%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX169^1 : 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 : n026.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 08:40:38 AM UTC 2026
% Result : Theorem 37.84s 5.79s
% Output : Refutation 39.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX169^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:12:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.39 % (794510)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.76/0.39 % (794519)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1224413732:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.76/0.39 % (794521)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.76/0.39 % (794521)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.76/0.39 % (794519)Instruction limit reached!
% 0.76/0.39 % (794519)------------------------------
% 0.76/0.39 % (794519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (794519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (794519)CaDiCaL version: 2.1.3
% 0.76/0.39 % (794519)Termination reason: Instruction limit
% 0.76/0.39 % (794519)Termination phase: shuffling
% 0.76/0.39 % (794519)Time elapsed: 0.005 s
% 0.76/0.39 % (794519)Peak memory usage: 10 MB
% 0.76/0.39 % (794519)Instructions burned: 24 (million)
% 0.76/0.39 % (794515)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1122629819:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.76/0.39 % (794516)lrs+10_16_si=on:nwc=1.5:random_seed=1224548774:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.76/0.39 % (794517)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3428723641:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.76/0.39 % (794518)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=2354775718:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.76/0.39 % (794520)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2481297789:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.76/0.39 % (794521)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=3712763171:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.76/0.39 % (794517)Instruction limit reached!
% 0.76/0.39 % (794517)------------------------------
% 0.76/0.39 % (794517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (794517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (794517)CaDiCaL version: 2.1.3
% 0.76/0.39 % (794517)Termination reason: Instruction limit
% 0.76/0.39 % (794517)Termination phase: shuffling
% 0.76/0.39 % (794517)Time elapsed: 0.002 s
% 0.76/0.39 % (794517)Peak memory usage: 9 MB
% 0.76/0.39 % (794517)Instructions burned: 5 (million)
% 0.76/0.39 % (794523)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2652799779:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.39 % (794516)Instruction limit reached!
% 0.76/0.39 % (794516)------------------------------
% 0.76/0.39 % (794516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (794516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (794516)CaDiCaL version: 2.1.3
% 0.76/0.39 % (794516)Termination reason: Instruction limit
% 0.76/0.39 % (794516)Termination phase: shuffling
% 0.76/0.39 % (794516)Time elapsed: 0.009 s
% 0.76/0.39 % (794516)Peak memory usage: 10 MB
% 0.76/0.39 % (794516)Instructions burned: 20 (million)
% 0.76/0.39 % (794523)Instruction limit reached!
% 0.76/0.39 % (794523)------------------------------
% 0.76/0.39 % (794523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (794523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (794523)CaDiCaL version: 2.1.3
% 0.76/0.39 % (794523)Termination reason: Instruction limit
% 0.76/0.39 % (794523)Termination phase: shuffling
% 0.76/0.39 % (794523)Time elapsed: 0.001 s
% 0.76/0.39 % (794523)Peak memory usage: 9 MB
% 0.76/0.39 % (794523)Instructions burned: 6 (million)
% 0.76/0.39 % (794533)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2107287100:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.76/0.39 % (794530)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=964979797:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.76/0.42 % (794533)Instruction limit reached!
% 0.76/0.42 % (794533)------------------------------
% 0.76/0.42 % (794533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.42 % (794533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.42 % (794533)CaDiCaL version: 2.1.3
% 0.76/0.42 % (794533)Termination reason: Instruction limit
% 0.76/0.42 % (794533)Termination phase: shuffling
% 0.76/0.42 % (794533)Time elapsed: 0.004 s
% 0.76/0.42 % (794533)Peak memory usage: 10 MB
% 0.76/0.42 % (794533)Instructions burned: 15 (million)
% 0.76/0.42 % (794530)Instruction limit reached!
% 0.76/0.42 % (794530)------------------------------
% 0.76/0.42 % (794530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.42 % (794530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.42 % (794530)CaDiCaL version: 2.1.3
% 0.76/0.42 % (794530)Termination reason: Instruction limit
% 0.76/0.42 % (794530)Termination phase: shuffling
% 0.76/0.42 % (794530)Time elapsed: 0.003 s
% 0.76/0.42 % (794530)Peak memory usage: 10 MB
% 0.76/0.42 % (794530)Instructions burned: 5 (million)
% 0.76/0.42 % (794532)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.42 % (794536)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.76/0.42 % (794536)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.42 % (794520)Instruction limit reached!
% 0.76/0.42 % (794520)------------------------------
% 0.76/0.42 % (794520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.42 % (794520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.42 % (794520)CaDiCaL version: 2.1.3
% 0.76/0.42 % (794520)Termination reason: Instruction limit
% 0.76/0.42 % (794520)Termination phase: Preprocessing 3
% 0.76/0.42 % (794520)Time elapsed: 0.035 s
% 0.76/0.42 % (794520)Peak memory usage: 12 MB
% 0.76/0.42 % (794520)Instructions burned: 76 (million)
% 0.76/0.42 % (794536)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=667854351:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.76/0.42 % (794532)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3482553819:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.76/0.42 % (794515)Instruction limit reached!
% 0.76/0.42 % (794515)------------------------------
% 0.76/0.42 % (794515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.42 % (794515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.42 % (794515)CaDiCaL version: 2.1.3
% 0.76/0.42 % (794515)Termination reason: Instruction limit
% 0.76/0.42 % (794515)Termination phase: Preprocessing 3
% 0.76/0.42 % (794515)Time elapsed: 0.042 s
% 0.76/0.42 % (794515)Peak memory usage: 12 MB
% 0.76/0.43 % (794515)Instructions burned: 90 (million)
% 0.76/0.43 % (794536)Instruction limit reached!
% 0.76/0.43 % (794536)------------------------------
% 0.76/0.43 % (794536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.43 % (794536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.43 % (794536)CaDiCaL version: 2.1.3
% 0.76/0.43 % (794536)Termination reason: Instruction limit
% 0.76/0.43 % (794536)Termination phase: shuffling
% 0.76/0.43 % (794536)Time elapsed: 0.007 s
% 0.76/0.43 % (794536)Peak memory usage: 10 MB
% 0.76/0.43 % (794536)Instructions burned: 31 (million)
% 0.76/0.43 % (794537)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=4267963197:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.76/0.43 % (794532)Instruction limit reached!
% 0.76/0.43 % (794532)------------------------------
% 0.76/0.43 % (794532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.43 % (794532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794532)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794532)Termination reason: Instruction limit
% 0.76/0.47 % (794532)Termination phase: shuffling
% 0.76/0.47 % (794532)Time elapsed: 0.004 s
% 0.76/0.47 % (794532)Peak memory usage: 10 MB
% 0.76/0.47 % (794532)Instructions burned: 7 (million)
% 0.76/0.47 % (794542)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1365924289:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.76/0.47 % (794540)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.76/0.47 % (794539)lrs+10_1_si=on:cs=on:random_seed=42429747:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.76/0.47 % (794540)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=3830069606:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.47 % (794539)Instruction limit reached!
% 0.76/0.47 % (794539)------------------------------
% 0.76/0.47 % (794539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794539)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794539)Termination reason: Instruction limit
% 0.76/0.47 % (794539)Termination phase: shuffling
% 0.76/0.47 % (794539)Time elapsed: 0.004 s
% 0.76/0.47 % (794539)Peak memory usage: 10 MB
% 0.76/0.47 % (794539)Instructions burned: 8 (million)
% 0.76/0.47 % (794540)Instruction limit reached!
% 0.76/0.47 % (794540)------------------------------
% 0.76/0.47 % (794540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794540)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794540)Termination reason: Instruction limit
% 0.76/0.47 % (794540)Termination phase: shuffling
% 0.76/0.47 % (794540)Time elapsed: 0.002 s
% 0.76/0.47 % (794540)Peak memory usage: 10 MB
% 0.76/0.47 % (794540)Instructions burned: 4 (million)
% 0.76/0.47 % (794542)Instruction limit reached!
% 0.76/0.47 % (794542)------------------------------
% 0.76/0.47 % (794542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794542)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794542)Termination reason: Instruction limit
% 0.76/0.47 % (794542)Termination phase: Property scanning
% 0.76/0.47 % (794542)Time elapsed: 0.009 s
% 0.76/0.47 % (794542)Peak memory usage: 11 MB
% 0.76/0.47 % (794542)Instructions burned: 41 (million)
% 0.76/0.47 % (794521)Instruction limit reached!
% 0.76/0.47 % (794521)------------------------------
% 0.76/0.47 % (794521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794521)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794521)Termination reason: Instruction limit
% 0.76/0.47 % (794521)Termination phase: Property scanning
% 0.76/0.47 % (794521)Time elapsed: 0.070 s
% 0.76/0.47 % (794521)Peak memory usage: 13 MB
% 0.76/0.47 % (794521)Instructions burned: 159 (million)
% 0.76/0.47 % (794549)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2641681628:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.76/0.47 % (794544)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2250554134:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.76/0.47 % (794549)Instruction limit reached!
% 0.76/0.47 % (794549)------------------------------
% 0.76/0.47 % (794549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (794549)CaDiCaL version: 2.1.3
% 0.76/0.47 % (794549)Termination reason: Instruction limit
% 0.76/0.47 % (794549)Termination phase: shuffling
% 0.76/0.47 % (794549)Time elapsed: 0.004 s
% 0.76/0.47 % (794549)Peak memory usage: 10 MB
% 0.76/0.47 % (794549)Instructions burned: 18 (million)
% 0.76/0.47 % (794537)Instruction limit reached!
% 0.76/0.47 % (794537)------------------------------
% 0.76/0.47 % (794537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (794537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794537)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794537)Termination reason: Instruction limit
% 1.44/0.53 % (794537)Termination phase: Saturation
% 1.44/0.53 % (794537)Time elapsed: 0.037 s
% 1.44/0.53 % (794537)Peak memory usage: 12 MB
% 1.44/0.53 % (794537)Instructions burned: 88 (million)
% 1.44/0.53 % (794548)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1466515956:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.44/0.53 % (794554)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3299925864: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)
% 1.44/0.53 % (794551)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2231481974:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.53 % (794550)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4275585839:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.44/0.53 % (794554)Instruction limit reached!
% 1.44/0.53 % (794554)------------------------------
% 1.44/0.53 % (794554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (794554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794554)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794554)Termination reason: Instruction limit
% 1.44/0.53 % (794554)Termination phase: shuffling
% 1.44/0.53 % (794554)Time elapsed: 0.003 s
% 1.44/0.53 % (794554)Peak memory usage: 10 MB
% 1.44/0.53 % (794554)Instructions burned: 12 (million)
% 1.44/0.53 % (794548)Instruction limit reached!
% 1.44/0.53 % (794548)------------------------------
% 1.44/0.53 % (794548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (794548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794548)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794548)Termination reason: Instruction limit
% 1.44/0.53 % (794548)Termination phase: Property scanning
% 1.44/0.53 % (794548)Time elapsed: 0.011 s
% 1.44/0.53 % (794548)Peak memory usage: 10 MB
% 1.44/0.53 % (794548)Instructions burned: 25 (million)
% 1.44/0.53 % (794551)Instruction limit reached!
% 1.44/0.53 % (794551)------------------------------
% 1.44/0.53 % (794551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (794551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794551)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794551)Termination reason: Instruction limit
% 1.44/0.53 % (794551)Termination phase: shuffling
% 1.44/0.53 % (794551)Time elapsed: 0.006 s
% 1.44/0.53 % (794551)Peak memory usage: 10 MB
% 1.44/0.53 % (794551)Instructions burned: 15 (million)
% 1.44/0.53 % (794555)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3985523259:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.44/0.53 % (794560)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1600207507:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.53 % (794560)Instruction limit reached!
% 1.44/0.53 % (794560)------------------------------
% 1.44/0.53 % (794560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (794560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794560)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794560)Termination reason: Instruction limit
% 1.44/0.53 % (794560)Termination phase: Property scanning
% 1.44/0.53 % (794560)Time elapsed: 0.006 s
% 1.44/0.53 % (794560)Peak memory usage: 10 MB
% 1.44/0.53 % (794560)Instructions burned: 27 (million)
% 1.44/0.53 % (794563)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
% 1.44/0.53 % (794563)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.44/0.53 % (794555)Instruction limit reached!
% 1.44/0.53 % (794555)------------------------------
% 1.44/0.53 % (794555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (794555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (794555)CaDiCaL version: 2.1.3
% 1.44/0.53 % (794555)Termination reason: Instruction limit
% 2.03/0.59 % (794555)Termination phase: shuffling
% 2.03/0.59 % (794555)Time elapsed: 0.012 s
% 2.03/0.59 % (794555)Peak memory usage: 10 MB
% 2.03/0.59 % (794555)Instructions burned: 26 (million)
% 2.03/0.59 % (794562)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=82822641:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.03/0.59 % (794563)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=1627584251:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.03/0.59 % (794563)Instruction limit reached!
% 2.03/0.59 % (794563)------------------------------
% 2.03/0.59 % (794563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (794563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (794563)CaDiCaL version: 2.1.3
% 2.03/0.59 % (794563)Termination reason: Instruction limit
% 2.03/0.59 % (794563)Termination phase: shuffling
% 2.03/0.59 % (794563)Time elapsed: 0.006 s
% 2.03/0.59 % (794563)Peak memory usage: 10 MB
% 2.03/0.59 % (794563)Instructions burned: 14 (million)
% 2.03/0.59 % (794570)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.03/0.59 % (794570)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=3687250700:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.03/0.59 % (794573)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=612256554:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.03/0.59 % (794570)Instruction limit reached!
% 2.03/0.59 % (794570)------------------------------
% 2.03/0.59 % (794570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (794570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (794570)CaDiCaL version: 2.1.3
% 2.03/0.59 % (794570)Termination reason: Instruction limit
% 2.03/0.59 % (794570)Termination phase: shuffling
% 2.03/0.59 % (794570)Time elapsed: 0.004 s
% 2.03/0.59 % (794570)Peak memory usage: 9 MB
% 2.03/0.59 % (794570)Instructions burned: 9 (million)
% 2.03/0.59 % (794579)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=549530772:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.03/0.59 % (794562)Instruction limit reached!
% 2.03/0.59 % (794562)------------------------------
% 2.03/0.59 % (794562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (794562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (794562)CaDiCaL version: 2.1.3
% 2.03/0.59 % (794562)Termination reason: Instruction limit
% 2.03/0.59 % (794562)Termination phase: Preprocessing 3
% 2.03/0.59 % (794562)Time elapsed: 0.027 s
% 2.03/0.59 % (794562)Peak memory usage: 11 MB
% 2.03/0.59 % (794562)Instructions burned: 60 (million)
% 2.03/0.59 % (794573)Instruction limit reached!
% 2.03/0.59 % (794573)------------------------------
% 2.03/0.59 % (794573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (794573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (794573)CaDiCaL version: 2.1.3
% 2.03/0.59 % (794573)Termination reason: Instruction limit
% 2.03/0.59 % (794573)Termination phase: Property scanning
% 2.03/0.59 % (794573)Time elapsed: 0.015 s
% 2.03/0.59 % (794573)Peak memory usage: 10 MB
% 2.03/0.59 % (794573)Instructions burned: 35 (million)
% 2.03/0.59 % (794579)Instruction limit reached!
% 2.03/0.59 % (794579)------------------------------
% 2.03/0.59 % (794579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.59 % (794579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.59 % (794579)CaDiCaL version: 2.1.3
% 2.03/0.59 % (794579)Termination reason: Instruction limit
% 2.03/0.59 % (794579)Termination phase: shuffling
% 2.03/0.59 % (794579)Time elapsed: 0.006 s
% 2.03/0.59 % (794579)Peak memory usage: 10 MB
% 2.03/0.59 % (794579)Instructions burned: 13 (million)
% 2.03/0.59 % (794586)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3403546395:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.03/0.59 % (794589)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=688673303:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.36/0.66 % (794589)Instruction limit reached!
% 2.36/0.66 % (794589)------------------------------
% 2.36/0.66 % (794589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794589)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794589)Termination reason: Instruction limit
% 2.36/0.66 % (794589)Termination phase: shuffling
% 2.36/0.66 % (794589)Time elapsed: 0.005 s
% 2.36/0.66 % (794589)Peak memory usage: 10 MB
% 2.36/0.66 % (794589)Instructions burned: 21 (million)
% 2.36/0.66 % (794586)Instruction limit reached!
% 2.36/0.66 % (794586)------------------------------
% 2.36/0.66 % (794586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794586)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794586)Termination reason: Instruction limit
% 2.36/0.66 % (794586)Termination phase: shuffling
% 2.36/0.66 % (794586)Time elapsed: 0.010 s
% 2.36/0.66 % (794586)Peak memory usage: 10 MB
% 2.36/0.66 % (794586)Instructions burned: 23 (million)
% 2.36/0.66 % (794592)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1961159779:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.36/0.66 % (794593)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2618656669:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.36/0.66 % (794599)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1928029180:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.36/0.66 % (794601)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2826793602:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.36/0.66 % (794544)Instruction limit reached!
% 2.36/0.66 % (794544)------------------------------
% 2.36/0.66 % (794544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794544)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794544)Termination reason: Instruction limit
% 2.36/0.66 % (794544)Termination phase: Saturation
% 2.36/0.66 % (794544)Time elapsed: 0.112 s
% 2.36/0.66 % (794544)Peak memory usage: 15 MB
% 2.36/0.66 % (794544)Instructions burned: 250 (million)
% 2.36/0.66 % (794601)Instruction limit reached!
% 2.36/0.66 % (794601)------------------------------
% 2.36/0.66 % (794601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794601)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794601)Termination reason: Instruction limit
% 2.36/0.66 % (794601)Termination phase: shuffling
% 2.36/0.66 % (794601)Time elapsed: 0.018 s
% 2.36/0.66 % (794601)Peak memory usage: 11 MB
% 2.36/0.66 % (794601)Instructions burned: 42 (million)
% 2.36/0.66 % (794617)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.36/0.66 % (794617)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2030747436:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.36/0.66 % (794617)Instruction limit reached!
% 2.36/0.66 % (794617)------------------------------
% 2.36/0.66 % (794617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794617)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794617)Termination reason: Instruction limit
% 2.36/0.66 % (794617)Termination phase: shuffling
% 2.36/0.66 % (794617)Time elapsed: 0.004 s
% 2.36/0.66 % (794617)Peak memory usage: 10 MB
% 2.36/0.66 % (794617)Instructions burned: 8 (million)
% 2.36/0.66 % (794599)Instruction limit reached!
% 2.36/0.66 % (794599)------------------------------
% 2.36/0.66 % (794599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.36/0.66 % (794599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/0.66 % (794599)CaDiCaL version: 2.1.3
% 2.36/0.66 % (794599)Termination reason: Instruction limit
% 2.36/0.66 % (794599)Termination phase: Property scanning
% 2.36/0.66 % (794599)Time elapsed: 0.045 s
% 2.56/0.75 % (794599)Peak memory usage: 13 MB
% 2.56/0.75 % (794599)Instructions burned: 195 (million)
% 2.56/0.75 % (794622)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1539053641:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.56/0.75 % (794631)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=1850628960: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)
% 2.56/0.75 % (794633)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.56/0.75 % (794593)Instruction limit reached!
% 2.56/0.75 % (794593)------------------------------
% 2.56/0.75 % (794593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.75 % (794593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.75 % (794593)CaDiCaL version: 2.1.3
% 2.56/0.75 % (794593)Termination reason: Instruction limit
% 2.56/0.75 % (794593)Termination phase: Function definition elimination
% 2.56/0.75 % (794593)Time elapsed: 0.064 s
% 2.56/0.75 % (794593)Peak memory usage: 13 MB
% 2.56/0.75 % (794593)Instructions burned: 145 (million)
% 2.56/0.75 % (794633)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=929699712:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.56/0.75 % (794633)Instruction limit reached!
