (($true = ((X301 @ X306 @ X305 @ (comp @ X307 @ X304)))) | ($true != ((X301 @ (comp @ X306 @ X307) @ (sub @ X305 @ X307) @ X304)))) | ~ ! [X303 : term,X302 : term] : (($true != ((X301 @ id @ X303 @ id))) | ($true != ((X301 @ id @ X302 @ id))) | ($true = ((X301 @ id @ (ap @ (sub @ X302 @ id) @ X303) @ id)))) | ($true = ((X301 @ id @ X300 @ id))) | ~ ! [X308 : (subst > term > term)] : (~ ! [X311 : subst,X312 : subst,X310 : term] : (((sub @ (X308 @ X311 @ X310) @ X312)) = ((X308 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312)))) | ($true = ((X301 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X309 : term] : (($true != ((X301 @ id @ X309 @ id))) | ($true = ((X301 @ id @ (X308 @ id @ X309) @ id))))) | ~ ! [X313 : term] : (($true = ((X301 @ id @ X313 @ id))) | ($true != ((var @ (sub @ X313 @ id)))))))))) & (apnotvar = $true) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X423 : (subst > term > subst > $o)] : ~ ! [X424 : (term > $o)] : ~ ! [X425 : term] : (((X423 @ id @ X425 @ id)) = ((X424 @ X425))) => (! [X427 : term,X426 : (term > $o)] : (~ ! [X431 : term] : (~ ! [X432 : term] : (($true = ((X426 @ (sub @ X431 @ (push @ X432 @ id))))) | ($true != ((X426 @ X432)))) | ($true = ((X426 @ (lam @ X431))))) | ~ ! [X430 : term] : ((((var @ X430)) != $true) | ($true = ((X426 @ X430)))) | ~ ! [X428 : term,X429 : term] : (($true = ((X426 @ (ap @ X429 @ X428)))) | ($true != ((X426 @ X428))) | ($true != ((X426 @ X429)))) | ($true = ((X426 @ X427)))) => (! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X434 : (term > $o),X435 : (subst > term > subst > $o),X436 : term] : (~ ! [X438 : (subst > term > term)] : (~ ! [X442 : term] : (($true = ((X435 @ id @ (X438 @ id @ X442) @ id))) | ($true != ((X435 @ id @ X442 @ id)))) | ~ ! [X440 : term,X439 : subst,X441 : subst] : (((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441))) = ((sub @ (X438 @ X439 @ X440) @ X441))) | ($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)))) | ($true = ((X434 @ (lam @ X436)))) | ~ ! [X443 : term] : (((X434 @ X443)) = ((X435 @ id @ X443 @ id))) | ~ ! [X437 : term] : ((((X434 @ X437)) != $true) | ($true = ((X434 @ (sub @ X436 @ (push @ X437 @ id))))))) => ! [X445 : (subst > term > subst > $o),X444 : term] : (~ ! [X458 : term,X459 : subst,X460 : subst,X461 : subst] : (($true = ((X445 @ X461 @ X458 @ (comp @ X459 @ X460)))) | ($true != ((X445 @ (comp @ X461 @ X459) @ (sub @ X458 @ X459) @ X460)))) | ~ ! [X456 : term,X457 : term] : (($true != ((X445 @ id @ X456 @ id))) | ($true != ((X445 @ id @ X457 @ id))) | ($true = ((X445 @ id @ (ap @ (sub @ X457 @ id) @ X456) @ id)))) | ($true = ((X445 @ id @ X444 @ id))) | ~ ! [X451 : term,X453 : subst,X454 : subst,X452 : subst] : ((((X445 @ X453 @ X451 @ (comp @ X454 @ X452))) != $true) | ($true = ((X445 @ (comp @ X453 @ X454) @ (sub @ X451 @ X454) @ X452)))) | ~ ! [X455 : term] : (($true != ((var @ (sub @ X455 @ id)))) | ($true = ((X445 @ id @ X455 @ id)))) | ~ ! [X446 : (subst > term > term)] : (($true = ((X445 @ id @ (lam @ (X446 @ sh @ one)) @ id))) | ~ ! [X448 : term,X449 : subst,X447 : subst] : (((sub @ (X446 @ X447 @ X448) @ X449)) = ((X446 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) | ~ ! [X450 : term] : (($true = ((X445 @ id @ (X446 @ id @ X450) @ id))) | ($true != ((X445 @ id @ X450 @ id))))))))))) & ((! [X419 : term] : (((sub @ X419 @ id)) = X419) => ! [X420 : term] : (((sub @ X420 @ id)) = X420)) <=> (termmset_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (pushprop_gthm = $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) = ((d2term @ X401))) => (X401 = X402)) & ((pushprop_lem1v2 = $true) <=> ! [X204 : subst,X207 : (term > $o),X205 : term,X206 : (term > $o)] : (~ ! [X208 : term] : (((X207 @ X208)) = ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | (((X207 @ one)) = $true) | ($true != ((X206 @ X205))))) & ((hoasinduction_lem3 = $true) <=> ! [X525 : term,X524 : (subst > term > subst > $o)] : (~ ! [X539 : subst,X538 : subst,X537 : term,X536 : subst] : (($true = ((X524 @ (comp @ X536 @ X539) @ (sub @ X537 @ X539) @ X538))) | ($true != ((X524 @ X536 @ X537 @ (comp @ X539 @ X538))))) | ~ ! [X533 : subst,X535 : subst,X534 : term,X532 : subst] : (($true = ((X524 @ X533 @ X534 @ (comp @ X532 @ X535)))) | ($true != ((X524 @ (comp @ X533 @ X532) @ (sub @ X534 @ X532) @ X535)))) | ($true = ((X524 @ id @ (lam @ X525) @ id))) | ~ ! [X526 : term] : (($true != ((X524 @ id @ X526 @ id))) | ($true = ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id)))) | ~ ! [X527 : (subst > term > term)] : (~ ! [X531 : term] : (($true = ((X524 @ id @ (X527 @ id @ X531) @ id))) | ($true != ((X524 @ id @ X531 @ id)))) | ($true = ((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id))) | ~ ! [X528 : subst,X530 : subst,X529 : term] : (((sub @ (X527 @ X528 @ X529) @ X530)) = ((X527 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))))))) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & ((hoasinduction_lem2 = $true) <=> ! [X39 : term,X40 : (subst > term > subst > $o),X38 : term] : (($true != ((X40 @ id @ X38 @ id))) | ~ ! [X45 : term,X46 : term] : (($true != ((X40 @ id @ X45 @ id))) | ($true != ((X40 @ id @ X46 @ id))) | ($true = ((X40 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id)))) | ($true != ((X40 @ id @ X39 @ id))) | ~ ! [X47 : subst,X48 : subst,X49 : term,X50 : subst] : (($true != ((X40 @ (comp @ X47 @ X50) @ (sub @ X49 @ X50) @ X48))) | (((X40 @ X47 @ X49 @ (comp @ X50 @ X48))) = $true)) | ($true = ((X40 @ id @ (ap @ X38 @ X39) @ id))) | ~ ! [X41 : subst,X43 : term,X44 : subst,X42 : subst] : (($true != ((X40 @ X42 @ X43 @ (comp @ X44 @ X41)))) | ($true = ((X40 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41)))))) & (! [X140 : subst,X138 : (term > $o),X139 : term] : (~ ! [X141 : term] : (~ ! [X142 : term] : ((((X138 @ (sub @ X141 @ (push @ X142 @ id)))) = $true) | ($true != ((X138 @ X142)))) | ($true = ((X138 @ (lam @ X141))))) | ($true = ((X138 @ (sub @ X139 @ X140)))) | ~ ! [X143 : term,X144 : term] : (($true = ((X138 @ (ap @ X144 @ X143)))) | ($true != ((X138 @ X143))) | ($true != ((X138 @ X144)))) | ~ ! [X145 : term] : (($true != ((var @ X145))) | ($true = ((X138 @ (sub @ X145 @ X140)))))) <=> (induction2lem = $true)) & (! [X485 : term] : ~ ! [X486 : (subst > term > term)] : (((X486 @ sh @ one)) != ((sub @ X485 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X73 : term] : (((sub @ X73 @ id)) = X73) => (! [X74 : term,X75 : (subst > term > subst > $o)] : (~ ! [X76 : term] : (($true = ((X75 @ id @ (sub @ X74 @ (push @ X76 @ id)) @ id))) | ($true != ((X75 @ id @ X76 @ id)))) | ~ ! [X77 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X77 @ sh @ one)) @ id)) = $true) | ~ ! [X80 : term,X79 : subst,X81 : subst] : (((sub @ (X77 @ X79 @ X80) @ X81)) = ((X77 @ (comp @ X79 @ X81) @ (sub @ X80 @ X81)))) | ~ ! [X78 : term] : (($true = ((X75 @ id @ (X77 @ id @ X78) @ id))) | ($true != ((X75 @ id @ X78 @ id))))) | ($true = ((X75 @ id @ (lam @ (sub @ X74 @ (push @ one @ sh))) @ id)))) => ! [X83 : term,X82 : (subst > term > subst > $o)] : (~ ! [X84 : (subst > term > term)] : (~ ! [X85 : subst,X86 : subst,X87 : term] : (((X84 @ (comp @ X86 @ X85) @ (sub @ X87 @ X85))) = ((sub @ (X84 @ X86 @ X87) @ X85))) | ~ ! [X88 : term] : (($true != ((X82 @ id @ X88 @ id))) | ($true = ((X82 @ id @ (X84 @ id @ X88) @ id)))) | ($true = ((X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)))) | ~ ! [X96 : term,X94 : subst,X97 : subst,X95 : subst] : (($true = ((X82 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95) @ X97))) | (((X82 @ X94 @ X96 @ (comp @ X95 @ X97))) != $true)) | ~ ! [X89 : term] : (($true = ((X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id))) | ($true != ((X82 @ id @ X89 @ id)))) | ($true = ((X82 @ id @ (lam @ X83) @ id))) | ~ ! [X91 : subst,X90 : subst,X93 : subst,X92 : term] : (($true = ((X82 @ X93 @ X92 @ (comp @ X90 @ X91)))) | ($true != ((X82 @ (comp @ X93 @ X90) @ (sub @ X92 @ X90) @ X91)))))))) & ((! [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) = X373) => (! [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) = X375) => ! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))))) <=> (pushprop_lem1_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) <=> (axscons = $true)) & ((! [X403 : subst] : (((comp @ id @ X403)) = X403) => (! [X404 : subst] : (((comp @ X404 @ id)) = X404) => (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)))) <=> (substmonoid_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X216 : term] : (((sub @ X216 @ id)) = X216) => (! [X219 : term,X217 : term,X220 : term,X218 : term] : ((((ap @ X218 @ X220)) != ((ap @ X219 @ X217))) | (X218 = X219)) => ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224))))) & ((axidr = $true) <=> ! [X71 : subst] : (((comp @ X71 @ id)) = X71)) & (hoasapnotvar_lthm = $true) & (((d2subst @ d_id)) = id) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X520 : term] : ~ ! [X521 : (subst > term > term)] : ~ ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522))))) & (lamnotap != $true) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) <=> (apinj2 = $true)) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X188 : (subst > term > subst > $o),X187 : term] : (~ ! [X191 : (subst > term > term)] : (~ ! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) | ~ ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195))) | ($true = ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id)))) | ($true = ((X188 @ id @ X187 @ id))) | ~ ! [X189 : term,X190 : term] : (($true = ((X188 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id))) | ($true != ((X188 @ id @ X189 @ id))) | ($true != ((X188 @ id @ X190 @ id)))))) & (ulamvarsh = $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) <=> (axshiftcons = $true)) & (lamnotvar = $true) & (one = ((d2term @ d_one))) & ((axvarcons = $true) <=> ! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408)) & (axabs = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X105 : term,X104 : term,X106 : (term > $o),X107 : (subst > term > subst > $o)] : ((((X106 @ (ap @ X105 @ X104))) = $true) | ~ ! [X110 : term] : (((X107 @ id @ X110 @ id)) = ((X106 @ X110))) | ~ ! [X112 : subst,X114 : subst,X111 : subst,X113 : term] : (($true != ((X107 @ X114 @ X113 @ (comp @ X111 @ X112)))) | ($true = ((X107 @ (comp @ X114 @ X111) @ (sub @ X113 @ X111) @ X112)))) | ($true != ((X106 @ X105))) | ~ ! [X117 : subst,X118 : subst,X116 : term,X115 : subst] : (($true = ((X107 @ X115 @ X116 @ (comp @ X118 @ X117)))) | ($true != ((X107 @ (comp @ X115 @ X118) @ (sub @ X116 @ X118) @ X117)))) | ~ ! [X109 : term,X108 : term] : (($true != ((X107 @ id @ X109 @ id))) | ($true = ((X107 @ id @ (ap @ (sub @ X109 @ id) @ X108) @ id))) | ($true != ((X107 @ id @ X108 @ id)))) | ($true != ((X106 @ X104))))) & ((! [X51 : term,X52 : subst] : (((sub @ one @ (push @ X51 @ X52))) = X51) => (! [X54 : subst,X53 : term] : (((comp @ sh @ (push @ X53 @ X54))) = X54) => (! [X56 : term,X55 : term] : ((X55 = X56) | (((lam @ X55)) != ((lam @ X56)))) => ! [X59 : term,X60 : (subst > term > term),X58 : (subst > term > term),X57 : subst] : ((((lam @ (X58 @ sh @ one))) != ((lam @ (X60 @ sh @ one)))) | ~ ! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X58 @ X65 @ X64) @ X66)) = ((X58 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | ~ ! [X63 : term,X61 : subst,X62 : subst] : (((sub @ (X60 @ X62 @ X63) @ X61)) = ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | (((X58 @ X57 @ X59)) = ((X60 @ X57 @ X59))))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X153 : subst,X152 : term] : (((X151 @ X153 @ X152)) = ((sub @ X150 @ (push @ X152 @ X153)))) => (! [X154 : term] : (((sub @ X154 @ id)) = X154) => ! [X156 : (subst > term > subst > $o),X155 : term,X157 : (term > $o)] : (~ ! [X163 : term] : (($true != ((X157 @ X163))) | (((X157 @ (sub @ X155 @ (push @ X163 @ id)))) = $true)) | ~ ! [X164 : term] : (((X156 @ id @ X164 @ id)) = ((X157 @ X164))) | ~ ! [X158 : (subst > term > term)] : (~ ! [X159 : term] : (($true != ((X156 @ id @ X159 @ id))) | ($true = ((X156 @ id @ (X158 @ id @ X159) @ id)))) | ~ ! [X161 : subst,X162 : term,X160 : subst] : (((X158 @ (comp @ X160 @ X161) @ (sub @ X162 @ X161))) = ((sub @ (X158 @ X160 @ X162) @ X161))) | ($true = ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ($true = ((X157 @ (lam @ X155)))))))) & ((induction = $true) <=> ! [X166 : term,X165 : (term > $o)] : (($true = ((X165 @ X166))) | ~ ! [X168 : term] : (($true = ((X165 @ (lam @ X168)))) | ($true != ((X165 @ X168)))) | ~ ! [X169 : term,X170 : term] : (($true != ((X165 @ X170))) | ($true = ((X165 @ (ap @ X170 @ X169)))) | ($true != ((X165 @ X169)))) | ~ ! [X167 : term] : (($true = ((X165 @ X167))) | ($true != ((var @ X167)))))) & (hoasinduction_lem1 = $true) & (axclos = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X248 : (subst > term > subst > $o),X246 : term,X247 : (term > $o)] : (($true = ((X247 @ (lam @ X246)))) | ~ ! [X258 : term] : (($true != ((X247 @ X258))) | ($true = ((X247 @ (sub @ X246 @ (push @ X258 @ id)))))) | ~ ! [X249 : term] : (((X248 @ id @ X249 @ id)) = ((X247 @ X249))) | ~ ! [X250 : subst,X253 : subst,X251 : term,X252 : subst] : (($true = ((X248 @ (comp @ X250 @ X253) @ (sub @ X251 @ X253) @ X252))) | ($true != ((X248 @ X250 @ X251 @ (comp @ X253 @ X252))))) | ~ ! [X257 : subst,X255 : term,X254 : subst,X256 : subst] : (($true != ((X248 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))) | ($true = ((X248 @ X254 @ X255 @ (comp @ X256 @ X257))))) | ~ ! [X259 : (subst > term > term)] : (~ ! [X263 : term] : (($true = ((X248 @ id @ (X259 @ id @ X263) @ id))) | ($true != ((X248 @ id @ X263 @ id)))) | ~ ! [X260 : term,X262 : subst,X261 : subst] : (((sub @ (X259 @ X261 @ X260) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X260 @ X262)))) | ($true = ((X248 @ id @ (lam @ (X259 @ sh @ one)) @ id)))))) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) <=> ! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X31 : (subst > term > subst > $o),X30 : term] : (~ ! [X32 : term] : (($true = ((X31 @ id @ (sub @ X30 @ (push @ X32 @ id)) @ id))) | ($true != ((X31 @ id @ X32 @ id)))) | ~ ! [X33 : (subst > term > term)] : (~ ! [X36 : subst,X37 : term,X35 : subst] : (((X33 @ (comp @ X35 @ X36) @ (sub @ X37 @ X36))) = ((sub @ (X33 @ X35 @ X37) @ X36))) | ($true = ((X31 @ id @ (lam @ (X33 @ sh @ one)) @ id))) | ~ ! [X34 : term] : (($true != ((X31 @ id @ X34 @ id))) | ($true = ((X31 @ id @ (X33 @ id @ X34) @ id))))) | ($true = ((X31 @ id @ (lam @ (sub @ X30 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1v2 = $true) & ! [X5 : d_subst] : (d_id = X5) & (! [X67 : term] : ~ ! [X68 : (subst > term > term)] : ~ ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop = $true) & ((shinj = $true) <=> ! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186))) & (pushprop_lem1_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)))))))))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X121 : (subst > term > term),X122 : subst,X123 : (subst > term > term),X124 : term] : (~ ! [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) = ((sub @ (X123 @ X128 @ X129) @ X130))) | ~ ! [X127 : subst,X126 : term,X125 : subst] : (((sub @ (X121 @ X125 @ X126) @ X127)) = ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one))))) <=> (hoaslaminj = $true)) & (axmap = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X517 : (subst > term > subst > $o)] : ~ ! [X518 : (term > $o)] : ~ ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id)))) & (hoaslamnotap_lthm = $true) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) <=> (substmonoid = $true)) & ((axvarid = $true) <=> ! [X381 : term] : (((sub @ X381 @ id)) = X381)) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) <=> (laminj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X226 : term,X225 : (subst > term > subst > $o)] : (~ ! [X227 : subst,X229 : subst,X230 : subst,X228 : term] : (($true != ((X225 @ X227 @ X228 @ (comp @ X229 @ X230)))) | ($true = ((X225 @ (comp @ X227 @ X229) @ (sub @ X228 @ X229) @ X230)))) | ~ ! [X231 : term] : (($true = ((X225 @ id @ X231 @ id))) | ($true != ((var @ (sub @ X231 @ id))))) | ($true = ((X225 @ id @ X226 @ id))) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : subst,X236 : subst,X237 : term] : (((X234 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))) = ((sub @ (X234 @ X236 @ X237) @ X235))) | ($true = ((X225 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X238 : term] : (($true != ((X225 @ id @ X238 @ id))) | ($true = ((X225 @ id @ (X234 @ id @ X238) @ id))))) | ~ ! [X240 : subst,X242 : subst,X241 : subst,X239 : term] : (($true != ((X225 @ (comp @ X240 @ X242) @ (sub @ X239 @ X242) @ X241))) | (((X225 @ X240 @ X239 @ (comp @ X242 @ X241))) = $true)) | ~ ! [X233 : term,X232 : term] : (($true = ((X225 @ id @ (ap @ (sub @ X233 @ id) @ X232) @ id))) | ($true != ((X225 @ id @ X233 @ id))) | ($true != ((X225 @ id @ X232 @ id)))))) & (axassoc = $true) & ! [X506 : d_subst,X507 : d_subst] : ((((d2subst @ X507)) = ((d2subst @ X506))) => (X506 = X507)) & ((! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X13 : term,X11 : (term > $o),X12 : subst] : (~ ! [X14 : term] : (~ ! [X15 : term] : ((((X11 @ X15)) != $true) | ($true = ((X11 @ (sub @ X14 @ (push @ X15 @ id)))))) | ($true = ((X11 @ (lam @ X14))))) | ~ ! [X16 : term] : (($true = ((X11 @ (sub @ X16 @ X12)))) | ($true != ((var @ X16)))) | ($true = ((X11 @ (sub @ X13 @ X12)))) | ~ ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ($true != ((X11 @ X18))) | (((X11 @ X17)) != $true))) => ! [X20 : (term > $o),X19 : term] : (~ ! [X23 : term,X22 : term] : ((((X20 @ (ap @ X22 @ X23))) = $true) | ($true != ((X20 @ X22))) | ($true != ((X20 @ X23)))) | ($true = ((X20 @ X19))) | ~ ! [X24 : term] : (~ ! [X25 : term] : (($true != ((X20 @ X25))) | ($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id)))))) | ($true = ((X20 @ (lam @ X24))))) | ~ ! [X21 : term] : (($true != ((var @ X21))) | ($true = ((X20 @ X21))))))) <=> (induction2_lthm = $true)) & (! [X1 : (term > $o),X0 : subst,X2 : term] : ~ ! [X3 : (term > $o)] : ~ ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (hoasinduction_lem1v2_gthm = $true) & (induction2lem_gthm = $true) & (! [X369 : term,X367 : subst,X368 : (term > $o)] : ~ ! [X370 : (term > $o)] : ~ ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) <=> (pushprop_lem0_lthm = $true)) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lthm = $true) & (! [X98 : (subst > term > term),X100 : term,X99 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ~ ! [X103 : subst,X102 : term,X101 : subst] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) = ((sub @ (X98 @ X103 @ X102) @ X101)))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X474 : (subst > term > subst > $o)] : ~ ! [X475 : (term > $o)] : ~ ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id)))) & ((! [X487 : term] : (((sub @ X487 @ id)) = X487) => ! [X489 : term,X490 : (subst > term > subst > $o),X488 : (term > $o)] : (~ ! [X497 : term] : (($true = ((X488 @ (sub @ X489 @ (push @ X497 @ id))))) | ($true != ((X488 @ X497)))) | ~ ! [X492 : (subst > term > term)] : (~ ! [X493 : term] : (($true = ((X490 @ id @ (X492 @ id @ X493) @ id))) | (((X490 @ id @ X493 @ id)) != $true)) | ($true = ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) | ~ ! [X496 : subst,X494 : term,X495 : subst] : (((sub @ (X492 @ X496 @ X494) @ X495)) = ((X492 @ (comp @ X496 @ X495) @ (sub @ X494 @ X495))))) | ($true = ((X488 @ (lam @ X489)))) | ~ ! [X505 : subst,X503 : subst,X504 : subst,X502 : term] : (($true != ((X490 @ (comp @ X503 @ X504) @ (sub @ X502 @ X504) @ X505))) | ($true = ((X490 @ X503 @ X502 @ (comp @ X504 @ X505))))) | ~ ! [X499 : subst,X500 : subst,X498 : subst,X501 : term] : (($true != ((X490 @ X498 @ X501 @ (comp @ X500 @ X499)))) | ($true = ((X490 @ (comp @ X498 @ X500) @ (sub @ X501 @ X500) @ X499)))) | ~ ! [X491 : term] : (((X488 @ X491)) = ((X490 @ id @ X491 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1_lthm = $true) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) <=> (hoasapinj2 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X462 : (subst > term > subst > $o),X463 : term] : (($true = ((X462 @ id @ (lam @ (sub @ X463 @ (push @ one @ sh))) @ id))) | ~ ! [X465 : (subst > term > term),X466 : term] : (~ ! [X468 : subst,X467 : term,X469 : subst] : (((sub @ (X465 @ X468 @ X467) @ X469)) = ((sub @ (sub @ X466 @ (push @ X467 @ X468)) @ X469))) | ($true = ((X462 @ id @ (lam @ (X465 @ sh @ one)) @ id))) | ~ ! [X470 : term] : (($true != ((X462 @ id @ X470 @ id))) | ($true = ((X462 @ id @ (X465 @ id @ X470) @ id)))) | ~ ! [X471 : subst,X473 : subst,X472 : term] : (((X465 @ (comp @ X471 @ X473) @ (sub @ X472 @ X473))) = ((sub @ X466 @ (push @ (sub @ X472 @ X473) @ (comp @ X471 @ X473)))))) | ~ ! [X464 : term] : (($true = ((X462 @ id @ (sub @ X463 @ (push @ X464 @ id)) @ id))) | ($true != ((X462 @ id @ X464 @ id))))))),
% 5.86/1.21 inference(flattening,[],[f8])).
% 5.86/1.21 thf(f10,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))))),
% 5.86/1.21 inference(flattening,[],[f7])).