% 2.56/0.75 % (794633)------------------------------
% 2.56/0.75 % (794633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.75 % (794633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.75 % (794633)CaDiCaL version: 2.1.3
% 2.56/0.75 % (794633)Termination reason: Instruction limit
% 2.56/0.75 % (794633)Termination phase: shuffling
% 2.56/0.75 % (794633)Time elapsed: 0.004 s
% 2.56/0.75 % (794633)Peak memory usage: 9 MB
% 2.56/0.75 % (794633)Instructions burned: 8 (million)
% 2.56/0.75 % (794550)Instruction limit reached!
% 2.56/0.75 % (794550)------------------------------
% 2.56/0.75 % (794550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.75 % (794550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.75 % (794550)CaDiCaL version: 2.1.3
% 2.56/0.75 % (794550)Termination reason: Instruction limit
% 2.56/0.75 % (794550)Termination phase: Saturation
% 2.56/0.75 % (794550)Time elapsed: 0.151 s
% 2.56/0.75 % (794550)Peak memory usage: 16 MB
% 2.56/0.75 % (794550)Instructions burned: 327 (million)
% 2.56/0.75 % (794645)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1376714688:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.56/0.75 % (794653)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4128194259:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.56/0.75 % (794655)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=4132550285:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.56/0.75 % (794645)Instruction limit reached!
% 2.56/0.75 % (794645)------------------------------
% 2.56/0.75 % (794645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.75 % (794645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.75 % (794645)CaDiCaL version: 2.1.3
% 2.56/0.75 % (794645)Termination reason: Instruction limit
% 2.56/0.75 % (794645)Termination phase: shuffling
% 2.56/0.75 % (794645)Time elapsed: 0.010 s
% 2.56/0.75 % (794645)Peak memory usage: 10 MB
% 2.56/0.75 % (794645)Instructions burned: 23 (million)
% 2.56/0.75 % (794653)Instruction limit reached!
% 2.56/0.75 % (794653)------------------------------
% 2.56/0.75 % (794653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.75 % (794653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.75 % (794653)CaDiCaL version: 2.1.3
% 2.56/0.75 % (794653)Termination reason: Instruction limit
% 2.56/0.75 % (794653)Termination phase: shuffling
% 2.56/0.75 % (794653)Time elapsed: 0.008 s
% 2.56/0.75 % (794653)Peak memory usage: 10 MB
% 2.56/0.75 % (794653)Instructions burned: 19 (million)
% 2.56/0.75 % (794631)Instruction limit reached!
% 2.56/0.75 % (794631)------------------------------
% 3.29/0.85 % (794631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.29/0.85 % (794631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.85 % (794631)CaDiCaL version: 2.1.3
% 3.29/0.85 % (794631)Termination reason: Instruction limit
% 3.29/0.85 % (794631)Termination phase: Property scanning
% 3.29/0.85 % (794631)Time elapsed: 0.046 s
% 3.29/0.85 % (794631)Peak memory usage: 13 MB
% 3.29/0.85 % (794631)Instructions burned: 170 (million)
% 3.29/0.85 % (794665)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=4114873259: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)
% 3.29/0.85 % (794666)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=4212239881: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)
% 3.29/0.85 % (794668)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=345915466:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.29/0.85 % (794622)Instruction limit reached!
% 3.29/0.85 % (794622)------------------------------
% 3.29/0.85 % (794622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.29/0.85 % (794622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.85 % (794622)CaDiCaL version: 2.1.3
% 3.29/0.85 % (794622)Termination reason: Instruction limit
% 3.29/0.85 % (794622)Termination phase: Saturation
% 3.29/0.85 % (794622)Time elapsed: 0.085 s
% 3.29/0.85 % (794622)Peak memory usage: 13 MB
% 3.29/0.85 % (794622)Instructions burned: 182 (million)
% 3.29/0.85 % (794666)Instruction limit reached!
% 3.29/0.85 % (794666)------------------------------
% 3.29/0.85 % (794666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.29/0.85 % (794666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.85 % (794666)CaDiCaL version: 2.1.3
% 3.29/0.85 % (794666)Termination reason: Instruction limit
% 3.29/0.85 % (794666)Termination phase: SInE selection
% 3.29/0.85 % (794666)Time elapsed: 0.019 s
% 3.29/0.85 % (794666)Peak memory usage: 11 MB
% 3.29/0.85 % (794666)Instructions burned: 46 (million)
% 3.29/0.85 % (794684)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3977965353: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)
% 3.29/0.85 % (794518)Instruction limit reached!
% 3.29/0.85 % (794518)------------------------------
% 3.29/0.85 % (794518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.29/0.85 % (794518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.85 % (794518)CaDiCaL version: 2.1.3
% 3.29/0.85 % (794518)Termination reason: Instruction limit
% 3.29/0.85 % (794518)Termination phase: Saturation
% 3.29/0.85 % (794518)Time elapsed: 0.329 s
% 3.29/0.85 % (794518)Peak memory usage: 19 MB
% 3.29/0.85 % (794518)Instructions burned: 634 (million)
% 3.29/0.85 % (794686)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.29/0.85 % (794684)Instruction limit reached!
% 3.29/0.85 % (794684)------------------------------
% 3.29/0.85 % (794684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.29/0.85 % (794684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.85 % (794684)CaDiCaL version: 2.1.3
% 3.29/0.85 % (794684)Termination reason: Instruction limit
% 3.29/0.85 % (794684)Termination phase: shuffling
% 3.29/0.85 % (794684)Time elapsed: 0.009 s
% 3.29/0.85 % (794684)Peak memory usage: 10 MB
% 3.29/0.85 % (794684)Instructions burned: 22 (million)
% 3.29/0.85 % (794686)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1154214428:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.29/0.85 % (794691)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2652234624:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.29/0.85 % (794692)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=438080096:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.16/1.07 % (794691)Instruction limit reached!
% 4.16/1.07 % (794691)------------------------------
% 4.16/1.07 % (794691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794691)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794691)Termination reason: Instruction limit
% 4.16/1.07 % (794691)Termination phase: shuffling
% 4.16/1.07 % (794691)Time elapsed: 0.006 s
% 4.16/1.07 % (794691)Peak memory usage: 10 MB
% 4.16/1.07 % (794691)Instructions burned: 14 (million)
% 4.16/1.07 % (794696)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3200795849:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 4.16/1.07 % (794692)Instruction limit reached!
% 4.16/1.07 % (794692)------------------------------
% 4.16/1.07 % (794692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794692)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794692)Termination reason: Instruction limit
% 4.16/1.07 % (794692)Termination phase: SInE selection
% 4.16/1.07 % (794692)Time elapsed: 0.033 s
% 4.16/1.07 % (794692)Peak memory usage: 11 MB
% 4.16/1.07 % (794692)Instructions burned: 66 (million)
% 4.16/1.07 % (794711)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3699294348:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 4.16/1.07 % (794696)Instruction limit reached!
% 4.16/1.07 % (794696)------------------------------
% 4.16/1.07 % (794696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794696)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794696)Termination reason: Instruction limit
% 4.16/1.07 % (794696)Termination phase: Preprocessing 3
% 4.16/1.07 % (794696)Time elapsed: 0.030 s
% 4.16/1.07 % (794696)Peak memory usage: 11 MB
% 4.16/1.07 % (794696)Instructions burned: 59 (million)
% 4.16/1.07 % (794711)Instruction limit reached!
% 4.16/1.07 % (794711)------------------------------
% 4.16/1.07 % (794711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794711)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794711)Termination reason: Instruction limit
% 4.16/1.07 % (794711)Termination phase: Property scanning
% 4.16/1.07 % (794711)Time elapsed: 0.014 s
% 4.16/1.07 % (794711)Peak memory usage: 10 MB
% 4.16/1.07 % (794711)Instructions burned: 32 (million)
% 4.16/1.07 % (794716)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2746574875:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.16/1.07 % (794668)Refutation not found, incomplete strategy
% 4.16/1.07 % (794668)------------------------------
% 4.16/1.07 % (794668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794668)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794668)Termination reason: Refutation not found, incomplete strategy
% 4.16/1.07 % (794668)Time elapsed: 0.140 s
% 4.16/1.07 % (794668)Peak memory usage: 16 MB
% 4.16/1.07 % (794668)Instructions burned: 275 (million)
% 4.16/1.07 % (794686)Instruction limit reached!
% 4.16/1.07 % (794686)------------------------------
% 4.16/1.07 % (794686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.16/1.07 % (794686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.07 % (794686)CaDiCaL version: 2.1.3
% 4.16/1.07 % (794686)Termination reason: Instruction limit
% 4.16/1.07 % (794686)Termination phase: Saturation
% 4.16/1.07 % (794686)Time elapsed: 0.101 s
% 4.16/1.07 % (794686)Peak memory usage: 14 MB
% 4.16/1.07 % (794686)Instructions burned: 201 (million)
% 4.16/1.07 % (794668)------------------------------
% 4.16/1.07 % (794668)------------------------------
% 4.16/1.07 % (794721)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=1342490267:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.16/1.07 % (794655)Instruction limit reached!
% 4.16/1.07 % (794655)------------------------------
% 4.16/1.07 % (794655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794655)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794655)Termination reason: Instruction limit
% 6.34/1.27 % (794655)Termination phase: Saturation
% 6.34/1.27 % (794655)Time elapsed: 0.179 s
% 6.34/1.27 % (794655)Peak memory usage: 16 MB
% 6.34/1.27 % (794655)Instructions burned: 316 (million)
% 6.34/1.27 % (794721)Instruction limit reached!
% 6.34/1.27 % (794721)------------------------------
% 6.34/1.27 % (794721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794721)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794721)Termination reason: Instruction limit
% 6.34/1.27 % (794721)Termination phase: Property scanning
% 6.34/1.27 % (794721)Time elapsed: 0.015 s
% 6.34/1.27 % (794721)Peak memory usage: 10 MB
% 6.34/1.27 % (794721)Instructions burned: 36 (million)
% 6.34/1.27 % (794727)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.34/1.27 % (794726)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1296967245:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 6.34/1.27 % (794730)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=601479935:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 6.34/1.27 % (794727)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3001268414:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 6.34/1.27 % (794734)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1978544755:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 6.34/1.27 % (794716)Instruction limit reached!
% 6.34/1.27 % (794716)------------------------------
% 6.34/1.27 % (794716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794716)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794716)Termination reason: Instruction limit
% 6.34/1.27 % (794716)Termination phase: Property scanning
% 6.34/1.27 % (794716)Time elapsed: 0.060 s
% 6.34/1.27 % (794716)Peak memory usage: 13 MB
% 6.34/1.27 % (794716)Instructions burned: 139 (million)
% 6.34/1.27 % (794726)Instruction limit reached!
% 6.34/1.27 % (794726)------------------------------
% 6.34/1.27 % (794726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794726)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794726)Termination reason: Instruction limit
% 6.34/1.27 % (794726)Termination phase: Preprocessing 3
% 6.34/1.27 % (794726)Time elapsed: 0.035 s
% 6.34/1.27 % (794726)Peak memory usage: 12 MB
% 6.34/1.27 % (794726)Instructions burned: 67 (million)
% 6.34/1.27 % (794749)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1580911241:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 6.34/1.27 % (794748)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1162988373:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 6.34/1.27 % (794734)Instruction limit reached!
% 6.34/1.27 % (794734)------------------------------
% 6.34/1.27 % (794734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794734)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794734)Termination reason: Instruction limit
% 6.34/1.27 % (794734)Termination phase: Property scanning
% 6.34/1.27 % (794734)Time elapsed: 0.043 s
% 6.34/1.27 % (794734)Peak memory usage: 12 MB
% 6.34/1.27 % (794734)Instructions burned: 96 (million)
% 6.34/1.27 % (794665)Instruction limit reached!
% 6.34/1.27 % (794665)------------------------------
% 6.34/1.27 % (794665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.27 % (794665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.27 % (794665)CaDiCaL version: 2.1.3
% 6.34/1.27 % (794665)Termination reason: Instruction limit
% 6.34/1.27 % (794665)Termination phase: Saturation
% 6.34/1.27 % (794665)Time elapsed: 0.238 s
% 6.34/1.27 % (794665)Peak memory usage: 19 MB
% 6.34/1.27 % (794665)Instructions burned: 855 (million)
% 6.34/1.27 % (794755)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=47494964:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 7.07/1.40 % (794754)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2099252801:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 7.07/1.40 % (794755)Instruction limit reached!
% 7.07/1.40 % (794755)------------------------------
% 7.07/1.40 % (794755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794755)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794755)Termination reason: Instruction limit
% 7.07/1.40 % (794755)Termination phase: Saturation
% 7.07/1.40 % (794755)Time elapsed: 0.031 s
% 7.07/1.40 % (794755)Peak memory usage: 13 MB
% 7.07/1.40 % (794755)Instructions burned: 131 (million)
% 7.07/1.40 % (794727)Instruction limit reached!
% 7.07/1.40 % (794727)------------------------------
% 7.07/1.40 % (794727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794727)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794727)Termination reason: Instruction limit
% 7.07/1.40 % (794727)Termination phase: Saturation
% 7.07/1.40 % (794727)Time elapsed: 0.103 s
% 7.07/1.40 % (794727)Peak memory usage: 12 MB
% 7.07/1.40 % (794727)Instructions burned: 181 (million)
% 7.07/1.40 % (794730)Instruction limit reached!
% 7.07/1.40 % (794730)------------------------------
% 7.07/1.40 % (794730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794730)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794730)Termination reason: Instruction limit
% 7.07/1.40 % (794730)Termination phase: Saturation
% 7.07/1.40 % (794730)Time elapsed: 0.115 s
% 7.07/1.40 % (794730)Peak memory usage: 15 MB
% 7.07/1.40 % (794730)Instructions burned: 246 (million)
% 7.07/1.40 % (794774)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=613526914:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 7.07/1.40 % (794775)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3118218869:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 7.07/1.40 % (794774)Instruction limit reached!
% 7.07/1.40 % (794774)------------------------------
% 7.07/1.40 % (794774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794774)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794774)Termination reason: Instruction limit
% 7.07/1.40 % (794774)Termination phase: Property scanning
% 7.07/1.40 % (794774)Time elapsed: 0.019 s
% 7.07/1.40 % (794774)Peak memory usage: 10 MB
% 7.07/1.40 % (794774)Instructions burned: 45 (million)
% 7.07/1.40 % (794776)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1248304449:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 7.07/1.40 % (794786)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3878584772:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 7.07/1.40 % (794786)Instruction limit reached!
% 7.07/1.40 % (794786)------------------------------
% 7.07/1.40 % (794786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794786)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794786)Termination reason: Instruction limit
% 7.07/1.40 % (794786)Termination phase: Property scanning
% 7.07/1.40 % (794786)Time elapsed: 0.097 s
% 7.07/1.40 % (794786)Peak memory usage: 13 MB
% 7.07/1.40 % (794786)Instructions burned: 95 (million)
% 7.07/1.40 % (794800)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=3066784663:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 7.07/1.40 % (794592)Instruction limit reached!
% 7.07/1.40 % (794592)------------------------------
% 7.07/1.40 % (794592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.07/1.40 % (794592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.07/1.40 % (794592)CaDiCaL version: 2.1.3
% 7.07/1.40 % (794592)Termination reason: Instruction limit
% 7.76/1.63 % (794592)Termination phase: Saturation
% 7.76/1.63 % (794592)Time elapsed: 0.586 s
% 7.76/1.63 % (794592)Peak memory usage: 14 MB
% 7.76/1.63 % (794592)Instructions burned: 1241 (million)
% 7.76/1.63 % (794800)Instruction limit reached!
% 7.76/1.63 % (794800)------------------------------
% 7.76/1.63 % (794800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.63 % (794800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.63 % (794800)CaDiCaL version: 2.1.3
% 7.76/1.63 % (794800)Termination reason: Instruction limit
% 7.76/1.63 % (794800)Termination phase: Property scanning
% 7.76/1.63 % (794800)Time elapsed: 0.030 s
% 7.76/1.63 % (794800)Peak memory usage: 11 MB
% 7.76/1.63 % (794800)Instructions burned: 67 (million)
% 7.76/1.63 % (794803)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=3860568849: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_2991 on theBenchmark for (2991ds/105Mi)
% 7.76/1.63 % (794804)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=1945370930: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)
% 7.76/1.63 % (794748)Instruction limit reached!
% 7.76/1.63 % (794748)------------------------------
% 7.76/1.63 % (794748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.63 % (794748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.63 % (794748)CaDiCaL version: 2.1.3
% 7.76/1.63 % (794748)Termination reason: Instruction limit
% 7.76/1.63 % (794748)Termination phase: Saturation
% 7.76/1.63 % (794748)Time elapsed: 0.303 s
% 7.76/1.63 % (794748)Peak memory usage: 14 MB
% 7.76/1.63 % (794748)Instructions burned: 427 (million)
% 7.76/1.63 % (794807)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1831276982:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 7.76/1.63 % (794803)Instruction limit reached!
% 7.76/1.63 % (794803)------------------------------
% 7.76/1.63 % (794803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.63 % (794803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.63 % (794803)CaDiCaL version: 2.1.3
% 7.76/1.63 % (794803)Termination reason: Instruction limit
% 7.76/1.63 % (794803)Termination phase: Saturation
% 7.76/1.63 % (794803)Time elapsed: 0.081 s
% 7.76/1.63 % (794803)Peak memory usage: 12 MB
% 7.76/1.63 % (794803)Instructions burned: 105 (million)
% 7.76/1.63 % (794775)Refutation not found, incomplete strategy
% 7.76/1.63 % (794775)------------------------------
% 7.76/1.63 % (794775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.63 % (794775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.63 % (794775)CaDiCaL version: 2.1.3
% 7.76/1.63 % (794775)Termination reason: Refutation not found, incomplete strategy
% 7.76/1.63 % (794775)Time elapsed: 0.304 s
% 7.76/1.63 % (794775)Peak memory usage: 17 MB
% 7.76/1.63 % (794775)Instructions burned: 361 (million)
% 7.76/1.63 % (794775)------------------------------
% 7.76/1.63 % (794775)------------------------------
% 7.76/1.63 % (794812)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3242867271:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/495Mi)
% 7.76/1.63 % (794816)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=866608885:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 7.76/1.63 % (794776)Instruction limit reached!
% 7.76/1.63 % (794776)------------------------------
% 7.76/1.63 % (794776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.76/1.63 % (794776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.76/1.63 % (794776)CaDiCaL version: 2.1.3
% 7.76/1.63 % (794776)Termination reason: Instruction limit
% 7.76/1.63 % (794776)Termination phase: Saturation
% 7.76/1.63 % (794776)Time elapsed: 0.346 s
% 7.76/1.63 % (794776)Peak memory usage: 17 MB
% 7.76/1.63 % (794776)Instructions burned: 451 (million)
% 7.76/1.63 % (794816)Instruction limit reached!
% 7.76/1.63 % (794816)------------------------------
% 8.94/1.77 % (794816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794816)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794816)Termination reason: Instruction limit
% 8.94/1.77 % (794816)Termination phase: Property scanning
% 8.94/1.77 % (794816)Time elapsed: 0.029 s
% 8.94/1.77 % (794816)Peak memory usage: 10 MB
% 8.94/1.77 % (794816)Instructions burned: 34 (million)
% 8.94/1.77 % (794754)Instruction limit reached!
% 8.94/1.77 % (794754)------------------------------
% 8.94/1.77 % (794754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794754)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794754)Termination reason: Instruction limit
% 8.94/1.77 % (794754)Termination phase: Saturation
% 8.94/1.77 % (794754)Time elapsed: 0.428 s
% 8.94/1.77 % (794754)Peak memory usage: 18 MB
% 8.94/1.77 % (794754)Instructions burned: 515 (million)
% 8.94/1.77 % (794821)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3795359052:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2989 on theBenchmark for (2989ds/91Mi)
% 8.94/1.77 % (794823)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4268203777:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 8.94/1.77 % (794822)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1327509774:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2989 on theBenchmark for (2989ds/66Mi)
% 8.94/1.77 % (794823)Instruction limit reached!
% 8.94/1.77 % (794823)------------------------------
% 8.94/1.77 % (794823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794823)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794823)Termination reason: Instruction limit
% 8.94/1.77 % (794823)Termination phase: shuffling
% 8.94/1.77 % (794823)Time elapsed: 0.019 s
% 8.94/1.77 % (794823)Peak memory usage: 10 MB
% 8.94/1.77 % (794823)Instructions burned: 23 (million)
% 8.94/1.77 % (794827)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=4017476080:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 8.94/1.77 % (794822)Instruction limit reached!
% 8.94/1.77 % (794822)------------------------------
% 8.94/1.77 % (794822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794822)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794822)Termination reason: Instruction limit
% 8.94/1.77 % (794822)Termination phase: Saturation
% 8.94/1.77 % (794822)Time elapsed: 0.054 s
% 8.94/1.77 % (794822)Peak memory usage: 12 MB
% 8.94/1.77 % (794822)Instructions burned: 67 (million)
% 8.94/1.77 % (794821)Instruction limit reached!
% 8.94/1.77 % (794821)------------------------------
% 8.94/1.77 % (794821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794821)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794821)Termination reason: Instruction limit
% 8.94/1.77 % (794821)Termination phase: Preprocessing 3
% 8.94/1.77 % (794821)Time elapsed: 0.075 s
% 8.94/1.77 % (794821)Peak memory usage: 12 MB
% 8.94/1.77 % (794821)Instructions burned: 91 (million)
% 8.94/1.77 % (794829)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3743602344:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/28Mi)
% 8.94/1.77 % (794829)Instruction limit reached!
% 8.94/1.77 % (794829)------------------------------
% 8.94/1.77 % (794829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.94/1.77 % (794829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.94/1.77 % (794829)CaDiCaL version: 2.1.3
% 8.94/1.77 % (794829)Termination reason: Instruction limit
% 8.94/1.77 % (794829)Termination phase: Property scanning
% 8.94/1.77 % (794829)Time elapsed: 0.013 s
% 8.94/1.77 % (794829)Peak memory usage: 10 MB
% 8.94/1.77 % (794829)Instructions burned: 29 (million)
% 8.94/1.77 % (794830)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 8.94/1.77 % (794830)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3853460785:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2988 on theBenchmark for (2988ds/137Mi)
% 9.70/1.99 % (794833)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=3705393957:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/340Mi)
% 9.70/1.99 % (794807)Instruction limit reached!
% 9.70/1.99 % (794807)------------------------------
% 9.70/1.99 % (794807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/1.99 % (794807)CaDiCaL version: 2.1.3
% 9.70/1.99 % (794807)Termination reason: Instruction limit
% 9.70/1.99 % (794807)Termination phase: Saturation
% 9.70/1.99 % (794807)Time elapsed: 0.311 s
% 9.70/1.99 % (794807)Peak memory usage: 16 MB
% 9.70/1.99 % (794807)Instructions burned: 376 (million)
% 9.70/1.99 % (794749)Instruction limit reached!
% 9.70/1.99 % (794749)------------------------------
% 9.70/1.99 % (794749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/1.99 % (794749)CaDiCaL version: 2.1.3
% 9.70/1.99 % (794749)Termination reason: Instruction limit
% 9.70/1.99 % (794749)Termination phase: Saturation
% 9.70/1.99 % (794749)Time elapsed: 0.670 s
% 9.70/1.99 % (794749)Peak memory usage: 18 MB
% 9.70/1.99 % (794749)Instructions burned: 874 (million)
% 9.70/1.99 % (794839)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2899609304:i=227:sd=1:bd=all:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/227Mi)
% 9.70/1.99 % (794830)Instruction limit reached!
% 9.70/1.99 % (794830)------------------------------
% 9.70/1.99 % (794830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/1.99 % (794830)CaDiCaL version: 2.1.3
% 9.70/1.99 % (794830)Termination reason: Instruction limit
% 9.70/1.99 % (794830)Termination phase: Saturation
% 9.70/1.99 % (794830)Time elapsed: 0.105 s
% 9.70/1.99 % (794830)Peak memory usage: 12 MB
% 9.70/1.99 % (794830)Instructions burned: 137 (million)
% 9.70/1.99 % (794840)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 9.70/1.99 % (794840)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3538776258:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/373Mi)
% 9.70/1.99 % (794842)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3765578923:i=116:ep=RSTC:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/116Mi)
% 9.70/1.99 % (794839)Refutation not found, incomplete strategy
% 9.70/1.99 % (794839)------------------------------
% 9.70/1.99 % (794839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/1.99 % (794839)CaDiCaL version: 2.1.3
% 9.70/1.99 % (794839)Termination reason: Refutation not found, incomplete strategy
% 9.70/1.99 % (794839)Time elapsed: 0.062 s
% 9.70/1.99 % (794839)Peak memory usage: 13 MB
% 9.70/1.99 % (794839)Instructions burned: 65 (million)
% 9.70/1.99 % (794839)------------------------------
% 9.70/1.99 % (794839)------------------------------
% 9.70/1.99 % (794850)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3372917086:i=575:rtra=on_2986 on theBenchmark for (2986ds/575Mi)
% 9.70/1.99 % (794827)Instruction limit reached!
% 9.70/1.99 % (794827)------------------------------
% 9.70/1.99 % (794827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/1.99 % (794827)CaDiCaL version: 2.1.3
% 9.70/1.99 % (794827)Termination reason: Instruction limit
% 9.70/1.99 % (794827)Termination phase: Saturation
% 9.70/1.99 % (794827)Time elapsed: 0.265 s
% 9.70/1.99 % (794827)Peak memory usage: 19 MB
% 9.70/1.99 % (794827)Instructions burned: 338 (million)
% 9.70/1.99 % (794812)Instruction limit reached!
% 9.70/1.99 % (794812)------------------------------
% 9.70/1.99 % (794812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.70/1.99 % (794812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.81/2.32 % (794812)CaDiCaL version: 2.1.3
% 13.81/2.32 % (794812)Termination reason: Instruction limit
% 13.81/2.32 % (794812)Termination phase: Saturation
% 13.81/2.32 % (794812)Time elapsed: 0.414 s
% 13.81/2.32 % (794812)Peak memory usage: 17 MB
% 13.81/2.32 % (794812)Instructions burned: 495 (million)
% 13.81/2.32 % (794842)Instruction limit reached!
% 13.81/2.32 % (794842)------------------------------
% 13.81/2.32 % (794842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.81/2.32 % (794842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.81/2.32 % (794842)CaDiCaL version: 2.1.3
% 13.81/2.32 % (794842)Termination reason: Instruction limit
% 13.81/2.32 % (794842)Termination phase: Property scanning
% 13.81/2.32 % (794842)Time elapsed: 0.096 s
% 13.81/2.32 % (794842)Peak memory usage: 13 MB
% 13.81/2.32 % (794842)Instructions burned: 117 (million)
% 13.81/2.32 % (794853)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=356546536:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2986 on theBenchmark for (2986ds/270Mi)
% 13.81/2.32 % (794854)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=3201250551:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2986 on theBenchmark for (2986ds/9840Mi)
% 13.81/2.32 % (794855)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3802661324:i=421:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/421Mi)
% 13.81/2.32 % (794833)Instruction limit reached!
% 13.81/2.32 % (794833)------------------------------
% 13.81/2.32 % (794833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.81/2.32 % (794833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.81/2.32 % (794833)CaDiCaL version: 2.1.3
% 13.81/2.32 % (794833)Termination reason: Instruction limit
% 13.81/2.32 % (794833)Termination phase: Saturation
% 13.81/2.32 % (794833)Time elapsed: 0.256 s
% 13.81/2.32 % (794833)Peak memory usage: 17 MB
% 13.81/2.32 % (794833)Instructions burned: 340 (million)
% 13.81/2.32 % (794859)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 13.81/2.32 % (794859)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3084146254:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/270Mi)
% 13.81/2.32 % (794855)Refutation not found, incomplete strategy
% 13.81/2.32 % (794855)------------------------------
% 13.81/2.32 % (794855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.81/2.32 % (794855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.81/2.32 % (794855)CaDiCaL version: 2.1.3
% 13.81/2.32 % (794855)Termination reason: Refutation not found, incomplete strategy
% 13.81/2.32 % (794855)Time elapsed: 0.051 s
% 13.81/2.32 % (794855)Peak memory usage: 13 MB
% 13.81/2.32 % (794855)Instructions burned: 63 (million)
% 13.81/2.32 % (794855)------------------------------
% 13.81/2.32 % (794855)------------------------------
% 13.81/2.32 % (794862)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=7788630:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/31Mi)
% 13.81/2.32 % (794840)Instruction limit reached!
% 13.81/2.32 % (794840)------------------------------
% 13.81/2.32 % (794840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.81/2.32 % (794840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.81/2.32 % (794840)CaDiCaL version: 2.1.3
% 13.81/2.32 % (794840)Termination reason: Instruction limit
% 13.81/2.32 % (794840)Termination phase: Saturation
% 13.81/2.32 % (794840)Time elapsed: 0.238 s
% 13.81/2.32 % (794840)Peak memory usage: 15 MB
% 13.81/2.32 % (794840)Instructions burned: 375 (million)
% 13.81/2.32 % (794865)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 13.81/2.32 % (794865)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
% 15.06/2.65 % (794865)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=1823620213:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2985 on theBenchmark for (2985ds/1440Mi)
% 15.06/2.65 % (794862)Instruction limit reached!
% 15.06/2.65 % (794862)------------------------------
% 15.06/2.65 % (794862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794862)CaDiCaL version: 2.1.3
% 15.06/2.65 % (794862)Termination reason: Instruction limit
% 15.06/2.65 % (794862)Termination phase: shuffling
% 15.06/2.65 % (794862)Time elapsed: 0.026 s
% 15.06/2.65 % (794862)Peak memory usage: 10 MB
% 15.06/2.65 % (794862)Instructions burned: 31 (million)
% 15.06/2.65 % (794867)dis+10_2_sil=128000:si=on:random_seed=1238150990:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2984 on theBenchmark for (2984ds/339Mi)
% 15.06/2.65 % (794853)Instruction limit reached!
% 15.06/2.65 % (794853)------------------------------
% 15.06/2.65 % (794853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794853)CaDiCaL version: 2.1.3
% 15.06/2.65 % (794853)Termination reason: Instruction limit
% 15.06/2.65 % (794853)Termination phase: Saturation
% 15.06/2.65 % (794853)Time elapsed: 0.204 s
% 15.06/2.65 % (794853)Peak memory usage: 12 MB
% 15.06/2.65 % (794853)Instructions burned: 271 (million)
% 15.06/2.65 % (794867)Instruction limit reached!
% 15.06/2.65 % (794867)------------------------------
% 15.06/2.65 % (794867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794867)CaDiCaL version: 2.1.3
% 15.06/2.65 % (794867)Termination reason: Instruction limit
% 15.06/2.65 % (794867)Termination phase: Saturation
% 15.06/2.65 % (794867)Time elapsed: 0.088 s
% 15.06/2.65 % (794867)Peak memory usage: 14 MB
% 15.06/2.65 % (794867)Instructions burned: 340 (million)
% 15.06/2.65 % (794869)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=44692190:i=111:add=on:fgj=on:rtra=on:fdi=1024_2984 on theBenchmark for (2984ds/111Mi)
% 15.06/2.65 % (794871)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=509498082:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2983 on theBenchmark for (2983ds/122Mi)
% 15.06/2.65 % (794859)Instruction limit reached!
% 15.06/2.65 % (794859)------------------------------
% 15.06/2.65 % (794859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794859)CaDiCaL version: 2.1.3
% 15.06/2.65 % (794859)Termination reason: Instruction limit
% 15.06/2.65 % (794859)Termination phase: Saturation
% 15.06/2.65 % (794859)Time elapsed: 0.222 s
% 15.06/2.65 % (794859)Peak memory usage: 15 MB
% 15.06/2.65 % (794859)Instructions burned: 270 (million)
% 15.06/2.65 % (794871)Instruction limit reached!
% 15.06/2.65 % (794871)------------------------------
% 15.06/2.65 % (794871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794871)CaDiCaL version: 2.1.3
% 15.06/2.65 % (794871)Termination reason: Instruction limit
% 15.06/2.65 % (794871)Termination phase: Property scanning
% 15.06/2.65 % (794871)Time elapsed: 0.052 s
% 15.06/2.65 % (794871)Peak memory usage: 13 MB
% 15.06/2.65 % (794871)Instructions burned: 122 (million)
% 15.06/2.65 % (794875)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=2220107185:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/136Mi)
% 15.06/2.65 % (794876)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=806039881:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2983 on theBenchmark for (2983ds/232Mi)
% 15.06/2.65 % (794869)Instruction limit reached!
% 15.06/2.65 % (794869)------------------------------
% 15.06/2.65 % (794869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.06/2.65 % (794869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.06/2.65 % (794869)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794869)Termination reason: Instruction limit
% 16.94/2.80 % (794869)Termination phase: Property scanning
% 16.94/2.80 % (794869)Time elapsed: 0.094 s
% 16.94/2.80 % (794869)Peak memory usage: 13 MB
% 16.94/2.80 % (794869)Instructions burned: 111 (million)
% 16.94/2.80 % (794882)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=1246963130:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2982 on theBenchmark for (2982ds/1254Mi)
% 16.94/2.80 % (794850)Instruction limit reached!
% 16.94/2.80 % (794850)------------------------------
% 16.94/2.80 % (794850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.94/2.80 % (794850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/2.80 % (794850)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794850)Termination reason: Instruction limit
% 16.94/2.80 % (794850)Termination phase: Saturation
% 16.94/2.80 % (794850)Time elapsed: 0.483 s
% 16.94/2.80 % (794850)Peak memory usage: 18 MB
% 16.94/2.80 % (794850)Instructions burned: 575 (million)
% 16.94/2.80 % (794875)Instruction limit reached!
% 16.94/2.80 % (794875)------------------------------
% 16.94/2.80 % (794875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.94/2.80 % (794875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/2.80 % (794875)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794875)Termination reason: Instruction limit
% 16.94/2.80 % (794875)Termination phase: Property scanning
% 16.94/2.80 % (794875)Time elapsed: 0.114 s
% 16.94/2.80 % (794875)Peak memory usage: 16 MB
% 16.94/2.80 % (794875)Instructions burned: 136 (million)
% 16.94/2.80 % (794885)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 16.94/2.80 % (794885)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2094409370:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2981 on theBenchmark for (2981ds/281Mi)
% 16.94/2.80 % (794886)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2501304450:i=619:add=on:rtra=on_2981 on theBenchmark for (2981ds/619Mi)
% 16.94/2.80 % (794876)Instruction limit reached!
% 16.94/2.80 % (794876)------------------------------
% 16.94/2.80 % (794876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.94/2.80 % (794876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/2.80 % (794876)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794876)Termination reason: Instruction limit
% 16.94/2.80 % (794876)Termination phase: Saturation
% 16.94/2.80 % (794876)Time elapsed: 0.161 s
% 16.94/2.80 % (794876)Peak memory usage: 14 MB
% 16.94/2.80 % (794876)Instructions burned: 232 (million)
% 16.94/2.80 % (794891)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=292462787:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/865Mi)
% 16.94/2.80 % (794882)Refutation not found, incomplete strategy
% 16.94/2.80 % (794882)------------------------------
% 16.94/2.80 % (794882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.94/2.80 % (794882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/2.80 % (794882)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794882)Termination reason: Refutation not found, incomplete strategy
% 16.94/2.80 % (794882)Time elapsed: 0.169 s
% 16.94/2.80 % (794882)Peak memory usage: 16 MB
% 16.94/2.80 % (794882)Instructions burned: 215 (million)
% 16.94/2.80 % (794882)------------------------------
% 16.94/2.80 % (794882)------------------------------
% 16.94/2.80 % (794893)lrs+10_1_sil=128000:si=on:urr=on:random_seed=695284105:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2980 on theBenchmark for (2980ds/212Mi)
% 16.94/2.80 % (794885)Instruction limit reached!
% 16.94/2.80 % (794885)------------------------------
% 16.94/2.80 % (794885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.94/2.80 % (794885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/2.80 % (794885)CaDiCaL version: 2.1.3
% 16.94/2.80 % (794885)Termination reason: Instruction limit
% 16.94/2.80 % (794885)Termination phase: Saturation
% 16.94/2.80 % (794885)Time elapsed: 0.166 s
% 16.94/2.80 % (794885)Peak memory usage: 12 MB
% 16.94/2.80 % (794885)Instructions burned: 281 (million)
% 16.94/2.80 % (794896)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3561614210:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/130Mi)
% 20.41/3.27 % (794893)Instruction limit reached!
% 20.41/3.27 % (794893)------------------------------
% 20.41/3.27 % (794893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794893)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794893)Termination reason: Instruction limit
% 20.41/3.27 % (794893)Termination phase: Saturation
% 20.41/3.27 % (794893)Time elapsed: 0.150 s
% 20.41/3.27 % (794893)Peak memory usage: 14 MB
% 20.41/3.27 % (794893)Instructions burned: 213 (million)
% 20.41/3.27 % (794901)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1191345107:st=1.5:i=346:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/346Mi)
% 20.41/3.27 % (794896)Instruction limit reached!
% 20.41/3.27 % (794896)------------------------------
% 20.41/3.27 % (794896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794896)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794896)Termination reason: Instruction limit
% 20.41/3.27 % (794896)Termination phase: Property scanning
% 20.41/3.27 % (794896)Time elapsed: 0.108 s
% 20.41/3.27 % (794896)Peak memory usage: 13 MB
% 20.41/3.27 % (794896)Instructions burned: 130 (million)
% 20.41/3.27 % (794903)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=48896094:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2978 on theBenchmark for (2978ds/152Mi)
% 20.41/3.27 % (794865)Instruction limit reached!
% 20.41/3.27 % (794865)------------------------------
% 20.41/3.27 % (794865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794865)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794865)Termination reason: Instruction limit
% 20.41/3.27 % (794865)Termination phase: Saturation
% 20.41/3.27 % (794865)Time elapsed: 0.676 s
% 20.41/3.27 % (794865)Peak memory usage: 21 MB
% 20.41/3.27 % (794865)Instructions burned: 1441 (million)
% 20.41/3.27 % (794905)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=256863442:i=75:ep=R:rtra=on:ntd=on_2978 on theBenchmark for (2978ds/75Mi)
% 20.41/3.27 % (794905)Instruction limit reached!