% 5.86/1.21 thf(f11,plain,(
% 5.86/1.21 (hoaslamnotvar = $true) & ((? [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) != X210) | ! [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true != ((X214 @ X211))) | (((X212 @ one)) = $true) | ? [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) != ((X212 @ X215))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true = ((X410 @ id @ X411 @ id))) & (((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id)) != $true)) | ? [X412 : (subst > term > term)] : (! [X416 : term] : (($true != ((X410 @ id @ X416 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X416) @ id)))) & ($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : subst,X414 : subst,X415 : term] : (((sub @ (X412 @ X413 @ X415) @ X414)) = ((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))))) | ($true = ((X410 @ id @ (lam @ X409) @ id)))) <=> (hoasinduction_lem3a = $true)) & (axapp = $true) & (((((! [X358 : term,X359 : (subst > term > subst > $o)] : (? [X366 : term,X365 : term] : (($true = ((X359 @ id @ X365 @ id))) & ($true != ((X359 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id))) & ($true = ((X359 @ id @ X366 @ id)))) | ($true = ((X359 @ id @ X358 @ id))) | ? [X360 : (subst > term > term)] : (! [X364 : term] : (($true = ((X359 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X359 @ id @ X364 @ id)))) & ($true != ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id))) & ! [X362 : subst,X361 : term,X363 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))))) | ? [X350 : (subst > term > subst > $o),X349 : (term > $o),X348 : term] : (($true != ((X349 @ (lam @ X348)))) & ! [X351 : (subst > term > term)] : (($true = ((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id))) | ? [X353 : term,X352 : subst,X354 : subst] : (((X351 @ (comp @ X354 @ X352) @ (sub @ X353 @ X352))) != ((sub @ (X351 @ X354 @ X353) @ X352))) | ? [X355 : term] : (($true != ((X350 @ id @ (X351 @ id @ X355) @ id))) & (((X350 @ id @ X355 @ id)) = $true))) & ! [X356 : term] : (($true = ((X349 @ (sub @ X348 @ (push @ X356 @ id))))) | ($true != ((X349 @ X356)))) & ! [X357 : term] : (((X349 @ X357)) = ((X350 @ id @ X357 @ id))))) | ? [X347 : term] : (((sub @ X347 @ id)) != X347)) | ? [X340 : (term > $o),X341 : term] : (($true != ((X340 @ X341))) & ! [X345 : term] : (? [X346 : term] : ((((X340 @ X346)) = $true) & ($true != ((X340 @ (sub @ X345 @ (push @ X346 @ id)))))) | (((X340 @ (lam @ X345))) = $true)) & ! [X342 : term,X343 : term] : ((((X340 @ X342)) != $true) | (((X340 @ (ap @ X342 @ X343))) = $true) | ($true != ((X340 @ X343)))) & ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344)))))) | ? [X337 : (subst > term > subst > $o)] : ! [X338 : (term > $o)] : ? [X339 : term] : (((X337 @ id @ X339 @ id)) != ((X338 @ X339)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (substmonoid_gthm = $true) & ((induction2 = $true) <=> ! [X131 : (term > $o),X132 : term] : (($true = ((X131 @ X132))) | ? [X137 : term] : (($true != ((X131 @ X137))) & ($true = ((var @ X137)))) | ? [X134 : term,X133 : term] : (($true = ((X131 @ X134))) & ($true = ((X131 @ X133))) & ($true != ((X131 @ (ap @ X134 @ X133))))) | ? [X135 : term] : (! [X136 : term] : (($true != ((X131 @ X136))) | ($true = ((X131 @ (sub @ X135 @ (push @ X136 @ id)))))) & ($true != ((X131 @ (lam @ X135))))))) & (! [X243 : term] : ? [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) = ((X244 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lthm_orig = $true) & (((! [X327 : term,X328 : (subst > term > subst > $o)] : (? [X329 : (subst > term > term)] : (! [X333 : term,X331 : subst,X332 : subst] : (((sub @ (X329 @ X331 @ X333) @ X332)) = ((X329 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)))) & ($true != ((X328 @ id @ (lam @ (X329 @ sh @ one)) @ id))) & ! [X330 : term] : (($true = ((X328 @ id @ (X329 @ id @ X330) @ id))) | ($true != ((X328 @ id @ X330 @ id))))) | ? [X334 : term] : (($true != ((X328 @ id @ (sub @ X327 @ (push @ X334 @ id)) @ id))) & ($true = ((X328 @ id @ X334 @ id)))) | ($true = ((X328 @ id @ (lam @ X327) @ id)))) | ? [X320 : (subst > term > subst > $o),X319 : term] : (($true != ((X320 @ id @ (lam @ (sub @ X319 @ (push @ one @ sh))) @ id))) & ! [X326 : term] : ((((X320 @ id @ X326 @ id)) != $true) | (((X320 @ id @ (sub @ X319 @ (push @ X326 @ id)) @ id)) = $true)) & ! [X321 : (subst > term > term)] : (? [X324 : subst,X322 : subst,X323 : term] : (((X321 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))) != ((sub @ (X321 @ X324 @ X323) @ X322))) | ($true = ((X320 @ id @ (lam @ (X321 @ sh @ one)) @ id))) | ? [X325 : term] : (($true = ((X320 @ id @ X325 @ id))) & ($true != ((X320 @ id @ (X321 @ id @ X325) @ id))))))) | ? [X318 : term] : (((sub @ X318 @ id)) != X318)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasapnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) <=> (apinj1 = $true)) & (hoasapinj1_gthm = $true) & (! [X172 : (term > $o),X171 : term,X173 : (subst > term > subst > $o)] : (($true = ((X172 @ (lam @ X171)))) | ? [X175 : (subst > term > term)] : (! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177)))) & ($true != ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) & ! [X176 : term] : (($true = ((X173 @ id @ (X175 @ id @ X176) @ id))) | ($true != ((X173 @ id @ X176 @ id))))) | ? [X174 : term] : (((X173 @ id @ X174 @ id)) != ((X172 @ X174))) | ? [X180 : term] : (($true = ((X172 @ X180))) & ($true != ((X172 @ (sub @ X171 @ (push @ X180 @ id))))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ! [X245 : d_term] : (d_one = X245) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axvarshift = $true) & (((((! [X395 : subst,X393 : term,X394 : (term > $o)] : (? [X399 : term] : (! [X400 : term] : (($true != ((X394 @ X400))) | ($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id)))))) & ($true != ((X394 @ (lam @ X399))))) | ? [X396 : term,X397 : term] : (($true = ((X394 @ X396))) & (((X394 @ (ap @ X396 @ X397))) != $true) & ($true = ((X394 @ X397)))) | ($true = ((X394 @ (sub @ X393 @ X395)))) | ? [X398 : term] : ((((X394 @ (sub @ X398 @ X395))) != $true) & ($true = ((var @ X398))))) | ? [X387 : (term > $o),X388 : term] : (! [X389 : term] : (($true = ((X387 @ X389))) | (((var @ X389)) != $true)) & ! [X392 : term,X391 : term] : ((((X387 @ X392)) != $true) | ($true = ((X387 @ (ap @ X392 @ X391)))) | ($true != ((X387 @ X391)))) & ($true != ((X387 @ X388))) & ! [X390 : term] : (($true != ((X387 @ X390))) | ($true = ((X387 @ (lam @ X390))))))) | ? [X386 : subst] : (((comp @ X386 @ id)) != X386)) | ? [X385 : term,X384 : subst] : (((comp @ sh @ (push @ X385 @ X384))) != X384)) | ? [X383 : term,X382 : subst] : (((sub @ one @ (push @ X383 @ X382))) != X383)) <=> (induction2lem_lthm = $true)) & (ulamvarind = $true) & ((hoasapinj2_lthm = $true) <=> (! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))) | ? [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 != X199) & (((ap @ X198 @ X196)) = ((ap @ X197 @ X199)))))) & (induction2_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X478 : term,X477 : (subst > term > subst > $o)] : (($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id))) | ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X477 @ id @ X481 @ id))) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id)))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X482 : term,X484 : subst,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ? [X479 : term] : (($true != ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id))) & ($true = ((X477 @ id @ X479 @ id)))))) & (ulamvar1 != $true) & ((hoasinduction_lthm = $true) <=> (((! [X301 : (subst > term > subst > $o),X300 : term] : (? [X313 : term] : (($true = ((var @ (sub @ X313 @ id)))) & ($true != ((X301 @ id @ X313 @ id)))) | ? [X308 : (subst > term > term)] : (! [X311 : subst,X312 : subst,X310 : term] : (((sub @ (X308 @ X311 @ X310) @ X312)) = ((X308 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312)))) & ! [X309 : term] : (($true != ((X301 @ id @ X309 @ id))) | ($true = ((X301 @ id @ (X308 @ id @ X309) @ id)))) & ($true != ((X301 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ? [X314 : subst,X317 : term,X316 : subst,X315 : subst] : (($true = ((X301 @ X316 @ X317 @ (comp @ X314 @ X315)))) & ($true != ((X301 @ (comp @ X316 @ X314) @ (sub @ X317 @ X314) @ X315)))) | ($true = ((X301 @ id @ X300 @ id))) | ? [X302 : term,X303 : term] : (($true = ((X301 @ id @ X303 @ id))) & ($true = ((X301 @ id @ X302 @ id))) & ($true != ((X301 @ id @ (ap @ (sub @ X302 @ id) @ X303) @ id)))) | ? [X307 : subst,X305 : term,X304 : subst,X306 : subst] : (($true = ((X301 @ (comp @ X306 @ X307) @ (sub @ X305 @ X307) @ X304))) & ($true != ((X301 @ X306 @ X305 @ (comp @ X307 @ X304)))))) | ? [X285 : term,X284 : (subst > term > subst > $o)] : (! [X299 : term] : (($true != ((X284 @ id @ X299 @ id))) | ($true = ((X284 @ id @ (sub @ X285 @ (push @ X299 @ id)) @ id)))) & ! [X286 : (subst > term > term)] : (? [X287 : term] : (($true != ((X284 @ id @ (X286 @ id @ X287) @ id))) & ($true = ((X284 @ id @ X287 @ id)))) | ($true = ((X284 @ id @ (lam @ (X286 @ sh @ one)) @ id))) | ? [X288 : subst,X290 : subst,X289 : term] : (((sub @ (X286 @ X290 @ X289) @ X288)) != ((X286 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))))) & ($true != ((X284 @ id @ (lam @ X285) @ id))) & ! [X296 : subst,X295 : subst,X298 : term,X297 : subst] : (($true != ((X284 @ (comp @ X297 @ X295) @ (sub @ X298 @ X295) @ X296))) | ($true = ((X284 @ X297 @ X298 @ (comp @ X295 @ X296))))) & ! [X291 : subst,X294 : subst,X292 : term,X293 : subst] : ((((X284 @ (comp @ X293 @ X291) @ (sub @ X292 @ X291) @ X294)) = $true) | (((X284 @ X293 @ X292 @ (comp @ X291 @ X294))) != $true)))) | ? [X273 : term,X271 : term,X272 : (subst > term > subst > $o)] : (! [X282 : term,X280 : subst,X281 : subst,X283 : subst] : (($true = ((X272 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281) @ X280))) | ($true != ((X272 @ X283 @ X282 @ (comp @ X281 @ X280))))) & ($true = ((X272 @ id @ X271 @ id))) & ($true != ((X272 @ id @ (ap @ X273 @ X271) @ id))) & ($true = ((X272 @ id @ X273 @ id))) & ! [X277 : subst,X276 : subst,X275 : subst,X274 : term] : (($true != ((X272 @ (comp @ X275 @ X277) @ (sub @ X274 @ X277) @ X276))) | ($true = ((X272 @ X275 @ X274 @ (comp @ X277 @ X276))))) & ! [X278 : term,X279 : term] : (($true != ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (ap @ (sub @ X279 @ id) @ X278) @ id))) | ($true != ((X272 @ id @ X279 @ id)))))) | ? [X264 : (term > $o),X265 : term] : (! [X269 : term,X268 : term] : (($true = ((X264 @ (ap @ X269 @ X268)))) | ($true != ((X264 @ X268))) | ($true != ((X264 @ X269)))) & ! [X270 : term] : ((((X264 @ X270)) = $true) | ($true != ((var @ X270)))) & ($true != ((X264 @ X265))) & ! [X266 : term] : (? [X267 : term] : (($true = ((X264 @ X267))) & ($true != ((X264 @ (sub @ X266 @ (push @ X267 @ id)))))) | ($true = ((X264 @ (lam @ X266)))))))) & (apnotvar = $true) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X444 : term,X445 : (subst > term > subst > $o)] : (? [X456 : term,X457 : term] : (($true = ((X445 @ id @ X456 @ id))) & ($true = ((X445 @ id @ X457 @ id))) & ($true != ((X445 @ id @ (ap @ (sub @ X457 @ id) @ X456) @ id)))) | ($true = ((X445 @ id @ X444 @ id))) | ? [X455 : term] : (($true != ((X445 @ id @ X455 @ id))) & ($true = ((var @ (sub @ X455 @ id))))) | ? [X453 : subst,X452 : subst,X454 : subst,X451 : term] : ((((X445 @ X453 @ X451 @ (comp @ X454 @ X452))) = $true) & ($true != ((X445 @ (comp @ X453 @ X454) @ (sub @ X451 @ X454) @ X452)))) | ? [X446 : (subst > term > term)] : (! [X450 : term] : (($true = ((X445 @ id @ (X446 @ id @ X450) @ id))) | ($true != ((X445 @ id @ X450 @ id)))) & ! [X448 : term,X449 : subst,X447 : subst] : (((sub @ (X446 @ X447 @ X448) @ X449)) = ((X446 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) & ($true != ((X445 @ id @ (lam @ (X446 @ sh @ one)) @ id)))) | ? [X461 : subst,X460 : subst,X458 : term,X459 : subst] : (($true != ((X445 @ X461 @ X458 @ (comp @ X459 @ X460)))) & ($true = ((X445 @ (comp @ X461 @ X459) @ (sub @ X458 @ X459) @ X460))))) | ? [X435 : (subst > term > subst > $o),X436 : term,X434 : (term > $o)] : (! [X437 : term] : ((((X434 @ X437)) != $true) | ($true = ((X434 @ (sub @ X436 @ (push @ X437 @ id)))))) & ! [X438 : (subst > term > term)] : (($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id))) | ? [X442 : term] : (($true = ((X435 @ id @ X442 @ id))) & ($true != ((X435 @ id @ (X438 @ id @ X442) @ id)))) | ? [X439 : subst,X441 : subst,X440 : term] : (((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441))) != ((sub @ (X438 @ X439 @ X440) @ X441)))) & ! [X443 : term] : (((X434 @ X443)) = ((X435 @ id @ X443 @ id))) & ($true != ((X434 @ (lam @ X436)))))) | ? [X433 : term] : (((sub @ X433 @ id)) != X433)) | ? [X427 : term,X426 : (term > $o)] : (! [X431 : term] : (($true = ((X426 @ (lam @ X431)))) | ? [X432 : term] : (($true != ((X426 @ (sub @ X431 @ (push @ X432 @ id))))) & ($true = ((X426 @ X432))))) & ! [X430 : term] : ((((var @ X430)) != $true) | ($true = ((X426 @ X430)))) & ($true != ((X426 @ X427))) & ! [X428 : term,X429 : term] : (($true = ((X426 @ (ap @ X429 @ X428)))) | ($true != ((X426 @ X428))) | ($true != ((X426 @ X429)))))) | ? [X423 : (subst > term > subst > $o)] : ! [X424 : (term > $o)] : ? [X425 : term] : (((X423 @ id @ X425 @ id)) != ((X424 @ X425))))) & ((! [X420 : term] : (((sub @ X420 @ id)) = X420) | ? [X419 : term] : (((sub @ X419 @ id)) != X419)) <=> (termmset_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (pushprop_gthm = $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) != ((d2term @ X401))) | (X401 = X402)) & (! [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) = $true) | ? [X208 : term] : (((X207 @ X208)) != ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | ($true != ((X206 @ X205)))) <=> (pushprop_lem1v2 = $true)) & (! [X524 : (subst > term > subst > $o),X525 : term] : (? [X532 : subst,X534 : term,X535 : subst,X533 : subst] : (($true = ((X524 @ (comp @ X533 @ X532) @ (sub @ X534 @ X532) @ X535))) & ($true != ((X524 @ X533 @ X534 @ (comp @ X532 @ X535))))) | ? [X537 : term,X538 : subst,X536 : subst,X539 : subst] : (($true != ((X524 @ (comp @ X536 @ X539) @ (sub @ X537 @ X539) @ X538))) & ($true = ((X524 @ X536 @ X537 @ (comp @ X539 @ X538))))) | ? [X527 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id))) & ! [X531 : term] : (($true = ((X524 @ id @ (X527 @ id @ X531) @ id))) | ($true != ((X524 @ id @ X531 @ id)))) & ! [X528 : subst,X530 : subst,X529 : term] : (((sub @ (X527 @ X528 @ X529) @ X530)) = ((X527 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))))) | ? [X526 : term] : (($true != ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id))) & ($true = ((X524 @ id @ X526 @ id)))) | ($true = ((X524 @ id @ (lam @ X525) @ id)))) <=> (hoasinduction_lem3 = $true)) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & ((hoasinduction_lem2 = $true) <=> ! [X38 : term,X40 : (subst > term > subst > $o),X39 : term] : (($true != ((X40 @ id @ X39 @ id))) | ? [X46 : term,X45 : term] : (($true = ((X40 @ id @ X45 @ id))) & ($true = ((X40 @ id @ X46 @ id))) & ($true != ((X40 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id)))) | ($true != ((X40 @ id @ X38 @ id))) | ($true = ((X40 @ id @ (ap @ X38 @ X39) @ id))) | ? [X47 : subst,X48 : subst,X49 : term,X50 : subst] : ((((X40 @ X47 @ X49 @ (comp @ X50 @ X48))) != $true) & ($true = ((X40 @ (comp @ X47 @ X50) @ (sub @ X49 @ X50) @ X48)))) | ? [X44 : subst,X43 : term,X42 : subst,X41 : subst] : (($true != ((X40 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X40 @ X42 @ X43 @ (comp @ X44 @ X41))))))) & ((induction2lem = $true) <=> ! [X139 : term,X140 : subst,X138 : (term > $o)] : (? [X143 : term,X144 : term] : (($true = ((X138 @ X144))) & ($true != ((X138 @ (ap @ X144 @ X143)))) & ($true = ((X138 @ X143)))) | ($true = ((X138 @ (sub @ X139 @ X140)))) | ? [X141 : term] : (! [X142 : term] : ((((X138 @ (sub @ X141 @ (push @ X142 @ id)))) = $true) | ($true != ((X138 @ X142)))) & ($true != ((X138 @ (lam @ X141))))) | ? [X145 : term] : (($true != ((X138 @ (sub @ X145 @ X140)))) & ($true = ((var @ X145)))))) & ((hoasinduction_lem3b = $true) <=> ! [X485 : term] : ? [X486 : (subst > term > term)] : (((X486 @ sh @ one)) = ((sub @ X485 @ (push @ one @ sh))))) & (termmset_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X82 : (subst > term > subst > $o),X83 : term] : (? [X89 : term] : (($true = ((X82 @ id @ X89 @ id))) & ($true != ((X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)))) | ? [X91 : subst,X93 : subst,X92 : term,X90 : subst] : (($true = ((X82 @ (comp @ X93 @ X90) @ (sub @ X92 @ X90) @ X91))) & ($true != ((X82 @ X93 @ X92 @ (comp @ X90 @ X91))))) | ? [X84 : (subst > term > term)] : (! [X88 : term] : (($true != ((X82 @ id @ X88 @ id))) | ($true = ((X82 @ id @ (X84 @ id @ X88) @ id)))) & ! [X85 : subst,X86 : subst,X87 : term] : (((X84 @ (comp @ X86 @ X85) @ (sub @ X87 @ X85))) = ((sub @ (X84 @ X86 @ X87) @ X85))) & ($true != ((X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)))) | ($true = ((X82 @ id @ (lam @ X83) @ id))) | ? [X96 : term,X95 : subst,X94 : subst,X97 : subst] : (($true != ((X82 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95) @ X97))) & (((X82 @ X94 @ X96 @ (comp @ X95 @ X97))) = $true))) | ? [X75 : (subst > term > subst > $o),X74 : term] : (! [X77 : (subst > term > term)] : (? [X79 : subst,X81 : subst,X80 : term] : (((sub @ (X77 @ X79 @ X80) @ X81)) != ((X77 @ (comp @ X79 @ X81) @ (sub @ X80 @ X81)))) | (((X75 @ id @ (lam @ (X77 @ sh @ one)) @ id)) = $true) | ? [X78 : term] : (($true = ((X75 @ id @ X78 @ id))) & ($true != ((X75 @ id @ (X77 @ id @ X78) @ id))))) & ($true != ((X75 @ id @ (lam @ (sub @ X74 @ (push @ one @ sh))) @ id))) & ! [X76 : term] : (($true = ((X75 @ id @ (sub @ X74 @ (push @ X76 @ id)) @ id))) | ($true != ((X75 @ id @ X76 @ id)))))) | ? [X73 : term] : (((sub @ X73 @ id)) != X73))) & (((! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))) | ? [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) != X375)) | ? [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) != X373)) <=> (pushprop_lem1_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) <=> (axscons = $true)) & ((((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404)) | ? [X403 : subst] : (((comp @ id @ X403)) != X403)) <=> (substmonoid_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224)) | ? [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 != X219) & (((ap @ X218 @ X220)) = ((ap @ X219 @ X217))))) | ? [X216 : term] : (((sub @ X216 @ id)) != X216))) & ((axidr = $true) <=> ! [X71 : subst] : (((comp @ X71 @ id)) = X71)) & (hoasapnotvar_lthm = $true) & (((d2subst @ d_id)) = id) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X520 : term] : ? [X521 : (subst > term > term)] : ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522))))) & (lamnotap != $true) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) <=> (apinj2 = $true)) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X188 : (subst > term > subst > $o),X187 : term] : (? [X191 : (subst > term > term)] : (! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) & ($true != ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))) | ? [X189 : term,X190 : term] : (($true = ((X188 @ id @ X190 @ id))) & ($true = ((X188 @ id @ X189 @ id))) & ($true != ((X188 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (ulamvarsh = $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) <=> (axshiftcons = $true)) & (lamnotvar = $true) & (one = ((d2term @ d_one))) & ((axvarcons = $true) <=> ! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408)) & (axabs = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X104 : term,X105 : term,X107 : (subst > term > subst > $o),X106 : (term > $o)] : (($true != ((X106 @ X104))) | ($true != ((X106 @ X105))) | ? [X110 : term] : (((X107 @ id @ X110 @ id)) != ((X106 @ X110))) | ? [X108 : term,X109 : term] : (($true != ((X107 @ id @ (ap @ (sub @ X109 @ id) @ X108) @ id))) & ($true = ((X107 @ id @ X108 @ id))) & ($true = ((X107 @ id @ X109 @ id)))) | (((X106 @ (ap @ X105 @ X104))) = $true) | ? [X118 : subst,X115 : subst,X116 : term,X117 : subst] : (($true = ((X107 @ (comp @ X115 @ X118) @ (sub @ X116 @ X118) @ X117))) & ($true != ((X107 @ X115 @ X116 @ (comp @ X118 @ X117))))) | ? [X114 : subst,X112 : subst,X111 : subst,X113 : term] : (($true = ((X107 @ X114 @ X113 @ (comp @ X111 @ X112)))) & ($true != ((X107 @ (comp @ X114 @ X111) @ (sub @ X113 @ X111) @ X112)))))) & ((((! [X58 : (subst > term > term),X60 : (subst > term > term),X59 : term,X57 : subst] : (? [X63 : term,X61 : subst,X62 : subst] : (((sub @ (X60 @ X62 @ X63) @ X61)) != ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | ? [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X58 @ X65 @ X64) @ X66)) != ((X58 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X58 @ X57 @ X59)) = ((X60 @ X57 @ X59))) | (((lam @ (X58 @ sh @ one))) != ((lam @ (X60 @ sh @ one))))) | ? [X56 : term,X55 : term] : ((((lam @ X55)) = ((lam @ X56))) & (X55 != X56))) | ? [X53 : term,X54 : subst] : (((comp @ sh @ (push @ X53 @ X54))) != X54)) | ? [X52 : subst,X51 : term] : (((sub @ one @ (push @ X51 @ X52))) != X51)) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X155 : term,X157 : (term > $o),X156 : (subst > term > subst > $o)] : (($true = ((X157 @ (lam @ X155)))) | ? [X158 : (subst > term > term)] : (! [X161 : subst,X162 : term,X160 : subst] : (((X158 @ (comp @ X160 @ X161) @ (sub @ X162 @ X161))) = ((sub @ (X158 @ X160 @ X162) @ X161))) & ! [X159 : term] : (($true != ((X156 @ id @ X159 @ id))) | ($true = ((X156 @ id @ (X158 @ id @ X159) @ id)))) & ($true != ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ? [X163 : term] : ((((X157 @ (sub @ X155 @ (push @ X163 @ id)))) != $true) & ($true = ((X157 @ X163)))) | ? [X164 : term] : (((X156 @ id @ X164 @ id)) != ((X157 @ X164)))) | ? [X154 : term] : (((sub @ X154 @ id)) != X154)) | ? [X150 : term] : ! [X151 : (subst > term > term)] : ? [X152 : term,X153 : subst] : (((X151 @ X153 @ X152)) != ((sub @ X150 @ (push @ X152 @ X153)))))) & ((induction = $true) <=> ! [X165 : (term > $o),X166 : term] : (? [X168 : term] : (($true != ((X165 @ (lam @ X168)))) & ($true = ((X165 @ X168)))) | ($true = ((X165 @ X166))) | ? [X167 : term] : (($true = ((var @ X167))) & ($true != ((X165 @ X167)))) | ? [X169 : term,X170 : term] : (($true = ((X165 @ X169))) & ($true = ((X165 @ X170))) & ($true != ((X165 @ (ap @ X170 @ X169))))))) & (hoasinduction_lem1 = $true) & (axclos = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X248 : (subst > term > subst > $o),X246 : term,X247 : (term > $o)] : (? [X259 : (subst > term > term)] : (! [X260 : term,X262 : subst,X261 : subst] : (((sub @ (X259 @ X261 @ X260) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X260 @ X262)))) & ($true != ((X248 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X263 : term] : (($true = ((X248 @ id @ (X259 @ id @ X263) @ id))) | ($true != ((X248 @ id @ X263 @ id))))) | ? [X257 : subst,X256 : subst,X255 : term,X254 : subst] : (($true = ((X248 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))) & ($true != ((X248 @ X254 @ X255 @ (comp @ X256 @ X257))))) | ? [X258 : term] : (($true = ((X247 @ X258))) & ($true != ((X247 @ (sub @ X246 @ (push @ X258 @ id)))))) | ? [X249 : term] : (((X248 @ id @ X249 @ id)) != ((X247 @ X249))) | ($true = ((X247 @ (lam @ X246)))) | ? [X253 : subst,X251 : term,X250 : subst,X252 : subst] : (($true = ((X248 @ X250 @ X251 @ (comp @ X253 @ X252)))) & ($true != ((X248 @ (comp @ X250 @ X253) @ (sub @ X251 @ X253) @ X252)))))) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) <=> ! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X31 : (subst > term > subst > $o),X30 : term] : (? [X33 : (subst > term > term)] : (($true != ((X31 @ id @ (lam @ (X33 @ sh @ one)) @ id))) & ! [X36 : subst,X37 : term,X35 : subst] : (((X33 @ (comp @ X35 @ X36) @ (sub @ X37 @ X36))) = ((sub @ (X33 @ X35 @ X37) @ X36))) & ! [X34 : term] : (($true != ((X31 @ id @ X34 @ id))) | ($true = ((X31 @ id @ (X33 @ id @ X34) @ id))))) | ? [X32 : term] : (($true = ((X31 @ id @ X32 @ id))) & ($true != ((X31 @ id @ (sub @ X30 @ (push @ X32 @ id)) @ id)))) | ($true = ((X31 @ id @ (lam @ (sub @ X30 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1v2 = $true) & ! [X5 : d_subst] : (d_id = X5) & (! [X67 : term] : ? [X68 : (subst > term > term)] : ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop = $true) & ((shinj = $true) <=> ! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186))) & (pushprop_lem1_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)))))))))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoaslaminj = $true) <=> ! [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (? [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) != ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | ? [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) != ((sub @ (X123 @ X128 @ X129) @ X130))))) & (axmap = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X517 : (subst > term > subst > $o)] : ? [X518 : (term > $o)] : ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id)))) & (hoaslamnotap_lthm = $true) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) <=> (substmonoid = $true)) & ((axvarid = $true) <=> ! [X381 : term] : (((sub @ X381 @ id)) = X381)) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) <=> (laminj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_gthm = $true) & (! [X225 : (subst > term > subst > $o),X226 : term] : (? [X242 : subst,X240 : subst,X239 : term,X241 : subst] : (($true = ((X225 @ (comp @ X240 @ X242) @ (sub @ X239 @ X242) @ X241))) & (((X225 @ X240 @ X239 @ (comp @ X242 @ X241))) != $true)) | ? [X227 : subst,X229 : subst,X230 : subst,X228 : term] : (($true = ((X225 @ X227 @ X228 @ (comp @ X229 @ X230)))) & ($true != ((X225 @ (comp @ X227 @ X229) @ (sub @ X228 @ X229) @ X230)))) | ? [X233 : term,X232 : term] : (($true != ((X225 @ id @ (ap @ (sub @ X233 @ id) @ X232) @ id))) & ($true = ((X225 @ id @ X232 @ id))) & ($true = ((X225 @ id @ X233 @ id)))) | ($true = ((X225 @ id @ X226 @ id))) | ? [X231 : term] : (($true != ((X225 @ id @ X231 @ id))) & ($true = ((var @ (sub @ X231 @ id))))) | ? [X234 : (subst > term > term)] : (! [X235 : subst,X236 : subst,X237 : term] : (((X234 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))) = ((sub @ (X234 @ X236 @ X237) @ X235))) & ! [X238 : term] : (($true != ((X225 @ id @ X238 @ id))) | ($true = ((X225 @ id @ (X234 @ id @ X238) @ id)))) & ($true != ((X225 @ id @ (lam @ (X234 @ sh @ one)) @ id))))) <=> (hoasinduction = $true)) & (axassoc = $true) & ! [X507 : d_subst,X506 : d_subst] : ((((d2subst @ X507)) != ((d2subst @ X506))) | (X506 = X507)) & (((! [X19 : term,X20 : (term > $o)] : (($true = ((X20 @ X19))) | ? [X21 : term] : (($true != ((X20 @ X21))) & ($true = ((var @ X21)))) | ? [X23 : term,X22 : term] : (($true = ((X20 @ X23))) & (((X20 @ (ap @ X22 @ X23))) != $true) & ($true = ((X20 @ X22)))) | ? [X24 : term] : (! [X25 : term] : (($true != ((X20 @ X25))) | ($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id)))))) & ($true != ((X20 @ (lam @ X24)))))) | ? [X12 : subst,X13 : term,X11 : (term > $o)] : (! [X14 : term] : (? [X15 : term] : (($true != ((X11 @ (sub @ X14 @ (push @ X15 @ id))))) & (((X11 @ X15)) = $true)) | ($true = ((X11 @ (lam @ X14))))) & ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ($true != ((X11 @ X18))) | (((X11 @ X17)) != $true)) & ($true != ((X11 @ (sub @ X13 @ X12)))) & ! [X16 : term] : (($true = ((X11 @ (sub @ X16 @ X12)))) | ($true != ((var @ X16)))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) <=> (induction2_lthm = $true)) & (! [X1 : (term > $o),X0 : subst,X2 : term] : ? [X3 : (term > $o)] : ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (hoasinduction_lem1v2_gthm = $true) & (induction2lem_gthm = $true) & (! [X368 : (term > $o),X369 : term,X367 : subst] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) <=> (pushprop_lem0_lthm = $true)) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lthm = $true) & (! [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ? [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) != ((sub @ (X98 @ X103 @ X102) @ X101)))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X474 : (subst > term > subst > $o)] : ? [X475 : (term > $o)] : ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X490 : (subst > term > subst > $o),X489 : term,X488 : (term > $o)] : (? [X491 : term] : (((X488 @ X491)) != ((X490 @ id @ X491 @ id))) | ? [X497 : term] : (($true != ((X488 @ (sub @ X489 @ (push @ X497 @ id))))) & ($true = ((X488 @ X497)))) | ? [X499 : subst,X501 : term,X498 : subst,X500 : subst] : (($true != ((X490 @ (comp @ X498 @ X500) @ (sub @ X501 @ X500) @ X499))) & ($true = ((X490 @ X498 @ X501 @ (comp @ X500 @ X499))))) | ? [X505 : subst,X503 : subst,X502 : term,X504 : subst] : (($true != ((X490 @ X503 @ X502 @ (comp @ X504 @ X505)))) & ($true = ((X490 @ (comp @ X503 @ X504) @ (sub @ X502 @ X504) @ X505)))) | ($true = ((X488 @ (lam @ X489)))) | ? [X492 : (subst > term > term)] : (($true != ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) & ! [X493 : term] : (($true = ((X490 @ id @ (X492 @ id @ X493) @ id))) | (((X490 @ id @ X493 @ id)) != $true)) & ! [X496 : subst,X494 : term,X495 : subst] : (((sub @ (X492 @ X496 @ X494) @ X495)) = ((X492 @ (comp @ X496 @ X495) @ (sub @ X494 @ X495)))))) | ? [X487 : term] : (((sub @ X487 @ id)) != X487))) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1_lthm = $true) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) <=> (hoasapinj2 = $true)) & (! [X463 : term,X462 : (subst > term > subst > $o)] : (? [X464 : term] : (($true = ((X462 @ id @ X464 @ id))) & ($true != ((X462 @ id @ (sub @ X463 @ (push @ X464 @ id)) @ id)))) | ($true = ((X462 @ id @ (lam @ (sub @ X463 @ (push @ one @ sh))) @ id))) | ? [X466 : term,X465 : (subst > term > term)] : (! [X471 : subst,X473 : subst,X472 : term] : (((X465 @ (comp @ X471 @ X473) @ (sub @ X472 @ X473))) = ((sub @ X466 @ (push @ (sub @ X472 @ X473) @ (comp @ X471 @ X473))))) & ! [X470 : term] : (($true != ((X462 @ id @ X470 @ id))) | ($true = ((X462 @ id @ (X465 @ id @ X470) @ id)))) & ($true != ((X462 @ id @ (lam @ (X465 @ sh @ one)) @ id))) & ! [X468 : subst,X467 : term,X469 : subst] : (((sub @ (X465 @ X468 @ X467) @ X469)) = ((sub @ (sub @ X466 @ (push @ X467 @ X468)) @ X469))))) <=> (hoasinduction_lem3aaa = $true))),
% 5.86/1.21 inference(ennf_transformation,[],[f9])).