% 20.41/3.27 % (794905)------------------------------
% 20.41/3.27 % (794905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794905)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794905)Termination reason: Instruction limit
% 20.41/3.27 % (794905)Termination phase: Property scanning
% 20.41/3.27 % (794905)Time elapsed: 0.031 s
% 20.41/3.27 % (794905)Peak memory usage: 11 MB
% 20.41/3.27 % (794905)Instructions burned: 75 (million)
% 20.41/3.27 % (794907)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=4205665724:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2977 on theBenchmark for (2977ds/387Mi)
% 20.41/3.27 % (794903)Instruction limit reached!
% 20.41/3.27 % (794903)------------------------------
% 20.41/3.27 % (794903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794903)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794903)Termination reason: Instruction limit
% 20.41/3.27 % (794903)Termination phase: Inequality splitting
% 20.41/3.27 % (794903)Time elapsed: 0.090 s
% 20.41/3.27 % (794903)Peak memory usage: 13 MB
% 20.41/3.27 % (794903)Instructions burned: 152 (million)
% 20.41/3.27 % (794909)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=1933728633:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2977 on theBenchmark for (2977ds/148Mi)
% 20.41/3.27 % (794909)Instruction limit reached!
% 20.41/3.27 % (794909)------------------------------
% 20.41/3.27 % (794909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.41/3.27 % (794909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.41/3.27 % (794909)CaDiCaL version: 2.1.3
% 20.41/3.27 % (794909)Termination reason: Instruction limit
% 20.41/3.27 % (794909)Termination phase: Saturation
% 20.41/3.27 % (794909)Time elapsed: 0.078 s
% 20.41/3.27 % (794909)Peak memory usage: 12 MB
% 20.41/3.27 % (794909)Instructions burned: 148 (million)
% 20.41/3.27 % (794886)Instruction limit reached!
% 21.73/3.45 % (794886)------------------------------
% 21.73/3.45 % (794886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794886)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794886)Termination reason: Instruction limit
% 21.73/3.45 % (794886)Termination phase: Saturation
% 21.73/3.45 % (794886)Time elapsed: 0.516 s
% 21.73/3.45 % (794886)Peak memory usage: 18 MB
% 21.73/3.45 % (794886)Instructions burned: 620 (million)
% 21.73/3.45 % (794911)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=899527381:i=161:piset=and:rtra=on:ntd=on_2976 on theBenchmark for (2976ds/161Mi)
% 21.73/3.45 % (794907)Instruction limit reached!
% 21.73/3.45 % (794907)------------------------------
% 21.73/3.45 % (794907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794907)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794907)Termination reason: Instruction limit
% 21.73/3.45 % (794907)Termination phase: Saturation
% 21.73/3.45 % (794907)Time elapsed: 0.151 s
% 21.73/3.45 % (794907)Peak memory usage: 12 MB
% 21.73/3.45 % (794907)Instructions burned: 388 (million)
% 21.73/3.45 % (794912)lrs+10_1_sil=128000:si=on:random_seed=2774785106:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2976 on theBenchmark for (2976ds/888Mi)
% 21.73/3.45 % (794901)Instruction limit reached!
% 21.73/3.45 % (794901)------------------------------
% 21.73/3.45 % (794901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794901)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794901)Termination reason: Instruction limit
% 21.73/3.45 % (794901)Termination phase: Saturation
% 21.73/3.45 % (794901)Time elapsed: 0.276 s
% 21.73/3.45 % (794901)Peak memory usage: 13 MB
% 21.73/3.45 % (794901)Instructions burned: 347 (million)
% 21.73/3.45 % (794914)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=2384795478:i=136:add=on:ins=4:rtra=on:sup=off_2975 on theBenchmark for (2975ds/136Mi)
% 21.73/3.45 % (794916)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=3522471381:i=88:s2at=3:nm=2:rtra=on:rawr=on_2975 on theBenchmark for (2975ds/88Mi)
% 21.73/3.45 % (794914)Instruction limit reached!
% 21.73/3.45 % (794914)------------------------------
% 21.73/3.45 % (794914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794914)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794914)Termination reason: Instruction limit
% 21.73/3.45 % (794914)Termination phase: Property scanning
% 21.73/3.45 % (794914)Time elapsed: 0.058 s
% 21.73/3.45 % (794914)Peak memory usage: 12 MB
% 21.73/3.45 % (794914)Instructions burned: 138 (million)
% 21.73/3.45 % (794920)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3659877850:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2975 on theBenchmark for (2975ds/93Mi)
% 21.73/3.45 % (794916)Instruction limit reached!
% 21.73/3.45 % (794916)------------------------------
% 21.73/3.45 % (794916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794916)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794916)Termination reason: Instruction limit
% 21.73/3.45 % (794916)Termination phase: Property scanning
% 21.73/3.45 % (794916)Time elapsed: 0.068 s
% 21.73/3.45 % (794916)Peak memory usage: 11 MB
% 21.73/3.45 % (794916)Instructions burned: 89 (million)
% 21.73/3.45 % (794911)Instruction limit reached!
% 21.73/3.45 % (794911)------------------------------
% 21.73/3.45 % (794911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.73/3.45 % (794911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.73/3.45 % (794911)CaDiCaL version: 2.1.3
% 21.73/3.45 % (794911)Termination reason: Instruction limit
% 21.73/3.45 % (794911)Termination phase: Property scanning
% 21.73/3.45 % (794911)Time elapsed: 0.126 s
% 21.73/3.45 % (794911)Peak memory usage: 13 MB
% 21.73/3.45 % (794911)Instructions burned: 162 (million)
% 21.73/3.45 % (794920)Instruction limit reached!
% 21.73/3.45 % (794920)------------------------------
% 22.48/3.58 % (794920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.48/3.58 % (794920)CaDiCaL version: 2.1.3
% 22.48/3.58 % (794920)Termination reason: Instruction limit
% 22.48/3.58 % (794920)Termination phase: Saturation
% 22.48/3.58 % (794920)Time elapsed: 0.038 s
% 22.48/3.58 % (794920)Peak memory usage: 12 MB
% 22.48/3.58 % (794920)Instructions burned: 95 (million)
% 22.48/3.58 % (794923)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1426700337:i=2186:rtra=on:ixr=off_2974 on theBenchmark for (2974ds/2186Mi)
% 22.48/3.58 % (794925)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=803789719:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2974 on theBenchmark for (2974ds/805Mi)
% 22.48/3.58 % (794924)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2016109197:s2a=on:i=240:rtra=on:ntd=on_2974 on theBenchmark for (2974ds/240Mi)
% 22.48/3.58 % (794891)Instruction limit reached!
% 22.48/3.58 % (794891)------------------------------
% 22.48/3.58 % (794891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.48/3.58 % (794891)CaDiCaL version: 2.1.3
% 22.48/3.58 % (794891)Termination reason: Instruction limit
% 22.48/3.58 % (794891)Termination phase: Saturation
% 22.48/3.58 % (794891)Time elapsed: 0.715 s
% 22.48/3.58 % (794891)Peak memory usage: 19 MB
% 22.48/3.58 % (794891)Instructions burned: 866 (million)
% 22.48/3.58 % (794929)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 22.48/3.58 % (794929)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2633818715:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2973 on theBenchmark for (2973ds/391Mi)
% 22.48/3.58 % (794924)Instruction limit reached!
% 22.48/3.58 % (794924)------------------------------
% 22.48/3.58 % (794924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.48/3.58 % (794924)CaDiCaL version: 2.1.3
% 22.48/3.58 % (794924)Termination reason: Instruction limit
% 22.48/3.58 % (794924)Termination phase: Saturation
% 22.48/3.58 % (794924)Time elapsed: 0.196 s
% 22.48/3.58 % (794924)Peak memory usage: 14 MB
% 22.48/3.58 % (794924)Instructions burned: 241 (million)
% 22.48/3.58 % (794931)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=320154668:i=355:av=off:fsr=off:rtra=on:ixr=off_2972 on theBenchmark for (2972ds/355Mi)
% 22.48/3.58 % (794925)Instruction limit reached!
% 22.48/3.58 % (794925)------------------------------
% 22.48/3.58 % (794925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.48/3.58 % (794925)CaDiCaL version: 2.1.3
% 22.48/3.58 % (794925)Termination reason: Instruction limit
% 22.48/3.58 % (794925)Termination phase: Saturation
% 22.48/3.58 % (794925)Time elapsed: 0.379 s
% 22.48/3.58 % (794925)Peak memory usage: 18 MB
% 22.48/3.58 % (794925)Instructions burned: 810 (million)
% 22.48/3.58 % (794929)Instruction limit reached!
% 22.48/3.58 % (794929)------------------------------
% 22.48/3.58 % (794929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.48/3.58 % (794929)CaDiCaL version: 2.1.3
% 22.48/3.58 % (794929)Termination reason: Instruction limit
% 22.48/3.58 % (794929)Termination phase: Saturation
% 22.48/3.58 % (794929)Time elapsed: 0.288 s
% 22.48/3.58 % (794929)Peak memory usage: 13 MB
% 22.48/3.58 % (794929)Instructions burned: 393 (million)
% 22.48/3.58 % (794933)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=1492768293:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/314Mi)
% 22.48/3.58 % (794934)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=560736407:s2a=on:i=251:fsr=off:rtra=on_2970 on theBenchmark for (2970ds/251Mi)
% 22.48/3.58 % (794931)Instruction limit reached!
% 22.48/3.58 % (794931)------------------------------
% 22.48/3.58 % (794931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.48/3.58 % (794931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794931)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794931)Termination reason: Instruction limit
% 24.16/3.84 % (794931)Termination phase: Saturation
% 24.16/3.84 % (794931)Time elapsed: 0.204 s
% 24.16/3.84 % (794931)Peak memory usage: 15 MB
% 24.16/3.84 % (794931)Instructions burned: 355 (million)
% 24.16/3.84 % (794938)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=1080291875:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2969 on theBenchmark for (2969ds/2470Mi)
% 24.16/3.84 % (794933)Refutation not found, incomplete strategy
% 24.16/3.84 % (794933)------------------------------
% 24.16/3.84 % (794933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.16/3.84 % (794933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794933)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794933)Termination reason: Refutation not found, incomplete strategy
% 24.16/3.84 % (794933)Time elapsed: 0.098 s
% 24.16/3.84 % (794933)Peak memory usage: 14 MB
% 24.16/3.84 % (794933)Instructions burned: 212 (million)
% 24.16/3.84 % (794933)------------------------------
% 24.16/3.84 % (794933)------------------------------
% 24.16/3.84 % (794940)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=3299916828:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2969 on theBenchmark for (2969ds/673Mi)
% 24.16/3.84 % (794912)Instruction limit reached!
% 24.16/3.84 % (794912)------------------------------
% 24.16/3.84 % (794912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.16/3.84 % (794912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794912)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794912)Termination reason: Instruction limit
% 24.16/3.84 % (794912)Termination phase: Saturation
% 24.16/3.84 % (794912)Time elapsed: 0.662 s
% 24.16/3.84 % (794912)Peak memory usage: 18 MB
% 24.16/3.84 % (794912)Instructions burned: 889 (million)
% 24.16/3.84 % (794934)Instruction limit reached!
% 24.16/3.84 % (794934)------------------------------
% 24.16/3.84 % (794934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.16/3.84 % (794934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794934)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794934)Termination reason: Instruction limit
% 24.16/3.84 % (794934)Termination phase: Saturation
% 24.16/3.84 % (794934)Time elapsed: 0.106 s
% 24.16/3.84 % (794934)Peak memory usage: 14 MB
% 24.16/3.84 % (794934)Instructions burned: 252 (million)
% 24.16/3.84 % (794942)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=447112121:i=116:ep=RSTC:rtra=on:ntd=on_2969 on theBenchmark for (2969ds/116Mi)
% 24.16/3.84 % (794943)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=972780644:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2969 on theBenchmark for (2969ds/270Mi)
% 24.16/3.84 % (794942)Instruction limit reached!
% 24.16/3.84 % (794942)------------------------------
% 24.16/3.84 % (794942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.16/3.84 % (794942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794942)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794942)Termination reason: Instruction limit
% 24.16/3.84 % (794942)Termination phase: Property scanning
% 24.16/3.84 % (794942)Time elapsed: 0.051 s
% 24.16/3.84 % (794942)Peak memory usage: 12 MB
% 24.16/3.84 % (794942)Instructions burned: 116 (million)
% 24.16/3.84 % (794965)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=1379641708:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2968 on theBenchmark for (2968ds/30Mi)
% 24.16/3.84 % (794965)Instruction limit reached!
% 24.16/3.84 % (794965)------------------------------
% 24.16/3.84 % (794965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.16/3.84 % (794965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.16/3.84 % (794965)CaDiCaL version: 2.1.3
% 24.16/3.84 % (794965)Termination reason: Instruction limit
% 24.16/3.84 % (794965)Termination phase: shuffling
% 26.50/4.08 % (794965)Time elapsed: 0.014 s
% 26.50/4.08 % (794965)Peak memory usage: 10 MB
% 26.50/4.08 % (794965)Instructions burned: 32 (million)
% 26.50/4.08 % (794983)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 26.50/4.08 % (794983)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2669275995:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2968 on theBenchmark for (2968ds/39Mi)
% 26.50/4.08 % (794943)Instruction limit reached!
% 26.50/4.08 % (794943)------------------------------
% 26.50/4.08 % (794943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (794943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.50/4.08 % (794943)CaDiCaL version: 2.1.3
% 26.50/4.08 % (794943)Termination reason: Instruction limit
% 26.50/4.08 % (794943)Termination phase: Saturation
% 26.50/4.08 % (794943)Time elapsed: 0.111 s
% 26.50/4.08 % (794943)Peak memory usage: 12 MB
% 26.50/4.08 % (794943)Instructions burned: 270 (million)
% 26.50/4.08 % (794983)Instruction limit reached!
% 26.50/4.08 % (794983)------------------------------
% 26.50/4.08 % (794983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (794983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.50/4.08 % (794983)CaDiCaL version: 2.1.3
% 26.50/4.08 % (794983)Termination reason: Instruction limit
% 26.50/4.08 % (794983)Termination phase: Property scanning
% 26.50/4.08 % (794983)Time elapsed: 0.017 s
% 26.50/4.08 % (794983)Peak memory usage: 10 MB
% 26.50/4.08 % (794983)Instructions burned: 40 (million)
% 26.50/4.08 % (794940)Instruction limit reached!
% 26.50/4.08 % (794940)------------------------------
% 26.50/4.08 % (794940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (794940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.50/4.08 % (794940)CaDiCaL version: 2.1.3
% 26.50/4.08 % (794940)Termination reason: Instruction limit
% 26.50/4.08 % (794940)Termination phase: Saturation
% 26.50/4.08 % (794940)Time elapsed: 0.156 s
% 26.50/4.08 % (794940)Peak memory usage: 17 MB
% 26.50/4.08 % (794940)Instructions burned: 674 (million)
% 26.50/4.08 % (794994)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1628662011:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2967 on theBenchmark for (2967ds/365Mi)
% 26.50/4.08 % (795002)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 26.50/4.08 % (795002)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=1072072420:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2967 on theBenchmark for (2967ds/252Mi)
% 26.50/4.08 % (794998)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3605224620:i=158:av=off:rtra=on_2967 on theBenchmark for (2967ds/158Mi)
% 26.50/4.08 % (795002)Instruction limit reached!
% 26.50/4.08 % (795002)------------------------------
% 26.50/4.08 % (795002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (795002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.50/4.08 % (795002)CaDiCaL version: 2.1.3
% 26.50/4.08 % (795002)Termination reason: Instruction limit
% 26.50/4.08 % (795002)Termination phase: Saturation
% 26.50/4.08 % (795002)Time elapsed: 0.059 s
% 26.50/4.08 % (795002)Peak memory usage: 15 MB
% 26.50/4.08 % (795002)Instructions burned: 255 (million)
% 26.50/4.08 % (795032)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=369639196:i=213:rtra=on:ss=axioms_2967 on theBenchmark for (2967ds/213Mi)
% 26.50/4.08 % (794998)Instruction limit reached!
% 26.50/4.08 % (794998)------------------------------
% 26.50/4.08 % (794998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (794998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.50/4.08 % (794998)CaDiCaL version: 2.1.3
% 26.50/4.08 % (794998)Termination reason: Instruction limit
% 26.50/4.08 % (794998)Termination phase: Saturation
% 26.50/4.08 % (794998)Time elapsed: 0.068 s
% 26.50/4.08 % (794998)Peak memory usage: 14 MB
% 26.50/4.08 % (794998)Instructions burned: 159 (million)
% 26.50/4.08 % (795032)Refutation not found, incomplete strategy
% 26.50/4.08 % (795032)------------------------------
% 26.50/4.08 % (795032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.50/4.08 % (795032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.22/4.19 % (795032)CaDiCaL version: 2.1.3
% 27.22/4.19 % (795032)Termination reason: Refutation not found, incomplete strategy
% 27.22/4.19 % (795032)Time elapsed: 0.009 s
% 27.22/4.19 % (795032)Peak memory usage: 13 MB
% 27.22/4.19 % (795032)Instructions burned: 40 (million)
% 27.22/4.19 % (795032)------------------------------
% 27.22/4.19 % (795032)------------------------------
% 27.22/4.19 % (795037)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=834653863:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2966 on theBenchmark for (2966ds/160Mi)
% 27.22/4.19 % (795042)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3972438309:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/763Mi)
% 27.22/4.19 % (794994)Instruction limit reached!
% 27.22/4.19 % (794994)------------------------------
% 27.22/4.19 % (794994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.22/4.19 % (794994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.22/4.19 % (794994)CaDiCaL version: 2.1.3
% 27.22/4.19 % (794994)Termination reason: Instruction limit
% 27.22/4.19 % (794994)Termination phase: Saturation
% 27.22/4.19 % (794994)Time elapsed: 0.161 s
% 27.22/4.19 % (794994)Peak memory usage: 16 MB
% 27.22/4.19 % (794994)Instructions burned: 365 (million)
% 27.22/4.19 % (795037)Instruction limit reached!
% 27.22/4.19 % (795037)------------------------------
% 27.22/4.19 % (795037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.22/4.19 % (795037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.22/4.19 % (795037)CaDiCaL version: 2.1.3
% 27.22/4.19 % (795037)Termination reason: Instruction limit
% 27.22/4.19 % (795037)Termination phase: Function definition elimination
% 27.22/4.19 % (795037)Time elapsed: 0.069 s
% 27.22/4.19 % (795037)Peak memory usage: 13 MB
% 27.22/4.19 % (795037)Instructions burned: 162 (million)
% 27.22/4.19 % (795067)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 27.22/4.19 % (795067)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=418992147:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2966 on theBenchmark for (2966ds/237Mi)
% 27.22/4.19 % (795068)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=57363341:s2a=on:i=386:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/386Mi)
% 27.22/4.19 % (795067)Instruction limit reached!
% 27.22/4.19 % (795067)------------------------------
% 27.22/4.19 % (795067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.22/4.19 % (795067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.22/4.19 % (795067)CaDiCaL version: 2.1.3
% 27.22/4.19 % (795067)Termination reason: Instruction limit
% 27.22/4.19 % (795067)Termination phase: Saturation
% 27.22/4.19 % (795067)Time elapsed: 0.105 s
% 27.22/4.19 % (795067)Peak memory usage: 15 MB
% 27.22/4.19 % (795067)Instructions burned: 238 (million)
% 27.22/4.19 % (795042)Instruction limit reached!