% 5.86/1.21 thf(f12,plain,(
% 5.86/1.21 (ulamvarind = $true) & ((induction2lem_lthm = $true) <=> (? [X383 : term,X382 : subst] : (((sub @ one @ (push @ X383 @ X382))) != X383) | ! [X395 : subst,X393 : term,X394 : (term > $o)] : (? [X399 : term] : (! [X400 : term] : (($true != ((X394 @ X400))) | ($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id)))))) & ($true != ((X394 @ (lam @ X399))))) | ? [X396 : term,X397 : term] : (($true = ((X394 @ X396))) & (((X394 @ (ap @ X396 @ X397))) != $true) & ($true = ((X394 @ X397)))) | ($true = ((X394 @ (sub @ X393 @ X395)))) | ? [X398 : term] : ((((X394 @ (sub @ X398 @ X395))) != $true) & ($true = ((var @ X398))))) | ? [X387 : (term > $o),X388 : term] : (! [X389 : term] : (($true = ((X387 @ X389))) | (((var @ X389)) != $true)) & ! [X392 : term,X391 : term] : ((((X387 @ X392)) != $true) | ($true = ((X387 @ (ap @ X392 @ X391)))) | ($true != ((X387 @ X391)))) & ($true != ((X387 @ X388))) & ! [X390 : term] : (($true != ((X387 @ X390))) | ($true = ((X387 @ (lam @ X390)))))) | ? [X385 : term,X384 : subst] : (((comp @ sh @ (push @ X385 @ X384))) != X384) | ? [X386 : subst] : (((comp @ X386 @ id)) != X386))) & (apnotvar = $true) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & ((axvarid = $true) <=> ! [X381 : term] : (((sub @ X381 @ id)) = X381)) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) <=> (apinj1 = $true)) & (! [X31 : (subst > term > subst > $o),X30 : term] : (? [X33 : (subst > term > term)] : (($true != ((X31 @ id @ (lam @ (X33 @ sh @ one)) @ id))) & ! [X36 : subst,X37 : term,X35 : subst] : (((X33 @ (comp @ X35 @ X36) @ (sub @ X37 @ X36))) = ((sub @ (X33 @ X35 @ X37) @ X36))) & ! [X34 : term] : (($true != ((X31 @ id @ X34 @ id))) | ($true = ((X31 @ id @ (X33 @ id @ X34) @ id))))) | ? [X32 : term] : (($true = ((X31 @ id @ X32 @ id))) & ($true != ((X31 @ id @ (sub @ X30 @ (push @ X32 @ id)) @ id)))) | ($true = ((X31 @ id @ (lam @ (sub @ X30 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (? [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) != ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | ? [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) != ((sub @ (X123 @ X128 @ X129) @ X130))))) & ((hoasinduction_lem0 = $true) <=> ! [X517 : (subst > term > subst > $o)] : ? [X518 : (term > $o)] : ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id)))) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & ((! [X444 : term,X445 : (subst > term > subst > $o)] : (? [X456 : term,X457 : term] : (($true = ((X445 @ id @ X456 @ id))) & ($true = ((X445 @ id @ X457 @ id))) & ($true != ((X445 @ id @ (ap @ (sub @ X457 @ id) @ X456) @ id)))) | ($true = ((X445 @ id @ X444 @ id))) | ? [X455 : term] : (($true != ((X445 @ id @ X455 @ id))) & ($true = ((var @ (sub @ X455 @ id))))) | ? [X453 : subst,X452 : subst,X454 : subst,X451 : term] : ((((X445 @ X453 @ X451 @ (comp @ X454 @ X452))) = $true) & ($true != ((X445 @ (comp @ X453 @ X454) @ (sub @ X451 @ X454) @ X452)))) | ? [X446 : (subst > term > term)] : (! [X450 : term] : (($true = ((X445 @ id @ (X446 @ id @ X450) @ id))) | ($true != ((X445 @ id @ X450 @ id)))) & ! [X448 : term,X449 : subst,X447 : subst] : (((sub @ (X446 @ X447 @ X448) @ X449)) = ((X446 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) & ($true != ((X445 @ id @ (lam @ (X446 @ sh @ one)) @ id)))) | ? [X461 : subst,X460 : subst,X458 : term,X459 : subst] : (($true != ((X445 @ X461 @ X458 @ (comp @ X459 @ X460)))) & ($true = ((X445 @ (comp @ X461 @ X459) @ (sub @ X458 @ X459) @ X460))))) | ? [X423 : (subst > term > subst > $o)] : ! [X424 : (term > $o)] : ? [X425 : term] : (((X423 @ id @ X425 @ id)) != ((X424 @ X425))) | ? [X427 : term,X426 : (term > $o)] : (! [X431 : term] : (($true = ((X426 @ (lam @ X431)))) | ? [X432 : term] : (($true != ((X426 @ (sub @ X431 @ (push @ X432 @ id))))) & ($true = ((X426 @ X432))))) & ! [X430 : term] : ((((var @ X430)) != $true) | ($true = ((X426 @ X430)))) & ($true != ((X426 @ X427))) & ! [X428 : term,X429 : term] : (($true = ((X426 @ (ap @ X429 @ X428)))) | ($true != ((X426 @ X428))) | ($true != ((X426 @ X429))))) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | ? [X435 : (subst > term > subst > $o),X436 : term,X434 : (term > $o)] : (! [X437 : term] : ((((X434 @ X437)) != $true) | ($true = ((X434 @ (sub @ X436 @ (push @ X437 @ id)))))) & ! [X438 : (subst > term > term)] : (($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id))) | ? [X442 : term] : (($true = ((X435 @ id @ X442 @ id))) & ($true != ((X435 @ id @ (X438 @ id @ X442) @ id)))) | ? [X439 : subst,X441 : subst,X440 : term] : (((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441))) != ((sub @ (X438 @ X439 @ X440) @ X441)))) & ! [X443 : term] : (((X434 @ X443)) = ((X435 @ id @ X443 @ id))) & ($true != ((X434 @ (lam @ X436)))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X340 : (term > $o),X341 : term] : (($true != ((X340 @ X341))) & ! [X345 : term] : (? [X346 : term] : ((((X340 @ X346)) = $true) & ($true != ((X340 @ (sub @ X345 @ (push @ X346 @ id)))))) | (((X340 @ (lam @ X345))) = $true)) & ! [X342 : term,X343 : term] : ((((X340 @ X342)) != $true) | (((X340 @ (ap @ X342 @ X343))) = $true) | ($true != ((X340 @ X343)))) & ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344))))) | ? [X350 : (subst > term > subst > $o),X349 : (term > $o),X348 : term] : (($true != ((X349 @ (lam @ X348)))) & ! [X351 : (subst > term > term)] : (($true = ((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id))) | ? [X353 : term,X352 : subst,X354 : subst] : (((X351 @ (comp @ X354 @ X352) @ (sub @ X353 @ X352))) != ((sub @ (X351 @ X354 @ X353) @ X352))) | ? [X355 : term] : (($true != ((X350 @ id @ (X351 @ id @ X355) @ id))) & (((X350 @ id @ X355 @ id)) = $true))) & ! [X356 : term] : (($true = ((X349 @ (sub @ X348 @ (push @ X356 @ id))))) | ($true != ((X349 @ X356)))) & ! [X357 : term] : (((X349 @ X357)) = ((X350 @ id @ X357 @ id)))) | ? [X347 : term] : (((sub @ X347 @ id)) != X347) | ! [X358 : term,X359 : (subst > term > subst > $o)] : (? [X366 : term,X365 : term] : (($true = ((X359 @ id @ X365 @ id))) & ($true != ((X359 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id))) & ($true = ((X359 @ id @ X366 @ id)))) | ($true = ((X359 @ id @ X358 @ id))) | ? [X360 : (subst > term > term)] : (! [X364 : term] : (($true = ((X359 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X359 @ id @ X364 @ id)))) & ($true != ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id))) & ! [X362 : subst,X361 : term,X363 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))))) | ? [X337 : (subst > term > subst > $o)] : ! [X338 : (term > $o)] : ? [X339 : term] : (((X337 @ id @ X339 @ id)) != ((X338 @ X339))))) & (! [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ? [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) != ((sub @ (X98 @ X103 @ X102) @ X101)))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (! [X463 : term,X462 : (subst > term > subst > $o)] : (? [X464 : term] : (($true = ((X462 @ id @ X464 @ id))) & ($true != ((X462 @ id @ (sub @ X463 @ (push @ X464 @ id)) @ id)))) | ($true = ((X462 @ id @ (lam @ (sub @ X463 @ (push @ one @ sh))) @ id))) | ? [X466 : term,X465 : (subst > term > term)] : (! [X471 : subst,X473 : subst,X472 : term] : (((X465 @ (comp @ X471 @ X473) @ (sub @ X472 @ X473))) = ((sub @ X466 @ (push @ (sub @ X472 @ X473) @ (comp @ X471 @ X473))))) & ! [X470 : term] : (($true != ((X462 @ id @ X470 @ id))) | ($true = ((X462 @ id @ (X465 @ id @ X470) @ id)))) & ($true != ((X462 @ id @ (lam @ (X465 @ sh @ one)) @ id))) & ! [X468 : subst,X467 : term,X469 : subst] : (((sub @ (X465 @ X468 @ X467) @ X469)) = ((sub @ (sub @ X466 @ (push @ X467 @ X468)) @ X469))))) <=> (hoasinduction_lem3aaa = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) != ((d2term @ X401))) | (X401 = X402)) & ((induction2 = $true) <=> ! [X131 : (term > $o),X132 : term] : (($true = ((X131 @ X132))) | ? [X137 : term] : (($true != ((X131 @ X137))) & ($true = ((var @ X137)))) | ? [X134 : term,X133 : term] : (($true = ((X131 @ X134))) & ($true = ((X131 @ X133))) & ($true != ((X131 @ (ap @ X134 @ X133))))) | ? [X135 : term] : (! [X136 : term] : (($true != ((X131 @ X136))) | ($true = ((X131 @ (sub @ X135 @ (push @ X136 @ id)))))) & ($true != ((X131 @ (lam @ X135))))))) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X150 : term] : ! [X151 : (subst > term > term)] : ? [X152 : term,X153 : subst] : (((X151 @ X153 @ X152)) != ((sub @ X150 @ (push @ X152 @ X153)))) | ? [X154 : term] : (((sub @ X154 @ id)) != X154) | ! [X155 : term,X157 : (term > $o),X156 : (subst > term > subst > $o)] : (($true = ((X157 @ (lam @ X155)))) | ? [X158 : (subst > term > term)] : (! [X161 : subst,X162 : term,X160 : subst] : (((X158 @ (comp @ X160 @ X161) @ (sub @ X162 @ X161))) = ((sub @ (X158 @ X160 @ X162) @ X161))) & ! [X159 : term] : (($true != ((X156 @ id @ X159 @ id))) | ($true = ((X156 @ id @ (X158 @ id @ X159) @ id)))) & ($true != ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ? [X163 : term] : ((((X157 @ (sub @ X155 @ (push @ X163 @ id)))) != $true) & ($true = ((X157 @ X163)))) | ? [X164 : term] : (((X156 @ id @ X164 @ id)) != ((X157 @ X164)))))) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))) | ? [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 != X199) & (((ap @ X198 @ X196)) = ((ap @ X197 @ X199)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X318 : term] : (((sub @ X318 @ id)) != X318) | ! [X327 : term,X328 : (subst > term > subst > $o)] : (? [X329 : (subst > term > term)] : (! [X333 : term,X331 : subst,X332 : subst] : (((sub @ (X329 @ X331 @ X333) @ X332)) = ((X329 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)))) & ($true != ((X328 @ id @ (lam @ (X329 @ sh @ one)) @ id))) & ! [X330 : term] : (($true = ((X328 @ id @ (X329 @ id @ X330) @ id))) | ($true != ((X328 @ id @ X330 @ id))))) | ? [X334 : term] : (($true != ((X328 @ id @ (sub @ X327 @ (push @ X334 @ id)) @ id))) & ($true = ((X328 @ id @ X334 @ id)))) | ($true = ((X328 @ id @ (lam @ X327) @ id)))) | ? [X320 : (subst > term > subst > $o),X319 : term] : (($true != ((X320 @ id @ (lam @ (sub @ X319 @ (push @ one @ sh))) @ id))) & ! [X326 : term] : ((((X320 @ id @ X326 @ id)) != $true) | (((X320 @ id @ (sub @ X319 @ (push @ X326 @ id)) @ id)) = $true)) & ! [X321 : (subst > term > term)] : (? [X324 : subst,X322 : subst,X323 : term] : (((X321 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))) != ((sub @ (X321 @ X324 @ X323) @ X322))) | ($true = ((X320 @ id @ (lam @ (X321 @ sh @ one)) @ id))) | ? [X325 : term] : (($true = ((X320 @ id @ X325 @ id))) & ($true != ((X320 @ id @ (X321 @ id @ X325) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X524 : (subst > term > subst > $o),X525 : term] : (? [X532 : subst,X534 : term,X535 : subst,X533 : subst] : (($true = ((X524 @ (comp @ X533 @ X532) @ (sub @ X534 @ X532) @ X535))) & ($true != ((X524 @ X533 @ X534 @ (comp @ X532 @ X535))))) | ? [X537 : term,X538 : subst,X536 : subst,X539 : subst] : (($true != ((X524 @ (comp @ X536 @ X539) @ (sub @ X537 @ X539) @ X538))) & ($true = ((X524 @ X536 @ X537 @ (comp @ X539 @ X538))))) | ? [X527 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id))) & ! [X531 : term] : (($true = ((X524 @ id @ (X527 @ id @ X531) @ id))) | ($true != ((X524 @ id @ X531 @ id)))) & ! [X528 : subst,X530 : subst,X529 : term] : (((sub @ (X527 @ X528 @ X529) @ X530)) = ((X527 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))))) | ? [X526 : term] : (($true != ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id))) & ($true = ((X524 @ id @ X526 @ id)))) | ($true = ((X524 @ id @ (lam @ X525) @ id)))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) <=> ! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X188 : (subst > term > subst > $o),X187 : term] : (? [X191 : (subst > term > term)] : (! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) & ($true != ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))) | ? [X189 : term,X190 : term] : (($true = ((X188 @ id @ X190 @ id))) & ($true = ((X188 @ id @ X189 @ id))) & ($true != ((X188 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X485 : term] : ? [X486 : (subst > term > term)] : (((X486 @ sh @ one)) = ((sub @ X485 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X5 : d_subst] : (d_id = X5) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1_lthm = $true) <=> (! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))) | ? [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) != X373) | ? [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) != X375))) & (ulamvar1 != $true) & (! [X225 : (subst > term > subst > $o),X226 : term] : (? [X242 : subst,X240 : subst,X239 : term,X241 : subst] : (($true = ((X225 @ (comp @ X240 @ X242) @ (sub @ X239 @ X242) @ X241))) & (((X225 @ X240 @ X239 @ (comp @ X242 @ X241))) != $true)) | ? [X227 : subst,X229 : subst,X230 : subst,X228 : term] : (($true = ((X225 @ X227 @ X228 @ (comp @ X229 @ X230)))) & ($true != ((X225 @ (comp @ X227 @ X229) @ (sub @ X228 @ X229) @ X230)))) | ? [X233 : term,X232 : term] : (($true != ((X225 @ id @ (ap @ (sub @ X233 @ id) @ X232) @ id))) & ($true = ((X225 @ id @ X232 @ id))) & ($true = ((X225 @ id @ X233 @ id)))) | ($true = ((X225 @ id @ X226 @ id))) | ? [X231 : term] : (($true != ((X225 @ id @ X231 @ id))) & ($true = ((var @ (sub @ X231 @ id))))) | ? [X234 : (subst > term > term)] : (! [X235 : subst,X236 : subst,X237 : term] : (((X234 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))) = ((sub @ (X234 @ X236 @ X237) @ X235))) & ! [X238 : term] : (($true != ((X225 @ id @ X238 @ id))) | ($true = ((X225 @ id @ (X234 @ id @ X238) @ id)))) & ($true != ((X225 @ id @ (lam @ (X234 @ sh @ one)) @ id))))) <=> (hoasinduction = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X38 : term,X40 : (subst > term > subst > $o),X39 : term] : (($true != ((X40 @ id @ X39 @ id))) | ? [X46 : term,X45 : term] : (($true = ((X40 @ id @ X45 @ id))) & ($true = ((X40 @ id @ X46 @ id))) & ($true != ((X40 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id)))) | ($true != ((X40 @ id @ X38 @ id))) | ($true = ((X40 @ id @ (ap @ X38 @ X39) @ id))) | ? [X47 : subst,X48 : subst,X49 : term,X50 : subst] : ((((X40 @ X47 @ X49 @ (comp @ X50 @ X48))) != $true) & ($true = ((X40 @ (comp @ X47 @ X50) @ (sub @ X49 @ X50) @ X48)))) | ? [X44 : subst,X43 : term,X42 : subst,X41 : subst] : (($true != ((X40 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X40 @ X42 @ X43 @ (comp @ X44 @ X41))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) <=> (laminj = $true)) & ((axidr = $true) <=> ! [X71 : subst] : (((comp @ X71 @ id)) = X71)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) <=> (axscons = $true)) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) <=> (hoasapinj2 = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & ((! [X301 : (subst > term > subst > $o),X300 : term] : (? [X313 : term] : (($true = ((var @ (sub @ X313 @ id)))) & ($true != ((X301 @ id @ X313 @ id)))) | ? [X308 : (subst > term > term)] : (! [X311 : subst,X312 : subst,X310 : term] : (((sub @ (X308 @ X311 @ X310) @ X312)) = ((X308 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312)))) & ! [X309 : term] : (($true != ((X301 @ id @ X309 @ id))) | ($true = ((X301 @ id @ (X308 @ id @ X309) @ id)))) & ($true != ((X301 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ? [X314 : subst,X317 : term,X316 : subst,X315 : subst] : (($true = ((X301 @ X316 @ X317 @ (comp @ X314 @ X315)))) & ($true != ((X301 @ (comp @ X316 @ X314) @ (sub @ X317 @ X314) @ X315)))) | ($true = ((X301 @ id @ X300 @ id))) | ? [X302 : term,X303 : term] : (($true = ((X301 @ id @ X303 @ id))) & ($true = ((X301 @ id @ X302 @ id))) & ($true != ((X301 @ id @ (ap @ (sub @ X302 @ id) @ X303) @ id)))) | ? [X307 : subst,X305 : term,X304 : subst,X306 : subst] : (($true = ((X301 @ (comp @ X306 @ X307) @ (sub @ X305 @ X307) @ X304))) & ($true != ((X301 @ X306 @ X305 @ (comp @ X307 @ X304)))))) | ? [X264 : (term > $o),X265 : term] : (! [X269 : term,X268 : term] : (($true = ((X264 @ (ap @ X269 @ X268)))) | ($true != ((X264 @ X268))) | ($true != ((X264 @ X269)))) & ! [X270 : term] : ((((X264 @ X270)) = $true) | ($true != ((var @ X270)))) & ($true != ((X264 @ X265))) & ! [X266 : term] : (? [X267 : term] : (($true = ((X264 @ X267))) & ($true != ((X264 @ (sub @ X266 @ (push @ X267 @ id)))))) | ($true = ((X264 @ (lam @ X266)))))) | ? [X273 : term,X271 : term,X272 : (subst > term > subst > $o)] : (! [X282 : term,X280 : subst,X281 : subst,X283 : subst] : (($true = ((X272 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281) @ X280))) | ($true != ((X272 @ X283 @ X282 @ (comp @ X281 @ X280))))) & ($true = ((X272 @ id @ X271 @ id))) & ($true != ((X272 @ id @ (ap @ X273 @ X271) @ id))) & ($true = ((X272 @ id @ X273 @ id))) & ! [X277 : subst,X276 : subst,X275 : subst,X274 : term] : (($true != ((X272 @ (comp @ X275 @ X277) @ (sub @ X274 @ X277) @ X276))) | ($true = ((X272 @ X275 @ X274 @ (comp @ X277 @ X276))))) & ! [X278 : term,X279 : term] : (($true != ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (ap @ (sub @ X279 @ id) @ X278) @ id))) | ($true != ((X272 @ id @ X279 @ id))))) | ? [X285 : term,X284 : (subst > term > subst > $o)] : (! [X299 : term] : (($true != ((X284 @ id @ X299 @ id))) | ($true = ((X284 @ id @ (sub @ X285 @ (push @ X299 @ id)) @ id)))) & ! [X286 : (subst > term > term)] : (? [X287 : term] : (($true != ((X284 @ id @ (X286 @ id @ X287) @ id))) & ($true = ((X284 @ id @ X287 @ id)))) | ($true = ((X284 @ id @ (lam @ (X286 @ sh @ one)) @ id))) | ? [X288 : subst,X290 : subst,X289 : term] : (((sub @ (X286 @ X290 @ X289) @ X288)) != ((X286 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))))) & ($true != ((X284 @ id @ (lam @ X285) @ id))) & ! [X296 : subst,X295 : subst,X298 : term,X297 : subst] : (($true != ((X284 @ (comp @ X297 @ X295) @ (sub @ X298 @ X295) @ X296))) | ($true = ((X284 @ X297 @ X298 @ (comp @ X295 @ X296))))) & ! [X291 : subst,X294 : subst,X292 : term,X293 : subst] : ((((X284 @ (comp @ X293 @ X291) @ (sub @ X292 @ X291) @ X294)) = $true) | (((X284 @ X293 @ X292 @ (comp @ X291 @ X294))) != $true)))) <=> (hoasinduction_lthm = $true)) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & ((hoaslaminj_lthm = $true) <=> (? [X52 : subst,X51 : term] : (((sub @ one @ (push @ X51 @ X52))) != X51) | ? [X53 : term,X54 : subst] : (((comp @ sh @ (push @ X53 @ X54))) != X54) | ! [X58 : (subst > term > term),X60 : (subst > term > term),X59 : term,X57 : subst] : (? [X63 : term,X61 : subst,X62 : subst] : (((sub @ (X60 @ X62 @ X63) @ X61)) != ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | ? [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X58 @ X65 @ X64) @ X66)) != ((X58 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X58 @ X57 @ X59)) = ((X60 @ X57 @ X59))) | (((lam @ (X58 @ sh @ one))) != ((lam @ (X60 @ sh @ one))))) | ? [X56 : term,X55 : term] : ((((lam @ X55)) = ((lam @ X56))) & (X55 != X56)))) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) <=> (axshiftcons = $true)) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X104 : term,X105 : term,X107 : (subst > term > subst > $o),X106 : (term > $o)] : (($true != ((X106 @ X104))) | ($true != ((X106 @ X105))) | ? [X110 : term] : (((X107 @ id @ X110 @ id)) != ((X106 @ X110))) | ? [X108 : term,X109 : term] : (($true != ((X107 @ id @ (ap @ (sub @ X109 @ id) @ X108) @ id))) & ($true = ((X107 @ id @ X108 @ id))) & ($true = ((X107 @ id @ X109 @ id)))) | (((X106 @ (ap @ X105 @ X104))) = $true) | ? [X118 : subst,X115 : subst,X116 : term,X117 : subst] : (($true = ((X107 @ (comp @ X115 @ X118) @ (sub @ X116 @ X118) @ X117))) & ($true != ((X107 @ X115 @ X116 @ (comp @ X118 @ X117))))) | ? [X114 : subst,X112 : subst,X111 : subst,X113 : term] : (($true = ((X107 @ X114 @ X113 @ (comp @ X111 @ X112)))) & ($true != ((X107 @ (comp @ X114 @ X111) @ (sub @ X113 @ X111) @ X112)))))) & ((? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X12 : subst,X13 : term,X11 : (term > $o)] : (! [X14 : term] : (? [X15 : term] : (($true != ((X11 @ (sub @ X14 @ (push @ X15 @ id))))) & (((X11 @ X15)) = $true)) | ($true = ((X11 @ (lam @ X14))))) & ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ($true != ((X11 @ X18))) | (((X11 @ X17)) != $true)) & ($true != ((X11 @ (sub @ X13 @ X12)))) & ! [X16 : term] : (($true = ((X11 @ (sub @ X16 @ X12)))) | ($true != ((var @ X16))))) | ! [X19 : term,X20 : (term > $o)] : (($true = ((X20 @ X19))) | ? [X21 : term] : (($true != ((X20 @ X21))) & ($true = ((var @ X21)))) | ? [X23 : term,X22 : term] : (($true = ((X20 @ X23))) & (((X20 @ (ap @ X22 @ X23))) != $true) & ($true = ((X20 @ X22)))) | ? [X24 : term] : (! [X25 : term] : (($true != ((X20 @ X25))) | ($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id)))))) & ($true != ((X20 @ (lam @ X24))))))) <=> (induction2_lthm = $true)) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) <=> (substmonoid = $true)) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((induction = $true) <=> ! [X165 : (term > $o),X166 : term] : (? [X168 : term] : (($true != ((X165 @ (lam @ X168)))) & ($true = ((X165 @ X168)))) | ($true = ((X165 @ X166))) | ? [X167 : term] : (($true = ((var @ X167))) & ($true != ((X165 @ X167)))) | ? [X169 : term,X170 : term] : (($true = ((X165 @ X169))) & ($true = ((X165 @ X170))) & ($true != ((X165 @ (ap @ X170 @ X169))))))) & ((? [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) != X210) | ! [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true != ((X214 @ X211))) | (((X212 @ one)) = $true) | ? [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) != ((X212 @ X215))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotap_lthm = $true) & (! [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) = $true) | ? [X208 : term] : (((X207 @ X208)) != ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | ($true != ((X206 @ X205)))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X490 : (subst > term > subst > $o),X489 : term,X488 : (term > $o)] : (? [X491 : term] : (((X488 @ X491)) != ((X490 @ id @ X491 @ id))) | ? [X497 : term] : (($true != ((X488 @ (sub @ X489 @ (push @ X497 @ id))))) & ($true = ((X488 @ X497)))) | ? [X499 : subst,X501 : term,X498 : subst,X500 : subst] : (($true != ((X490 @ (comp @ X498 @ X500) @ (sub @ X501 @ X500) @ X499))) & ($true = ((X490 @ X498 @ X501 @ (comp @ X500 @ X499))))) | ? [X505 : subst,X503 : subst,X502 : term,X504 : subst] : (($true != ((X490 @ X503 @ X502 @ (comp @ X504 @ X505)))) & ($true = ((X490 @ (comp @ X503 @ X504) @ (sub @ X502 @ X504) @ X505)))) | ($true = ((X488 @ (lam @ X489)))) | ? [X492 : (subst > term > term)] : (($true != ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) & ! [X493 : term] : (($true = ((X490 @ id @ (X492 @ id @ X493) @ id))) | (((X490 @ id @ X493 @ id)) != $true)) & ! [X496 : subst,X494 : term,X495 : subst] : (((sub @ (X492 @ X496 @ X494) @ X495)) = ((X492 @ (comp @ X496 @ X495) @ (sub @ X494 @ X495)))))) | ? [X487 : term] : (((sub @ X487 @ id)) != X487))) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((axvarcons = $true) <=> ! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408)) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X368 : (term > $o),X369 : term,X367 : subst] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) <=> (pushprop_lem0_lthm = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X474 : (subst > term > subst > $o)] : ? [X475 : (term > $o)] : ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id)))) & (! [X243 : term] : ? [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) = ((X244 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X420 : term] : (((sub @ X420 @ id)) = X420) | ? [X419 : term] : (((sub @ X419 @ id)) != X419)) <=> (termmset_lthm = $true)) & ((shinj = $true) <=> ! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186))) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((substmonoid_lthm = $true) <=> ((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)) | ? [X403 : subst] : (((comp @ id @ X403)) != X403) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404))) & ((induction2lem = $true) <=> ! [X139 : term,X140 : subst,X138 : (term > $o)] : (? [X143 : term,X144 : term] : (($true = ((X138 @ X144))) & ($true != ((X138 @ (ap @ X144 @ X143)))) & ($true = ((X138 @ X143)))) | ($true = ((X138 @ (sub @ X139 @ X140)))) | ? [X141 : term] : (! [X142 : term] : ((((X138 @ (sub @ X141 @ (push @ X142 @ id)))) = $true) | ($true != ((X138 @ X142)))) & ($true != ((X138 @ (lam @ X141))))) | ? [X145 : term] : (($true != ((X138 @ (sub @ X145 @ X140)))) & ($true = ((var @ X145)))))) & (! [X67 : term] : ? [X68 : (subst > term > term)] : ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X245 : d_term] : (d_one = X245) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X507 : d_subst,X506 : d_subst] : ((((d2subst @ X507)) != ((d2subst @ X506))) | (X506 = X507)) & (axvarshift = $true) & (axmap = $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)))))))))))))) & (! [X172 : (term > $o),X171 : term,X173 : (subst > term > subst > $o)] : (($true = ((X172 @ (lam @ X171)))) | ? [X175 : (subst > term > term)] : (! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177)))) & ($true != ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) & ! [X176 : term] : (($true = ((X173 @ id @ (X175 @ id @ X176) @ id))) | ($true != ((X173 @ id @ X176 @ id))))) | ? [X174 : term] : (((X173 @ id @ X174 @ id)) != ((X172 @ X174))) | ? [X180 : term] : (($true = ((X172 @ X180))) & ($true != ((X172 @ (sub @ X171 @ (push @ X180 @ id))))))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj1_lthm = $true) <=> (? [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 != X219) & (((ap @ X218 @ X220)) = ((ap @ X219 @ X217)))) | ? [X216 : term] : (((sub @ X216 @ id)) != X216) | ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224)))) & (hoaslamnotap_gthm = $true) & (! [X1 : (term > $o),X0 : subst,X2 : term] : ? [X3 : (term > $o)] : ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X248 : (subst > term > subst > $o),X246 : term,X247 : (term > $o)] : (? [X259 : (subst > term > term)] : (! [X260 : term,X262 : subst,X261 : subst] : (((sub @ (X259 @ X261 @ X260) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X260 @ X262)))) & ($true != ((X248 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X263 : term] : (($true = ((X248 @ id @ (X259 @ id @ X263) @ id))) | ($true != ((X248 @ id @ X263 @ id))))) | ? [X257 : subst,X256 : subst,X255 : term,X254 : subst] : (($true = ((X248 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))) & ($true != ((X248 @ X254 @ X255 @ (comp @ X256 @ X257))))) | ? [X258 : term] : (($true = ((X247 @ X258))) & ($true != ((X247 @ (sub @ X246 @ (push @ X258 @ id)))))) | ? [X249 : term] : (((X248 @ id @ X249 @ id)) != ((X247 @ X249))) | ($true = ((X247 @ (lam @ X246)))) | ? [X253 : subst,X251 : term,X250 : subst,X252 : subst] : (($true = ((X248 @ X250 @ X251 @ (comp @ X253 @ X252)))) & ($true != ((X248 @ (comp @ X250 @ X253) @ (sub @ X251 @ X253) @ X252)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X520 : term] : ? [X521 : (subst > term > term)] : ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522))))) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) <=> (apinj2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3aa = $true) <=> ! [X478 : term,X477 : (subst > term > subst > $o)] : (($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id))) | ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X477 @ id @ X481 @ id))) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id)))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X482 : term,X484 : subst,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ? [X479 : term] : (($true != ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id))) & ($true = ((X477 @ id @ X479 @ id)))))) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & (induction2_gthm = $true) & ((? [X75 : (subst > term > subst > $o),X74 : term] : (! [X77 : (subst > term > term)] : (? [X79 : subst,X81 : subst,X80 : term] : (((sub @ (X77 @ X79 @ X80) @ X81)) != ((X77 @ (comp @ X79 @ X81) @ (sub @ X80 @ X81)))) | (((X75 @ id @ (lam @ (X77 @ sh @ one)) @ id)) = $true) | ? [X78 : term] : (($true = ((X75 @ id @ X78 @ id))) & ($true != ((X75 @ id @ (X77 @ id @ X78) @ id))))) & ($true != ((X75 @ id @ (lam @ (sub @ X74 @ (push @ one @ sh))) @ id))) & ! [X76 : term] : (($true = ((X75 @ id @ (sub @ X74 @ (push @ X76 @ id)) @ id))) | ($true != ((X75 @ id @ X76 @ id))))) | ! [X82 : (subst > term > subst > $o),X83 : term] : (? [X89 : term] : (($true = ((X82 @ id @ X89 @ id))) & ($true != ((X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)))) | ? [X91 : subst,X93 : subst,X92 : term,X90 : subst] : (($true = ((X82 @ (comp @ X93 @ X90) @ (sub @ X92 @ X90) @ X91))) & ($true != ((X82 @ X93 @ X92 @ (comp @ X90 @ X91))))) | ? [X84 : (subst > term > term)] : (! [X88 : term] : (($true != ((X82 @ id @ X88 @ id))) | ($true = ((X82 @ id @ (X84 @ id @ X88) @ id)))) & ! [X85 : subst,X86 : subst,X87 : term] : (((X84 @ (comp @ X86 @ X85) @ (sub @ X87 @ X85))) = ((sub @ (X84 @ X86 @ X87) @ X85))) & ($true != ((X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)))) | ($true = ((X82 @ id @ (lam @ X83) @ id))) | ? [X96 : term,X95 : subst,X94 : subst,X97 : subst] : (($true != ((X82 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95) @ X97))) & (((X82 @ X94 @ X96 @ (comp @ X95 @ X97))) = $true))) | ? [X73 : term] : (((sub @ X73 @ id)) != X73)) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (ulamvarsh = $true) & (! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true = ((X410 @ id @ X411 @ id))) & (((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id)) != $true)) | ? [X412 : (subst > term > term)] : (! [X416 : term] : (($true != ((X410 @ id @ X416 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X416) @ id)))) & ($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : subst,X414 : subst,X415 : term] : (((sub @ (X412 @ X413 @ X415) @ X414)) = ((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))))) | ($true = ((X410 @ id @ (lam @ X409) @ id)))) <=> (hoasinduction_lem3a = $true))),
% 5.86/1.21 inference(flattening,[],[f11])).
% 5.86/1.21 thf(f13,definition,(
% 5.86/1.21 ($true = sP0) <=> ! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true = ((X410 @ id @ X411 @ id))) & (((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id)) != $true)) | ? [X412 : (subst > term > term)] : (! [X416 : term] : (($true != ((X410 @ id @ X416 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X416) @ id)))) & ($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : subst,X414 : subst,X415 : term] : (((sub @ (X412 @ X413 @ X415) @ X414)) = ((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))))) | ($true = ((X410 @ id @ (lam @ X409) @ id))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f14,definition,(
% 5.86/1.21 ! [X82 : (subst > term > subst > $o)] : (($true = ((sP1 @ X82))) <=> ? [X84 : (subst > term > term)] : (! [X88 : term] : (($true != ((X82 @ id @ X88 @ id))) | ($true = ((X82 @ id @ (X84 @ id @ X88) @ id)))) & ! [X85 : subst,X86 : subst,X87 : term] : (((X84 @ (comp @ X86 @ X85) @ (sub @ X87 @ X85))) = ((sub @ (X84 @ X86 @ X87) @ X85))) & ($true != ((X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f15,definition,(
% 5.86/1.21 ($true = sP2) <=> ? [X75 : (subst > term > subst > $o),X74 : term] : (! [X77 : (subst > term > term)] : (? [X79 : subst,X81 : subst,X80 : term] : (((sub @ (X77 @ X79 @ X80) @ X81)) != ((X77 @ (comp @ X79 @ X81) @ (sub @ X80 @ X81)))) | (((X75 @ id @ (lam @ (X77 @ sh @ one)) @ id)) = $true) | ? [X78 : term] : (($true = ((X75 @ id @ X78 @ id))) & ($true != ((X75 @ id @ (X77 @ id @ X78) @ id))))) & ($true != ((X75 @ id @ (lam @ (sub @ X74 @ (push @ one @ sh))) @ id))) & ! [X76 : term] : (($true = ((X75 @ id @ (sub @ X74 @ (push @ X76 @ id)) @ id))) | ($true != ((X75 @ id @ X76 @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f16,definition,(
% 5.86/1.21 ($true = sP3) <=> (($true = sP2) | ! [X82 : (subst > term > subst > $o),X83 : term] : (? [X89 : term] : (($true = ((X82 @ id @ X89 @ id))) & ($true != ((X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)))) | ? [X91 : subst,X93 : subst,X92 : term,X90 : subst] : (($true = ((X82 @ (comp @ X93 @ X90) @ (sub @ X92 @ X90) @ X91))) & ($true != ((X82 @ X93 @ X92 @ (comp @ X90 @ X91))))) | ($true = ((sP1 @ X82))) | ($true = ((X82 @ id @ (lam @ X83) @ id))) | ? [X96 : term,X95 : subst,X94 : subst,X97 : subst] : (($true != ((X82 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95) @ X97))) & (((X82 @ X94 @ X96 @ (comp @ X95 @ X97))) = $true))) | ? [X73 : term] : (((sub @ X73 @ id)) != X73))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f17,definition,(
% 5.86/1.21 (sP4 = $true) <=> ! [X478 : term,X477 : (subst > term > subst > $o)] : (($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id))) | ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X477 @ id @ X481 @ id))) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id)))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X482 : term,X484 : subst,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ? [X479 : term] : (($true != ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id))) & ($true = ((X477 @ id @ X479 @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f18,definition,(
% 5.86/1.21 ! [X248 : (subst > term > subst > $o)] : (($true = ((sP5 @ X248))) <=> ? [X259 : (subst > term > term)] : (! [X260 : term,X262 : subst,X261 : subst] : (((sub @ (X259 @ X261 @ X260) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X260 @ X262)))) & ($true != ((X248 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X263 : term] : (($true = ((X248 @ id @ (X259 @ id @ X263) @ id))) | ($true != ((X248 @ id @ X263 @ id))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f19,definition,(
% 5.86/1.21 ($true = sP6) <=> ! [X248 : (subst > term > subst > $o),X246 : term,X247 : (term > $o)] : (($true = ((sP5 @ X248))) | ? [X257 : subst,X256 : subst,X255 : term,X254 : subst] : (($true = ((X248 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))) & ($true != ((X248 @ X254 @ X255 @ (comp @ X256 @ X257))))) | ? [X258 : term] : (($true = ((X247 @ X258))) & ($true != ((X247 @ (sub @ X246 @ (push @ X258 @ id)))))) | ? [X249 : term] : (((X248 @ id @ X249 @ id)) != ((X247 @ X249))) | ($true = ((X247 @ (lam @ X246)))) | ? [X253 : subst,X251 : term,X250 : subst,X252 : subst] : (($true = ((X248 @ X250 @ X251 @ (comp @ X253 @ X252)))) & ($true != ((X248 @ (comp @ X250 @ X253) @ (sub @ X251 @ X253) @ X252)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f20,definition,(
% 5.86/1.21 ($true = sP7) <=> ! [X172 : (term > $o),X171 : term,X173 : (subst > term > subst > $o)] : (($true = ((X172 @ (lam @ X171)))) | ? [X175 : (subst > term > term)] : (! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177)))) & ($true != ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) & ! [X176 : term] : (($true = ((X173 @ id @ (X175 @ id @ X176) @ id))) | ($true != ((X173 @ id @ X176 @ id))))) | ? [X174 : term] : (((X173 @ id @ X174 @ id)) != ((X172 @ X174))) | ? [X180 : term] : (($true = ((X172 @ X180))) & ($true != ((X172 @ (sub @ X171 @ (push @ X180 @ id)))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f21,definition,(
% 5.86/1.21 ! [X138 : (term > $o)] : ((((sP8 @ X138)) = $true) <=> ? [X143 : term,X144 : term] : (($true = ((X138 @ X144))) & ($true != ((X138 @ (ap @ X144 @ X143)))) & ($true = ((X138 @ X143)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f22,definition,(
% 5.86/1.21 ($true = sP9) <=> ! [X139 : term,X140 : subst,X138 : (term > $o)] : ((((sP8 @ X138)) = $true) | ($true = ((X138 @ (sub @ X139 @ X140)))) | ? [X141 : term] : (! [X142 : term] : ((((X138 @ (sub @ X141 @ (push @ X142 @ id)))) = $true) | ($true != ((X138 @ X142)))) & ($true != ((X138 @ (lam @ X141))))) | ? [X145 : term] : (($true != ((X138 @ (sub @ X145 @ X140)))) & ($true = ((var @ X145)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f23,definition,(
% 5.86/1.21 ! [X490 : (subst > term > subst > $o)] : ((((sP10 @ X490)) = $true) <=> ? [X492 : (subst > term > term)] : (($true != ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) & ! [X493 : term] : (($true = ((X490 @ id @ (X492 @ id @ X493) @ id))) | (((X490 @ id @ X493 @ id)) != $true)) & ! [X496 : subst,X494 : term,X495 : subst] : (((sub @ (X492 @ X496 @ X494) @ X495)) = ((X492 @ (comp @ X496 @ X495) @ (sub @ X494 @ X495))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f24,definition,(
% 5.86/1.21 ($true = sP11) <=> (! [X490 : (subst > term > subst > $o),X489 : term,X488 : (term > $o)] : (? [X491 : term] : (((X488 @ X491)) != ((X490 @ id @ X491 @ id))) | ? [X497 : term] : (($true != ((X488 @ (sub @ X489 @ (push @ X497 @ id))))) & ($true = ((X488 @ X497)))) | ? [X499 : subst,X501 : term,X498 : subst,X500 : subst] : (($true != ((X490 @ (comp @ X498 @ X500) @ (sub @ X501 @ X500) @ X499))) & ($true = ((X490 @ X498 @ X501 @ (comp @ X500 @ X499))))) | ? [X505 : subst,X503 : subst,X502 : term,X504 : subst] : (($true != ((X490 @ X503 @ X502 @ (comp @ X504 @ X505)))) & ($true = ((X490 @ (comp @ X503 @ X504) @ (sub @ X502 @ X504) @ X505)))) | ($true = ((X488 @ (lam @ X489)))) | (((sP10 @ X490)) = $true)) | ? [X487 : term] : (((sub @ X487 @ id)) != X487))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f25,definition,(
% 5.86/1.21 ! [X165 : (term > $o)] : (($true = ((sP12 @ X165))) <=> ? [X169 : term,X170 : term] : (($true = ((X165 @ X169))) & ($true = ((X165 @ X170))) & ($true != ((X165 @ (ap @ X170 @ X169))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f26,definition,(
% 5.86/1.21 ! [X20 : (term > $o)] : (($true = ((sP13 @ X20))) <=> ? [X23 : term,X22 : term] : (($true = ((X20 @ X23))) & (((X20 @ (ap @ X22 @ X23))) != $true) & ($true = ((X20 @ X22)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f27,definition,(
% 5.86/1.21 ! [X11 : (term > $o)] : (($true = ((sP14 @ X11))) <=> ! [X17 : term,X18 : term] : (($true = ((X11 @ (ap @ X18 @ X17)))) | ($true != ((X11 @ X18))) | (((X11 @ X17)) != $true)))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f28,definition,(
% 5.86/1.21 ($true = sP15) <=> ! [X19 : term,X20 : (term > $o)] : (($true = ((X20 @ X19))) | ? [X21 : term] : (($true != ((X20 @ X21))) & ($true = ((var @ X21)))) | ($true = ((sP13 @ X20))) | ? [X24 : term] : (! [X25 : term] : (($true != ((X20 @ X25))) | ($true = ((X20 @ (sub @ X24 @ (push @ X25 @ id)))))) & ($true != ((X20 @ (lam @ X24))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f29,definition,(
% 5.86/1.21 (sP16 = $true) <=> (? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X12 : subst,X13 : term,X11 : (term > $o)] : (! [X14 : term] : (? [X15 : term] : (($true != ((X11 @ (sub @ X14 @ (push @ X15 @ id))))) & (((X11 @ X15)) = $true)) | ($true = ((X11 @ (lam @ X14))))) & ($true = ((sP14 @ X11))) & ($true != ((X11 @ (sub @ X13 @ X12)))) & ! [X16 : term] : (($true = ((X11 @ (sub @ X16 @ X12)))) | ($true != ((var @ X16))))) | ($true = sP15))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f30,definition,(
% 5.86/1.21 ! [X107 : (subst > term > subst > $o)] : (($true = ((sP17 @ X107))) <=> ? [X108 : term,X109 : term] : (($true != ((X107 @ id @ (ap @ (sub @ X109 @ id) @ X108) @ id))) & ($true = ((X107 @ id @ X108 @ id))) & ($true = ((X107 @ id @ X109 @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f31,definition,(
% 5.86/1.21 ($true = sP18) <=> ! [X104 : term,X105 : term,X107 : (subst > term > subst > $o),X106 : (term > $o)] : (($true != ((X106 @ X104))) | ($true != ((X106 @ X105))) | ? [X110 : term] : (((X107 @ id @ X110 @ id)) != ((X106 @ X110))) | ($true = ((sP17 @ X107))) | (((X106 @ (ap @ X105 @ X104))) = $true) | ? [X118 : subst,X115 : subst,X116 : term,X117 : subst] : (($true = ((X107 @ (comp @ X115 @ X118) @ (sub @ X116 @ X118) @ X117))) & ($true != ((X107 @ X115 @ X116 @ (comp @ X118 @ X117))))) | ? [X114 : subst,X112 : subst,X111 : subst,X113 : term] : (($true = ((X107 @ X114 @ X113 @ (comp @ X111 @ X112)))) & ($true != ((X107 @ (comp @ X114 @ X111) @ (sub @ X113 @ X111) @ X112)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f32,definition,(
% 5.86/1.21 ($true = sP19) <=> (? [X52 : subst,X51 : term] : (((sub @ one @ (push @ X51 @ X52))) != X51) | ? [X53 : term,X54 : subst] : (((comp @ sh @ (push @ X53 @ X54))) != X54) | ! [X58 : (subst > term > term),X60 : (subst > term > term),X59 : term,X57 : subst] : (? [X63 : term,X61 : subst,X62 : subst] : (((sub @ (X60 @ X62 @ X63) @ X61)) != ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | ? [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X58 @ X65 @ X64) @ X66)) != ((X58 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X58 @ X57 @ X59)) = ((X60 @ X57 @ X59))) | (((lam @ (X58 @ sh @ one))) != ((lam @ (X60 @ sh @ one))))) | ? [X56 : term,X55 : term] : ((((lam @ X55)) = ((lam @ X56))) & (X55 != X56)))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f33,definition,(
% 5.86/1.21 ! [X284 : (subst > term > subst > $o)] : (($true = ((sP20 @ X284))) <=> ! [X286 : (subst > term > term)] : (? [X287 : term] : (($true != ((X284 @ id @ (X286 @ id @ X287) @ id))) & ($true = ((X284 @ id @ X287 @ id)))) | ($true = ((X284 @ id @ (lam @ (X286 @ sh @ one)) @ id))) | ? [X288 : subst,X290 : subst,X289 : term] : (((sub @ (X286 @ X290 @ X289) @ X288)) != ((X286 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f34,definition,(
% 5.86/1.21 ! [X272 : (subst > term > subst > $o)] : (($true = ((sP21 @ X272))) <=> ! [X278 : term,X279 : term] : (($true != ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (ap @ (sub @ X279 @ id) @ X278) @ id))) | ($true != ((X272 @ id @ X279 @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f35,definition,(
% 5.86/1.21 ! [X264 : (term > $o)] : (($true = ((sP22 @ X264))) <=> ! [X269 : term,X268 : term] : (($true = ((X264 @ (ap @ X269 @ X268)))) | ($true != ((X264 @ X268))) | ($true != ((X264 @ X269)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f36,definition,(
% 5.86/1.21 ! [X301 : (subst > term > subst > $o)] : (($true = ((sP23 @ X301))) <=> ? [X302 : term,X303 : term] : (($true = ((X301 @ id @ X303 @ id))) & ($true = ((X301 @ id @ X302 @ id))) & ($true != ((X301 @ id @ (ap @ (sub @ X302 @ id) @ X303) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f37,definition,(
% 5.86/1.21 ! [X301 : (subst > term > subst > $o)] : (($true = ((sP24 @ X301))) <=> ? [X308 : (subst > term > term)] : (! [X311 : subst,X312 : subst,X310 : term] : (((sub @ (X308 @ X311 @ X310) @ X312)) = ((X308 @ (comp @ X311 @ X312) @ (sub @ X310 @ X312)))) & ! [X309 : term] : (($true != ((X301 @ id @ X309 @ id))) | ($true = ((X301 @ id @ (X308 @ id @ X309) @ id)))) & ($true != ((X301 @ id @ (lam @ (X308 @ sh @ one)) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f38,definition,(
% 5.86/1.21 ($true = sP25) <=> ? [X285 : term,X284 : (subst > term > subst > $o)] : (! [X299 : term] : (($true != ((X284 @ id @ X299 @ id))) | ($true = ((X284 @ id @ (sub @ X285 @ (push @ X299 @ id)) @ id)))) & ($true = ((sP20 @ X284))) & ($true != ((X284 @ id @ (lam @ X285) @ id))) & ! [X296 : subst,X295 : subst,X298 : term,X297 : subst] : (($true != ((X284 @ (comp @ X297 @ X295) @ (sub @ X298 @ X295) @ X296))) | ($true = ((X284 @ X297 @ X298 @ (comp @ X295 @ X296))))) & ! [X291 : subst,X294 : subst,X292 : term,X293 : subst] : ((((X284 @ (comp @ X293 @ X291) @ (sub @ X292 @ X291) @ X294)) = $true) | (((X284 @ X293 @ X292 @ (comp @ X291 @ X294))) != $true)))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f39,definition,(
% 5.86/1.21 ($true = sP26) <=> ! [X301 : (subst > term > subst > $o),X300 : term] : (? [X313 : term] : (($true = ((var @ (sub @ X313 @ id)))) & ($true != ((X301 @ id @ X313 @ id)))) | ($true = ((sP24 @ X301))) | ? [X314 : subst,X317 : term,X316 : subst,X315 : subst] : (($true = ((X301 @ X316 @ X317 @ (comp @ X314 @ X315)))) & ($true != ((X301 @ (comp @ X316 @ X314) @ (sub @ X317 @ X314) @ X315)))) | ($true = ((X301 @ id @ X300 @ id))) | ($true = ((sP23 @ X301))) | ? [X307 : subst,X305 : term,X304 : subst,X306 : subst] : (($true = ((X301 @ (comp @ X306 @ X307) @ (sub @ X305 @ X307) @ X304))) & ($true != ((X301 @ X306 @ X305 @ (comp @ X307 @ X304))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f40,definition,(
% 5.86/1.21 ($true = sP27) <=> ? [X273 : term,X271 : term,X272 : (subst > term > subst > $o)] : (! [X282 : term,X280 : subst,X281 : subst,X283 : subst] : (($true = ((X272 @ (comp @ X283 @ X281) @ (sub @ X282 @ X281) @ X280))) | ($true != ((X272 @ X283 @ X282 @ (comp @ X281 @ X280))))) & ($true = ((X272 @ id @ X271 @ id))) & ($true != ((X272 @ id @ (ap @ X273 @ X271) @ id))) & ($true = ((X272 @ id @ X273 @ id))) & ! [X277 : subst,X276 : subst,X275 : subst,X274 : term] : (($true != ((X272 @ (comp @ X275 @ X277) @ (sub @ X274 @ X277) @ X276))) | ($true = ((X272 @ X275 @ X274 @ (comp @ X277 @ X276))))) & ($true = ((sP21 @ X272))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f41,definition,(
% 5.86/1.21 ($true = sP28) <=> (($true = sP26) | ? [X264 : (term > $o),X265 : term] : (($true = ((sP22 @ X264))) & ! [X270 : term] : ((((X264 @ X270)) = $true) | ($true != ((var @ X270)))) & ($true != ((X264 @ X265))) & ! [X266 : term] : (? [X267 : term] : (($true = ((X264 @ X267))) & ($true != ((X264 @ (sub @ X266 @ (push @ X267 @ id)))))) | ($true = ((X264 @ (lam @ X266)))))) | ($true = sP27) | ($true = sP25))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f42,definition,(
% 5.86/1.21 ! [X40 : (subst > term > subst > $o)] : ((((sP29 @ X40)) = $true) <=> ? [X46 : term,X45 : term] : (($true = ((X40 @ id @ X45 @ id))) & ($true = ((X40 @ id @ X46 @ id))) & ($true != ((X40 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f43,definition,(
% 5.86/1.21 ($true = sP30) <=> ! [X38 : term,X40 : (subst > term > subst > $o),X39 : term] : (($true != ((X40 @ id @ X39 @ id))) | (((sP29 @ X40)) = $true) | ($true != ((X40 @ id @ X38 @ id))) | ($true = ((X40 @ id @ (ap @ X38 @ X39) @ id))) | ? [X47 : subst,X48 : subst,X49 : term,X50 : subst] : ((((X40 @ X47 @ X49 @ (comp @ X50 @ X48))) != $true) & ($true = ((X40 @ (comp @ X47 @ X50) @ (sub @ X49 @ X50) @ X48)))) | ? [X44 : subst,X43 : term,X42 : subst,X41 : subst] : (($true != ((X40 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X40 @ X42 @ X43 @ (comp @ X44 @ X41))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f44,definition,(
% 5.86/1.21 ! [X225 : (subst > term > subst > $o)] : (($true = ((sP31 @ X225))) <=> ? [X234 : (subst > term > term)] : (! [X235 : subst,X236 : subst,X237 : term] : (((X234 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))) = ((sub @ (X234 @ X236 @ X237) @ X235))) & ! [X238 : term] : (($true != ((X225 @ id @ X238 @ id))) | ($true = ((X225 @ id @ (X234 @ id @ X238) @ id)))) & ($true != ((X225 @ id @ (lam @ (X234 @ sh @ one)) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f45,definition,(
% 5.86/1.21 ! [X225 : (subst > term > subst > $o)] : (($true = ((sP32 @ X225))) <=> ? [X233 : term,X232 : term] : (($true != ((X225 @ id @ (ap @ (sub @ X233 @ id) @ X232) @ id))) & ($true = ((X225 @ id @ X232 @ id))) & ($true = ((X225 @ id @ X233 @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f46,definition,(
% 5.86/1.21 ($true = sP33) <=> ! [X225 : (subst > term > subst > $o),X226 : term] : (? [X242 : subst,X240 : subst,X239 : term,X241 : subst] : (($true = ((X225 @ (comp @ X240 @ X242) @ (sub @ X239 @ X242) @ X241))) & (((X225 @ X240 @ X239 @ (comp @ X242 @ X241))) != $true)) | ? [X227 : subst,X229 : subst,X230 : subst,X228 : term] : (($true = ((X225 @ X227 @ X228 @ (comp @ X229 @ X230)))) & ($true != ((X225 @ (comp @ X227 @ X229) @ (sub @ X228 @ X229) @ X230)))) | ($true = ((sP32 @ X225))) | ($true = ((X225 @ id @ X226 @ id))) | ? [X231 : term] : (($true != ((X225 @ id @ X231 @ id))) & ($true = ((var @ (sub @ X231 @ id))))) | ($true = ((sP31 @ X225))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f47,definition,(
% 5.86/1.21 ! [X188 : (subst > term > subst > $o)] : (($true = ((sP34 @ X188))) <=> ? [X189 : term,X190 : term] : (($true = ((X188 @ id @ X190 @ id))) & ($true = ((X188 @ id @ X189 @ id))) & ($true != ((X188 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f48,definition,(
% 5.86/1.21 ! [X524 : (subst > term > subst > $o)] : ((((sP35 @ X524)) = $true) <=> ? [X527 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id))) & ! [X531 : term] : (($true = ((X524 @ id @ (X527 @ id @ X531) @ id))) | ($true != ((X524 @ id @ X531 @ id)))) & ! [X528 : subst,X530 : subst,X529 : term] : (((sub @ (X527 @ X528 @ X529) @ X530)) = ((X527 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f49,definition,(
% 5.86/1.21 ($true = sP36) <=> ! [X524 : (subst > term > subst > $o),X525 : term] : (? [X532 : subst,X534 : term,X535 : subst,X533 : subst] : (($true = ((X524 @ (comp @ X533 @ X532) @ (sub @ X534 @ X532) @ X535))) & ($true != ((X524 @ X533 @ X534 @ (comp @ X532 @ X535))))) | ? [X537 : term,X538 : subst,X536 : subst,X539 : subst] : (($true != ((X524 @ (comp @ X536 @ X539) @ (sub @ X537 @ X539) @ X538))) & ($true = ((X524 @ X536 @ X537 @ (comp @ X539 @ X538))))) | (((sP35 @ X524)) = $true) | ? [X526 : term] : (($true != ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id))) & ($true = ((X524 @ id @ X526 @ id)))) | ($true = ((X524 @ id @ (lam @ X525) @ id))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f50,definition,(
% 5.86/1.21 ($true = sP37) <=> ? [X320 : (subst > term > subst > $o),X319 : term] : (($true != ((X320 @ id @ (lam @ (sub @ X319 @ (push @ one @ sh))) @ id))) & ! [X326 : term] : ((((X320 @ id @ X326 @ id)) != $true) | (((X320 @ id @ (sub @ X319 @ (push @ X326 @ id)) @ id)) = $true)) & ! [X321 : (subst > term > term)] : (? [X324 : subst,X322 : subst,X323 : term] : (((X321 @ (comp @ X324 @ X322) @ (sub @ X323 @ X322))) != ((sub @ (X321 @ X324 @ X323) @ X322))) | ($true = ((X320 @ id @ (lam @ (X321 @ sh @ one)) @ id))) | ? [X325 : term] : (($true = ((X320 @ id @ X325 @ id))) & ($true != ((X320 @ id @ (X321 @ id @ X325) @ id))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f51,definition,(
% 5.86/1.21 ($true = sP38) <=> (? [X318 : term] : (((sub @ X318 @ id)) != X318) | ! [X327 : term,X328 : (subst > term > subst > $o)] : (? [X329 : (subst > term > term)] : (! [X333 : term,X331 : subst,X332 : subst] : (((sub @ (X329 @ X331 @ X333) @ X332)) = ((X329 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332)))) & ($true != ((X328 @ id @ (lam @ (X329 @ sh @ one)) @ id))) & ! [X330 : term] : (($true = ((X328 @ id @ (X329 @ id @ X330) @ id))) | ($true != ((X328 @ id @ X330 @ id))))) | ? [X334 : term] : (($true != ((X328 @ id @ (sub @ X327 @ (push @ X334 @ id)) @ id))) & ($true = ((X328 @ id @ X334 @ id)))) | ($true = ((X328 @ id @ (lam @ X327) @ id)))) | ($true = sP37))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f52,definition,(
% 5.86/1.21 ($true = sP39) <=> (? [X150 : term] : ! [X151 : (subst > term > term)] : ? [X152 : term,X153 : subst] : (((X151 @ X153 @ X152)) != ((sub @ X150 @ (push @ X152 @ X153)))) | ? [X154 : term] : (((sub @ X154 @ id)) != X154) | ! [X155 : term,X157 : (term > $o),X156 : (subst > term > subst > $o)] : (($true = ((X157 @ (lam @ X155)))) | ? [X158 : (subst > term > term)] : (! [X161 : subst,X162 : term,X160 : subst] : (((X158 @ (comp @ X160 @ X161) @ (sub @ X162 @ X161))) = ((sub @ (X158 @ X160 @ X162) @ X161))) & ! [X159 : term] : (($true != ((X156 @ id @ X159 @ id))) | ($true = ((X156 @ id @ (X158 @ id @ X159) @ id)))) & ($true != ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ? [X163 : term] : ((((X157 @ (sub @ X155 @ (push @ X163 @ id)))) != $true) & ($true = ((X157 @ X163)))) | ? [X164 : term] : (((X156 @ id @ X164 @ id)) != ((X157 @ X164)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f53,definition,(
% 5.86/1.21 ! [X131 : (term > $o)] : (($true = ((sP40 @ X131))) <=> ? [X134 : term,X133 : term] : (($true = ((X131 @ X134))) & ($true = ((X131 @ X133))) & ($true != ((X131 @ (ap @ X134 @ X133))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f54,definition,(
% 5.86/1.21 ($true = sP41) <=> ! [X131 : (term > $o),X132 : term] : (($true = ((X131 @ X132))) | ? [X137 : term] : (($true != ((X131 @ X137))) & ($true = ((var @ X137)))) | ($true = ((sP40 @ X131))) | ? [X135 : term] : (! [X136 : term] : (($true != ((X131 @ X136))) | ($true = ((X131 @ (sub @ X135 @ (push @ X136 @ id)))))) & ($true != ((X131 @ (lam @ X135))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f55,definition,(
% 5.86/1.21 ($true = sP42) <=> ! [X463 : term,X462 : (subst > term > subst > $o)] : (? [X464 : term] : (($true = ((X462 @ id @ X464 @ id))) & ($true != ((X462 @ id @ (sub @ X463 @ (push @ X464 @ id)) @ id)))) | ($true = ((X462 @ id @ (lam @ (sub @ X463 @ (push @ one @ sh))) @ id))) | ? [X466 : term,X465 : (subst > term > term)] : (! [X471 : subst,X473 : subst,X472 : term] : (((X465 @ (comp @ X471 @ X473) @ (sub @ X472 @ X473))) = ((sub @ X466 @ (push @ (sub @ X472 @ X473) @ (comp @ X471 @ X473))))) & ! [X470 : term] : (($true != ((X462 @ id @ X470 @ id))) | ($true = ((X462 @ id @ (X465 @ id @ X470) @ id)))) & ($true != ((X462 @ id @ (lam @ (X465 @ sh @ one)) @ id))) & ! [X468 : subst,X467 : term,X469 : subst] : (((sub @ (X465 @ X468 @ X467) @ X469)) = ((sub @ (sub @ X466 @ (push @ X467 @ X468)) @ X469)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f56,definition,(
% 5.86/1.21 ! [X359 : (subst > term > subst > $o)] : (($true = ((sP43 @ X359))) <=> ? [X360 : (subst > term > term)] : (! [X364 : term] : (($true = ((X359 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X359 @ id @ X364 @ id)))) & ($true != ((X359 @ id @ (lam @ (X360 @ sh @ one)) @ id))) & ! [X362 : subst,X361 : term,X363 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f57,definition,(
% 5.86/1.21 ! [X340 : (term > $o)] : (($true = ((sP44 @ X340))) <=> ! [X342 : term,X343 : term] : ((((X340 @ X342)) != $true) | (((X340 @ (ap @ X342 @ X343))) = $true) | ($true != ((X340 @ X343)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f58,definition,(
% 5.86/1.21 ($true = sP45) <=> ? [X350 : (subst > term > subst > $o),X349 : (term > $o),X348 : term] : (($true != ((X349 @ (lam @ X348)))) & ! [X351 : (subst > term > term)] : (($true = ((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id))) | ? [X353 : term,X352 : subst,X354 : subst] : (((X351 @ (comp @ X354 @ X352) @ (sub @ X353 @ X352))) != ((sub @ (X351 @ X354 @ X353) @ X352))) | ? [X355 : term] : (($true != ((X350 @ id @ (X351 @ id @ X355) @ id))) & (((X350 @ id @ X355 @ id)) = $true))) & ! [X356 : term] : (($true = ((X349 @ (sub @ X348 @ (push @ X356 @ id))))) | ($true != ((X349 @ X356)))) & ! [X357 : term] : (((X349 @ X357)) = ((X350 @ id @ X357 @ id))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f59,definition,(
% 5.86/1.21 (sP46 = $true) <=> ? [X340 : (term > $o),X341 : term] : (($true != ((X340 @ X341))) & ! [X345 : term] : (? [X346 : term] : ((((X340 @ X346)) = $true) & ($true != ((X340 @ (sub @ X345 @ (push @ X346 @ id)))))) | (((X340 @ (lam @ X345))) = $true)) & ($true = ((sP44 @ X340))) & ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f60,definition,(
% 5.86/1.21 ($true = sP47) <=> ((sP46 = $true) | ($true = sP45) | ? [X347 : term] : (((sub @ X347 @ id)) != X347) | ! [X358 : term,X359 : (subst > term > subst > $o)] : (? [X366 : term,X365 : term] : (($true = ((X359 @ id @ X365 @ id))) & ($true != ((X359 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id))) & ($true = ((X359 @ id @ X366 @ id)))) | ($true = ((X359 @ id @ X358 @ id))) | ($true = ((sP43 @ X359)))) | ? [X337 : (subst > term > subst > $o)] : ! [X338 : (term > $o)] : ? [X339 : term] : (((X337 @ id @ X339 @ id)) != ((X338 @ X339))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f61,definition,(
% 5.86/1.21 ! [X426 : (term > $o)] : (($true = ((sP48 @ X426))) <=> ! [X428 : term,X429 : term] : (($true = ((X426 @ (ap @ X429 @ X428)))) | ($true != ((X426 @ X428))) | ($true != ((X426 @ X429)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f62,definition,(
% 5.86/1.21 ! [X445 : (subst > term > subst > $o)] : (($true = ((sP49 @ X445))) <=> ? [X446 : (subst > term > term)] : (! [X450 : term] : (($true = ((X445 @ id @ (X446 @ id @ X450) @ id))) | ($true != ((X445 @ id @ X450 @ id)))) & ! [X448 : term,X449 : subst,X447 : subst] : (((sub @ (X446 @ X447 @ X448) @ X449)) = ((X446 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449)))) & ($true != ((X445 @ id @ (lam @ (X446 @ sh @ one)) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f63,definition,(
% 5.86/1.21 ! [X445 : (subst > term > subst > $o)] : (($true = ((sP50 @ X445))) <=> ? [X456 : term,X457 : term] : (($true = ((X445 @ id @ X456 @ id))) & ($true = ((X445 @ id @ X457 @ id))) & ($true != ((X445 @ id @ (ap @ (sub @ X457 @ id) @ X456) @ id)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f64,definition,(
% 5.86/1.21 ($true = sP51) <=> ? [X435 : (subst > term > subst > $o),X436 : term,X434 : (term > $o)] : (! [X437 : term] : ((((X434 @ X437)) != $true) | ($true = ((X434 @ (sub @ X436 @ (push @ X437 @ id)))))) & ! [X438 : (subst > term > term)] : (($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id))) | ? [X442 : term] : (($true = ((X435 @ id @ X442 @ id))) & ($true != ((X435 @ id @ (X438 @ id @ X442) @ id)))) | ? [X439 : subst,X441 : subst,X440 : term] : (((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441))) != ((sub @ (X438 @ X439 @ X440) @ X441)))) & ! [X443 : term] : (((X434 @ X443)) = ((X435 @ id @ X443 @ id))) & ($true != ((X434 @ (lam @ X436)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f65,definition,(
% 5.86/1.21 ($true = sP52) <=> ! [X444 : term,X445 : (subst > term > subst > $o)] : (($true = ((sP50 @ X445))) | ($true = ((X445 @ id @ X444 @ id))) | ? [X455 : term] : (($true != ((X445 @ id @ X455 @ id))) & ($true = ((var @ (sub @ X455 @ id))))) | ? [X453 : subst,X452 : subst,X454 : subst,X451 : term] : ((((X445 @ X453 @ X451 @ (comp @ X454 @ X452))) = $true) & ($true != ((X445 @ (comp @ X453 @ X454) @ (sub @ X451 @ X454) @ X452)))) | ($true = ((sP49 @ X445))) | ? [X461 : subst,X460 : subst,X458 : term,X459 : subst] : (($true != ((X445 @ X461 @ X458 @ (comp @ X459 @ X460)))) & ($true = ((X445 @ (comp @ X461 @ X459) @ (sub @ X458 @ X459) @ X460)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f66,definition,(