% 27.22/4.19 % (795042)------------------------------
% 27.22/4.19 % (795042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.22/4.19 % (795042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.22/4.19 % (795042)CaDiCaL version: 2.1.3
% 27.22/4.19 % (795042)Termination reason: Instruction limit
% 27.22/4.19 % (795042)Termination phase: Saturation
% 27.22/4.19 % (795042)Time elapsed: 0.195 s
% 27.22/4.19 % (795042)Peak memory usage: 17 MB
% 27.22/4.19 % (795042)Instructions burned: 763 (million)
% 27.22/4.19 % (795077)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=1228593762:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2964 on theBenchmark for (2964ds/567Mi)
% 27.22/4.19 % (795074)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=1668323253:i=300:piset=and:nm=32:rtra=on_2964 on theBenchmark for (2964ds/300Mi)
% 27.22/4.19 % (795068)Instruction limit reached!
% 27.22/4.19 % (795068)------------------------------
% 27.22/4.19 % (795068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.22/4.19 % (795068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (795068)CaDiCaL version: 2.1.3
% 28.00/4.36 % (795068)Termination reason: Instruction limit
% 28.00/4.36 % (795068)Termination phase: Saturation
% 28.00/4.36 % (795068)Time elapsed: 0.157 s
% 28.00/4.36 % (795068)Peak memory usage: 12 MB
% 28.00/4.36 % (795068)Instructions burned: 386 (million)
% 28.00/4.36 % (795099)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=1532223399:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2964 on theBenchmark for (2964ds/379Mi)
% 28.00/4.36 % (795077)Instruction limit reached!
% 28.00/4.36 % (795077)------------------------------
% 28.00/4.36 % (795077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (795077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (795077)CaDiCaL version: 2.1.3
% 28.00/4.36 % (795077)Termination reason: Instruction limit
% 28.00/4.36 % (795077)Termination phase: Saturation
% 28.00/4.36 % (795077)Time elapsed: 0.124 s
% 28.00/4.36 % (795077)Peak memory usage: 12 MB
% 28.00/4.36 % (795077)Instructions burned: 572 (million)
% 28.00/4.36 % (795124)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3728588570:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2963 on theBenchmark for (2963ds/429Mi)
% 28.00/4.36 % (795074)Instruction limit reached!
% 28.00/4.36 % (795074)------------------------------
% 28.00/4.36 % (795074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (795074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (795074)CaDiCaL version: 2.1.3
% 28.00/4.36 % (795074)Termination reason: Instruction limit
% 28.00/4.36 % (795074)Termination phase: Saturation
% 28.00/4.36 % (795074)Time elapsed: 0.137 s
% 28.00/4.36 % (795074)Peak memory usage: 13 MB
% 28.00/4.36 % (795074)Instructions burned: 300 (million)
% 28.00/4.36 % (794923)Instruction limit reached!
% 28.00/4.36 % (794923)------------------------------
% 28.00/4.36 % (794923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (794923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (794923)CaDiCaL version: 2.1.3
% 28.00/4.36 % (794923)Termination reason: Instruction limit
% 28.00/4.36 % (794923)Termination phase: Saturation
% 28.00/4.36 % (794923)Time elapsed: 1.141 s
% 28.00/4.36 % (794923)Peak memory usage: 16 MB
% 28.00/4.36 % (794923)Instructions burned: 2186 (million)
% 28.00/4.36 % (795126)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=1873945261:i=478:bd=all:rtra=on_2963 on theBenchmark for (2963ds/478Mi)
% 28.00/4.36 % (795127)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=38916394:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2963 on theBenchmark for (2963ds/445Mi)
% 28.00/4.36 % (795099)Instruction limit reached!
% 28.00/4.36 % (795099)------------------------------
% 28.00/4.36 % (795099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (795099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (795099)CaDiCaL version: 2.1.3
% 28.00/4.36 % (795099)Termination reason: Instruction limit
% 28.00/4.36 % (795099)Termination phase: Saturation
% 28.00/4.36 % (795099)Time elapsed: 0.170 s
% 28.00/4.36 % (795099)Peak memory usage: 16 MB
% 28.00/4.36 % (795099)Instructions burned: 380 (million)
% 28.00/4.36 % (795124)Instruction limit reached!
% 28.00/4.36 % (795124)------------------------------
% 28.00/4.36 % (795124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (795124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.00/4.36 % (795124)CaDiCaL version: 2.1.3
% 28.00/4.36 % (795124)Termination reason: Instruction limit
% 28.00/4.36 % (795124)Termination phase: Saturation
% 28.00/4.36 % (795124)Time elapsed: 0.107 s
% 28.00/4.36 % (795124)Peak memory usage: 17 MB
% 28.00/4.36 % (795124)Instructions burned: 433 (million)
% 28.00/4.36 % (795130)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2295298237:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2962 on theBenchmark for (2962ds/71Mi)
% 28.00/4.36 % (795131)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4066073422:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2962 on theBenchmark for (2962ds/302Mi)
% 28.00/4.36 % (795130)Instruction limit reached!
% 28.00/4.36 % (795130)------------------------------
% 28.00/4.36 % (795130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.00/4.36 % (795130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795130)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795130)Termination reason: Instruction limit
% 28.96/4.55 % (795130)Termination phase: Property scanning
% 28.96/4.55 % (795130)Time elapsed: 0.029 s
% 28.96/4.55 % (795130)Peak memory usage: 11 MB
% 28.96/4.55 % (795130)Instructions burned: 71 (million)
% 28.96/4.55 % (795134)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=802385957:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2961 on theBenchmark for (2961ds/4980Mi)
% 28.96/4.55 % (795134)Refutation not found, incomplete strategy
% 28.96/4.55 % (795134)------------------------------
% 28.96/4.55 % (795134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.55 % (795134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795134)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795134)Termination reason: Refutation not found, incomplete strategy
% 28.96/4.55 % (795134)Time elapsed: 0.018 s
% 28.96/4.55 % (795134)Peak memory usage: 12 MB
% 28.96/4.55 % (795134)Instructions burned: 42 (million)
% 28.96/4.55 % (795134)------------------------------
% 28.96/4.55 % (795134)------------------------------
% 28.96/4.55 % (795131)Instruction limit reached!
% 28.96/4.55 % (795131)------------------------------
% 28.96/4.55 % (795131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.55 % (795131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795131)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795131)Termination reason: Instruction limit
% 28.96/4.55 % (795131)Termination phase: Saturation
% 28.96/4.55 % (795131)Time elapsed: 0.075 s
% 28.96/4.55 % (795131)Peak memory usage: 14 MB
% 28.96/4.55 % (795131)Instructions burned: 302 (million)
% 28.96/4.55 % (795136)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
% 28.96/4.55 % (795136)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 28.96/4.55 % (795136)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=318485935:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2961 on theBenchmark for (2961ds/100Mi)
% 28.96/4.55 % (795137)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=2335664319:i=76:piset=equals:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/76Mi)
% 28.96/4.55 % (795137)Instruction limit reached!
% 28.96/4.55 % (795137)------------------------------
% 28.96/4.55 % (795137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.55 % (795137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795137)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795137)Termination reason: Instruction limit
% 28.96/4.55 % (795137)Termination phase: Saturation
% 28.96/4.55 % (795137)Time elapsed: 0.017 s
% 28.96/4.55 % (795137)Peak memory usage: 12 MB
% 28.96/4.55 % (795137)Instructions burned: 80 (million)
% 28.96/4.55 % (795140)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=3007993856:i=289:rtra=on_2961 on theBenchmark for (2961ds/289Mi)
% 28.96/4.55 % (795136)Instruction limit reached!
% 28.96/4.55 % (795136)------------------------------
% 28.96/4.55 % (795136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.55 % (795136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795136)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795136)Termination reason: Instruction limit
% 28.96/4.55 % (795136)Termination phase: Twee Goal Transformation
% 28.96/4.55 % (795136)Time elapsed: 0.042 s
% 28.96/4.55 % (795136)Peak memory usage: 11 MB
% 28.96/4.55 % (795136)Instructions burned: 102 (million)
% 28.96/4.55 % (795127)Instruction limit reached!
% 28.96/4.55 % (795127)------------------------------
% 28.96/4.55 % (795127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.96/4.55 % (795127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.96/4.55 % (795127)CaDiCaL version: 2.1.3
% 28.96/4.55 % (795127)Termination reason: Instruction limit
% 28.96/4.55 % (795127)Termination phase: Saturation
% 28.96/4.55 % (795127)Time elapsed: 0.205 s
% 28.96/4.55 % (795127)Peak memory usage: 16 MB
% 28.96/4.55 % (795127)Instructions burned: 445 (million)
% 28.96/4.55 % (795126)Instruction limit reached!
% 30.60/4.72 % (795126)------------------------------
% 30.60/4.72 % (795126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.60/4.72 % (795126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.60/4.72 % (795126)CaDiCaL version: 2.1.3
% 30.60/4.72 % (795126)Termination reason: Instruction limit
% 30.60/4.72 % (795126)Termination phase: Saturation
% 30.60/4.72 % (795126)Time elapsed: 0.232 s
% 30.60/4.72 % (795126)Peak memory usage: 18 MB
% 30.60/4.72 % (795126)Instructions burned: 478 (million)
% 30.60/4.72 % (795142)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=4223868191:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2960 on theBenchmark for (2960ds/493Mi)
% 30.60/4.72 % (795143)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=2822927376:cond=on:i=34:hud=10:nm=10:rtra=on_2960 on theBenchmark for (2960ds/34Mi)
% 30.60/4.72 % (795144)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 30.60/4.72 % (795144)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=157261790:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2960 on theBenchmark for (2960ds/372Mi)
% 30.60/4.72 % (795143)Instruction limit reached!
% 30.60/4.72 % (795143)------------------------------
% 30.60/4.72 % (795143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.60/4.72 % (795143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.60/4.72 % (795143)CaDiCaL version: 2.1.3
% 30.60/4.72 % (795143)Termination reason: Instruction limit
% 30.60/4.72 % (795143)Termination phase: Property scanning
% 30.60/4.72 % (795143)Time elapsed: 0.015 s
% 30.60/4.72 % (795143)Peak memory usage: 10 MB
% 30.60/4.72 % (795143)Instructions burned: 35 (million)
% 30.60/4.72 % (795148)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=1281035628:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2960 on theBenchmark for (2960ds/670Mi)
% 30.60/4.72 % (795140)Instruction limit reached!
% 30.60/4.72 % (795140)------------------------------
% 30.60/4.72 % (795140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.60/4.72 % (795140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.60/4.72 % (795140)CaDiCaL version: 2.1.3
% 30.60/4.72 % (795140)Termination reason: Instruction limit
% 30.60/4.72 % (795140)Termination phase: Saturation
% 30.60/4.72 % (795140)Time elapsed: 0.070 s
% 30.60/4.72 % (795140)Peak memory usage: 15 MB
% 30.60/4.72 % (795140)Instructions burned: 289 (million)
% 30.60/4.72 % (794804)Instruction limit reached!
% 30.60/4.72 % (794804)------------------------------
% 30.60/4.72 % (794804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.60/4.72 % (794804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.60/4.72 % (794804)CaDiCaL version: 2.1.3
% 30.60/4.72 % (794804)Termination reason: Instruction limit
% 30.60/4.72 % (794804)Termination phase: Saturation
% 30.60/4.72 % (794804)Time elapsed: 3.128 s
% 30.60/4.72 % (794804)Peak memory usage: 38 MB
% 30.60/4.72 % (794804)Instructions burned: 5756 (million)
% 30.60/4.72 % (795150)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4077685233:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2960 on theBenchmark for (2960ds/647Mi)
% 30.60/4.72 % (795152)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=523766260:i=857:add=off:kws=frequency:rtra=on:ntd=on_2960 on theBenchmark for (2960ds/857Mi)
% 30.60/4.72 % (794938)Instruction limit reached!
% 30.60/4.72 % (794938)------------------------------
% 30.60/4.72 % (794938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.60/4.72 % (794938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.60/4.72 % (794938)CaDiCaL version: 2.1.3
% 30.60/4.72 % (794938)Termination reason: Instruction limit
% 30.60/4.72 % (794938)Termination phase: Saturation
% 30.60/4.72 % (794938)Time elapsed: 1.055 s
% 30.60/4.72 % (794938)Peak memory usage: 18 MB
% 30.60/4.72 % (794938)Instructions burned: 2470 (million)
% 30.60/4.72 % (795154)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=4195147235:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2959 on theBenchmark for (2959ds/693Mi)
% 33.57/5.09 % (795144)Instruction limit reached!
% 33.57/5.09 % (795144)------------------------------
% 33.57/5.09 % (795144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795144)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795144)Termination reason: Instruction limit
% 33.57/5.09 % (795144)Termination phase: Saturation
% 33.57/5.09 % (795144)Time elapsed: 0.166 s
% 33.57/5.09 % (795144)Peak memory usage: 16 MB
% 33.57/5.09 % (795144)Instructions burned: 373 (million)
% 33.57/5.09 % (795156)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=3524516873:i=285:hud=10:bd=all:rtra=on:ss=axioms_2958 on theBenchmark for (2958ds/285Mi)
% 33.57/5.09 % (795150)Instruction limit reached!
% 33.57/5.09 % (795150)------------------------------
% 33.57/5.09 % (795150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795150)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795150)Termination reason: Instruction limit
% 33.57/5.09 % (795150)Termination phase: Saturation
% 33.57/5.09 % (795150)Time elapsed: 0.166 s
% 33.57/5.09 % (795150)Peak memory usage: 18 MB
% 33.57/5.09 % (795150)Instructions burned: 650 (million)
% 33.57/5.09 % (795158)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 33.57/5.09 % (795158)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3200321200:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2958 on theBenchmark for (2958ds/52Mi)
% 33.57/5.09 % (795158)Instruction limit reached!
% 33.57/5.09 % (795158)------------------------------
% 33.57/5.09 % (795158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795158)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795158)Termination reason: Instruction limit
% 33.57/5.09 % (795158)Termination phase: Preprocessing 3
% 33.57/5.09 % (795158)Time elapsed: 0.024 s
% 33.57/5.09 % (795158)Peak memory usage: 11 MB
% 33.57/5.09 % (795158)Instructions burned: 54 (million)
% 33.57/5.09 % (795142)Instruction limit reached!
% 33.57/5.09 % (795142)------------------------------
% 33.57/5.09 % (795142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795142)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795142)Termination reason: Instruction limit
% 33.57/5.09 % (795142)Termination phase: Saturation
% 33.57/5.09 % (795142)Time elapsed: 0.268 s
% 33.57/5.09 % (795142)Peak memory usage: 15 MB
% 33.57/5.09 % (795142)Instructions burned: 494 (million)
% 33.57/5.09 % (795160)dis+10_1_si=on:random_seed=2208804868:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2958 on theBenchmark for (2958ds/407Mi)
% 33.57/5.09 % (795161)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=1291980295:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2958 on theBenchmark for (2958ds/2240Mi)
% 33.57/5.09 % (795156)Instruction limit reached!
% 33.57/5.09 % (795156)------------------------------
% 33.57/5.09 % (795156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795156)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795156)Termination reason: Instruction limit
% 33.57/5.09 % (795156)Termination phase: Saturation
% 33.57/5.09 % (795156)Time elapsed: 0.136 s
% 33.57/5.09 % (795156)Peak memory usage: 14 MB
% 33.57/5.09 % (795156)Instructions burned: 285 (million)
% 33.57/5.09 % (795148)Instruction limit reached!
% 33.57/5.09 % (795148)------------------------------
% 33.57/5.09 % (795148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.57/5.09 % (795148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.57/5.09 % (795148)CaDiCaL version: 2.1.3
% 33.57/5.09 % (795148)Termination reason: Instruction limit
% 33.57/5.09 % (795148)Termination phase: Saturation
% 33.57/5.09 % (795148)Time elapsed: 0.315 s
% 33.57/5.09 % (795148)Peak memory usage: 18 MB
% 35.27/5.37 % (795148)Instructions burned: 671 (million)
% 35.27/5.37 % (795164)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=4155315633:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2957 on theBenchmark for (2957ds/336Mi)
% 35.27/5.37 % (795165)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=3125731591:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2957 on theBenchmark for (2957ds/1142Mi)
% 35.27/5.37 % (795160)Instruction limit reached!
% 35.27/5.37 % (795160)------------------------------
% 35.27/5.37 % (795160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.27/5.37 % (795160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.27/5.37 % (795160)CaDiCaL version: 2.1.3
% 35.27/5.37 % (795160)Termination reason: Instruction limit
% 35.27/5.37 % (795160)Termination phase: Saturation
% 35.27/5.37 % (795160)Time elapsed: 0.110 s
% 35.27/5.37 % (795160)Peak memory usage: 17 MB
% 35.27/5.37 % (795160)Instructions burned: 408 (million)
% 35.27/5.37 % (795168)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1936464861:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2956 on theBenchmark for (2956ds/376Mi)
% 35.27/5.37 % (795152)Instruction limit reached!
% 35.27/5.37 % (795152)------------------------------
% 35.27/5.37 % (795152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.27/5.37 % (795152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.27/5.37 % (795152)CaDiCaL version: 2.1.3
% 35.27/5.37 % (795152)Termination reason: Instruction limit
% 35.27/5.37 % (795152)Termination phase: Saturation
% 35.27/5.37 % (795152)Time elapsed: 0.370 s
% 35.27/5.37 % (795152)Peak memory usage: 17 MB
% 35.27/5.37 % (795152)Instructions burned: 857 (million)
% 35.27/5.37 % (795154)Instruction limit reached!
% 35.27/5.37 % (795154)------------------------------
% 35.27/5.37 % (795154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.27/5.37 % (795154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.27/5.37 % (795154)CaDiCaL version: 2.1.3
% 35.27/5.37 % (795154)Termination reason: Instruction limit
% 35.27/5.37 % (795154)Termination phase: Saturation
% 35.27/5.37 % (795154)Time elapsed: 0.285 s
% 35.27/5.37 % (795154)Peak memory usage: 13 MB
% 35.27/5.37 % (795154)Instructions burned: 693 (million)
% 35.27/5.37 % (795170)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=3169699282:i=766:bd=all:rtra=on_2956 on theBenchmark for (2956ds/766Mi)
% 35.27/5.37 % (795171)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 35.27/5.37 % (795171)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=1159961062:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2956 on theBenchmark for (2956ds/959Mi)
% 35.27/5.37 % (795168)Instruction limit reached!
% 35.27/5.37 % (795168)------------------------------
% 35.27/5.37 % (795168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.27/5.37 % (795168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.27/5.37 % (795168)CaDiCaL version: 2.1.3
% 35.27/5.37 % (795168)Termination reason: Instruction limit
% 35.27/5.37 % (795168)Termination phase: Saturation
% 35.27/5.37 % (795168)Time elapsed: 0.091 s
% 35.27/5.37 % (795168)Peak memory usage: 16 MB
% 35.27/5.37 % (795168)Instructions burned: 377 (million)
% 35.27/5.37 % (795164)Instruction limit reached!
% 35.27/5.37 % (795164)------------------------------
% 35.27/5.37 % (795164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.27/5.37 % (795164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.27/5.37 % (795164)CaDiCaL version: 2.1.3
% 35.27/5.37 % (795164)Termination reason: Instruction limit
% 35.27/5.37 % (795164)Termination phase: Saturation
% 35.27/5.37 % (795164)Time elapsed: 0.149 s
% 35.27/5.37 % (795164)Peak memory usage: 16 MB
% 35.27/5.37 % (795164)Instructions burned: 337 (million)
% 35.27/5.37 % (795174)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=3932155256:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2955 on theBenchmark for (2955ds/6359Mi)
% 35.27/5.37 % (795175)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2458013252:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2955 on theBenchmark for (2955ds/35Mi)
% 36.65/5.53 % (795175)Instruction limit reached!