% 5.86/1.21 ($true = sP53) <=> (($true = sP52) | ? [X423 : (subst > term > subst > $o)] : ! [X424 : (term > $o)] : ? [X425 : term] : (((X423 @ id @ X425 @ id)) != ((X424 @ X425))) | ? [X427 : term,X426 : (term > $o)] : (! [X431 : term] : (($true = ((X426 @ (lam @ X431)))) | ? [X432 : term] : (($true != ((X426 @ (sub @ X431 @ (push @ X432 @ id))))) & ($true = ((X426 @ X432))))) & ! [X430 : term] : ((((var @ X430)) != $true) | ($true = ((X426 @ X430)))) & ($true != ((X426 @ X427))) & ($true = ((sP48 @ X426)))) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | ($true = sP51))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f67,definition,(
% 5.86/1.21 ($true = sP54) <=> ! [X31 : (subst > term > subst > $o),X30 : term] : (? [X33 : (subst > term > term)] : (($true != ((X31 @ id @ (lam @ (X33 @ sh @ one)) @ id))) & ! [X36 : subst,X37 : term,X35 : subst] : (((X33 @ (comp @ X35 @ X36) @ (sub @ X37 @ X36))) = ((sub @ (X33 @ X35 @ X37) @ X36))) & ! [X34 : term] : (($true != ((X31 @ id @ X34 @ id))) | ($true = ((X31 @ id @ (X33 @ id @ X34) @ id))))) | ? [X32 : term] : (($true = ((X31 @ id @ X32 @ id))) & ($true != ((X31 @ id @ (sub @ X30 @ (push @ X32 @ id)) @ id)))) | ($true = ((X31 @ id @ (lam @ (sub @ X30 @ (push @ one @ sh))) @ id))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f68,definition,(
% 5.86/1.21 ! [X387 : (term > $o)] : (($true = ((sP55 @ X387))) <=> ! [X392 : term,X391 : term] : ((((X387 @ X392)) != $true) | ($true = ((X387 @ (ap @ X392 @ X391)))) | ($true != ((X387 @ X391)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f69,definition,(
% 5.86/1.21 ! [X394 : (term > $o)] : (($true = ((sP56 @ X394))) <=> ? [X396 : term,X397 : term] : (($true = ((X394 @ X396))) & (((X394 @ (ap @ X396 @ X397))) != $true) & ($true = ((X394 @ X397)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f70,definition,(
% 5.86/1.21 ($true = sP57) <=> ! [X395 : subst,X393 : term,X394 : (term > $o)] : (? [X399 : term] : (! [X400 : term] : (($true != ((X394 @ X400))) | ($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id)))))) & ($true != ((X394 @ (lam @ X399))))) | ($true = ((sP56 @ X394))) | ($true = ((X394 @ (sub @ X393 @ X395)))) | ? [X398 : term] : ((((X394 @ (sub @ X398 @ X395))) != $true) & ($true = ((var @ X398)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f71,definition,(
% 5.86/1.21 ($true = sP58) <=> (? [X383 : term,X382 : subst] : (((sub @ one @ (push @ X383 @ X382))) != X383) | ($true = sP57) | ? [X387 : (term > $o),X388 : term] : (! [X389 : term] : (($true = ((X387 @ X389))) | (((var @ X389)) != $true)) & ($true = ((sP55 @ X387))) & ($true != ((X387 @ X388))) & ! [X390 : term] : (($true != ((X387 @ X390))) | ($true = ((X387 @ (lam @ X390)))))) | ? [X385 : term,X384 : subst] : (((comp @ sh @ (push @ X385 @ X384))) != X384) | ? [X386 : subst] : (((comp @ X386 @ id)) != X386))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.86/1.21 thf(f72,plain,(
% 5.86/1.21 (ulamvarind = $true) & ((induction2lem_lthm = $true) <=> ($true = sP58)) & (apnotvar = $true) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & ((axvarid = $true) <=> ! [X381 : term] : (((sub @ X381 @ id)) = X381)) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) <=> (apinj1 = $true)) & (($true = sP54) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (? [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) != ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | ? [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) != ((sub @ (X123 @ X128 @ X129) @ X130))))) & ((hoasinduction_lem0 = $true) <=> ! [X517 : (subst > term > subst > $o)] : ? [X518 : (term > $o)] : ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id)))) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (($true = sP53) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP47)) & (! [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ? [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) != ((sub @ (X98 @ X103 @ X102) @ X101)))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (($true = sP42) <=> (hoasinduction_lem3aaa = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) != ((d2term @ X401))) | (X401 = X402)) & ((induction2 = $true) <=> ($true = sP41)) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ($true = sP39)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))) | ? [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 != X199) & (((ap @ X198 @ X196)) = ((ap @ X197 @ X199)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP38) <=> (hoasinduction_lem3a_lthm = $true)) & (($true = sP36) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) <=> ! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X188 : (subst > term > subst > $o),X187 : term] : (? [X191 : (subst > term > term)] : (! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) & ($true != ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))) | ($true = ((sP34 @ X188)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X485 : term] : ? [X486 : (subst > term > term)] : (((X486 @ sh @ one)) = ((sub @ X485 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X5 : d_subst] : (d_id = X5) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1_lthm = $true) <=> (! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))) | ? [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) != X373) | ? [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) != X375))) & (ulamvar1 != $true) & (($true = sP33) <=> (hoasinduction = $true)) & ((hoasinduction_lem2 = $true) <=> ($true = sP30)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) <=> (laminj = $true)) & ((axidr = $true) <=> ! [X71 : subst] : (((comp @ X71 @ id)) = X71)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) <=> (axscons = $true)) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) <=> (hoasapinj2 = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (($true = sP28) <=> (hoasinduction_lthm = $true)) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & ((hoaslaminj_lthm = $true) <=> ($true = sP19)) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) <=> (axshiftcons = $true)) & ((hoasapinj1 = $true) <=> ! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9))) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP18)) & ((sP16 = $true) <=> (induction2_lthm = $true)) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) <=> (substmonoid = $true)) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((induction = $true) <=> ! [X165 : (term > $o),X166 : term] : (? [X168 : term] : (($true != ((X165 @ (lam @ X168)))) & ($true = ((X165 @ X168)))) | ($true = ((X165 @ X166))) | ? [X167 : term] : (($true = ((var @ X167))) & ($true != ((X165 @ X167)))) | ($true = ((sP12 @ X165))))) & ((? [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) != X210) | ! [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true != ((X214 @ X211))) | (((X212 @ one)) = $true) | ? [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) != ((X212 @ X215))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotap_lthm = $true) & (! [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) = $true) | ? [X208 : term] : (((X207 @ X208)) != ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | ($true != ((X206 @ X205)))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> ($true = sP11)) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((axvarcons = $true) <=> ! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408)) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X368 : (term > $o),X369 : term,X367 : subst] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) <=> (pushprop_lem0_lthm = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X474 : (subst > term > subst > $o)] : ? [X475 : (term > $o)] : ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id)))) & (! [X243 : term] : ? [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) = ((X244 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X420 : term] : (((sub @ X420 @ id)) = X420) | ? [X419 : term] : (((sub @ X419 @ id)) != X419)) <=> (termmset_lthm = $true)) & ((shinj = $true) <=> ! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186))) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((substmonoid_lthm = $true) <=> ((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)) | ? [X403 : subst] : (((comp @ id @ X403)) != X403) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404))) & ((induction2lem = $true) <=> ($true = sP9)) & (! [X67 : term] : ? [X68 : (subst > term > term)] : ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X245 : d_term] : (d_one = X245) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X507 : d_subst,X506 : d_subst] : ((((d2subst @ X507)) != ((d2subst @ X506))) | (X506 = X507)) & (axvarshift = $true) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (($true = sP7) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj1_lthm = $true) <=> (? [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 != X219) & (((ap @ X218 @ X220)) = ((ap @ X219 @ X217)))) | ? [X216 : term] : (((sub @ X216 @ id)) != X216) | ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224)))) & (hoaslamnotap_gthm = $true) & (! [X1 : (term > $o),X0 : subst,X2 : term] : ? [X3 : (term > $o)] : ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP6)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X520 : term] : ? [X521 : (subst > term > term)] : ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522))))) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) <=> (apinj2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3aa = $true) <=> (sP4 = $true)) & ((termmset = $true) <=> ! [X26 : term] : (((sub @ X26 @ id)) = X26)) & (induction2_gthm = $true) & (($true = sP3) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (ulamvarsh = $true) & (($true = sP0) <=> (hoasinduction_lem3a = $true))),
% 5.86/1.21 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 5.86/1.21 thf(f235,plain,(
% 5.86/1.21 (($true = sP7) | ? [X172 : (term > $o),X171 : term,X173 : (subst > term > subst > $o)] : (($true != ((X172 @ (lam @ X171)))) & ! [X175 : (subst > term > term)] : (? [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) != ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177)))) | ($true = ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) | ? [X176 : term] : (($true != ((X173 @ id @ (X175 @ id @ X176) @ id))) & ($true = ((X173 @ id @ X176 @ id))))) & ! [X174 : term] : (((X173 @ id @ X174 @ id)) = ((X172 @ X174))) & ! [X180 : term] : (($true != ((X172 @ X180))) | ($true = ((X172 @ (sub @ X171 @ (push @ X180 @ id)))))))) & (! [X172 : (term > $o),X171 : term,X173 : (subst > term > subst > $o)] : (($true = ((X172 @ (lam @ X171)))) | ? [X175 : (subst > term > term)] : (! [X177 : subst,X179 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X179) @ X177)) = ((X175 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177)))) & ($true != ((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id))) & ! [X176 : term] : (($true = ((X173 @ id @ (X175 @ id @ X176) @ id))) | ($true != ((X173 @ id @ X176 @ id))))) | ? [X174 : term] : (((X173 @ id @ X174 @ id)) != ((X172 @ X174))) | ? [X180 : term] : (($true = ((X172 @ X180))) & ($true != ((X172 @ (sub @ X171 @ (push @ X180 @ id))))))) | ($true != sP7))),
% 5.86/1.21 inference(nnf_transformation,[],[f20])).
% 5.86/1.21 thf(f236,plain,(
% 5.86/1.21 (($true = sP7) | ? [X0 : (term > $o),X1 : term,X2 : (subst > term > subst > $o)] : (($true != ((X0 @ (lam @ X1)))) & ! [X3 : (subst > term > term)] : (? [X4 : subst,X5 : term,X6 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) != ((sub @ (X3 @ X6 @ X5) @ X4))) | ($true = ((X2 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ? [X7 : term] : ((((X2 @ id @ (X3 @ id @ X7) @ id)) != $true) & ($true = ((X2 @ id @ X7 @ id))))) & ! [X8 : term] : (((X0 @ X8)) = ((X2 @ id @ X8 @ id))) & ! [X9 : term] : (($true != ((X0 @ X9))) | ($true = ((X0 @ (sub @ X1 @ (push @ X9 @ id)))))))) & (! [X10 : (term > $o),X11 : term,X12 : (subst > term > subst > $o)] : (($true = ((X10 @ (lam @ X11)))) | ? [X13 : (subst > term > term)] : (! [X14 : subst,X15 : term,X16 : subst] : (((X13 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) = ((sub @ (X13 @ X16 @ X15) @ X14))) & ($true != ((X12 @ id @ (lam @ (X13 @ sh @ one)) @ id))) & ! [X17 : term] : ((((X12 @ id @ (X13 @ id @ X17) @ id)) = $true) | ($true != ((X12 @ id @ X17 @ id))))) | ? [X18 : term] : (((X12 @ id @ X18 @ id)) != ((X10 @ X18))) | ? [X19 : term] : (($true = ((X10 @ X19))) & ($true != ((X10 @ (sub @ X11 @ (push @ X19 @ id))))))) | ($true != sP7))),
% 5.86/1.21 inference(rectify,[],[f235])).
% 5.86/1.21 thf(f237,plain,(
% 5.86/1.21 (($true = sP7) | (($true != ((sK385 @ (lam @ sK386)))) & ! [X3 : (subst > term > term)] : ((((X3 @ (comp @ (sK390 @ X3) @ (sK388 @ X3)) @ (sub @ (sK389 @ X3) @ (sK388 @ X3)))) != ((sub @ (X3 @ (sK390 @ X3) @ (sK389 @ X3)) @ (sK388 @ X3)))) | ($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | (($true != ((sK387 @ id @ (X3 @ id @ (sK391 @ X3)) @ id))) & ($true = ((sK387 @ id @ (sK391 @ X3) @ id))))) & ! [X8 : term] : (((sK387 @ id @ X8 @ id)) = ((sK385 @ X8))) & ! [X9 : term] : (($true != ((sK385 @ X9))) | ($true = ((sK385 @ (sub @ sK386 @ (push @ X9 @ id)))))))) & (! [X10 : (term > $o),X11 : term,X12 : (subst > term > subst > $o)] : (($true = ((X10 @ (lam @ X11)))) | (! [X14 : subst,X15 : term,X16 : subst] : (((sub @ (sK392 @ X12 @ X16 @ X15) @ X14)) = ((sK392 @ X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14)))) & ($true != ((X12 @ id @ (lam @ (sK392 @ X12 @ sh @ one)) @ id))) & ! [X17 : term] : (($true = ((X12 @ id @ (sK392 @ X12 @ id @ X17) @ id))) | ($true != ((X12 @ id @ X17 @ id))))) | (((X12 @ id @ (sK393 @ X12 @ X10) @ id)) != ((X10 @ (sK393 @ X12 @ X10)))) | (($true = ((X10 @ (sK394 @ X11 @ X10)))) & ($true != ((X10 @ (sub @ X11 @ (push @ (sK394 @ X11 @ X10) @ id))))))) | ($true != sP7))),
% 5.86/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK385,sK386,sK387,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK385),skolemize(X1,sK386),skolemize(X2,sK387),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2)],[f236])).
% 5.86/1.21 thf(f260,plain,(
% 5.86/1.21 (ulamvarind = $true) & (((induction2lem_lthm = $true) | ($true != sP58)) & (($true = sP58) | (induction2lem_lthm != $true))) & (apnotvar = $true) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & (((axvarid = $true) | ? [X381 : term] : (((sub @ X381 @ id)) != X381)) & (! [X381 : term] : (((sub @ X381 @ id)) = X381) | (axvarid != $true))) & ((! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 != X147) & (((ap @ X147 @ X148)) = ((ap @ X146 @ X149)))))) & ((($true = sP54) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP54))) & (((hoaslaminj = $true) | ? [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (! [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) = ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) & (((lam @ (X123 @ sh @ one))) = ((lam @ (X121 @ sh @ one)))) & (((X121 @ X122 @ X124)) != ((X123 @ X122 @ X124))) & ! [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) = ((sub @ (X123 @ X128 @ X129) @ X130))))) & (! [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (? [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) != ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | ? [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) != ((sub @ (X123 @ X128 @ X129) @ X130)))) | (hoaslaminj != $true))) & (((hoasinduction_lem0 = $true) | ? [X517 : (subst > term > subst > $o)] : ! [X518 : (term > $o)] : ? [X519 : term] : (((X518 @ X519)) != ((X517 @ id @ X519 @ id)))) & (! [X517 : (subst > term > subst > $o)] : ? [X518 : (term > $o)] : ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id))) | (hoasinduction_lem0 != $true))) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & ((($true = sP53) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP53))) & (pushprop_lem2v2 = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_no_psi_cond_lthm != $true))) & ((! [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ? [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) != ((sub @ (X98 @ X103 @ X102) @ X101)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) = ((ap @ (sub @ X100 @ id) @ X99))) & ! [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) = ((sub @ (X98 @ X103 @ X102) @ X101)))))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & ((($true = sP42) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP42))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) != ((d2term @ X401))) | (X401 = X402)) & (((induction2 = $true) | ($true != sP41)) & (($true = sP41) | (induction2 != $true))) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & (((hoasinduction_lem3v2a_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3v2a_lthm != $true))) & (hoasinduction_lem1_gthm = $true) & (((hoasapinj2_lthm = $true) | (? [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 != X202) & (((ap @ (sub @ X200 @ id) @ X202)) = ((ap @ (sub @ X203 @ id) @ X201)))) & ! [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 = X199) | (((ap @ X198 @ X196)) != ((ap @ X197 @ X199)))))) & ((! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))) | ? [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 != X199) & (((ap @ X198 @ X196)) = ((ap @ X197 @ X199))))) | (hoasapinj2_lthm != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((($true = sP38) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP38))) & ((($true = sP36) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP36))) & (pushprop_lem3v2 = $true) & (((pushprop_lem1 = $true) | ? [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true = ((X512 @ X513))) & ($true != ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516)))))) | (pushprop_lem1 != $true))) & ((! [X188 : (subst > term > subst > $o),X187 : term] : (? [X191 : (subst > term > term)] : (! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) & ($true != ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))) | ($true = ((sP34 @ X188)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X188 : (subst > term > subst > $o),X187 : term] : (! [X191 : (subst > term > term)] : (? [X192 : term] : (($true != ((X188 @ id @ (X191 @ id @ X192) @ id))) & (((X188 @ id @ X192 @ id)) = $true)) | ($true = ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) | ? [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) != ((sub @ (X191 @ X194 @ X193) @ X195)))) & ($true != ((X188 @ id @ X187 @ id))) & ($true != ((sP34 @ X188)))))) & (((hoasinduction_lem3b = $true) | ? [X485 : term] : ! [X486 : (subst > term > term)] : (((X486 @ sh @ one)) != ((sub @ X485 @ (push @ one @ sh))))) & (! [X485 : term] : ? [X486 : (subst > term > term)] : (((X486 @ sh @ one)) = ((sub @ X485 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X5 : d_subst] : (d_id = X5) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((pushprop_lem1_lthm = $true) | (? [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true != ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) & ($true = ((X377 @ X379)))) & ! [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) = X373) & ! [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) = X375))) & ((! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))) | ? [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) != X373) | ? [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) != X375)) | (pushprop_lem1_lthm != $true))) & (ulamvar1 != $true) & ((($true = sP33) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP33))) & (((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & ((! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) | (laminj != $true)) & ((laminj = $true) | ? [X421 : term,X422 : term] : ((((lam @ X422)) = ((lam @ X421))) & (X421 != X422)))) & (((axidr = $true) | ? [X71 : subst] : (((comp @ X71 @ id)) != X71)) & (! [X71 : subst] : (((comp @ X71 @ id)) = X71) | (axidr != $true))) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) | (axscons != $true)) & ((axscons = $true) | ? [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) != X27))) & ((! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) = ((ap @ (sub @ X184 @ id) @ X183))) & (X182 != X183)))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & ((($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28))) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & (((hoaslaminj_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoaslaminj_lthm != $true))) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & ((! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) != X28))) & (((hoasapinj1 = $true) | ? [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) = ((ap @ (sub @ X8 @ id) @ X6))) & (X8 != X9))) & (! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9)) | (hoasapinj1 != $true))) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP18)) & (($true = sP18) | (hoasinduction_lem2v2 != $true))) & (((sP16 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP16 != $true))) & (((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X335 : subst] : (((comp @ id @ X335)) != X335) | ? [X336 : subst] : (((comp @ X336 @ id)) != X336)))) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((induction = $true) | ? [X165 : (term > $o),X166 : term] : (! [X168 : term] : (($true = ((X165 @ (lam @ X168)))) | ($true != ((X165 @ X168)))) & ($true != ((X165 @ X166))) & ! [X167 : term] : (($true != ((var @ X167))) | ($true = ((X165 @ X167)))) & ($true != ((sP12 @ X165))))) & (! [X165 : (term > $o),X166 : term] : (? [X168 : term] : (($true != ((X165 @ (lam @ X168)))) & ($true = ((X165 @ X168)))) | ($true = ((X165 @ X166))) | ? [X167 : term] : (($true = ((var @ X167))) & ($true != ((X165 @ X167)))) | ($true = ((sP12 @ X165)))) | (induction != $true))) & (((? [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) != X210) | ! [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true != ((X214 @ X211))) | (((X212 @ one)) = $true) | ? [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) != ((X212 @ X215))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) = X210) & ? [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true = ((X214 @ X211))) & (((X212 @ one)) != $true) & ! [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) = ((X212 @ X215))))))) & (hoaslamnotap_lthm = $true) & ((! [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) = $true) | ? [X208 : term] : (((X207 @ X208)) != ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | ($true != ((X206 @ X205)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) != $true) & ! [X208 : term] : (((X207 @ X208)) = ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) & ($true = ((X206 @ X205)))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & (((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true))) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & (((axvarcons = $true) | ? [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) != X408)) & (! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408) | (axvarcons != $true))) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X368 : (term > $o),X369 : term,X367 : subst] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X368 : (term > $o),X369 : term,X367 : subst] : ! [X370 : (term > $o)] : ? [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) != ((X370 @ X371))))) & (((hoasinduction_lem0_lthm = $true) | ? [X474 : (subst > term > subst > $o)] : ! [X475 : (term > $o)] : ? [X476 : term] : (((X475 @ X476)) != ((X474 @ id @ X476 @ id)))) & (! [X474 : (subst > term > subst > $o)] : ? [X475 : (term > $o)] : ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id))) | (hoasinduction_lem0_lthm != $true))) & ((! [X243 : term] : ? [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) = ((X244 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X243 : term] : ! [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) != ((X244 @ sh @ one))))) & (((! [X420 : term] : (((sub @ X420 @ id)) = X420) | ? [X419 : term] : (((sub @ X419 @ id)) != X419)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X420 : term] : (((sub @ X420 @ id)) != X420) & ! [X419 : term] : (((sub @ X419 @ id)) = X419)))) & (((shinj = $true) | ? [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) = ((sub @ X185 @ sh))) & (X185 != X186))) & (! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186)) | (shinj != $true))) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (((substmonoid_lthm = $true) | ((? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X406 : subst] : (((comp @ id @ X406)) != X406)) & ! [X403 : subst] : (((comp @ id @ X403)) = X403) & ! [X404 : subst] : (((comp @ X404 @ id)) = X404))) & (((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)) | ? [X403 : subst] : (((comp @ id @ X403)) != X403) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404)) | (substmonoid_lthm != $true))) & (((induction2lem = $true) | ($true != sP9)) & (($true = sP9) | (induction2lem != $true))) & ((! [X67 : term] : ? [X68 : (subst > term > term)] : ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X67 : term] : ! [X68 : (subst > term > term)] : ? [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) != ((X68 @ X69 @ X70))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X245 : d_term] : (d_one = X245) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X507 : d_subst,X506 : d_subst] : ((((d2subst @ X507)) != ((d2subst @ X506))) | (X506 = X507)) & (axvarshift = $true) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((($true = sP7) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP7))) & (((hoasapinj1_lthm = $true) | (! [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 = X219) | (((ap @ X218 @ X220)) != ((ap @ X219 @ X217)))) & ! [X216 : term] : (((sub @ X216 @ id)) = X216) & ? [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) = ((ap @ (sub @ X223 @ id) @ X221))) & (X223 != X224)))) & ((? [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 != X219) & (((ap @ X218 @ X220)) = ((ap @ X219 @ X217)))) | ? [X216 : term] : (((sub @ X216 @ id)) != X216) | ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224))) | (hoasapinj1_lthm != $true))) & (hoaslamnotap_gthm = $true) & ((! [X1 : (term > $o),X0 : subst,X2 : term] : ? [X3 : (term > $o)] : ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X1 : (term > $o),X0 : subst,X2 : term] : ! [X3 : (term > $o)] : ? [X4 : term] : (((X3 @ X4)) != ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))))) & (hoasinduction_lem2v2_gthm = $true) & (((hoasinduction_lem3v2 = $true) | ($true != sP6)) & (($true = sP6) | (hoasinduction_lem3v2 != $true))) & (((hoasinduction_lem3v2_f = $true) | ? [X520 : term] : ! [X521 : (subst > term > term)] : ? [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) != ((sub @ X520 @ (push @ X523 @ X522))))) & (! [X520 : term] : ? [X521 : (subst > term > term)] : ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522)))) | (hoasinduction_lem3v2_f != $true))) & ((! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) = ((ap @ X511 @ X509))) & (X508 != X509)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((hoasinduction_lem3aa = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3aa != $true))) & (((termmset = $true) | ? [X26 : term] : (((sub @ X26 @ id)) != X26)) & (! [X26 : term] : (((sub @ X26 @ id)) = X26) | (termmset != $true))) & (induction2_gthm = $true) & ((($true = sP3) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP3))) & (hoasinduction_lem3b_gthm = $true) & (((axidl = $true) | ? [X72 : subst] : (((comp @ id @ X72)) != X72)) & (! [X72 : subst] : (((comp @ id @ X72)) = X72) | (axidl != $true))) & (ulamvarsh = $true) & ((($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0)))),
% 5.86/1.21 inference(nnf_transformation,[],[f72])).
% 5.86/1.21 thf(f261,plain,(
% 5.86/1.21 (ulamvarind = $true) & ((induction2lem_lthm = $true) | ($true != sP58)) & (($true = sP58) | (induction2lem_lthm != $true)) & (apnotvar = $true) & ! [X417 : term] : ? [X418 : d_term] : (((d2term @ X418)) = X417) & ((axvarid = $true) | ? [X381 : term] : (((sub @ X381 @ id)) != X381)) & (! [X381 : term] : (((sub @ X381 @ id)) = X381) | (axvarid != $true)) & (! [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 = X147) | (((ap @ X147 @ X148)) != ((ap @ X146 @ X149)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X148 : term,X147 : term,X149 : term,X146 : term] : ((X146 != X147) & (((ap @ X147 @ X148)) = ((ap @ X146 @ X149))))) & (($true = sP54) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP54)) & ((hoaslaminj = $true) | ? [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (! [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) = ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) & (((lam @ (X123 @ sh @ one))) = ((lam @ (X121 @ sh @ one)))) & (((X121 @ X122 @ X124)) != ((X123 @ X122 @ X124))) & ! [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) = ((sub @ (X123 @ X128 @ X129) @ X130))))) & (! [X123 : (subst > term > term),X124 : term,X122 : subst,X121 : (subst > term > term)] : (? [X127 : subst,X125 : subst,X126 : term] : (((sub @ (X121 @ X125 @ X126) @ X127)) != ((X121 @ (comp @ X125 @ X127) @ (sub @ X126 @ X127)))) | (((lam @ (X123 @ sh @ one))) != ((lam @ (X121 @ sh @ one)))) | (((X121 @ X122 @ X124)) = ((X123 @ X122 @ X124))) | ? [X130 : subst,X128 : subst,X129 : term] : (((X123 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130))) != ((sub @ (X123 @ X128 @ X129) @ X130)))) | (hoaslaminj != $true)) & ((hoasinduction_lem0 = $true) | ? [X517 : (subst > term > subst > $o)] : ! [X518 : (term > $o)] : ? [X519 : term] : (((X518 @ X519)) != ((X517 @ id @ X519 @ id)))) & (! [X517 : (subst > term > subst > $o)] : ? [X518 : (term > $o)] : ! [X519 : term] : (((X518 @ X519)) = ((X517 @ id @ X519 @ id))) | (hoasinduction_lem0 != $true)) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (($true = sP53) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP53)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) != ((ap @ (sub @ X100 @ id) @ X99))) | ? [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) != ((sub @ (X98 @ X103 @ X102) @ X101)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X99 : term,X98 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) = ((ap @ (sub @ X100 @ id) @ X99))) & ! [X101 : subst,X103 : subst,X102 : term] : (((X98 @ (comp @ X103 @ X101) @ (sub @ X102 @ X101))) = ((sub @ (X98 @ X103 @ X102) @ X101))))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (($true = sP42) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X401 : d_term,X402 : d_term] : ((((d2term @ X402)) != ((d2term @ X401))) | (X401 = X402)) & ((induction2 = $true) | ($true != sP41)) & (($true = sP41) | (induction2 != $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2_lthm = $true) | (? [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 != X202) & (((ap @ (sub @ X200 @ id) @ X202)) = ((ap @ (sub @ X203 @ id) @ X201)))) & ! [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 = X199) | (((ap @ X198 @ X196)) != ((ap @ X197 @ X199)))))) & (! [X203 : term,X201 : term,X202 : term,X200 : term] : ((X201 = X202) | (((ap @ (sub @ X200 @ id) @ X202)) != ((ap @ (sub @ X203 @ id) @ X201)))) | ? [X197 : term,X198 : term,X196 : term,X199 : term] : ((X196 != X199) & (((ap @ X198 @ X196)) = ((ap @ X197 @ X199)))) | (hoasapinj2_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP38) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP38)) & (($true = sP36) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP36)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) | ? [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true = ((X512 @ X513))) & ($true != ((X514 @ (sub @ X513 @ (push @ X515 @ X516))))))) & (! [X513 : term,X514 : (term > $o),X512 : (term > $o),X516 : subst,X515 : term] : (($true != ((X512 @ X513))) | ($true = ((X514 @ (sub @ X513 @ (push @ X515 @ X516)))))) | (pushprop_lem1 != $true)) & (! [X188 : (subst > term > subst > $o),X187 : term] : (? [X191 : (subst > term > term)] : (! [X192 : term] : (($true = ((X188 @ id @ (X191 @ id @ X192) @ id))) | (((X188 @ id @ X192 @ id)) != $true)) & ($true != ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X191 @ X194 @ X193) @ X195)))) | ($true = ((X188 @ id @ X187 @ id))) | ($true = ((sP34 @ X188)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X188 : (subst > term > subst > $o),X187 : term] : (! [X191 : (subst > term > term)] : (? [X192 : term] : (($true != ((X188 @ id @ (X191 @ id @ X192) @ id))) & (((X188 @ id @ X192 @ id)) = $true)) | ($true = ((X188 @ id @ (lam @ (X191 @ sh @ one)) @ id))) | ? [X194 : subst,X195 : subst,X193 : term] : (((X191 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) != ((sub @ (X191 @ X194 @ X193) @ X195)))) & ($true != ((X188 @ id @ X187 @ id))) & ($true != ((sP34 @ X188))))) & ((hoasinduction_lem3b = $true) | ? [X485 : term] : ! [X486 : (subst > term > term)] : (((X486 @ sh @ one)) != ((sub @ X485 @ (push @ one @ sh))))) & (! [X485 : term] : ? [X486 : (subst > term > term)] : (((X486 @ sh @ one)) = ((sub @ X485 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X5 : d_subst] : (d_id = X5) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1_lthm = $true) | (? [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true != ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) & ($true = ((X377 @ X379)))) & ! [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) = X373) & ! [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) = X375))) & (! [X378 : subst,X376 : term,X377 : (term > $o),X379 : term,X380 : (term > $o)] : (($true = ((X380 @ (sub @ X379 @ (push @ X376 @ X378))))) | ($true != ((X377 @ X379)))) | ? [X373 : term,X372 : subst] : (((sub @ one @ (push @ X373 @ X372))) != X373) | ? [X374 : term,X375 : subst] : (((comp @ sh @ (push @ X374 @ X375))) != X375) | (pushprop_lem1_lthm != $true)) & (ulamvar1 != $true) & (($true = sP33) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP33)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X421 : term,X422 : term] : ((((lam @ X422)) != ((lam @ X421))) | (X421 = X422)) | (laminj != $true)) & ((laminj = $true) | ? [X421 : term,X422 : term] : ((((lam @ X422)) = ((lam @ X421))) & (X421 != X422))) & ((axidr = $true) | ? [X71 : subst] : (((comp @ X71 @ id)) != X71)) & (! [X71 : subst] : (((comp @ X71 @ id)) = X71) | (axidr != $true)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) = X27) | (axscons != $true)) & ((axscons = $true) | ? [X27 : subst] : (((push @ (sub @ one @ X27) @ (comp @ sh @ X27))) != X27)) & (! [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) != ((ap @ (sub @ X184 @ id) @ X183))) | (X182 = X183)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X182 : term,X184 : term,X181 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) = ((ap @ (sub @ X184 @ id) @ X183))) & (X182 != X183))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & ! [X119 : subst] : ? [X120 : d_subst] : (((d2subst @ X120)) = X119) & ((hoaslaminj_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoaslaminj_lthm != $true)) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) = X28) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X29 : term,X28 : subst] : (((comp @ sh @ (push @ X29 @ X28))) != X28)) & ((hoasapinj1 = $true) | ? [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) = ((ap @ (sub @ X8 @ id) @ X6))) & (X8 != X9))) & (! [X9 : term,X8 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X9 @ id) @ X7)) != ((ap @ (sub @ X8 @ id) @ X6))) | (X8 = X9)) | (hoasapinj1 != $true)) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP18)) & (($true = sP18) | (hoasinduction_lem2v2 != $true)) & ((sP16 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP16 != $true)) & ((! [X335 : subst] : (((comp @ id @ X335)) = X335) & ! [X336 : subst] : (((comp @ X336 @ id)) = X336)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X335 : subst] : (((comp @ id @ X335)) != X335) | ? [X336 : subst] : (((comp @ X336 @ id)) != X336)) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((induction = $true) | ? [X165 : (term > $o),X166 : term] : (! [X168 : term] : (($true = ((X165 @ (lam @ X168)))) | ($true != ((X165 @ X168)))) & ($true != ((X165 @ X166))) & ! [X167 : term] : (($true != ((var @ X167))) | ($true = ((X165 @ X167)))) & ($true != ((sP12 @ X165))))) & (! [X165 : (term > $o),X166 : term] : (? [X168 : term] : (($true != ((X165 @ (lam @ X168)))) & ($true = ((X165 @ X168)))) | ($true = ((X165 @ X166))) | ? [X167 : term] : (($true = ((var @ X167))) & ($true != ((X165 @ X167)))) | ($true = ((sP12 @ X165)))) | (induction != $true)) & (? [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) != X210) | ! [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true != ((X214 @ X211))) | (((X212 @ one)) = $true) | ? [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) != ((X212 @ X215)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X209 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X209))) = X210) & ? [X212 : (term > $o),X213 : subst,X211 : term,X214 : (term > $o)] : (($true = ((X214 @ X211))) & (((X212 @ one)) != $true) & ! [X215 : term] : (((X214 @ (sub @ X215 @ (push @ X211 @ X213)))) = ((X212 @ X215)))))) & (hoaslamnotap_lthm = $true) & (! [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) = $true) | ? [X208 : term] : (((X207 @ X208)) != ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) | ($true != ((X206 @ X205)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X206 : (term > $o),X204 : subst,X207 : (term > $o),X205 : term] : ((((X207 @ one)) != $true) & ! [X208 : term] : (((X207 @ X208)) = ((X206 @ (sub @ X208 @ (push @ X205 @ X204))))) & ($true = ((X206 @ X205))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((axvarcons = $true) | ? [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) != X408)) & (! [X408 : term,X407 : subst] : (((sub @ one @ (push @ X408 @ X407))) = X408) | (axvarcons != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X368 : (term > $o),X369 : term,X367 : subst] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) = ((X370 @ X371))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X368 : (term > $o),X369 : term,X367 : subst] : ! [X370 : (term > $o)] : ? [X371 : term] : (((X368 @ (sub @ X371 @ (push @ X369 @ X367)))) != ((X370 @ X371)))) & ((hoasinduction_lem0_lthm = $true) | ? [X474 : (subst > term > subst > $o)] : ! [X475 : (term > $o)] : ? [X476 : term] : (((X475 @ X476)) != ((X474 @ id @ X476 @ id)))) & (! [X474 : (subst > term > subst > $o)] : ? [X475 : (term > $o)] : ! [X476 : term] : (((X475 @ X476)) = ((X474 @ id @ X476 @ id))) | (hoasinduction_lem0_lthm != $true)) & (! [X243 : term] : ? [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) = ((X244 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X243 : term] : ! [X244 : (subst > term > term)] : (((sub @ X243 @ (push @ one @ sh))) != ((X244 @ sh @ one)))) & (! [X420 : term] : (((sub @ X420 @ id)) = X420) | ? [X419 : term] : (((sub @ X419 @ id)) != X419) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X420 : term] : (((sub @ X420 @ id)) != X420) & ! [X419 : term] : (((sub @ X419 @ id)) = X419))) & ((shinj = $true) | ? [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) = ((sub @ X185 @ sh))) & (X185 != X186))) & (! [X185 : term,X186 : term] : ((((sub @ X186 @ sh)) != ((sub @ X185 @ sh))) | (X185 = X186)) | (shinj != $true)) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((substmonoid_lthm = $true) | ((? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X406 : subst] : (((comp @ id @ X406)) != X406)) & ! [X403 : subst] : (((comp @ id @ X403)) = X403) & ! [X404 : subst] : (((comp @ X404 @ id)) = X404))) & ((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X406 : subst] : (((comp @ id @ X406)) = X406)) | ? [X403 : subst] : (((comp @ id @ X403)) != X403) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | ($true != sP9)) & (($true = sP9) | (induction2lem != $true)) & (! [X67 : term] : ? [X68 : (subst > term > term)] : ! [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) = ((X68 @ X69 @ X70))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X67 : term] : ! [X68 : (subst > term > term)] : ? [X70 : term,X69 : subst] : (((sub @ X67 @ (push @ X70 @ X69))) != ((X68 @ X69 @ X70)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X245 : d_term] : (d_one = X245) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X507 : d_subst,X506 : d_subst] : ((((d2subst @ X507)) != ((d2subst @ X506))) | (X506 = X507)) & (axvarshift = $true) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (($true = sP7) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP7)) & ((hoasapinj1_lthm = $true) | (! [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 = X219) | (((ap @ X218 @ X220)) != ((ap @ X219 @ X217)))) & ! [X216 : term] : (((sub @ X216 @ id)) = X216) & ? [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) = ((ap @ (sub @ X223 @ id) @ X221))) & (X223 != X224)))) & (? [X218 : term,X219 : term,X220 : term,X217 : term] : ((X218 != X219) & (((ap @ X218 @ X220)) = ((ap @ X219 @ X217)))) | ? [X216 : term] : (((sub @ X216 @ id)) != X216) | ! [X224 : term,X223 : term,X222 : term,X221 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) != ((ap @ (sub @ X223 @ id) @ X221))) | (X223 = X224)) | (hoasapinj1_lthm != $true)) & (hoaslamnotap_gthm = $true) & (! [X1 : (term > $o),X0 : subst,X2 : term] : ? [X3 : (term > $o)] : ! [X4 : term] : (((X3 @ X4)) = ((X1 @ (sub @ X4 @ (push @ X2 @ X0))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X1 : (term > $o),X0 : subst,X2 : term] : ! [X3 : (term > $o)] : ? [X4 : term] : (((X3 @ X4)) != ((X1 @ (sub @ X4 @ (push @ X2 @ X0)))))) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP6)) & (($true = sP6) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X520 : term] : ! [X521 : (subst > term > term)] : ? [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) != ((sub @ X520 @ (push @ X523 @ X522))))) & (! [X520 : term] : ? [X521 : (subst > term > term)] : ! [X523 : term,X522 : subst] : (((X521 @ X522 @ X523)) = ((sub @ X520 @ (push @ X523 @ X522)))) | (hoasinduction_lem3v2_f != $true)) & (! [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) != ((ap @ X511 @ X509))) | (X508 = X509)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X508 : term,X511 : term,X510 : term,X509 : term] : ((((ap @ X510 @ X508)) = ((ap @ X511 @ X509))) & (X508 != X509))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3aa = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3aa != $true)) & ((termmset = $true) | ? [X26 : term] : (((sub @ X26 @ id)) != X26)) & (! [X26 : term] : (((sub @ X26 @ id)) = X26) | (termmset != $true)) & (induction2_gthm = $true) & (($true = sP3) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP3)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | ? [X72 : subst] : (((comp @ id @ X72)) != X72)) & (! [X72 : subst] : (((comp @ id @ X72)) = X72) | (axidl != $true)) & (ulamvarsh = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0))),
% 5.86/1.21 inference(flattening,[],[f260])).
% 5.86/1.21 thf(f262,plain,(
% 5.86/1.21 (ulamvarind = $true) & ((induction2lem_lthm = $true) | ($true != sP58)) & (($true = sP58) | (induction2lem_lthm != $true)) & (apnotvar = $true) & ! [X0 : term] : ? [X1 : d_term] : (((d2term @ X1)) = X0) & ((axvarid = $true) | ? [X2 : term] : (((sub @ X2 @ id)) != X2)) & (! [X3 : term] : (((sub @ X3 @ id)) = X3) | (axvarid != $true)) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X5 = X7) | (((ap @ X5 @ X4)) != ((ap @ X7 @ X6)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X8 : term,X9 : term,X10 : term,X11 : term] : ((X9 != X11) & (((ap @ X11 @ X10)) = ((ap @ X9 @ X8))))) & (($true = sP54) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP54)) & ((hoaslaminj = $true) | ? [X12 : (subst > term > term),X13 : term,X14 : subst,X15 : (subst > term > term)] : (! [X16 : subst,X17 : subst,X18 : term] : (((sub @ (X15 @ X17 @ X18) @ X16)) = ((X15 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) & (((lam @ (X12 @ sh @ one))) = ((lam @ (X15 @ sh @ one)))) & (((X15 @ X14 @ X13)) != ((X12 @ X14 @ X13))) & ! [X19 : subst,X20 : subst,X21 : term] : (((sub @ (X12 @ X20 @ X21) @ X19)) = ((X12 @ (comp @ X20 @ X19) @ (sub @ X21 @ X19)))))) & (! [X22 : (subst > term > term),X23 : term,X24 : subst,X25 : (subst > term > term)] : (? [X26 : subst,X27 : subst,X28 : term] : (((X25 @ (comp @ X27 @ X26) @ (sub @ X28 @ X26))) != ((sub @ (X25 @ X27 @ X28) @ X26))) | (((lam @ (X25 @ sh @ one))) != ((lam @ (X22 @ sh @ one)))) | (((X22 @ X24 @ X23)) = ((X25 @ X24 @ X23))) | ? [X29 : subst,X30 : subst,X31 : term] : (((sub @ (X22 @ X30 @ X31) @ X29)) != ((X22 @ (comp @ X30 @ X29) @ (sub @ X31 @ X29))))) | (hoaslaminj != $true)) & ((hoasinduction_lem0 = $true) | ? [X32 : (subst > term > subst > $o)] : ! [X33 : (term > $o)] : ? [X34 : term] : (((X33 @ X34)) != ((X32 @ id @ X34 @ id)))) & (! [X35 : (subst > term > subst > $o)] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X35 @ id @ X37 @ id)) = ((X36 @ X37))) | (hoasinduction_lem0 != $true)) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (($true = sP53) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP53)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X38 : term,X39 : (subst > term > term),X40 : term] : ((((ap @ (sub @ X40 @ id) @ X38)) != ((lam @ (X39 @ sh @ one)))) | ? [X41 : subst,X42 : subst,X43 : term] : (((X39 @ (comp @ X42 @ X41) @ (sub @ X43 @ X41))) != ((sub @ (X39 @ X42 @ X43) @ X41)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X44 : term,X45 : (subst > term > term),X46 : term] : ((((ap @ (sub @ X46 @ id) @ X44)) = ((lam @ (X45 @ sh @ one)))) & ! [X47 : subst,X48 : subst,X49 : term] : (((sub @ (X45 @ X48 @ X49) @ X47)) = ((X45 @ (comp @ X48 @ X47) @ (sub @ X49 @ X47)))))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (($true = sP42) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X50 : d_term,X51 : d_term] : ((((d2term @ X50)) != ((d2term @ X51))) | (X50 = X51)) & ((induction2 = $true) | ($true != sP41)) & (($true = sP41) | (induction2 != $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2_lthm = $true) | (? [X52 : term,X53 : term,X54 : term,X55 : term] : ((X53 != X54) & (((ap @ (sub @ X52 @ id) @ X53)) = ((ap @ (sub @ X55 @ id) @ X54)))) & ! [X56 : term,X57 : term,X58 : term,X59 : term] : ((X58 = X59) | (((ap @ X57 @ X58)) != ((ap @ X56 @ X59)))))) & (! [X60 : term,X61 : term,X62 : term,X63 : term] : ((X61 = X62) | (((ap @ (sub @ X60 @ id) @ X61)) != ((ap @ (sub @ X63 @ id) @ X62)))) | ? [X64 : term,X65 : term,X66 : term,X67 : term] : ((X66 != X67) & (((ap @ X65 @ X66)) = ((ap @ X64 @ X67)))) | (hoasapinj2_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP38) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP38)) & (($true = sP36) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP36)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) | ? [X68 : term,X69 : (term > $o),X70 : (term > $o),X71 : subst,X72 : term] : (($true = ((X70 @ X68))) & ($true != ((X69 @ (sub @ X68 @ (push @ X72 @ X71))))))) & (! [X73 : term,X74 : (term > $o),X75 : (term > $o),X76 : subst,X77 : term] : (($true != ((X75 @ X73))) | ($true = ((X74 @ (sub @ X73 @ (push @ X77 @ X76)))))) | (pushprop_lem1 != $true)) & (! [X78 : (subst > term > subst > $o),X79 : term] : (? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X78 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X78 @ id @ X81 @ id)))) & ($true != ((X78 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X82 : subst,X83 : subst,X84 : term] : (((sub @ (X80 @ X82 @ X84) @ X83)) = ((X80 @ (comp @ X82 @ X83) @ (sub @ X84 @ X83))))) | (((X78 @ id @ X79 @ id)) = $true) | ($true = ((sP34 @ X78)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X85 : (subst > term > subst > $o),X86 : term] : (! [X87 : (subst > term > term)] : (? [X88 : term] : (($true != ((X85 @ id @ (X87 @ id @ X88) @ id))) & ($true = ((X85 @ id @ X88 @ id)))) | ($true = ((X85 @ id @ (lam @ (X87 @ sh @ one)) @ id))) | ? [X89 : subst,X90 : subst,X91 : term] : (((X87 @ (comp @ X89 @ X90) @ (sub @ X91 @ X90))) != ((sub @ (X87 @ X89 @ X91) @ X90)))) & (((X85 @ id @ X86 @ id)) != $true) & ($true != ((sP34 @ X85))))) & ((hoasinduction_lem3b = $true) | ? [X92 : term] : ! [X93 : (subst > term > term)] : (((sub @ X92 @ (push @ one @ sh))) != ((X93 @ sh @ one)))) & (! [X94 : term] : ? [X95 : (subst > term > term)] : (((X95 @ sh @ one)) = ((sub @ X94 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X96 : d_subst] : (d_id = X96) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1_lthm = $true) | (? [X97 : subst,X98 : term,X99 : (term > $o),X100 : term,X101 : (term > $o)] : (($true != ((X101 @ (sub @ X100 @ (push @ X98 @ X97))))) & ($true = ((X99 @ X100)))) & ! [X102 : term,X103 : subst] : (((sub @ one @ (push @ X102 @ X103))) = X102) & ! [X104 : term,X105 : subst] : (((comp @ sh @ (push @ X104 @ X105))) = X105))) & (! [X106 : subst,X107 : term,X108 : (term > $o),X109 : term,X110 : (term > $o)] : (($true = ((X110 @ (sub @ X109 @ (push @ X107 @ X106))))) | ($true != ((X108 @ X109)))) | ? [X111 : term,X112 : subst] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ? [X113 : term,X114 : subst] : (((comp @ sh @ (push @ X113 @ X114))) != X114) | (pushprop_lem1_lthm != $true)) & (ulamvar1 != $true) & (($true = sP33) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP33)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X115 : term,X116 : term] : ((((lam @ X116)) != ((lam @ X115))) | (X115 = X116)) | (laminj != $true)) & ((laminj = $true) | ? [X117 : term,X118 : term] : ((((lam @ X118)) = ((lam @ X117))) & (X117 != X118))) & ((axidr = $true) | ? [X119 : subst] : (((comp @ X119 @ id)) != X119)) & (! [X120 : subst] : (((comp @ X120 @ id)) = X120) | (axidr != $true)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X121 : subst] : (((push @ (sub @ one @ X121) @ (comp @ sh @ X121))) = X121) | (axscons != $true)) & ((axscons = $true) | ? [X122 : subst] : (((push @ (sub @ one @ X122) @ (comp @ sh @ X122))) != X122)) & (! [X123 : term,X124 : term,X125 : term,X126 : term] : ((((ap @ (sub @ X125 @ id) @ X123)) != ((ap @ (sub @ X124 @ id) @ X126))) | (X123 = X126)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X127 : term,X128 : term,X129 : term,X130 : term] : ((((ap @ (sub @ X129 @ id) @ X127)) = ((ap @ (sub @ X128 @ id) @ X130))) & (X127 != X130))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & ! [X131 : subst] : ? [X132 : d_subst] : (((d2subst @ X132)) = X131) & ((hoaslaminj_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoaslaminj_lthm != $true)) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X133 : term,X134 : subst] : (((comp @ sh @ (push @ X133 @ X134))) = X134) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X135 : term,X136 : subst] : (((comp @ sh @ (push @ X135 @ X136))) != X136)) & ((hoasapinj1 = $true) | ? [X137 : term,X138 : term,X139 : term,X140 : term] : ((((ap @ (sub @ X137 @ id) @ X140)) = ((ap @ (sub @ X138 @ id) @ X139))) & (X137 != X138))) & (! [X141 : term,X142 : term,X143 : term,X144 : term] : ((((ap @ (sub @ X141 @ id) @ X144)) != ((ap @ (sub @ X142 @ id) @ X143))) | (X141 = X142)) | (hoasapinj1 != $true)) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP18)) & (($true = sP18) | (hoasinduction_lem2v2 != $true)) & ((sP16 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP16 != $true)) & ((! [X145 : subst] : (((comp @ id @ X145)) = X145) & ! [X146 : subst] : (((comp @ X146 @ id)) = X146)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X147 : subst] : (((comp @ id @ X147)) != X147) | ? [X148 : subst] : (((comp @ X148 @ id)) != X148)) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((induction = $true) | ? [X149 : (term > $o),X150 : term] : (! [X151 : term] : (($true = ((X149 @ (lam @ X151)))) | ($true != ((X149 @ X151)))) & ($true != ((X149 @ X150))) & ! [X152 : term] : (($true != ((var @ X152))) | ($true = ((X149 @ X152)))) & ($true != ((sP12 @ X149))))) & (! [X153 : (term > $o),X154 : term] : (? [X155 : term] : ((((X153 @ (lam @ X155))) != $true) & ($true = ((X153 @ X155)))) | ($true = ((X153 @ X154))) | ? [X156 : term] : (($true = ((var @ X156))) & ($true != ((X153 @ X156)))) | ($true = ((sP12 @ X153)))) | (induction != $true)) & (? [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) != X158) | ! [X159 : (term > $o),X160 : subst,X161 : term,X162 : (term > $o)] : ((((X162 @ X161)) != $true) | ($true = ((X159 @ one))) | ? [X163 : term] : (((X159 @ X163)) != ((X162 @ (sub @ X163 @ (push @ X161 @ X160)))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X164 : subst,X165 : term] : (((sub @ one @ (push @ X165 @ X164))) = X165) & ? [X166 : (term > $o),X167 : subst,X168 : term,X169 : (term > $o)] : (($true = ((X169 @ X168))) & ($true != ((X166 @ one))) & ! [X170 : term] : (((X166 @ X170)) = ((X169 @ (sub @ X170 @ (push @ X168 @ X167)))))))) & (hoaslamnotap_lthm = $true) & (! [X171 : (term > $o),X172 : subst,X173 : (term > $o),X174 : term] : (($true = ((X173 @ one))) | ? [X175 : term] : (((X171 @ (sub @ X175 @ (push @ X174 @ X172)))) != ((X173 @ X175))) | ($true != ((X171 @ X174)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X176 : (term > $o),X177 : subst,X178 : (term > $o),X179 : term] : (($true != ((X178 @ one))) & ! [X180 : term] : (((X176 @ (sub @ X180 @ (push @ X179 @ X177)))) = ((X178 @ X180))) & ($true = ((X176 @ X179))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((axvarcons = $true) | ? [X181 : term,X182 : subst] : (((sub @ one @ (push @ X181 @ X182))) != X181)) & (! [X183 : term,X184 : subst] : (((sub @ one @ (push @ X183 @ X184))) = X183) | (axvarcons != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X185 : (term > $o),X186 : term,X187 : subst] : ? [X188 : (term > $o)] : ! [X189 : term] : (((X185 @ (sub @ X189 @ (push @ X186 @ X187)))) = ((X188 @ X189))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X190 : (term > $o),X191 : term,X192 : subst] : ! [X193 : (term > $o)] : ? [X194 : term] : (((X193 @ X194)) != ((X190 @ (sub @ X194 @ (push @ X191 @ X192)))))) & ((hoasinduction_lem0_lthm = $true) | ? [X195 : (subst > term > subst > $o)] : ! [X196 : (term > $o)] : ? [X197 : term] : (((X196 @ X197)) != ((X195 @ id @ X197 @ id)))) & (! [X198 : (subst > term > subst > $o)] : ? [X199 : (term > $o)] : ! [X200 : term] : (((X198 @ id @ X200 @ id)) = ((X199 @ X200))) | (hoasinduction_lem0_lthm != $true)) & (! [X201 : term] : ? [X202 : (subst > term > term)] : (((X202 @ sh @ one)) = ((sub @ X201 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X203 : term] : ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ X203 @ (push @ one @ sh))))) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) | ? [X206 : term] : (((sub @ X206 @ id)) != X206) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X207 : term] : (((sub @ X207 @ id)) != X207) & ! [X208 : term] : (((sub @ X208 @ id)) = X208))) & ((shinj = $true) | ? [X209 : term,X210 : term] : ((((sub @ X209 @ sh)) = ((sub @ X210 @ sh))) & (X209 != X210))) & (! [X211 : term,X212 : term] : ((((sub @ X212 @ sh)) != ((sub @ X211 @ sh))) | (X211 = X212)) | (shinj != $true)) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((substmonoid_lthm = $true) | ((? [X213 : subst] : (((comp @ X213 @ id)) != X213) | ? [X214 : subst] : (((comp @ id @ X214)) != X214)) & ! [X215 : subst] : (((comp @ id @ X215)) = X215) & ! [X216 : subst] : (((comp @ X216 @ id)) = X216))) & ((! [X217 : subst] : (((comp @ X217 @ id)) = X217) & ! [X218 : subst] : (((comp @ id @ X218)) = X218)) | ? [X219 : subst] : (((comp @ id @ X219)) != X219) | ? [X220 : subst] : (((comp @ X220 @ id)) != X220) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | ($true != sP9)) & (($true = sP9) | (induction2lem != $true)) & (! [X221 : term] : ? [X222 : (subst > term > term)] : ! [X223 : term,X224 : subst] : (((X222 @ X224 @ X223)) = ((sub @ X221 @ (push @ X223 @ X224)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X225 : term] : ! [X226 : (subst > term > term)] : ? [X227 : term,X228 : subst] : (((X226 @ X228 @ X227)) != ((sub @ X225 @ (push @ X227 @ X228))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X229 : d_term] : (d_one = X229) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X230 : d_subst,X231 : d_subst] : ((((d2subst @ X230)) != ((d2subst @ X231))) | (X230 = X231)) & (axvarshift = $true) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (($true = sP7) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP7)) & ((hoasapinj1_lthm = $true) | (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X232 = X233) | (((ap @ X233 @ X235)) != ((ap @ X232 @ X234)))) & ! [X236 : term] : (((sub @ X236 @ id)) = X236) & ? [X237 : term,X238 : term,X239 : term,X240 : term] : ((((ap @ (sub @ X237 @ id) @ X239)) = ((ap @ (sub @ X238 @ id) @ X240))) & (X237 != X238)))) & (? [X241 : term,X242 : term,X243 : term,X244 : term] : ((X241 != X242) & (((ap @ X242 @ X244)) = ((ap @ X241 @ X243)))) | ? [X245 : term] : (((sub @ X245 @ id)) != X245) | ! [X246 : term,X247 : term,X248 : term,X249 : term] : ((((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X246 @ id) @ X248))) | (X246 = X247)) | (hoasapinj1_lthm != $true)) & (hoaslamnotap_gthm = $true) & (! [X250 : (term > $o),X251 : subst,X252 : term] : ? [X253 : (term > $o)] : ! [X254 : term] : (((X250 @ (sub @ X254 @ (push @ X252 @ X251)))) = ((X253 @ X254))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X255 : (term > $o),X256 : subst,X257 : term] : ! [X258 : (term > $o)] : ? [X259 : term] : (((X255 @ (sub @ X259 @ (push @ X257 @ X256)))) != ((X258 @ X259)))) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP6)) & (($true = sP6) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X260 : term] : ! [X261 : (subst > term > term)] : ? [X262 : term,X263 : subst] : (((sub @ X260 @ (push @ X262 @ X263))) != ((X261 @ X263 @ X262)))) & (! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : term,X267 : subst] : (((sub @ X264 @ (push @ X266 @ X267))) = ((X265 @ X267 @ X266))) | (hoasinduction_lem3v2_f != $true)) & (! [X268 : term,X269 : term,X270 : term,X271 : term] : ((((ap @ X270 @ X268)) != ((ap @ X269 @ X271))) | (X268 = X271)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X272 : term,X273 : term,X274 : term,X275 : term] : ((((ap @ X273 @ X275)) = ((ap @ X274 @ X272))) & (X272 != X275))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3aa = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3aa != $true)) & ((termmset = $true) | ? [X276 : term] : (((sub @ X276 @ id)) != X276)) & (! [X277 : term] : (((sub @ X277 @ id)) = X277) | (termmset != $true)) & (induction2_gthm = $true) & (($true = sP3) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP3)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | ? [X278 : subst] : (((comp @ id @ X278)) != X278)) & (! [X279 : subst] : (((comp @ id @ X279)) = X279) | (axidl != $true)) & (ulamvarsh = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0))),
% 5.86/1.21 inference(rectify,[],[f261])).