% 36.65/5.53 % (795175)------------------------------
% 36.65/5.53 % (795175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795175)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795175)Termination reason: Instruction limit
% 36.65/5.53 % (795175)Termination phase: SInE selection
% 36.65/5.53 % (795175)Time elapsed: 0.015 s
% 36.65/5.53 % (795175)Peak memory usage: 10 MB
% 36.65/5.53 % (795175)Instructions burned: 36 (million)
% 36.65/5.53 % (795178)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=384098414:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2955 on theBenchmark for (2955ds/53Mi)
% 36.65/5.53 % (795178)Instruction limit reached!
% 36.65/5.53 % (795178)------------------------------
% 36.65/5.53 % (795178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795178)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795178)Termination reason: Instruction limit
% 36.65/5.53 % (795178)Termination phase: Property scanning
% 36.65/5.53 % (795178)Time elapsed: 0.022 s
% 36.65/5.53 % (795178)Peak memory usage: 10 MB
% 36.65/5.53 % (795178)Instructions burned: 53 (million)
% 36.65/5.53 % (795180)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=2140772412:s2a=on:i=876:s2at=6:nm=2:rtra=on_2954 on theBenchmark for (2954ds/876Mi)
% 36.65/5.53 % (795170)Instruction limit reached!
% 36.65/5.53 % (795170)------------------------------
% 36.65/5.53 % (795170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795170)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795170)Termination reason: Instruction limit
% 36.65/5.53 % (795170)Termination phase: Saturation
% 36.65/5.53 % (795170)Time elapsed: 0.367 s
% 36.65/5.53 % (795170)Peak memory usage: 20 MB
% 36.65/5.53 % (795170)Instructions burned: 767 (million)
% 36.65/5.53 % (795182)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2633232062:i=57:ep=R:rtra=on:ntd=on_2952 on theBenchmark for (2952ds/57Mi)
% 36.65/5.53 % (795165)Refutation not found, incomplete strategy
% 36.65/5.53 % (795165)------------------------------
% 36.65/5.53 % (795165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795165)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795165)Termination reason: Refutation not found, incomplete strategy
% 36.65/5.53 % (795165)Time elapsed: 0.496 s
% 36.65/5.53 % (795165)Peak memory usage: 19 MB
% 36.65/5.53 % (795165)Instructions burned: 944 (million)
% 36.65/5.53 % (795165)------------------------------
% 36.65/5.53 % (795165)------------------------------
% 36.65/5.53 % (795182)Instruction limit reached!
% 36.65/5.53 % (795182)------------------------------
% 36.65/5.53 % (795182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795182)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795182)Termination reason: Instruction limit
% 36.65/5.53 % (795182)Termination phase: Property scanning
% 36.65/5.53 % (795182)Time elapsed: 0.024 s
% 36.65/5.53 % (795182)Peak memory usage: 11 MB
% 36.65/5.53 % (795182)Instructions burned: 58 (million)
% 36.65/5.53 % (795184)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 36.65/5.53 % (795171)Instruction limit reached!
% 36.65/5.53 % (795171)------------------------------
% 36.65/5.53 % (795171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.65/5.53 % (795171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.65/5.53 % (795171)CaDiCaL version: 2.1.3
% 36.65/5.53 % (795171)Termination reason: Instruction limit
% 36.65/5.53 % (795171)Termination phase: Saturation
% 36.65/5.53 % (795171)Time elapsed: 0.419 s
% 36.65/5.53 % (795171)Peak memory usage: 19 MB
% 36.65/5.53 % (795171)Instructions burned: 959 (million)
% 36.65/5.53 % (795184)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=2447082424:i=306:bd=all:rtra=on_2951 on theBenchmark for (2951ds/306Mi)
% 37.84/5.72 % (795185)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=2534154790:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2951 on theBenchmark for (2951ds/262Mi)
% 37.84/5.72 % (795187)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 37.84/5.72 % (795187)ott+1002_16_sil=128000:si=on:random_seed=2253286186:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2951 on theBenchmark for (2951ds/409Mi)
% 37.84/5.72 % (795185)Instruction limit reached!
% 37.84/5.72 % (795185)------------------------------
% 37.84/5.72 % (795185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.72 % (795185)CaDiCaL version: 2.1.3
% 37.84/5.72 % (795185)Termination reason: Instruction limit
% 37.84/5.72 % (795185)Termination phase: Saturation
% 37.84/5.72 % (795185)Time elapsed: 0.113 s
% 37.84/5.72 % (795185)Peak memory usage: 15 MB
% 37.84/5.72 % (795185)Instructions burned: 263 (million)
% 37.84/5.72 % (795190)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=2309879068:s2a=on:i=381:rtra=on_2950 on theBenchmark for (2950ds/381Mi)
% 37.84/5.72 % (795184)Instruction limit reached!
% 37.84/5.72 % (795184)------------------------------
% 37.84/5.72 % (795184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.72 % (795184)CaDiCaL version: 2.1.3
% 37.84/5.72 % (795184)Termination reason: Instruction limit
% 37.84/5.72 % (795184)Termination phase: Saturation
% 37.84/5.72 % (795184)Time elapsed: 0.138 s
% 37.84/5.72 % (795184)Peak memory usage: 16 MB
% 37.84/5.72 % (795184)Instructions burned: 306 (million)
% 37.84/5.72 % (795180)Instruction limit reached!
% 37.84/5.72 % (795180)------------------------------
% 37.84/5.72 % (795180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.72 % (795180)CaDiCaL version: 2.1.3
% 37.84/5.72 % (795180)Termination reason: Instruction limit
% 37.84/5.72 % (795180)Termination phase: Saturation
% 37.84/5.72 % (795180)Time elapsed: 0.437 s
% 37.84/5.72 % (795180)Peak memory usage: 17 MB
% 37.84/5.72 % (795180)Instructions burned: 876 (million)
% 37.84/5.72 % (795192)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3816066405:cond=on:i=324:rtra=on:ntd=on_2950 on theBenchmark for (2950ds/324Mi)
% 37.84/5.72 % (795193)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=2475524655:i=240:kws=inv_precedence:rtra=on_2950 on theBenchmark for (2950ds/240Mi)
% 37.84/5.72 % (795187)Instruction limit reached!
% 37.84/5.72 % (795187)------------------------------
% 37.84/5.72 % (795187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.72 % (795187)CaDiCaL version: 2.1.3
% 37.84/5.72 % (795187)Termination reason: Instruction limit
% 37.84/5.72 % (795187)Termination phase: Saturation
% 37.84/5.72 % (795187)Time elapsed: 0.184 s
% 37.84/5.72 % (795187)Peak memory usage: 17 MB
% 37.84/5.72 % (795187)Instructions burned: 409 (million)
% 37.84/5.72 % (795196)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 37.84/5.72 % (795196)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3840164789:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2949 on theBenchmark for (2949ds/124Mi)
% 37.84/5.72 % (795196)Instruction limit reached!
% 37.84/5.72 % (795196)------------------------------
% 37.84/5.72 % (795196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.72 % (795196)CaDiCaL version: 2.1.3
% 37.84/5.72 % (795196)Termination reason: Instruction limit
% 37.84/5.72 % (795196)Termination phase: Property scanning
% 37.84/5.72 % (795196)Time elapsed: 0.055 s
% 37.84/5.72 % (795196)Peak memory usage: 13 MB
% 37.84/5.72 % (795196)Instructions burned: 126 (million)
% 37.84/5.72 % (795193)Instruction limit reached!
% 37.84/5.72 % (795193)------------------------------
% 37.84/5.72 % (795193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.72 % (795193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795193)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795193)Termination reason: Instruction limit
% 37.84/5.78 % (795193)Termination phase: Saturation
% 37.84/5.78 % (795193)Time elapsed: 0.116 s
% 37.84/5.78 % (795193)Peak memory usage: 16 MB
% 37.84/5.78 % (795193)Instructions burned: 241 (million)
% 37.84/5.78 % (795198)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=3131165491:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2948 on theBenchmark for (2948ds/223Mi)
% 37.84/5.78 % (795199)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3188407172:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2948 on theBenchmark for (2948ds/282Mi)
% 37.84/5.78 % (795190)Instruction limit reached!
% 37.84/5.78 % (795190)------------------------------
% 37.84/5.78 % (795190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.78 % (795190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795190)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795190)Termination reason: Instruction limit
% 37.84/5.78 % (795190)Termination phase: Saturation
% 37.84/5.78 % (795190)Time elapsed: 0.173 s
% 37.84/5.78 % (795190)Peak memory usage: 17 MB
% 37.84/5.78 % (795190)Instructions burned: 381 (million)
% 37.84/5.78 % (795192)Instruction limit reached!
% 37.84/5.78 % (795192)------------------------------
% 37.84/5.78 % (795192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.78 % (795192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795192)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795192)Termination reason: Instruction limit
% 37.84/5.78 % (795192)Termination phase: Saturation
% 37.84/5.78 % (795192)Time elapsed: 0.149 s
% 37.84/5.78 % (795192)Peak memory usage: 16 MB
% 37.84/5.78 % (795192)Instructions burned: 325 (million)
% 37.84/5.78 % (795202)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=655419664:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2948 on theBenchmark for (2948ds/464Mi)
% 37.84/5.78 % (795203)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=1248268160:i=88:s2at=3:nm=2:rtra=on:rawr=on_2948 on theBenchmark for (2948ds/88Mi)
% 37.84/5.78 % (795203)Instruction limit reached!
% 37.84/5.78 % (795203)------------------------------
% 37.84/5.78 % (795203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.78 % (795203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795203)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795203)Termination reason: Instruction limit
% 37.84/5.78 % (795203)Termination phase: Property scanning
% 37.84/5.78 % (795203)Time elapsed: 0.037 s
% 37.84/5.78 % (795203)Peak memory usage: 11 MB
% 37.84/5.78 % (795203)Instructions burned: 90 (million)
% 37.84/5.78 % (795206)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1648228299:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2948 on theBenchmark for (2948ds/280Mi)
% 37.84/5.78 % (795198)Instruction limit reached!
% 37.84/5.78 % (795198)------------------------------
% 37.84/5.78 % (795198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.78 % (795198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795198)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795198)Termination reason: Instruction limit
% 37.84/5.78 % (795198)Termination phase: Saturation
% 37.84/5.78 % (795198)Time elapsed: 0.096 s
% 37.84/5.78 % (795198)Peak memory usage: 14 MB
% 37.84/5.78 % (795198)Instructions burned: 223 (million)
% 37.84/5.78 % (795208)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 37.84/5.78 % (795208)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1487305698:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2947 on theBenchmark for (2947ds/4386Mi)
% 37.84/5.78 % (795199)Instruction limit reached!
% 37.84/5.78 % (795199)------------------------------
% 37.84/5.78 % (795199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.78 % (795199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.78 % (795199)CaDiCaL version: 2.1.3
% 37.84/5.78 % (795199)Termination reason: Instruction limit
% 37.84/5.78 % (795199)Termination phase: Saturation
% 37.84/5.78 % (795199)Time elapsed: 0.124 s
% 37.84/5.78 % (795199)Peak memory usage: 15 MB
% 37.84/5.78 % (795199)Instructions burned: 283 (million)
% 37.84/5.78 % (795210)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 37.84/5.79 % (795210)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 37.84/5.79 % (795210)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=1271476260:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2947 on theBenchmark for (2947ds/483Mi)
% 37.84/5.79 % (795206)Instruction limit reached!
% 37.84/5.79 % (795206)------------------------------
% 37.84/5.79 % (795206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795206)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795206)Termination reason: Instruction limit
% 37.84/5.79 % (795206)Termination phase: Saturation
% 37.84/5.79 % (795206)Time elapsed: 0.118 s
% 37.84/5.79 % (795206)Peak memory usage: 13 MB
% 37.84/5.79 % (795206)Instructions burned: 282 (million)
% 37.84/5.79 % (795212)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3102164698:i=73:rtra=on_2946 on theBenchmark for (2946ds/73Mi)
% 37.84/5.79 % (795202)Instruction limit reached!
% 37.84/5.79 % (795202)------------------------------
% 37.84/5.79 % (795202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795202)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795202)Termination reason: Instruction limit
% 37.84/5.79 % (795202)Termination phase: Saturation
% 37.84/5.79 % (795202)Time elapsed: 0.199 s
% 37.84/5.79 % (795202)Peak memory usage: 17 MB
% 37.84/5.79 % (795202)Instructions burned: 465 (million)
% 37.84/5.79 % (795214)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2404501898:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2946 on theBenchmark for (2946ds/176Mi)
% 37.84/5.79 % (795212)Instruction limit reached!
% 37.84/5.79 % (795212)------------------------------
% 37.84/5.79 % (795212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795212)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795212)Termination reason: Instruction limit
% 37.84/5.79 % (795212)Termination phase: Preprocessing 3
% 37.84/5.79 % (795212)Time elapsed: 0.033 s
% 37.84/5.79 % (795212)Peak memory usage: 12 MB
% 37.84/5.79 % (795212)Instructions burned: 74 (million)
% 37.84/5.79 % (795216)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 37.84/5.79 % (795216)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=272547032:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2946 on theBenchmark for (2946ds/39Mi)
% 37.84/5.79 % (795216)Instruction limit reached!
% 37.84/5.79 % (795216)------------------------------
% 37.84/5.79 % (795216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795216)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795216)Termination reason: Instruction limit
% 37.84/5.79 % (795216)Termination phase: Property scanning
% 37.84/5.79 % (795216)Time elapsed: 0.017 s
% 37.84/5.79 % (795216)Peak memory usage: 10 MB
% 37.84/5.79 % (795216)Instructions burned: 40 (million)
% 37.84/5.79 % (795218)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=60283272:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2945 on theBenchmark for (2945ds/708Mi)
% 37.84/5.79 % (795214)Instruction limit reached!
% 37.84/5.79 % (795214)------------------------------
% 37.84/5.79 % (795214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795214)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795214)Termination reason: Instruction limit
% 37.84/5.79 % (795214)Termination phase: Saturation
% 37.84/5.79 % (795214)Time elapsed: 0.073 s
% 37.84/5.79 % (795214)Peak memory usage: 12 MB
% 37.84/5.79 % (795214)Instructions burned: 177 (million)
% 37.84/5.79 % (795220)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 37.84/5.79 % (795220)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2286541393:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2945 on theBenchmark for (2945ds/252Mi)
% 37.84/5.79 % (795174) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-794510-795174"...
% 37.84/5.79 % (795210)Instruction limit reached!
% 37.84/5.79 % (795210)------------------------------
% 37.84/5.79 % (795210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.84/5.79 % (795210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.84/5.79 % (795210)CaDiCaL version: 2.1.3
% 37.84/5.79 % (795210)Termination reason: Instruction limit
% 37.84/5.79 % (795210)Termination phase: Saturation
% 37.84/5.79 % (795210)Time elapsed: 0.223 s
% 37.84/5.79 % (795210)Peak memory usage: 17 MB
% 37.84/5.79 % (795210)Instructions burned: 485 (million)
% 37.84/5.79 % (795174)...printing done.
% 37.84/5.79 % (795222)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=1883704229:i=823:fsr=off:rtra=on_2945 on theBenchmark for (2945ds/823Mi)
% 37.84/5.79 % (795174)Refutation found. Thanks to Tanya!
% 37.84/5.79 % SZS status Theorem for theBenchmark
% 37.84/5.79 % SZS output start Proof for theBenchmark
% 37.84/5.79 thf(type_def_5, type, term: $tType).
% 37.84/5.79 thf(type_def_6, type, subst: $tType).
% 37.84/5.79 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 37.84/5.79 thf(type_def_8, type, d_term: $tType).
% 37.84/5.79 thf(type_def_9, type, d_subst: $tType).
% 37.84/5.79 thf(func_def_0, type, one: term).
% 37.84/5.79 thf(func_def_1, type, ap: (term > term > term)).
% 37.84/5.79 thf(func_def_2, type, lam: (term > term)).
% 37.84/5.79 thf(func_def_3, type, sub: (term > subst > term)).
% 37.84/5.79 thf(func_def_4, type, id: subst).
% 37.84/5.79 thf(func_def_5, type, sh: subst).
% 37.84/5.79 thf(func_def_6, type, push: (term > subst > subst)).
% 37.84/5.79 thf(func_def_7, type, comp: (subst > subst > subst)).
% 37.84/5.79 thf(func_def_8, type, var: (term > $o)).
% 37.84/5.79 thf(func_def_9, type, pushprop_lem1v2: $o).
% 37.84/5.79 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 37.84/5.79 thf(func_def_11, type, axmap: $o).
% 37.84/5.79 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 37.84/5.79 thf(func_def_13, type, shinj: $o).
% 37.84/5.79 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 37.84/5.79 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 37.84/5.79 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 37.84/5.79 thf(func_def_17, type, induction2lem: $o).
% 37.84/5.79 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 37.84/5.79 thf(func_def_19, type, axvarshift: $o).
% 37.84/5.79 thf(func_def_20, type, hoasapinj2: $o).
% 37.84/5.79 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 37.84/5.79 thf(func_def_22, type, hoasapinj1: $o).
% 37.84/5.79 thf(func_def_23, type, ulamvar1: $o).
% 37.84/5.79 thf(func_def_24, type, induction2lem_lthm: $o).
% 37.84/5.79 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 37.84/5.79 thf(func_def_26, type, apnotvar: $o).
% 37.84/5.79 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 37.84/5.79 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 37.84/5.79 thf(func_def_29, type, hoasinduction_lthm: $o).
% 37.84/5.79 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 37.84/5.79 thf(func_def_31, type, hoaslaminj: $o).
% 37.84/5.79 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 37.84/5.79 thf(func_def_33, type, induction2lem_gthm: $o).
% 37.84/5.79 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 37.84/5.79 thf(func_def_35, type, hoasinduction_lem3: $o).
% 37.84/5.79 thf(func_def_36, type, hoasinduction_lem2: $o).
% 37.84/5.79 thf(func_def_37, type, termmset_lthm: $o).
% 37.84/5.79 thf(func_def_38, type, hoasinduction_lem1: $o).
% 37.84/5.79 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 37.84/5.79 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 37.84/5.79 thf(func_def_41, type, hoasapnotvar: $o).
% 37.84/5.79 thf(func_def_42, type, hoasinduction_lem0: $o).
% 37.84/5.79 thf(func_def_43, type, hoasinduction: $o).
% 37.84/5.79 thf(func_def_44, type, hoasinduction_gthm: $o).
% 37.84/5.79 thf(func_def_45, type, axapp: $o).
% 37.84/5.79 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 37.84/5.79 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 37.84/5.79 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 37.84/5.79 thf(func_def_49, type, ulamvarind: $o).
% 37.84/5.79 thf(func_def_50, type, induction: $o).
% 37.84/5.79 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 37.84/5.79 thf(func_def_52, type, termmset_gthm: $o).
% 37.84/5.79 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 37.84/5.79 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 37.84/5.79 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 37.84/5.79 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 37.84/5.79 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 37.84/5.79 thf(func_def_58, type, pushprop_lem2v2: $o).
% 37.84/5.79 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 37.84/5.79 thf(func_def_60, type, axclos: $o).
% 37.84/5.79 thf(func_def_61, type, axassoc: $o).
% 37.84/5.79 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 37.84/5.79 thf(func_def_63, type, pushprop_lthm: $o).
% 37.84/5.79 thf(func_def_64, type, apinj2: $o).
% 37.84/5.79 thf(func_def_65, type, apinj1: $o).