% 5.86/1.21 thf(f263,plain,(
% 5.86/1.21 (ulamvarind = $true) & ((induction2lem_lthm = $true) | ($true != sP58)) & (($true = sP58) | (induction2lem_lthm != $true)) & (apnotvar = $true) & ! [X0 : term] : (((d2term @ (sK454 @ X0))) = X0) & ((axvarid = $true) | (((sub @ sK455 @ id)) != sK455)) & (! [X3 : term] : (((sub @ X3 @ id)) = X3) | (axvarid != $true)) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X5 = X7) | (((ap @ X5 @ X4)) != ((ap @ X7 @ X6)))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK459 != sK457) & (((ap @ sK457 @ sK456)) = ((ap @ sK459 @ sK458))))) & (($true = sP54) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP54)) & ((hoaslaminj = $true) | (! [X16 : subst,X17 : subst,X18 : term] : (((sK463 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16))) = ((sub @ (sK463 @ X17 @ X18) @ X16))) & (((lam @ (sK463 @ sh @ one))) = ((lam @ (sK460 @ sh @ one)))) & (((sK463 @ sK462 @ sK461)) != ((sK460 @ sK462 @ sK461))) & ! [X19 : subst,X20 : subst,X21 : term] : (((sub @ (sK460 @ X20 @ X21) @ X19)) = ((sK460 @ (comp @ X20 @ X19) @ (sub @ X21 @ X19)))))) & (! [X22 : (subst > term > term),X23 : term,X24 : subst,X25 : (subst > term > term)] : ((((sub @ (X25 @ (sK465 @ X25) @ (sK466 @ X25)) @ (sK464 @ X25))) != ((X25 @ (comp @ (sK465 @ X25) @ (sK464 @ X25)) @ (sub @ (sK466 @ X25) @ (sK464 @ X25))))) | (((lam @ (X25 @ sh @ one))) != ((lam @ (X22 @ sh @ one)))) | (((X22 @ X24 @ X23)) = ((X25 @ X24 @ X23))) | (((sub @ (X22 @ (sK468 @ X22) @ (sK469 @ X22)) @ (sK467 @ X22))) != ((X22 @ (comp @ (sK468 @ X22) @ (sK467 @ X22)) @ (sub @ (sK469 @ X22) @ (sK467 @ X22)))))) | (hoaslaminj != $true)) & ((hoasinduction_lem0 = $true) | ! [X33 : (term > $o)] : (((X33 @ (sK471 @ X33))) != ((sK470 @ id @ (sK471 @ X33) @ id)))) & (! [X35 : (subst > term > subst > $o)] : ! [X37 : term] : (((sK472 @ X35 @ X37)) = ((X35 @ id @ X37 @ id))) | (hoasinduction_lem0 != $true)) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (($true = sP53) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP53)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X38 : term,X39 : (subst > term > term),X40 : term] : ((((ap @ (sub @ X40 @ id) @ X38)) != ((lam @ (X39 @ sh @ one)))) | (((X39 @ (comp @ (sK474 @ X39) @ (sK473 @ X39)) @ (sub @ (sK475 @ X39) @ (sK473 @ X39)))) != ((sub @ (X39 @ (sK474 @ X39) @ (sK475 @ X39)) @ (sK473 @ X39))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ((((lam @ (sK477 @ sh @ one))) = ((ap @ (sub @ sK478 @ id) @ sK476))) & ! [X47 : subst,X48 : subst,X49 : term] : (((sub @ (sK477 @ X48 @ X49) @ X47)) = ((sK477 @ (comp @ X48 @ X47) @ (sub @ X49 @ X47)))))) & (pushprop_lem0_gthm = $true) & (lamnotap != $true) & (($true = sP42) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X50 : d_term,X51 : d_term] : ((((d2term @ X50)) != ((d2term @ X51))) | (X50 = X51)) & ((induction2 = $true) | ($true != sP41)) & (($true = sP41) | (induction2 != $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2_lthm = $true) | (((sK480 != sK481) & (((ap @ (sub @ sK482 @ id) @ sK481)) = ((ap @ (sub @ sK479 @ id) @ sK480)))) & ! [X56 : term,X57 : term,X58 : term,X59 : term] : ((X58 = X59) | (((ap @ X57 @ X58)) != ((ap @ X56 @ X59)))))) & (! [X60 : term,X61 : term,X62 : term,X63 : term] : ((X61 = X62) | (((ap @ (sub @ X60 @ id) @ X61)) != ((ap @ (sub @ X63 @ id) @ X62)))) | ((sK485 != sK486) & (((ap @ sK483 @ sK486)) = ((ap @ sK484 @ sK485)))) | (hoasapinj2_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP38) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP38)) & (($true = sP36) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP36)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) | (($true = ((sK489 @ sK487))) & (((sK488 @ (sub @ sK487 @ (push @ sK491 @ sK490)))) != $true))) & (! [X73 : term,X74 : (term > $o),X75 : (term > $o),X76 : subst,X77 : term] : (($true != ((X75 @ X73))) | ($true = ((X74 @ (sub @ X73 @ (push @ X77 @ X76)))))) | (pushprop_lem1 != $true)) & (! [X78 : (subst > term > subst > $o),X79 : term] : ((! [X81 : term] : (($true = ((X78 @ id @ (sK492 @ X78 @ id @ X81) @ id))) | ($true != ((X78 @ id @ X81 @ id)))) & ($true != ((X78 @ id @ (lam @ (sK492 @ X78 @ sh @ one)) @ id))) & ! [X82 : subst,X83 : subst,X84 : term] : (((sK492 @ X78 @ (comp @ X82 @ X83) @ (sub @ X84 @ X83))) = ((sub @ (sK492 @ X78 @ X82 @ X84) @ X83)))) | (((X78 @ id @ X79 @ id)) = $true) | ($true = ((sP34 @ X78)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X87 : (subst > term > term)] : ((($true != ((sK493 @ id @ (X87 @ id @ (sK495 @ X87)) @ id))) & ($true = ((sK493 @ id @ (sK495 @ X87) @ id)))) | ($true = ((sK493 @ id @ (lam @ (X87 @ sh @ one)) @ id))) | (((sub @ (X87 @ (sK496 @ X87) @ (sK498 @ X87)) @ (sK497 @ X87))) != ((X87 @ (comp @ (sK496 @ X87) @ (sK497 @ X87)) @ (sub @ (sK498 @ X87) @ (sK497 @ X87)))))) & ($true != ((sK493 @ id @ sK494 @ id))) & ($true != ((sP34 @ sK493))))) & ((hoasinduction_lem3b = $true) | ! [X93 : (subst > term > term)] : (((sub @ sK499 @ (push @ one @ sh))) != ((X93 @ sh @ one)))) & (! [X94 : term] : (((sK500 @ X94 @ sh @ one)) = ((sub @ X94 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (((d2subst @ d_id)) = id) & (axabs = $true) & ! [X96 : d_subst] : (d_id = X96) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1_lthm = $true) | ((($true != ((sK505 @ (sub @ sK504 @ (push @ sK502 @ sK501))))) & ($true = ((sK503 @ sK504)))) & ! [X102 : term,X103 : subst] : (((sub @ one @ (push @ X102 @ X103))) = X102) & ! [X104 : term,X105 : subst] : (((comp @ sh @ (push @ X104 @ X105))) = X105))) & (! [X106 : subst,X107 : term,X108 : (term > $o),X109 : term,X110 : (term > $o)] : (($true = ((X110 @ (sub @ X109 @ (push @ X107 @ X106))))) | ($true != ((X108 @ X109)))) | (((sub @ one @ (push @ sK506 @ sK507))) != sK506) | (((comp @ sh @ (push @ sK508 @ sK509))) != sK509) | (pushprop_lem1_lthm != $true)) & (ulamvar1 != $true) & (($true = sP33) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP33)) & ((hoasinduction_lem2 = $true) | ($true != sP30)) & (($true = sP30) | (hoasinduction_lem2 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X115 : term,X116 : term] : ((((lam @ X116)) != ((lam @ X115))) | (X115 = X116)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK511)) = ((lam @ sK510))) & (sK511 != sK510))) & ((axidr = $true) | (sK512 != ((comp @ sK512 @ id)))) & (! [X120 : subst] : (((comp @ X120 @ id)) = X120) | (axidr != $true)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X121 : subst] : (((push @ (sub @ one @ X121) @ (comp @ sh @ X121))) = X121) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK513) @ (comp @ sh @ sK513))) != sK513)) & (! [X123 : term,X124 : term,X125 : term,X126 : term] : ((((ap @ (sub @ X125 @ id) @ X123)) != ((ap @ (sub @ X124 @ id) @ X126))) | (X123 = X126)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK516 @ id) @ sK514)) = ((ap @ (sub @ sK515 @ id) @ sK517))) & (sK514 != sK517))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & ! [X131 : subst] : (((d2subst @ (sK518 @ X131))) = X131) & ((hoaslaminj_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoaslaminj_lthm != $true)) & (axassoc = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X133 : term,X134 : subst] : (((comp @ sh @ (push @ X133 @ X134))) = X134) | (axshiftcons != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK519 @ sK520))) != sK520)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK522 @ id) @ sK523)) = ((ap @ (sub @ sK521 @ id) @ sK524))) & (sK522 != sK521))) & (! [X141 : term,X142 : term,X143 : term,X144 : term] : ((((ap @ (sub @ X141 @ id) @ X144)) != ((ap @ (sub @ X142 @ id) @ X143))) | (X141 = X142)) | (hoasapinj1 != $true)) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP18)) & (($true = sP18) | (hoasinduction_lem2v2 != $true)) & ((sP16 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP16 != $true)) & ((! [X145 : subst] : (((comp @ id @ X145)) = X145) & ! [X146 : subst] : (((comp @ X146 @ id)) = X146)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK525 != ((comp @ id @ sK525))) | (((comp @ sK526 @ id)) != sK526)) & (hoasapnotvar = $true) & (axclos = $true) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((induction = $true) | (! [X151 : term] : (($true = ((sK527 @ (lam @ X151)))) | (((sK527 @ X151)) != $true)) & ($true != ((sK527 @ sK528))) & ! [X152 : term] : (($true != ((var @ X152))) | ($true = ((sK527 @ X152)))) & ($true != ((sP12 @ sK527))))) & (! [X153 : (term > $o),X154 : term] : ((($true != ((X153 @ (lam @ (sK529 @ X153))))) & ($true = ((X153 @ (sK529 @ X153))))) | ($true = ((X153 @ X154))) | (($true = ((var @ (sK530 @ X153)))) & ($true != ((X153 @ (sK530 @ X153))))) | ($true = ((sP12 @ X153)))) | (induction != $true)) & ((sK532 != ((sub @ one @ (push @ sK532 @ sK531)))) | ! [X159 : (term > $o),X160 : subst,X161 : term,X162 : (term > $o)] : ((((X162 @ X161)) != $true) | ($true = ((X159 @ one))) | (((X159 @ (sK533 @ X162 @ X161 @ X160 @ X159))) != ((X162 @ (sub @ (sK533 @ X162 @ X161 @ X160 @ X159) @ (push @ X161 @ X160)))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X164 : subst,X165 : term] : (((sub @ one @ (push @ X165 @ X164))) = X165) & ((((sK537 @ sK536)) = $true) & ($true != ((sK534 @ one))) & ! [X170 : term] : (((sK537 @ (sub @ X170 @ (push @ sK536 @ sK535)))) = ((sK534 @ X170)))))) & (hoaslamnotap_lthm = $true) & (! [X171 : (term > $o),X172 : subst,X173 : (term > $o),X174 : term] : (($true = ((X173 @ one))) | (((X173 @ (sK538 @ X174 @ X173 @ X172 @ X171))) != ((X171 @ (sub @ (sK538 @ X174 @ X173 @ X172 @ X171) @ (push @ X174 @ X172))))) | ($true != ((X171 @ X174)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ((((sK541 @ one)) != $true) & ! [X180 : term] : (((sK541 @ X180)) = ((sK539 @ (sub @ X180 @ (push @ sK542 @ sK540))))) & ($true = ((sK539 @ sK542))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((axvarcons = $true) | (sK543 != ((sub @ one @ (push @ sK543 @ sK544))))) & (! [X183 : term,X184 : subst] : (((sub @ one @ (push @ X183 @ X184))) = X183) | (axvarcons != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X185 : (term > $o),X186 : term,X187 : subst] : ! [X189 : term] : (((sK545 @ X187 @ X186 @ X185 @ X189)) = ((X185 @ (sub @ X189 @ (push @ X186 @ X187))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X193 : (term > $o)] : (((sK546 @ (sub @ (sK549 @ X193) @ (push @ sK547 @ sK548)))) != ((X193 @ (sK549 @ X193))))) & ((hoasinduction_lem0_lthm = $true) | ! [X196 : (term > $o)] : (((sK550 @ id @ (sK551 @ X196) @ id)) != ((X196 @ (sK551 @ X196))))) & (! [X198 : (subst > term > subst > $o)] : ! [X200 : term] : (((X198 @ id @ X200 @ id)) = ((sK552 @ X198 @ X200))) | (hoasinduction_lem0_lthm != $true)) & (! [X201 : term] : (((sK553 @ X201 @ sh @ one)) = ((sub @ X201 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ sK554 @ (push @ one @ sh))))) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) | (sK555 != ((sub @ sK555 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK556 @ id)) != sK556) & ! [X208 : term] : (((sub @ X208 @ id)) = X208))) & ((shinj = $true) | ((((sub @ sK558 @ sh)) = ((sub @ sK557 @ sh))) & (sK557 != sK558))) & (! [X211 : term,X212 : term] : ((((sub @ X212 @ sh)) != ((sub @ X211 @ sh))) | (X211 = X212)) | (shinj != $true)) & (axapp = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((substmonoid_lthm = $true) | (((sK559 != ((comp @ sK559 @ id))) | (sK560 != ((comp @ id @ sK560)))) & ! [X215 : subst] : (((comp @ id @ X215)) = X215) & ! [X216 : subst] : (((comp @ X216 @ id)) = X216))) & ((! [X217 : subst] : (((comp @ X217 @ id)) = X217) & ! [X218 : subst] : (((comp @ id @ X218)) = X218)) | (((comp @ id @ sK561)) != sK561) | (sK562 != ((comp @ sK562 @ id))) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | ($true != sP9)) & (($true = sP9) | (induction2lem != $true)) & (! [X221 : term] : ! [X223 : term,X224 : subst] : (((sub @ X221 @ (push @ X223 @ X224))) = ((sK563 @ X221 @ X224 @ X223))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X226 : (subst > term > term)] : (((sub @ sK564 @ (push @ (sK565 @ X226) @ (sK566 @ X226)))) != ((X226 @ (sK566 @ X226) @ (sK565 @ X226))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X229 : d_term] : (d_one = X229) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X230 : d_subst,X231 : d_subst] : ((((d2subst @ X230)) != ((d2subst @ X231))) | (X230 = X231)) & (axvarshift = $true) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (($true = sP7) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP7)) & ((hoasapinj1_lthm = $true) | (! [X232 : term,X233 : term,X234 : term,X235 : term] : ((X232 = X233) | (((ap @ X233 @ X235)) != ((ap @ X232 @ X234)))) & ! [X236 : term] : (((sub @ X236 @ id)) = X236) & ((((ap @ (sub @ sK567 @ id) @ sK569)) = ((ap @ (sub @ sK568 @ id) @ sK570))) & (sK568 != sK567)))) & (((sK572 != sK571) & (((ap @ sK571 @ sK573)) = ((ap @ sK572 @ sK574)))) | (sK575 != ((sub @ sK575 @ id))) | ! [X246 : term,X247 : term,X248 : term,X249 : term] : ((((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X246 @ id) @ X248))) | (X246 = X247)) | (hoasapinj1_lthm != $true)) & (hoaslamnotap_gthm = $true) & (! [X250 : (term > $o),X251 : subst,X252 : term] : ! [X254 : term] : (((X250 @ (sub @ X254 @ (push @ X252 @ X251)))) = ((sK576 @ X252 @ X251 @ X250 @ X254))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X258 : (term > $o)] : (((sK577 @ (sub @ (sK580 @ X258) @ (push @ sK579 @ sK578)))) != ((X258 @ (sK580 @ X258))))) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP6)) & (($true = sP6) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X261 : (subst > term > term)] : (((X261 @ (sK583 @ X261) @ (sK582 @ X261))) != ((sub @ sK581 @ (push @ (sK582 @ X261) @ (sK583 @ X261)))))) & (! [X264 : term] : ! [X266 : term,X267 : subst] : (((sub @ X264 @ (push @ X266 @ X267))) = ((sK584 @ X264 @ X267 @ X266))) | (hoasinduction_lem3v2_f != $true)) & (! [X268 : term,X269 : term,X270 : term,X271 : term] : ((((ap @ X270 @ X268)) != ((ap @ X269 @ X271))) | (X268 = X271)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK586 @ sK588)) = ((ap @ sK587 @ sK585))) & (sK588 != sK585))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3aa = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3aa != $true)) & ((termmset = $true) | (sK589 != ((sub @ sK589 @ id)))) & (! [X277 : term] : (((sub @ X277 @ id)) = X277) | (termmset != $true)) & (induction2_gthm = $true) & (($true = sP3) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP3)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | (sK590 != ((comp @ id @ sK590)))) & (! [X279 : subst] : (((comp @ id @ X279)) = X279) | (axidl != $true)) & (ulamvarsh = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0))),
% 5.86/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK470,vAPP,vAPP,vAPP,vAPP,vAPP,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,vAPP,sK493,sK494,vAPP,vAPP,vAPP,vAPP,sK499,vAPP,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,vAPP,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,vAPP,vAPP,sK531,sK532,vAPP,sK534,sK535,sK536,sK537,vAPP,sK539,sK540,sK541,sK542,sK543,sK544,vAPP,sK546,sK547,sK548,vAPP,sK550,vAPP,vAPP,vAPP,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,vAPP,sK564,vAPP,vAPP,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,vAPP,sK577,sK578,sK579,vAPP,sK581,vAPP,vAPP,vAPP,sK585,sK586,sK587,sK588,sK589,sK590]),skolemize(X5,sK60 @ X2),skolemize(X2,sK455),skolemize(X8,sK456),skolemize(X9,sK457),skolemize(X10,sK458),skolemize(X11,sK459),skolemize(X12,sK460),skolemize(X13,sK461),skolemize(X14,sK462),skolemize(X15,sK463),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X32,sK470),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X44,sK476),skolemize(X45,sK477),skolemize(X46,sK478),skolemize(X52,sK479),skolemize(X53,sK480),skolemize(X54,sK481),skolemize(X55,sK482),skolemize(X64,sK483),skolemize(X65,sK484),skolemize(X66,sK485),skolemize(X67,sK486),skolemize(X68,sK487),skolemize(X69,sK488),skolemize(X70,sK489),skolemize(X71,sK490),skolemize(X72,sK491),skolemize(X5,sK60 @ X2),skolemize(X85,sK493),skolemize(X86,sK494),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X92,sK499),skolemize(X5,sK60 @ X2),skolemize(X97,sK501),skolemize(X98,sK502),skolemize(X99,sK503),skolemize(X100,sK504),skolemize(X101,sK505),skolemize(X111,sK506),skolemize(X112,sK507),skolemize(X113,sK508),skolemize(X114,sK509),skolemize(X117,sK510),skolemize(X118,sK511),skolemize(X119,sK512),skolemize(X122,sK513),skolemize(X127,sK514),skolemize(X128,sK515),skolemize(X129,sK516),skolemize(X130,sK517),skolemize(X5,sK60 @ X2),skolemize(X135,sK519),skolemize(X136,sK520),skolemize(X137,sK521),skolemize(X138,sK522),skolemize(X139,sK523),skolemize(X140,sK524),skolemize(X147,sK525),skolemize(X148,sK526),skolemize(X149,sK527),skolemize(X150,sK528),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X157,sK531),skolemize(X158,sK532),skolemize(X5,sK60 @ X2),skolemize(X166,sK534),skolemize(X167,sK535),skolemize(X168,sK536),skolemize(X169,sK537),skolemize(X5,sK60 @ X2),skolemize(X176,sK539),skolemize(X177,sK540),skolemize(X178,sK541),skolemize(X179,sK542),skolemize(X181,sK543),skolemize(X182,sK544),skolemize(X5,sK60 @ X2),skolemize(X190,sK546),skolemize(X191,sK547),skolemize(X192,sK548),skolemize(X5,sK60 @ X2),skolemize(X195,sK550),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X203,sK554),skolemize(X206,sK555),skolemize(X207,sK556),skolemize(X209,sK557),skolemize(X210,sK558),skolemize(X213,sK559),skolemize(X214,sK560),skolemize(X219,sK561),skolemize(X220,sK562),skolemize(X5,sK60 @ X2),skolemize(X225,sK564),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X237,sK567),skolemize(X238,sK568),skolemize(X239,sK569),skolemize(X240,sK570),skolemize(X241,sK571),skolemize(X242,sK572),skolemize(X243,sK573),skolemize(X244,sK574),skolemize(X245,sK575),skolemize(X5,sK60 @ X2),skolemize(X255,sK577),skolemize(X256,sK578),skolemize(X257,sK579),skolemize(X5,sK60 @ X2),skolemize(X260,sK581),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X5,sK60 @ X2),skolemize(X272,sK585),skolemize(X273,sK586),skolemize(X274,sK587),skolemize(X275,sK588),skolemize(X276,sK589),skolemize(X278,sK590)],[f262])).
% 5.86/1.21 thf(f264,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))))),
% 5.86/1.21 inference(cnf_transformation,[],[f10])).
% 5.86/1.21 thf(f680,plain,(
% 5.86/1.21 ( ! [X8 : term] : ((((sK387 @ id @ X8 @ id)) = ((sK385 @ X8))) | ($true = sP7)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f237])).
% 5.86/1.21 thf(f681,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : (($true = sP7) | (((X3 @ (comp @ (sK390 @ X3) @ (sK388 @ X3)) @ (sub @ (sK389 @ X3) @ (sK388 @ X3)))) != ((sub @ (X3 @ (sK390 @ X3) @ (sK389 @ X3)) @ (sK388 @ X3)))) | ($true = ((sK387 @ id @ (sK391 @ X3) @ id))) | ($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id)))) )),
% 5.86/1.21 inference(cnf_transformation,[],[f237])).
% 5.86/1.21 thf(f683,plain,(
% 5.86/1.21 ($true != ((sK385 @ (lam @ sK386)))) | ($true = sP7)),
% 5.86/1.21 inference(cnf_transformation,[],[f237])).
% 5.86/1.21 thf(f766,plain,(
% 5.86/1.21 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id))))))))),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f768,plain,(
% 5.86/1.21 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f786,plain,(
% 5.86/1.21 ($true != sP7) | (hoasinduction_lem3v2a = $true)),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f794,plain,(
% 5.86/1.21 ( ! [X229 : d_term] : ((d_one = X229)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f810,plain,(
% 5.86/1.21 ( ! [X212 : term,X211 : term] : ((shinj != $true) | (((sub @ X212 @ sh)) != ((sub @ X211 @ sh))) | (X211 = X212)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f811,plain,(
% 5.86/1.21 (shinj = $true) | (sK557 != sK558)),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f874,plain,(
% 5.86/1.21 ( ! [X131 : subst] : ((((d2subst @ (sK518 @ X131))) = X131)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f908,plain,(
% 5.86/1.21 (((d2subst @ d_id)) = sh)),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f910,plain,(
% 5.86/1.21 ( ! [X96 : d_subst] : ((d_id = X96)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f912,plain,(
% 5.86/1.21 (((d2subst @ d_id)) = id)),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f974,plain,(
% 5.86/1.21 ( ! [X0 : term] : ((((d2term @ (sK454 @ X0))) = X0)) )),
% 5.86/1.21 inference(cnf_transformation,[],[f263])).
% 5.86/1.21 thf(f981,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))))),
% 5.86/1.21 inference(definition_unfolding,[],[f264,f768,f766])).
% 5.86/1.21 thf(f982,definition,(
% 5.86/1.21 (sF591 = ((d2term @ d_one)))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[sF591])],[function_definition])).
% 5.86/1.21 thf(f983,plain,(
% 5.86/1.21 (((d2term @ d_one)) = sF591)),
% 5.86/1.21 inference(reorient_equations,[],[f982])).
% 5.86/1.21 thf(f984,definition,(
% 5.86/1.21 (sF592 = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (sF591)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[sF592])],[function_definition])).
% 5.86/1.21 thf(f985,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a != sF592)),
% 5.86/1.21 inference(definition_folding,[],[f981,f984,f983])).
% 5.86/1.21 thf(f1011,plain,(
% 5.86/1.21 ( ! [X8 : term] : (($true = ((sK385 @ X8))) | (((sK387 @ id @ X8 @ id)) = $false) | ($true = sP7)) )),
% 5.86/1.21 inference(iff_proxy_clausification,[],[f680])).
% 5.86/1.21 thf(f1022,plain,(
% 5.86/1.21 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (sF591)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))))) = $false) | ($true = sF592)),
% 5.86/1.21 inference(iff_proxy_clausification,[],[f984])).
% 5.86/1.21 thf(f1099,plain,(
% 5.86/1.21 ($true = sF592) | ($false = (((^[Y0 : subst > term > subst > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y4 @ Y3) @ Y5) = (Y2 @ (comp @ Y4 @ Y5) @ (sub @ Y3 @ Y5))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y0 @ id @ Y3 @ id) => (Y0 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y0 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (sF591)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y0 @ Y1) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (Y1 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y1 @ (lam @ Y2)))))))))) @ sK599)))),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1022])).
% 5.86/1.21 thf(f1100,plain,(
% 5.86/1.21 ($true = sF592) | ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((sK599 @ id @ Y2 @ id) => (sK599 @ id @ (Y1 @ id @ Y2) @ id)))) => (sK599 @ id @ sF591 @ id))))) => ((!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK599 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ id)))))) => (Y0 @ (lam @ Y1)))))))))))),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1099])).
% 5.86/1.21 thf(f1101,plain,(
% 5.86/1.21 ($true = sF592) | ($false = (((^[Y0 : term > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((sK599 @ id @ Y2 @ id) => (sK599 @ id @ (Y1 @ id @ Y2) @ id)))) => (sK599 @ id @ sF591 @ id))))) => ((!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK599 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => (Y0 @ (sub @ Y1 @ (push @ Y2 @ id)))))) => (Y0 @ (lam @ Y1)))))))) @ sK600)))),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1100])).
% 5.86/1.21 thf(f1102,plain,(
% 5.86/1.21 ($false = (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK599 @ id @ Y1 @ id) => (sK599 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK599 @ id @ sF591 @ id))))) => ((!! @ term @ (^[Y0 : term]: ((sK600 @ Y0) = (sK599 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK600 @ Y1) => (sK600 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK600 @ (lam @ Y0))))))))) | ($true = sF592)),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1101])).
% 5.86/1.21 thf(f1103,plain,(
% 5.86/1.21 ((((!! @ term @ (^[Y0 : term]: ((sK600 @ Y0) = (sK599 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK600 @ Y1) => (sK600 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK600 @ (lam @ Y0))))))) = $false) | ($true = sF592)),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1102])).
% 5.86/1.21 thf(f1104,plain,(
% 5.86/1.21 ($true = sF592) | ($true = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK599 @ id @ Y1 @ id) => (sK599 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK599 @ id @ sF591 @ id)))))))),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1102])).
% 5.86/1.21 thf(f1105,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = sF592) | ($true = (((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK599 @ id @ Y1 @ id) => (sK599 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK599 @ id @ sF591 @ id)))) @ X1)))) )),
% 5.86/1.21 inference(pi_proxy_clausification,[],[f1104])).
% 5.86/1.21 thf(f1106,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK599 @ id @ Y0 @ id) => (sK599 @ id @ (X1 @ id @ Y0) @ id)))) => (sK599 @ id @ sF591 @ id))))) | ($true = sF592)) )),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1105])).
% 5.86/1.21 thf(f1107,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))))) | ($true = sF592) | ($true = (((!! @ term @ (^[Y0 : term]: ((sK599 @ id @ Y0 @ id) => (sK599 @ id @ (X1 @ id @ Y0) @ id)))) => (sK599 @ id @ sF591 @ id))))) )),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1106])).