% 37.84/5.79 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 37.84/5.79 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 37.84/5.79 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 37.84/5.79 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 37.84/5.79 thf(func_def_70, type, axvarcons: $o).
% 37.84/5.79 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 37.84/5.79 thf(func_def_72, type, axscons: $o).
% 37.84/5.79 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 37.84/5.79 thf(func_def_74, type, axidr: $o).
% 37.84/5.79 thf(func_def_75, type, pushprop_lem1: $o).
% 37.84/5.79 thf(func_def_76, type, laminj: $o).
% 37.84/5.79 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 37.84/5.79 thf(func_def_78, type, pushprop_lem0: $o).
% 37.84/5.79 thf(func_def_79, type, pushprop_gthm: $o).
% 37.84/5.79 thf(func_def_80, type, axabs: $o).
% 37.84/5.79 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 37.84/5.79 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 37.84/5.79 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 37.84/5.79 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 37.84/5.79 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 37.84/5.79 thf(func_def_86, type, lamnotap: $o).
% 37.84/5.79 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 37.84/5.79 thf(func_def_88, type, hoaslamnotvar: $o).
% 37.84/5.79 thf(func_def_89, type, axidl: $o).
% 37.84/5.79 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 37.84/5.79 thf(func_def_91, type, induction2_lthm: $o).
% 37.84/5.79 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 37.84/5.79 thf(func_def_93, type, substmonoid_lthm: $o).
% 37.84/5.79 thf(func_def_94, type, pushprop: $o).
% 37.84/5.79 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 37.84/5.79 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 37.84/5.79 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 37.84/5.79 thf(func_def_98, type, substmonoid: $o).
% 37.84/5.79 thf(func_def_99, type, lamnotvar: $o).
% 37.84/5.79 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 37.84/5.79 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 37.84/5.79 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 37.84/5.79 thf(func_def_103, type, induction2_gthm: $o).
% 37.84/5.79 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 37.84/5.79 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_106, type, hoaslamnotap: $o).
% 37.84/5.79 thf(func_def_107, type, substmonoid_gthm: $o).
% 37.84/5.79 thf(func_def_108, type, ulamvarsh: $o).
% 37.84/5.79 thf(func_def_109, type, induction2: $o).
% 37.84/5.79 thf(func_def_110, type, pushprop_lem3v2: $o).
% 37.84/5.79 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 37.84/5.79 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 37.84/5.79 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 37.84/5.79 thf(func_def_114, type, axshiftcons: $o).
% 37.84/5.79 thf(func_def_115, type, termmset: $o).
% 37.84/5.79 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 37.84/5.79 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 37.84/5.79 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 37.84/5.79 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 37.84/5.79 thf(func_def_120, type, axvarid: $o).
% 37.84/5.79 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 37.84/5.79 thf(func_def_122, type, d2term: (d_term > term)).
% 37.84/5.79 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 37.84/5.79 thf(func_def_124, type, d_one: d_term).
% 37.84/5.79 thf(func_def_125, type, d_id: d_subst).
% 37.84/5.79 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 37.84/5.79 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 37.84/5.79 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 37.84/5.79 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)).
% 37.84/5.79 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)).
% 37.84/5.79 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)).
% 37.84/5.79 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 37.84/5.79 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 37.84/5.79 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_138, type, sP1: $o).
% 37.84/5.79 thf(func_def_139, type, sP2: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_140, type, sP3: $o).
% 37.84/5.79 thf(func_def_141, type, sP4: $o).
% 37.84/5.79 thf(func_def_142, type, sP5: $o).
% 37.84/5.79 thf(func_def_143, type, sP6: $o).
% 37.84/5.79 thf(func_def_144, type, sP7: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_145, type, sP8: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_146, type, sP9: $o).
% 37.84/5.79 thf(func_def_147, type, sP10: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_149, type, sP12: $o).
% 37.84/5.79 thf(func_def_150, type, sP13: $o).
% 37.84/5.79 thf(func_def_151, type, sP14: $o).
% 37.84/5.79 thf(func_def_152, type, sP15: $o).
% 37.84/5.79 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_154, type, sP17: $o).
% 37.84/5.79 thf(func_def_155, type, sP18: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_156, type, sP19: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_157, type, sP20: $o).
% 37.84/5.79 thf(func_def_158, type, sP21: $o).
% 37.84/5.79 thf(func_def_159, type, sP22: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_160, type, sP23: $o).
% 37.84/5.79 thf(func_def_161, type, sP24: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_162, type, sP25: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_163, type, sP26: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_164, type, sP27: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_165, type, sP28: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_166, type, sP29: $o).
% 37.84/5.79 thf(func_def_167, type, sP30: $o).
% 37.84/5.79 thf(func_def_168, type, sP31: $o).
% 37.84/5.79 thf(func_def_169, type, sP32: $o).
% 37.84/5.79 thf(func_def_170, type, sP33: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_171, type, sP34: $o).
% 37.84/5.79 thf(func_def_172, type, sP35: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_173, type, sP36: $o).
% 37.84/5.79 thf(func_def_174, type, sP37: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_175, type, sP38: $o).
% 37.84/5.79 thf(func_def_176, type, sP39: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_177, type, sP40: $o).
% 37.84/5.79 thf(func_def_178, type, sP41: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_179, type, sP42: $o).
% 37.84/5.79 thf(func_def_180, type, sP43: $o).
% 37.84/5.79 thf(func_def_181, type, sP44: $o).
% 37.84/5.79 thf(func_def_182, type, sP45: $o).
% 37.84/5.79 thf(func_def_183, type, sP46: $o).
% 37.84/5.79 thf(func_def_184, type, sP47: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_185, type, sP48: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_186, type, sP49: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_187, type, sP50: $o).
% 37.84/5.79 thf(func_def_188, type, sP51: $o).
% 37.84/5.79 thf(func_def_189, type, sP52: $o).
% 37.84/5.79 thf(func_def_190, type, sP53: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_191, type, sP54: $o).
% 37.84/5.79 thf(func_def_192, type, sP55: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_193, type, sP56: ((term > $o) > $o)).
% 37.84/5.79 thf(func_def_194, type, sP57: $o).
% 37.84/5.79 thf(func_def_195, type, sP58: $o).
% 37.84/5.79 thf(func_def_196, type, sP59: $o).
% 37.84/5.79 thf(func_def_197, type, sP60: ((subst > term > subst > $o) > $o)).
% 37.84/5.79 thf(func_def_198, type, sK61: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_199, type, sK62: term).
% 37.84/5.79 thf(func_def_200, type, sK63: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_202, type, sK65: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_203, type, sK66: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_204, type, sK67: (term > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_205, type, sK68: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_206, type, sK69: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_207, type, sK70: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_209, type, sK72: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_210, type, sK73: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_211, type, sK74: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_212, type, sK75: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_213, type, sK76: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_214, type, sK77: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_215, type, sK78: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_216, type, sK79: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_217, type, sK80: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_218, type, sK81: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_219, type, sK82: term).
% 37.84/5.79 thf(func_def_220, type, sK83: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_221, type, sK84: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_222, type, sK85: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_223, type, sK86: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_224, type, sK87: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_225, type, sK88: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_226, type, sK89: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_227, type, sK90: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_228, type, sK91: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_229, type, sK92: subst).
% 37.84/5.79 thf(func_def_230, type, sK93: (term > $o)).
% 37.84/5.79 thf(func_def_231, type, sK94: term).
% 37.84/5.79 thf(func_def_232, type, sK95: subst).
% 37.84/5.79 thf(func_def_233, type, sK96: term).
% 37.84/5.79 thf(func_def_234, type, sK97: subst).
% 37.84/5.79 thf(func_def_235, type, sK98: term).
% 37.84/5.79 thf(func_def_236, type, sK99: (term > $o)).
% 37.84/5.79 thf(func_def_237, type, sK100: subst).
% 37.84/5.79 thf(func_def_238, type, sK101: term).
% 37.84/5.79 thf(func_def_239, type, sK102: (term > term)).
% 37.84/5.79 thf(func_def_240, type, sK103: (subst > (term > $o) > term)).
% 37.84/5.79 thf(func_def_241, type, sK104: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_242, type, sK105: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_243, type, sK106: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_244, type, sK107: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_245, type, sK108: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_246, type, sK109: (term > $o)).
% 37.84/5.79 thf(func_def_247, type, sK110: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_248, type, sK111: term).
% 37.84/5.79 thf(func_def_249, type, sK112: term).
% 37.84/5.79 thf(func_def_250, type, sK113: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_251, type, sK114: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_252, type, sK115: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_253, type, sK116: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_256, type, sK119: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > (term > $o) > term)).
% 37.84/5.79 thf(func_def_259, type, sK122: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_260, type, sK123: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_261, type, sK124: ((subst > term > subst > $o) > term > $o)).
% 37.84/5.79 thf(func_def_262, type, sK125: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_263, type, sK126: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_264, type, sK127: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_265, type, sK128: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_266, type, sK129: term).
% 37.84/5.79 thf(func_def_267, type, sK130: (term > $o)).
% 37.84/5.79 thf(func_def_268, type, sK131: term).
% 37.84/5.79 thf(func_def_269, type, sK132: (term > term)).
% 37.84/5.79 thf(func_def_270, type, sK133: ((subst > term > subst > $o) > (term > $o) > term)).
% 37.84/5.79 thf(func_def_271, type, sK134: ((term > $o) > term > term)).
% 37.84/5.79 thf(func_def_272, type, sK135: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_273, type, sK136: term).
% 37.84/5.79 thf(func_def_274, type, sK137: (term > $o)).
% 37.84/5.79 thf(func_def_275, type, sK138: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_276, type, sK139: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_277, type, sK140: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_278, type, sK141: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_279, type, sK142: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_280, type, sK143: term).
% 37.84/5.79 thf(func_def_281, type, sK144: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_282, type, sK145: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_283, type, sK146: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_284, type, sK147: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_285, type, sK148: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_286, type, sK149: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_287, type, sK150: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_288, type, sK151: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_289, type, sK152: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_290, type, sK153: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_291, type, sK154: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_292, type, sK155: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_293, type, sK156: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_294, type, sK157: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_295, type, sK158: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_296, type, sK159: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_297, type, sK160: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_298, type, sK161: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_299, type, sK162: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_300, type, sK163: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_301, type, sK164: term).
% 37.84/5.79 thf(func_def_302, type, sK165: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_303, type, sK166: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_304, type, sK167: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_305, type, sK168: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_306, type, sK169: (term > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_308, type, sK171: term).
% 37.84/5.79 thf(func_def_309, type, sK172: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_310, type, sK173: (term > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_311, type, sK174: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_312, type, sK175: term).
% 37.84/5.79 thf(func_def_313, type, sK176: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_314, type, sK177: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_315, type, sK178: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_316, type, sK179: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_317, type, sK180: subst).
% 37.84/5.79 thf(func_def_318, type, sK181: (subst > term > term)).
% 37.84/5.79 thf(func_def_319, type, sK182: term).
% 37.84/5.79 thf(func_def_320, type, sK183: (subst > term > term)).
% 37.84/5.79 thf(func_def_321, type, sK184: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_322, type, sK185: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_323, type, sK186: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_324, type, sK187: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_325, type, sK188: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_326, type, sK189: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_327, type, sK190: term).
% 37.84/5.79 thf(func_def_328, type, sK191: subst).
% 37.84/5.79 thf(func_def_329, type, sK192: term).
% 37.84/5.79 thf(func_def_330, type, sK193: term).
% 37.84/5.79 thf(func_def_331, type, sK194: term).
% 37.84/5.79 thf(func_def_332, type, sK195: subst).
% 37.84/5.79 thf(func_def_333, type, sK196: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_334, type, sK197: term).
% 37.84/5.79 thf(func_def_335, type, sK198: (term > $o)).
% 37.84/5.79 thf(func_def_336, type, sK199: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_337, type, sK200: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_338, type, sK201: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_339, type, sK202: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_340, type, sK203: ((term > $o) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_341, type, sK204: ((term > $o) > term > term)).
% 37.84/5.79 thf(func_def_342, type, sK205: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_343, type, sK206: term).
% 37.84/5.79 thf(func_def_344, type, sK207: term).
% 37.84/5.79 thf(func_def_345, type, sK208: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_346, type, sK209: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_347, type, sK210: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_348, type, sK211: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_349, type, sK212: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_350, type, sK213: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_351, type, sK214: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_352, type, sK215: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_354, type, sK217: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_355, type, sK218: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_356, type, sK219: subst).
% 37.84/5.79 thf(func_def_357, type, sK220: (term > $o)).
% 37.84/5.79 thf(func_def_358, type, sK221: term).
% 37.84/5.79 thf(func_def_359, type, sK222: (term > term)).
% 37.84/5.79 thf(func_def_360, type, sK223: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_361, type, sK224: ((term > $o) > subst > term)).
% 37.84/5.79 thf(func_def_362, type, sK225: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_363, type, sK226: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_364, type, sK227: (term > $o)).
% 37.84/5.79 thf(func_def_365, type, sK228: term).
% 37.84/5.79 thf(func_def_366, type, sK229: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_367, type, sK230: term).
% 37.84/5.79 thf(func_def_368, type, sK231: (term > (term > $o) > term)).
% 37.84/5.79 thf(func_def_369, type, sK232: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_370, type, sK233: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_371, type, sK234: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_372, type, sK235: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_373, type, sK236: ((subst > term > subst > $o) > (term > $o) > term)).
% 37.84/5.79 thf(func_def_374, type, sK237: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_375, type, sK238: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_378, type, sK241: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_379, type, sK242: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_380, type, sK243: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_381, type, sK244: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_382, type, sK245: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_383, type, sK246: term).
% 37.84/5.79 thf(func_def_384, type, sK247: (term > $o)).
% 37.84/5.79 thf(func_def_385, type, sK248: (term > term)).
% 37.84/5.79 thf(func_def_386, type, sK249: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_387, type, sK250: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_388, type, sK251: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_389, type, sK252: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_390, type, sK253: term).
% 37.84/5.79 thf(func_def_391, type, sK254: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_392, type, sK255: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_393, type, sK256: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_394, type, sK257: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_395, type, sK258: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_396, type, sK259: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_398, type, sK261: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_399, type, sK262: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_400, type, sK263: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_401, type, sK264: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_402, type, sK265: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_403, type, sK266: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_404, type, sK267: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_405, type, sK268: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_406, type, sK269: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_407, type, sK270: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_408, type, sK271: term).
% 37.84/5.79 thf(func_def_409, type, sK272: (term > $o)).
% 37.84/5.79 thf(func_def_410, type, sK273: (term > term)).
% 37.84/5.79 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_413, type, sK276: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_414, type, sK277: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_415, type, sK278: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_417, type, sK280: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_418, type, sK281: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_419, type, sK282: term).
% 37.84/5.79 thf(func_def_420, type, sK283: term).
% 37.84/5.79 thf(func_def_421, type, sK284: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_422, type, sK285: term).
% 37.84/5.79 thf(func_def_423, type, sK286: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_424, type, sK287: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_425, type, sK288: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_426, type, sK289: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_427, type, sK290: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_428, type, sK291: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_429, type, sK292: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_430, type, sK293: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_431, type, sK294: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_432, type, sK295: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_433, type, sK296: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_434, type, sK297: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_435, type, sK298: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_436, type, sK299: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_437, type, sK300: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_438, type, sK301: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_439, type, sK302: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_440, type, sK303: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_441, type, sK304: (term > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_442, type, sK305: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_443, type, sK306: term).
% 37.84/5.79 thf(func_def_444, type, sK307: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_445, type, sK308: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_446, type, sK309: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_447, type, sK310: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_448, type, sK311: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_449, type, sK312: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_450, type, sK313: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_451, type, sK314: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_452, type, sK315: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_453, type, sK316: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_454, type, sK317: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_455, type, sK318: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_456, type, sK319: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_457, type, sK320: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_458, type, sK321: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_459, type, sK322: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_460, type, sK323: term).
% 37.84/5.79 thf(func_def_461, type, sK324: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_462, type, sK325: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_463, type, sK326: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_464, type, sK327: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_465, type, sK328: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_466, type, sK329: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_467, type, sK330: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_468, type, sK331: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_469, type, sK332: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_470, type, sK333: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_471, type, sK334: ((term > $o) > subst > term)).
% 37.84/5.79 thf(func_def_472, type, sK335: term).
% 37.84/5.79 thf(func_def_473, type, sK336: subst).
% 37.84/5.79 thf(func_def_474, type, sK337: term).
% 37.84/5.79 thf(func_def_475, type, sK338: (term > $o)).
% 37.84/5.79 thf(func_def_476, type, sK339: (term > term)).
% 37.84/5.79 thf(func_def_477, type, sK340: term).
% 37.84/5.79 thf(func_def_478, type, sK341: (term > $o)).
% 37.84/5.79 thf(func_def_479, type, sK342: (term > term)).
% 37.84/5.79 thf(func_def_480, type, sK343: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_481, type, sK344: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_482, type, sK345: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_483, type, sK346: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_484, type, sK347: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_485, type, sK348: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_486, type, sK349: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_487, type, sK350: (term > $o)).
% 37.84/5.79 thf(func_def_488, type, sK351: term).
% 37.84/5.79 thf(func_def_489, type, sK352: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_490, type, sK353: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_491, type, sK354: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_492, type, sK355: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_493, type, sK356: ((term > $o) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_494, type, sK357: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_495, type, sK358: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_496, type, sK359: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_497, type, sK360: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_498, type, sK361: (term > (term > $o) > term)).
% 37.84/5.79 thf(func_def_499, type, sK362: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_500, type, sK363: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_501, type, sK364: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_502, type, sK365: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_503, type, sK366: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_504, type, sK367: term).
% 37.84/5.79 thf(func_def_505, type, sK368: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_506, type, sK369: (term > (subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_507, type, sK370: (term > (subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_508, type, sK371: (term > (subst > term > term) > term)).
% 37.84/5.79 thf(func_def_509, type, sK372: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_510, type, sK373: (term > (subst > term > term) > term)).
% 37.84/5.79 thf(func_def_511, type, sK374: (term > (subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_512, type, sK375: (term > (subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_513, type, sK376: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_514, type, sK377: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_516, type, sK379: term).
% 37.84/5.79 thf(func_def_517, type, sK380: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_518, type, sK381: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_519, type, sK382: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_520, type, sK383: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_521, type, sK384: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_522, type, sK385: ((subst > term > subst > $o) > term > $o)).
% 37.84/5.79 thf(func_def_523, type, sK386: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_524, type, sK387: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_525, type, sK388: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_526, type, sK389: term).
% 37.84/5.79 thf(func_def_527, type, sK390: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_528, type, sK391: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_529, type, sK392: (term > $o)).
% 37.84/5.79 thf(func_def_530, type, sK393: term).
% 37.84/5.79 thf(func_def_531, type, sK394: (term > term)).
% 37.84/5.79 thf(func_def_532, type, sK395: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_533, type, sK396: ((subst > term > subst > $o) > (term > $o) > term)).
% 37.84/5.79 thf(func_def_534, type, sK397: (term > (term > $o) > term)).
% 37.84/5.79 thf(func_def_535, type, sK398: (term > $o)).
% 37.84/5.79 thf(func_def_536, type, sK399: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_537, type, sK400: term).
% 37.84/5.79 thf(func_def_538, type, sK401: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_539, type, sK402: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_540, type, sK403: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_541, type, sK404: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_542, type, sK405: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_543, type, sK406: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_544, type, sK407: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_545, type, sK408: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_546, type, sK409: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_547, type, sK410: term).