% 5.86/1.21 thf(f1108,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: ((sK599 @ id @ Y0 @ id) => (sK599 @ id @ (X1 @ id @ Y0) @ id)))) => (sK599 @ id @ sF591 @ id)))) | ($true = sF592) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK601 @ X1))))) )),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1107])).
% 5.86/1.21 thf(f1109,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : ((((!! @ term @ (^[Y0 : term]: ((sK599 @ id @ Y0 @ id) => (sK599 @ id @ (X1 @ id @ Y0) @ id))))) = $false) | ($true = sF592) | ($true = ((sK599 @ id @ sF591 @ id))) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK601 @ X1))))) )),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1108])).
% 5.86/1.21 thf(f1110,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = ((sK599 @ id @ sF591 @ id))) | ($true = sF592) | ((((^[Y0 : term]: ((sK599 @ id @ Y0 @ id) => (sK599 @ id @ (X1 @ id @ Y0) @ id))) @ (sK602 @ X1))) = $false) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK601 @ X1))))) )),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1109])).
% 5.86/1.21 thf(f1111,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = sF592) | ($false = (((sK599 @ id @ (sK602 @ X1) @ id) => (sK599 @ id @ (X1 @ id @ (sK602 @ X1)) @ id)))) | ($true = ((sK599 @ id @ sF591 @ id))) | (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK601 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK601 @ X1) @ Y1)))))))) = $false)) )),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1110])).
% 5.86/1.21 thf(f1113,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK601 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK601 @ X1) @ Y1)))))))) = $false) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | ($true = ((sK599 @ id @ sF591 @ id))) | ($true = sF592)) )),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1111])).
% 5.86/1.21 thf(f1114,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = sF592) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | ((((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK601 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK601 @ X1) @ Y1)))))) @ (sK603 @ X1))) = $false) | ($true = ((sK599 @ id @ sF591 @ id)))) )),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1113])).
% 5.86/1.21 thf(f1115,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = ((sK599 @ id @ sF591 @ id))) | ($false = ((!! @ subst @ (^[Y0 : subst]: ((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ Y0) = (X1 @ (comp @ (sK603 @ X1) @ Y0) @ (sub @ (sK601 @ X1) @ Y0))))))) | ($true = sF592) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true)) )),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1114])).
% 5.86/1.21 thf(f1116,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($false = (((^[Y0 : subst]: ((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ Y0) = (X1 @ (comp @ (sK603 @ X1) @ Y0) @ (sub @ (sK601 @ X1) @ Y0)))) @ (sK604 @ X1)))) | ($true = sF592) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | ($true = ((sK599 @ id @ sF591 @ id)))) )),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1115])).
% 5.86/1.21 thf(f1117,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = sF592) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | ($true = ((sK599 @ id @ sF591 @ id))) | ((((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ (sK604 @ X1)) = (X1 @ (comp @ (sK603 @ X1) @ (sK604 @ X1)) @ (sub @ (sK601 @ X1) @ (sK604 @ X1))))) = $false)) )),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1116])).
% 5.86/1.21 thf(f1118,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = ((sK599 @ id @ sF591 @ id))) | (((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | ($true = sF592) | (((X1 @ (comp @ (sK603 @ X1) @ (sK604 @ X1)) @ (sub @ (sK601 @ X1) @ (sK604 @ X1)))) != ((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ (sK604 @ X1))))) )),
% 5.86/1.21 inference(equality_proxy_clausification,[],[f1117])).
% 5.86/1.21 thf(f1124,plain,(
% 5.86/1.21 ($true = sF592) | ($false = ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK600 @ Y1) => (sK600 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK600 @ (lam @ Y0)))))))),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1103])).
% 5.86/1.21 thf(f1125,plain,(
% 5.86/1.21 (((!! @ term @ (^[Y0 : term]: ((sK600 @ Y0) = (sK599 @ id @ Y0 @ id))))) = $true) | ($true = sF592)),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1103])).
% 5.86/1.21 thf(f1126,plain,(
% 5.86/1.21 ( ! [X1 : term] : (($true = (((^[Y0 : term]: ((sK600 @ Y0) = (sK599 @ id @ Y0 @ id))) @ X1))) | ($true = sF592)) )),
% 5.86/1.21 inference(pi_proxy_clausification,[],[f1125])).
% 5.86/1.21 thf(f1127,plain,(
% 5.86/1.21 ( ! [X1 : term] : (($true = (((sK600 @ X1) = (sK599 @ id @ X1 @ id)))) | ($true = sF592)) )),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1126])).
% 5.86/1.21 thf(f1128,plain,(
% 5.86/1.21 ( ! [X1 : term] : (($true = sF592) | (((sK600 @ X1)) = ((sK599 @ id @ X1 @ id)))) )),
% 5.86/1.21 inference(equality_proxy_clausification,[],[f1127])).
% 5.86/1.21 thf(f1129,plain,(
% 5.86/1.21 ( ! [X1 : term] : ((((sK599 @ id @ X1 @ id)) = $false) | ($true = sF592) | (((sK600 @ X1)) = $true)) )),
% 5.86/1.21 inference(iff_proxy_clausification,[],[f1128])).
% 5.86/1.21 thf(f1131,plain,(
% 5.86/1.21 ($false = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK600 @ Y1) => (sK600 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK600 @ (lam @ Y0)))) @ sK607))) | ($true = sF592)),
% 5.86/1.21 inference(sigma_proxy_clausification,[],[f1124])).
% 5.86/1.21 thf(f1132,plain,(
% 5.86/1.21 ($true = sF592) | ((((!! @ term @ (^[Y0 : term]: ((sK600 @ Y0) => (sK600 @ (sub @ sK607 @ (push @ Y0 @ id)))))) => (sK600 @ (lam @ sK607)))) = $false)),
% 5.86/1.21 inference(beta-eta_normalization,[],[f1131])).
% 5.86/1.21 thf(f1133,plain,(
% 5.86/1.21 ($true = sF592) | (((sK600 @ (lam @ sK607))) = $false)),
% 5.86/1.21 inference(imp_proxy_clausification,[],[f1132])).
% 5.86/1.21 thf(f1149,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a = $false) | (sF592 = $false)),
% 5.86/1.21 inference(xor_proxy_clausification,[],[f985])).
% 5.86/1.21 thf(f1659,definition,(
% 5.86/1.21 spl608_99 <=> ($true = sP7)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_99])],[avatar_definition])).
% 5.86/1.21 thf(f1718,definition,(
% 5.86/1.21 spl608_113 <=> ($true = ((sK385 @ (lam @ sK386))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_113])],[avatar_definition])).
% 5.86/1.21 thf(f1720,plain,(
% 5.86/1.21 ($true != ((sK385 @ (lam @ sK386)))) | spl608_113),
% 5.86/1.21 inference(avatar_component_clause,[],[f1718])).
% 5.86/1.21 thf(f1721,plain,(
% 5.86/1.21 ~spl608_113 | spl608_99),
% 5.86/1.21 inference(avatar_split_clause,[],[f683,f1659,f1718])).
% 5.86/1.21 thf(f1723,definition,(
% 5.86/1.21 spl608_114 <=> ! [X3 : (subst > term > term)] : ((((X3 @ (comp @ (sK390 @ X3) @ (sK388 @ X3)) @ (sub @ (sK389 @ X3) @ (sK388 @ X3)))) != ((sub @ (X3 @ (sK390 @ X3) @ (sK389 @ X3)) @ (sK388 @ X3)))) | ($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = ((sK387 @ id @ (sK391 @ X3) @ id))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_114])],[avatar_definition])).
% 5.86/1.21 thf(f1724,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : (($true = ((sK387 @ id @ (sK391 @ X3) @ id))) | ($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | (((X3 @ (comp @ (sK390 @ X3) @ (sK388 @ X3)) @ (sub @ (sK389 @ X3) @ (sK388 @ X3)))) != ((sub @ (X3 @ (sK390 @ X3) @ (sK389 @ X3)) @ (sK388 @ X3))))) ) | ~spl608_114),
% 5.86/1.21 inference(avatar_component_clause,[],[f1723])).
% 5.86/1.21 thf(f1725,plain,(
% 5.86/1.21 spl608_99 | spl608_114),
% 5.86/1.21 inference(avatar_split_clause,[],[f681,f1723,f1659])).
% 5.86/1.21 thf(f1822,definition,(
% 5.86/1.21 spl608_138 <=> ! [X8 : term] : (($true = ((sK385 @ X8))) | (((sK387 @ id @ X8 @ id)) = $false))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_138])],[avatar_definition])).
% 5.86/1.21 thf(f1823,plain,(
% 5.86/1.21 ( ! [X8 : term] : ((((sK387 @ id @ X8 @ id)) = $false) | ($true = ((sK385 @ X8)))) ) | ~spl608_138),
% 5.86/1.21 inference(avatar_component_clause,[],[f1822])).
% 5.86/1.21 thf(f1824,plain,(
% 5.86/1.21 spl608_138 | spl608_99),
% 5.86/1.21 inference(avatar_split_clause,[],[f1011,f1659,f1822])).
% 5.86/1.21 thf(f1963,definition,(
% 5.86/1.21 spl608_172 <=> (sF592 = $false)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_172])],[avatar_definition])).
% 5.86/1.21 thf(f1965,plain,(
% 5.86/1.21 (sF592 = $false) | ~spl608_172),
% 5.86/1.21 inference(avatar_component_clause,[],[f1963])).
% 5.86/1.21 thf(f2015,definition,(
% 5.86/1.21 spl608_185 <=> ! [X1 : (subst > term > term)] : ((((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | (((X1 @ (comp @ (sK603 @ X1) @ (sK604 @ X1)) @ (sub @ (sK601 @ X1) @ (sK604 @ X1)))) != ((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ (sK604 @ X1)))))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_185])],[avatar_definition])).
% 5.86/1.21 thf(f2016,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : ((((sK599 @ id @ (sK602 @ X1) @ id)) = $true) | (((X1 @ (comp @ (sK603 @ X1) @ (sK604 @ X1)) @ (sub @ (sK601 @ X1) @ (sK604 @ X1)))) != ((sub @ (X1 @ (sK603 @ X1) @ (sK601 @ X1)) @ (sK604 @ X1))))) ) | ~spl608_185),
% 5.86/1.21 inference(avatar_component_clause,[],[f2015])).
% 5.86/1.21 thf(f2018,definition,(
% 5.86/1.21 spl608_186 <=> ($true = sF592)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_186])],[avatar_definition])).
% 5.86/1.21 thf(f2020,plain,(
% 5.86/1.21 ($true = sF592) | ~spl608_186),
% 5.86/1.21 inference(avatar_component_clause,[],[f2018])).
% 5.86/1.21 thf(f2022,definition,(
% 5.86/1.21 spl608_187 <=> ($true = ((sK599 @ id @ sF591 @ id)))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_187])],[avatar_definition])).
% 5.86/1.21 thf(f2023,plain,(
% 5.86/1.21 ($true != ((sK599 @ id @ sF591 @ id))) | spl608_187),
% 5.86/1.21 inference(avatar_component_clause,[],[f2022])).
% 5.86/1.21 thf(f2024,plain,(
% 5.86/1.21 ($true = ((sK599 @ id @ sF591 @ id))) | ~spl608_187),
% 5.86/1.21 inference(avatar_component_clause,[],[f2022])).
% 5.86/1.21 thf(f2025,plain,(
% 5.86/1.21 spl608_185 | spl608_186 | spl608_187),
% 5.86/1.21 inference(avatar_split_clause,[],[f1118,f2022,f2018,f2015])).
% 5.86/1.21 thf(f2035,definition,(
% 5.86/1.21 spl608_190 <=> ! [X1 : term] : ((((sK599 @ id @ X1 @ id)) = $false) | (((sK600 @ X1)) = $true))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_190])],[avatar_definition])).
% 5.86/1.21 thf(f2036,plain,(
% 5.86/1.21 ( ! [X1 : term] : ((((sK599 @ id @ X1 @ id)) = $false) | (((sK600 @ X1)) = $true)) ) | ~spl608_190),
% 5.86/1.21 inference(avatar_component_clause,[],[f2035])).
% 5.86/1.21 thf(f2037,plain,(
% 5.86/1.21 spl608_190 | spl608_186),
% 5.86/1.21 inference(avatar_split_clause,[],[f1129,f2018,f2035])).
% 5.86/1.21 thf(f2043,definition,(
% 5.86/1.21 spl608_192 <=> (((sK600 @ (lam @ sK607))) = $false)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_192])],[avatar_definition])).
% 5.86/1.21 thf(f2045,plain,(
% 5.86/1.21 (((sK600 @ (lam @ sK607))) = $false) | ~spl608_192),
% 5.86/1.21 inference(avatar_component_clause,[],[f2043])).
% 5.86/1.21 thf(f2046,plain,(
% 5.86/1.21 spl608_192 | spl608_186),
% 5.86/1.21 inference(avatar_split_clause,[],[f1133,f2018,f2043])).
% 5.86/1.21 thf(f2312,definition,(
% 5.86/1.21 spl608_252 <=> (hoasinduction_lem3v2a = $false)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_252])],[avatar_definition])).
% 5.86/1.21 thf(f2314,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a = $false) | ~spl608_252),
% 5.86/1.21 inference(avatar_component_clause,[],[f2312])).
% 5.86/1.21 thf(f2315,plain,(
% 5.86/1.21 spl608_172 | spl608_252),
% 5.86/1.21 inference(avatar_split_clause,[],[f1149,f2312,f1963])).
% 5.86/1.21 thf(f2317,definition,(
% 5.86/1.21 spl608_253 <=> (hoasinduction_lem3v2a = $true)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_253])],[avatar_definition])).
% 5.86/1.21 thf(f2319,plain,(
% 5.86/1.21 (hoasinduction_lem3v2a = $true) | ~spl608_253),
% 5.86/1.21 inference(avatar_component_clause,[],[f2317])).
% 5.86/1.21 thf(f3666,plain,(
% 5.86/1.21 spl608_253 | ~spl608_99),
% 5.86/1.21 inference(avatar_split_clause,[],[f786,f1659,f2317])).
% 5.86/1.21 thf(f3821,definition,(
% 5.86/1.21 spl608_597 <=> (shinj = $true)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_597])],[avatar_definition])).
% 5.86/1.21 thf(f3919,definition,(
% 5.86/1.21 spl608_620 <=> ! [X212 : term,X211 : term] : ((((sub @ X212 @ sh)) != ((sub @ X211 @ sh))) | (X211 = X212))),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_620])],[avatar_definition])).
% 5.86/1.21 thf(f3920,plain,(
% 5.86/1.21 ( ! [X212 : term,X211 : term] : ((X211 = X212) | (((sub @ X212 @ sh)) != ((sub @ X211 @ sh)))) ) | ~spl608_620),
% 5.86/1.21 inference(avatar_component_clause,[],[f3919])).
% 5.86/1.21 thf(f3921,plain,(
% 5.86/1.21 spl608_620 | ~spl608_597),
% 5.86/1.21 inference(avatar_split_clause,[],[f810,f3821,f3919])).
% 5.86/1.21 thf(f4009,definition,(
% 5.86/1.21 spl608_641 <=> (sK557 = sK558)),
% 5.86/1.21 introduced(definition,[new_symbols(definition,[spl608_641])],[avatar_definition])).
% 5.86/1.21 thf(f4011,plain,(
% 5.86/1.21 (sK557 != sK558) | spl608_641),
% 5.86/1.21 inference(avatar_component_clause,[],[f4009])).
% 5.86/1.21 thf(f4012,plain,(
% 5.86/1.21 spl608_597 | ~spl608_641),
% 5.86/1.21 inference(avatar_split_clause,[],[f811,f4009,f3821])).
% 5.86/1.21 thf(f4044,plain,(
% 5.86/1.21 ( ! [X0 : d_subst] : ((sh = ((d2subst @ X0)))) )),
% 5.86/1.21 inference(superposition,[],[f908,f910])).
% 5.86/1.21 thf(f4052,plain,(
% 5.86/1.21 ($true = $false) | (~spl608_172 | ~spl608_186)),
% 5.86/1.21 inference(superposition,[],[f2020,f1965])).
% 5.86/1.21 thf(f4055,plain,(
% 5.86/1.21 $false | (~spl608_172 | ~spl608_186)),
% 5.86/1.21 inference(trivial_inequality_removal,[],[f4052])).
% 5.86/1.21 thf(f4056,plain,(
% 5.86/1.21 ~spl608_172 | ~spl608_186),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f4055])).
% 5.86/1.21 thf(f4058,plain,(
% 5.86/1.21 (id = sh)),
% 5.86/1.21 inference(forward_demodulation,[],[f912,f908])).
% 5.86/1.21 thf(f4062,plain,(
% 5.86/1.21 ( ! [X0 : d_term] : ((((d2term @ X0)) = sF591)) )),
% 5.86/1.21 inference(superposition,[],[f983,f794])).
% 5.86/1.21 thf(f4075,plain,(
% 5.86/1.21 ( ! [X131 : subst] : ((sh = X131)) )),
% 5.86/1.21 inference(forward_demodulation,[],[f874,f4044])).
% 5.86/1.21 thf(f4085,plain,(
% 5.86/1.21 ( ! [X0 : term] : ((sF591 = X0)) )),
% 5.86/1.21 inference(forward_demodulation,[],[f974,f4062])).
% 5.86/1.21 thf(f4091,plain,(
% 5.86/1.21 (sK557 != sF591) | spl608_641),
% 5.86/1.21 inference(superposition,[],[f4011,f4085])).
% 5.86/1.21 thf(f4092,plain,(
% 5.86/1.21 $false | spl608_641),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f4091,f4085])).
% 5.86/1.21 thf(f4093,plain,(
% 5.86/1.21 spl608_641),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f4092])).
% 5.86/1.21 thf(f4095,plain,(
% 5.86/1.21 ( ! [X212 : term,X211 : term] : ((X211 = X212) | (((sub @ X212 @ sh)) != sF591)) ) | ~spl608_620),
% 5.86/1.21 inference(forward_demodulation,[],[f3920,f4085])).
% 5.86/1.21 thf(f4096,plain,(
% 5.86/1.21 ( ! [X212 : term,X211 : term] : ((X211 = X212)) ) | ~spl608_620),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f4095,f4085])).
% 5.86/1.21 thf(f4164,plain,(
% 5.86/1.21 ($false = ((sK600 @ sF591))) | ~spl608_192),
% 5.86/1.21 inference(forward_demodulation,[],[f2045,f4085])).
% 5.86/1.21 thf(f4165,plain,(
% 5.86/1.21 ( ! [X0 : term] : (($false = ((sK600 @ X0)))) ) | ~spl608_192),
% 5.86/1.21 inference(superposition,[],[f4164,f4085])).
% 5.86/1.21 thf(f4769,plain,(
% 5.86/1.21 ($true = ((sK599 @ sh @ sF591 @ sh))) | ~spl608_187),
% 5.86/1.21 inference(forward_demodulation,[],[f2024,f4058])).
% 5.86/1.21 thf(f4779,plain,(
% 5.86/1.21 ( ! [X0 : term] : (($true = ((sK599 @ sh @ X0 @ sh)))) ) | ~spl608_187),
% 5.86/1.21 inference(superposition,[],[f4769,f4085])).
% 5.86/1.21 thf(f4785,plain,(
% 5.86/1.21 ( ! [X0 : subst,X1 : term] : (($true = ((sK599 @ X0 @ X1 @ X0)))) ) | ~spl608_187),
% 5.86/1.21 inference(superposition,[],[f4779,f4075])).
% 5.86/1.21 thf(f5546,plain,(
% 5.86/1.21 ( ! [X1 : term] : (($true = $false) | (((sK600 @ X1)) = $true)) ) | (~spl608_187 | ~spl608_190)),
% 5.86/1.21 inference(forward_demodulation,[],[f2036,f4785])).
% 5.86/1.21 thf(f5547,plain,(
% 5.86/1.21 ( ! [X1 : term] : ((((sK600 @ X1)) = $true)) ) | (~spl608_187 | ~spl608_190)),
% 5.86/1.21 inference(trivial_inequality_removal,[],[f5546])).
% 5.86/1.21 thf(f5548,plain,(
% 5.86/1.21 ($true = $false) | (~spl608_187 | ~spl608_190 | ~spl608_192)),
% 5.86/1.21 inference(forward_demodulation,[],[f5547,f4165])).
% 5.86/1.21 thf(f5549,plain,(
% 5.86/1.21 $false | (~spl608_187 | ~spl608_190 | ~spl608_192)),
% 5.86/1.21 inference(trivial_inequality_removal,[],[f5548])).
% 5.86/1.21 thf(f5550,plain,(
% 5.86/1.21 ~spl608_187 | ~spl608_190 | ~spl608_192),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f5549])).
% 5.86/1.21 thf(f5552,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : ((((sK599 @ id @ (sK602 @ X1) @ id)) = $true)) ) | (~spl608_185 | ~spl608_620)),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f2016,f4096])).
% 5.86/1.21 thf(f5554,plain,(
% 5.86/1.21 ($true != ((sK599 @ sh @ sF591 @ sh))) | spl608_187),
% 5.86/1.21 inference(forward_demodulation,[],[f2023,f4058])).
% 5.86/1.21 thf(f5556,plain,(
% 5.86/1.21 ( ! [X1 : (subst > term > term)] : (($true = ((sK599 @ sh @ (sK602 @ X1) @ sh)))) ) | (~spl608_185 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5552,f4058])).
% 5.86/1.21 thf(f5560,plain,(
% 5.86/1.21 ($true = ((sK599 @ sh @ sF591 @ sh))) | (~spl608_185 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5556,f4085])).
% 5.86/1.21 thf(f5576,plain,(
% 5.86/1.21 $false | (~spl608_185 | spl608_187 | ~spl608_620)),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f5560,f5554])).
% 5.86/1.21 thf(f5577,plain,(
% 5.86/1.21 ~spl608_185 | spl608_187 | ~spl608_620),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f5576])).
% 5.86/1.21 thf(f5637,plain,(
% 5.86/1.21 ($true = $false) | (~spl608_252 | ~spl608_253)),
% 5.86/1.21 inference(superposition,[],[f2314,f2319])).
% 5.86/1.21 thf(f5641,plain,(
% 5.86/1.21 $false | (~spl608_252 | ~spl608_253)),
% 5.86/1.21 inference(trivial_inequality_removal,[],[f5637])).
% 5.86/1.21 thf(f5642,plain,(
% 5.86/1.21 ~spl608_252 | ~spl608_253),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f5641])).
% 5.86/1.21 thf(f5644,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : (($true = ((sK387 @ id @ (sK391 @ X3) @ id))) | ($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f1724,f4096])).
% 5.86/1.21 thf(f5647,plain,(
% 5.86/1.21 ($true != ((sK385 @ sF591))) | spl608_113),
% 5.86/1.21 inference(forward_demodulation,[],[f1720,f4085])).
% 5.86/1.21 thf(f5648,plain,(
% 5.86/1.21 ( ! [X8 : term] : (($true = ((sK385 @ X8))) | (((sK387 @ sh @ X8 @ sh)) = $false)) ) | ~spl608_138),
% 5.86/1.21 inference(forward_demodulation,[],[f1823,f4058])).
% 5.86/1.21 thf(f5650,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : (($true = ((sK387 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = ((sK387 @ sh @ (sK391 @ X3) @ sh)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5644,f4058])).
% 5.86/1.21 thf(f5652,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : (($true = ((sK387 @ sh @ (lam @ (X3 @ sh @ one)) @ sh))) | ($true = ((sK387 @ sh @ (sK391 @ X3) @ sh)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5650,f4058])).
% 5.86/1.21 thf(f5654,plain,(
% 5.86/1.21 ( ! [X3 : (subst > term > term)] : ((((sK387 @ sh @ sF591 @ sh)) = $true) | ($true = ((sK387 @ sh @ (sK391 @ X3) @ sh)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5652,f4085])).
% 5.86/1.21 thf(f5656,plain,(
% 5.86/1.21 (((sK387 @ sh @ sF591 @ sh)) = $true) | (((sK387 @ sh @ sF591 @ sh)) = $true) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5654,f4085])).
% 5.86/1.21 thf(f5657,plain,(
% 5.86/1.21 (((sK387 @ sh @ sF591 @ sh)) = $true) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(duplicate_literal_removal,[],[f5656])).
% 5.86/1.21 thf(f5660,plain,(
% 5.86/1.21 ( ! [X0 : term] : (($true != ((sK385 @ X0)))) ) | spl608_113),
% 5.86/1.21 inference(superposition,[],[f5647,f4085])).
% 5.86/1.21 thf(f5663,plain,(
% 5.86/1.21 ( ! [X0 : term] : (($true = ((sK387 @ sh @ X0 @ sh)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(superposition,[],[f5657,f4085])).
% 5.86/1.21 thf(f5683,plain,(
% 5.86/1.21 ( ! [X0 : subst,X1 : term] : (($true = ((sK387 @ X0 @ X1 @ X0)))) ) | (~spl608_114 | ~spl608_620)),
% 5.86/1.21 inference(superposition,[],[f5663,f4075])).
% 5.86/1.21 thf(f5800,plain,(
% 5.86/1.21 ( ! [X8 : term] : ((((sK387 @ sh @ X8 @ sh)) = $false)) ) | (spl608_113 | ~spl608_138)),
% 5.86/1.21 inference(forward_subsumption_resolution,[],[f5648,f5660])).
% 5.86/1.21 thf(f5801,plain,(
% 5.86/1.21 ($true = $false) | (spl608_113 | ~spl608_114 | ~spl608_138 | ~spl608_620)),
% 5.86/1.21 inference(forward_demodulation,[],[f5800,f5683])).
% 5.86/1.21 thf(f5802,plain,(
% 5.86/1.21 $false | (spl608_113 | ~spl608_114 | ~spl608_138 | ~spl608_620)),
% 5.86/1.21 inference(trivial_inequality_removal,[],[f5801])).
% 5.86/1.21 thf(f5803,plain,(
% 5.86/1.21 spl608_113 | ~spl608_114 | ~spl608_138 | ~spl608_620),
% 5.86/1.21 inference(avatar_contradiction_clause,[],[f5802])).
% 5.86/1.21 cnf(s68, plain, spl608_99 | ~spl608_113, inference(sat_conversion,[],[f1721])).
% 5.86/1.21 cnf(s69, plain, spl608_99 | spl608_114, inference(sat_conversion,[],[f1725])).
% 5.86/1.21 cnf(s87, plain, spl608_99 | spl608_138, inference(sat_conversion,[],[f1824])).
% 5.86/1.21 cnf(s125, plain, spl608_185 | spl608_186 | spl608_187, inference(sat_conversion,[],[f2025])).
% 5.86/1.21 cnf(s128, plain, spl608_186 | spl608_190, inference(sat_conversion,[],[f2037])).
% 5.86/1.21 cnf(s130, plain, spl608_186 | spl608_192, inference(sat_conversion,[],[f2046])).
% 5.86/1.21 cnf(s191, plain, spl608_172 | spl608_252, inference(sat_conversion,[],[f2315])).
% 5.86/1.21 cnf(s523, plain, ~spl608_99 | spl608_253, inference(sat_conversion,[],[f3666])).
% 5.86/1.21 cnf(s589, plain, ~spl608_597 | spl608_620, inference(sat_conversion,[],[f3921])).
% 5.86/1.21 cnf(s614, plain, spl608_597 | ~spl608_641, inference(sat_conversion,[],[f4012])).
% 5.86/1.21 cnf(s624, plain, ~spl608_172 | ~spl608_186, inference(sat_conversion,[],[f4056])).
% 5.86/1.21 cnf(s625, plain, spl608_641, inference(sat_conversion,[],[f4093])).
% 5.86/1.21 cnf(s740, plain, ~spl608_187 | ~spl608_190 | ~spl608_192, inference(sat_conversion,[],[f5550])).
% 5.86/1.21 cnf(s741, plain, ~spl608_185 | spl608_187 | ~spl608_620, inference(sat_conversion,[],[f5577])).
% 5.86/1.21 cnf(s747, plain, ~spl608_252 | ~spl608_253, inference(sat_conversion,[],[f5642])).
% 5.86/1.21 cnf(s748, plain, spl608_113 | ~spl608_114 | ~spl608_138 | ~spl608_620, inference(sat_conversion,[],[f5803])).
% 5.86/1.21 cnf(s752, plain, spl608_597, inference(rat,[],[s614,s625])).
% 5.86/1.21 cnf(s753, plain, spl608_620, inference(rat,[],[s589,s752])).
% 5.86/1.21 cnf(s866, plain, spl608_99, inference(rat,[],[s748,s68,s69,s87,s753])).
% 5.86/1.21 cnf(s867, plain, spl608_253, inference(rat,[],[s523,s866])).
% 5.86/1.21 cnf(s880, plain, ~spl608_252, inference(rat,[],[s747,s867])).
% 5.86/1.21 cnf(s881, plain, spl608_172, inference(rat,[],[s191,s880])).
% 5.86/1.21 cnf(s882, plain, ~spl608_186, inference(rat,[],[s624,s881])).
% 5.86/1.21 cnf(s883, plain, spl608_192, inference(rat,[],[s130,s882])).
% 5.86/1.21 cnf(s885, plain, spl608_190, inference(rat,[],[s128,s882])).
% 5.86/1.21 cnf(s887, plain, ~spl608_187, inference(rat,[],[s740,s883,s885])).
% 5.86/1.21 cnf(s888, plain, ~spl608_185, inference(rat,[],[s741,s753,s887])).
% 5.86/1.21 cnf(s890, plain, $false, inference(rat,[],[s125,s882,s887,s888])).
% 5.86/1.21 thf(f5804,plain,(
% 5.86/1.21 $false),
% 5.86/1.21 inference(avatar_sat_refutation,[],[s890])).
% 5.86/1.21 % SZS output end Proof for theBenchmark
% 5.86/1.21 % (519341)------------------------------
% 5.86/1.21 % (519341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.21 % (519341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.21 % (519341)CaDiCaL version: 2.1.3
% 5.86/1.21 % (519341)Termination reason: Refutation
% 5.86/1.21 % (519341)Time elapsed: 0.260 s
% 5.86/1.21 % (519341)Peak memory usage: 18 MB
% 5.86/1.21 % (519341)Instructions burned: 560 (million)
% 5.86/1.21 % (519211)Success in time 0.932 s
% 5.86/1.21 % Vampire exiting
%------------------------------------------------------------------------------