% 37.84/5.79 thf(func_def_548, type, sK411: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_549, type, sK412: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_550, type, sK413: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_551, type, sK414: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_552, type, sK415: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_553, type, sK416: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_554, type, sK417: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_555, type, sK418: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_556, type, sK419: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_557, type, sK420: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_558, type, sK421: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_559, type, sK422: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_560, type, sK423: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_562, type, sK425: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_563, type, sK426: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_564, type, sK427: (term > subst > term > term)).
% 37.84/5.79 thf(func_def_565, type, sK428: term).
% 37.84/5.79 thf(func_def_566, type, sK429: (term > $o)).
% 37.84/5.79 thf(func_def_567, type, sK430: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_568, type, sK431: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_569, type, sK432: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_570, type, sK433: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_571, type, sK434: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_572, type, sK435: term).
% 37.84/5.79 thf(func_def_573, type, sK436: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_574, type, sK437: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_575, type, sK438: term).
% 37.84/5.79 thf(func_def_576, type, sK439: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_577, type, sK440: ((term > $o) > term > term)).
% 37.84/5.79 thf(func_def_578, type, sK441: ((subst > term > subst > $o) > (term > $o) > term)).
% 37.84/5.79 thf(func_def_579, type, sK442: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_580, type, sK443: term).
% 37.84/5.79 thf(func_def_581, type, sK444: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_582, type, sK445: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_583, type, sK446: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_584, type, sK447: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_585, type, sK448: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_586, type, sK449: (term > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_587, type, sK450: term).
% 37.84/5.79 thf(func_def_588, type, sK451: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_589, type, sK452: term).
% 37.84/5.79 thf(func_def_590, type, sK453: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_591, type, sK454: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_592, type, sK455: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_593, type, sK456: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_594, type, sK457: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_595, type, sK458: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_596, type, sK459: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_597, type, sK460: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_598, type, sK461: ((subst > term > subst > $o) > subst)).
% 37.84/5.79 thf(func_def_599, type, sK462: ((subst > term > subst > $o) > term > term)).
% 37.84/5.79 thf(func_def_600, type, sK463: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_601, type, sK464: term).
% 37.84/5.79 thf(func_def_602, type, sK465: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_603, type, sK466: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_604, type, sK467: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_605, type, sK468: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_606, type, sK469: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_607, type, sK470: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_608, type, sK471: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_609, type, sK472: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_610, type, sK473: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_611, type, sK474: ((subst > term > subst > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_612, type, sK475: term).
% 37.84/5.79 thf(func_def_613, type, sK476: term).
% 37.84/5.79 thf(func_def_614, type, sK477: term).
% 37.84/5.79 thf(func_def_615, type, sK478: term).
% 37.84/5.79 thf(func_def_616, type, sK479: term).
% 37.84/5.79 thf(func_def_617, type, sK480: term).
% 37.84/5.79 thf(func_def_618, type, sK481: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_619, type, sK482: term).
% 37.84/5.79 thf(func_def_620, type, sK483: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_621, type, sK484: ((subst > term > subst > $o) > term)).
% 37.84/5.79 thf(func_def_622, type, sK485: term).
% 37.84/5.79 thf(func_def_623, type, sK486: subst).
% 37.84/5.79 thf(func_def_624, type, sK487: term).
% 37.84/5.79 thf(func_def_625, type, sK488: subst).
% 37.84/5.79 thf(func_def_626, type, sK489: (term > $o)).
% 37.84/5.79 thf(func_def_627, type, sK490: (term > $o)).
% 37.84/5.79 thf(func_def_628, type, sK491: ((term > $o) > (term > $o) > subst > term > term)).
% 37.84/5.79 thf(func_def_629, type, sK492: term).
% 37.84/5.79 thf(func_def_630, type, sK493: term).
% 37.84/5.79 thf(func_def_631, type, sK494: term).
% 37.84/5.79 thf(func_def_632, type, sK495: term).
% 37.84/5.79 thf(func_def_633, type, sK496: subst).
% 37.84/5.79 thf(func_def_634, type, sK497: term).
% 37.84/5.79 thf(func_def_635, type, sK498: (subst > term > (term > $o) > term > $o)).
% 37.84/5.79 thf(func_def_636, type, sK499: (term > $o)).
% 37.84/5.79 thf(func_def_637, type, sK500: term).
% 37.84/5.79 thf(func_def_638, type, sK501: subst).
% 37.84/5.79 thf(func_def_639, type, sK502: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_640, type, sK503: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_641, type, sK504: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_642, type, sK505: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_643, type, sK506: term).
% 37.84/5.79 thf(func_def_644, type, sK507: term).
% 37.84/5.79 thf(func_def_645, type, sK508: (subst > term > term)).
% 37.84/5.79 thf(func_def_646, type, sK509: term).
% 37.84/5.79 thf(func_def_647, type, sK510: term).
% 37.84/5.79 thf(func_def_648, type, sK511: term).
% 37.84/5.79 thf(func_def_649, type, sK512: term).
% 37.84/5.79 thf(func_def_650, type, sK513: term).
% 37.84/5.79 thf(func_def_651, type, sK514: term).
% 37.84/5.79 thf(func_def_652, type, sK515: term).
% 37.84/5.79 thf(func_def_653, type, sK516: term).
% 37.84/5.79 thf(func_def_654, type, sK517: ((subst > term > subst > $o) > term > $o)).
% 37.84/5.79 thf(func_def_655, type, sK518: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_656, type, sK519: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_657, type, sK520: term).
% 37.84/5.79 thf(func_def_658, type, sK521: term).
% 37.84/5.79 thf(func_def_659, type, sK522: term).
% 37.84/5.79 thf(func_def_660, type, sK523: term).
% 37.84/5.79 thf(func_def_661, type, sK524: term).
% 37.84/5.79 thf(func_def_662, type, sK525: subst).
% 37.84/5.79 thf(func_def_663, type, sK526: subst).
% 37.84/5.79 thf(func_def_664, type, sK527: (subst > term > subst > $o)).
% 37.84/5.79 thf(func_def_665, type, sK528: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_666, type, sK529: ((subst > term > subst > $o) > term > $o)).
% 37.84/5.79 thf(func_def_667, type, sK530: subst).
% 37.84/5.79 thf(func_def_668, type, sK531: subst).
% 37.84/5.79 thf(func_def_669, type, sK532: subst).
% 37.84/5.79 thf(func_def_670, type, sK533: subst).
% 37.84/5.79 thf(func_def_671, type, sK534: (term > subst > term > term)).
% 37.84/5.79 thf(func_def_672, type, sK535: term).
% 37.84/5.79 thf(func_def_673, type, sK536: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_674, type, sK537: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_675, type, sK538: subst).
% 37.84/5.79 thf(func_def_676, type, sK539: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_677, type, sK540: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_678, type, sK541: (term > $o)).
% 37.84/5.79 thf(func_def_679, type, sK542: term).
% 37.84/5.79 thf(func_def_680, type, sK543: (term > $o)).
% 37.84/5.79 thf(func_def_681, type, sK544: term).
% 37.84/5.79 thf(func_def_682, type, sK545: (term > $o)).
% 37.84/5.79 thf(func_def_683, type, sK546: term).
% 37.84/5.79 thf(func_def_684, type, sK547: subst).
% 37.84/5.79 thf(func_def_685, type, sK548: term).
% 37.84/5.79 thf(func_def_686, type, sK549: term).
% 37.84/5.79 thf(func_def_687, type, sK550: (term > $o)).
% 37.84/5.79 thf(func_def_688, type, sK551: term).
% 37.84/5.79 thf(func_def_689, type, sK552: subst).
% 37.84/5.79 thf(func_def_690, type, sK553: (term > $o)).
% 37.84/5.79 thf(func_def_691, type, sK554: ((term > $o) > subst > term > (term > $o) > term)).
% 37.84/5.79 thf(func_def_692, type, sK555: subst).
% 37.84/5.79 thf(func_def_693, type, sK556: term).
% 37.84/5.79 thf(func_def_694, type, sK557: term).
% 37.84/5.79 thf(func_def_695, type, sK558: (term > $o)).
% 37.84/5.79 thf(func_def_696, type, sK559: subst).
% 37.84/5.79 thf(func_def_697, type, sK560: term).
% 37.84/5.79 thf(func_def_698, type, sK561: ((term > $o) > term)).
% 37.84/5.79 thf(func_def_699, type, sK562: (term > subst > (term > $o) > term > $o)).
% 37.84/5.79 thf(func_def_700, type, sK563: term).
% 37.84/5.79 thf(func_def_701, type, sK564: (term > subst > term > term)).
% 37.84/5.79 thf(func_def_702, type, sK565: (term > subst > term > term)).
% 37.84/5.79 thf(func_def_703, type, sK566: term).
% 37.84/5.79 thf(func_def_704, type, sK567: (subst > d_subst)).
% 37.84/5.79 thf(func_def_705, type, sK568: subst).
% 37.84/5.79 thf(func_def_706, type, sK569: term).
% 37.84/5.79 thf(func_def_707, type, sK570: term).
% 37.84/5.79 thf(func_def_708, type, sK571: term).
% 37.84/5.79 thf(func_def_709, type, sK572: term).
% 37.84/5.79 thf(func_def_710, type, sK573: term).
% 37.84/5.79 thf(func_def_711, type, sK574: term).
% 37.84/5.79 thf(func_def_712, type, sK575: term).
% 37.84/5.79 thf(func_def_713, type, sK576: term).
% 37.84/5.79 thf(func_def_714, type, sK577: term).
% 37.84/5.79 thf(func_def_715, type, sK578: (term > d_term)).
% 37.84/5.79 thf(func_def_716, type, sK579: subst).
% 37.84/5.79 thf(func_def_717, type, sK580: (subst > term > term)).
% 37.84/5.79 thf(func_def_718, type, sK581: term).
% 37.84/5.79 thf(func_def_719, type, sK582: (subst > term > term)).
% 37.84/5.79 thf(func_def_720, type, sK583: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_721, type, sK584: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_722, type, sK585: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_723, type, sK586: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_724, type, sK587: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_725, type, sK588: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_726, type, sK589: term).
% 37.84/5.79 thf(func_def_727, type, sK590: subst).
% 37.84/5.79 thf(func_def_728, type, sK591: subst).
% 37.84/5.79 thf(func_def_729, type, sK592: term).
% 37.84/5.79 thf(func_def_730, type, sK593: (term > $o)).
% 37.84/5.79 thf(func_def_731, type, sK594: term).
% 37.84/5.79 thf(func_def_732, type, sK595: term).
% 37.84/5.79 thf(func_def_733, type, sK596: subst).
% 37.84/5.79 thf(func_def_734, type, sK597: (term > $o)).
% 37.84/5.79 thf(func_def_735, type, sK598: term).
% 37.84/5.79 thf(func_def_736, type, sK599: term).
% 37.84/5.79 thf(func_def_737, type, sK600: term).
% 37.84/5.79 thf(func_def_738, type, sK601: term).
% 37.84/5.79 thf(func_def_739, type, sK602: subst).
% 37.84/5.79 thf(func_def_740, type, sK603: term).
% 37.84/5.79 thf(func_def_741, type, sK604: ((subst > term > term) > term)).
% 37.84/5.79 thf(func_def_742, type, sK605: ((subst > term > term) > subst)).
% 37.84/5.79 thf(func_def_743, type, sK606: (term > subst > term > term)).
% 37.84/5.79 thf(func_def_744, type, sK607: term).
% 37.84/5.79 thf(func_def_745, type, sK608: term).
% 37.84/5.79 thf(func_def_746, type, vNOT: ($o > $o)).
% 37.84/5.79 thf(f1,axiom,(
% 37.84/5.79 (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoasapinj1_gthm & hoasinduction_lem1_gthm & pushprop & ulamvarind & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & substmonoid_gthm & axvarshift & hoasinduction_lem3a_gthm & (! [X10 : (term > $o),X11 : (term > $o),X14 : subst,X13 : term] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)) <=> pushprop_lem1v2) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & hoasinduction_lem2_gthm & pushprop_lthm_orig & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & hoaslaminj_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapinj2_gthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))) & hoasinduction_lem1_lthm & pushprop_lem0_gthm & (hoaslaminj <=> ! [X31 : (subst > term > term),X33 : term,X32 : subst,X18 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X15 : term,X13 : term,X26 : (term > $o),X14 : subst] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & (hoasapinj1 <=> ! [X19 : term,X15 : term,X20 : term,X13 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) <=> hoasinduction_lem3v2) & ((! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id)) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : ((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] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) <=> hoasinduction_lthm) & (! [X18 : (subst > term > term),X46 : term,X47 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslamnotap) & ~ulamvar1 & pushprop_gthm & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & pushprop_lem1v2_gthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [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)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) <=> hoasinduction_lthm_3) & (! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))) <=> induction2lem) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (hoasinduction_lem3v2a <=> ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)))) & hoasinduction_lem3b_gthm & (hoasapinj2 <=> ! [X20 : term,X15 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & ~lamnotap & induction2lem_gthm & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (apinj1 <=> ! [X19 : term,X13 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (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)))))))) & (! [X10 : (subst > term > subst > $o),X42 : term] : ((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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3aa_lthm) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoaslamnotvar & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X14 : subst,X10 : (term > $o),X13 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13))) <=> pushprop_lem1v2_lthm) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & hoasinduction_lem3v2_gthm & (! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ((! [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,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & hoasinduction_lem2_lthm & (! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X36 : subst,X38 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X41 : subst,X39 : subst,X40 : term] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & (hoasinduction_lem2v2 <=> ! [X45 : term,X44 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : ((X11 @ (ap @ X44 @ X45)) | ~(X11 @ X44) | ~(X11 @ X45) | ~ ! [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,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & pushprop_lem1_gthm & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [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 @ X15) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)))))) & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & termmset_gthm & hoaslamnotap_lthm & pushprop_lem3v2 & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & (axshiftcons <=> ! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & hoasapnotvar & ((! [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 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))))))) <=> induction2lem_lthm) & hoasinduction_lem1v2_gthm & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (laminj <=> ! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & axmap & (! [X20 : term,X15 : term,X13 : term,X19 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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))))))) <=> hoasinduction_lem3v2_lthm) & hoasinduction_lem1 & pushprop_lem2v2_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & pushprop_lem3v2_lthm & ulamvarsh & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & pushprop_lem2v2 & axabs & (sh = ((d2subst @ d_id))) & pushprop_lthm & hoasinduction_lem2v2_gthm & axclos & ! [X1 : d_term] : (X1 = d_one) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [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))) <=> hoasinduction_lem3aa) & hoasapnotvar_gthm & (induction <=> ! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)))) & hoasapnotvar_lthm & (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id)) <=> hoasinduction_lem2) & axapp & apnotvar & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & axassoc & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ! [X5 : d_subst] : (X5 = d_id) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (shinj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & induction2_gthm & (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & hoasinduction_lem1v2 & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotvar_gthm & hoasinduction_gthm & hoasinduction_lem3_gthm & (hoasapinj2_lthm <=> (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)))) & pushprop_lem2v2_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) <=> hoasinduction_lem3_lthm) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X31 : (subst > term > term),X18 : (subst > term > term),X33 : term,X32 : subst] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))))) <=> hoaslaminj_lthm) & (! [X10 : (term > $o),X14 : subst,X26 : (term > $o),X15 : term,X13 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & lamnotvar & hoaslamnotvar_lthm & (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) <=> induction2) & (! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,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)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3a) & (one = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & (! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & hoaslamnotap_gthm & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))))),
% 37.84/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 37.84/5.79 thf(f2,conjecture,(
% 37.84/5.79 (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X1 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X2 : term,X3 : subst,X1 : subst,X4 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X5 : (subst > term > term)] : (! [X3 : subst,X2 : term,X1 : subst] : (((sub @ (X5 @ X1 @ X2) @ X3)) = ((X5 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X5 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X5 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (sub @ X2 @ (push @ X6 @ id)) @ id)) => (X0 @ id @ (lam @ X2) @ id))))) = hoasinduction_lem3)),
% 37.84/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3)).
% 37.84/5.79 thf(f3,negated_conjecture,(
% 37.84/5.79 ~ (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X1 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X2 : term,X3 : subst,X1 : subst,X4 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X5 : (subst > term > term)] : (! [X3 : subst,X2 : term,X1 : subst] : (((sub @ (X5 @ X1 @ X2) @ X3)) = ((X5 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X5 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X5 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (sub @ X2 @ (push @ X6 @ id)) @ id)) => (X0 @ id @ (lam @ X2) @ id))))) = hoasinduction_lem3)),
% 37.84/5.79 inference(negated_conjecture,[status(cth)],[f2])).
% 37.84/5.79 thf(f4,plain,(
% 37.84/5.79 (hoasinduction_no_psi_cond_lthm <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : ((X3 @ X4) | ~ ! [X5 : term] : ((X3 @ X5) | ~(var @ X5)) | ~ ! [X6 : term] : (~ ! [X7 : term] : (~(X3 @ X7) | (X3 @ (sub @ X6 @ (push @ X7 @ id)))) | (X3 @ (lam @ X6))) | ~ ! [X8 : term,X9 : term] : ((X3 @ (ap @ X8 @ X9)) | ~(X3 @ X8) | ~(X3 @ X9))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (term > $o),X13 : (subst > term > subst > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : (~(X13 @ id @ X15 @ id) | (X13 @ id @ (X14 @ id @ X15) @ id)) | ~ ! [X16 : subst,X17 : subst,X18 : term] : (((sub @ (X14 @ X17 @ X18) @ X16)) = ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | (X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) | ~ ! [X20 : term] : ((X12 @ (sub @ X11 @ (push @ X20 @ id))) | ~(X12 @ X20)) | (X12 @ (lam @ X11))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((X21 @ id @ X22 @ id) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : term] : ((X21 @ id @ (X23 @ id @ X24) @ id) | ~(X21 @ id @ X24 @ id)) | (X21 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X25 : subst,X26 : subst,X27 : term] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25))))) | ~ ! [X28 : term,X29 : term] : (~(X21 @ id @ X28 @ id) | ~(X21 @ id @ X29 @ id) | (X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)))))))) & (! [X30 : term] : ~ ! [X31 : (subst > term > term)] : ~ ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) <=> hoasinduction_lem3v2_f_lthm) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & hoasapinj1_gthm & hoasinduction_lem1_gthm & pushprop & ulamvarind & (! [X36 : term] : ~ ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & substmonoid_gthm & axvarshift & hoasinduction_lem3a_gthm & (! [X38 : (term > $o),X39 : (term > $o),X40 : subst,X41 : term] : ((X39 @ one) | ~ ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) | ~(X38 @ X41)) <=> pushprop_lem1v2) & (! [X43 : (subst > term > subst > $o)] : ~ ! [X44 : (term > $o)] : ~ ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id))) <=> hoasinduction_lem0_lthm) & hoasinduction_lem2_gthm & pushprop_lthm_orig & ((^[X46 : subst, X47 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & hoaslaminj_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapinj2_gthm & ((! [X48 : subst] : (((comp @ id @ X48)) = X48) => (! [X49 : subst] : (((comp @ X49 @ id)) = X49) => (! [X50 : subst] : (((comp @ id @ X50)) = X50) & ! [X51 : subst] : (((comp @ X51 @ id)) = X51)))) <=> substmonoid_lthm) & (substmonoid <=> (! [X52 : subst] : (((comp @ id @ X52)) = X52) & ! [X53 : subst] : (((comp @ X53 @ id)) = X53))) & hoasinduction_lem1_lthm & pushprop_lem0_gthm & (hoaslaminj <=> ! [X54 : (subst > term > term),X55 : term,X56 : subst,X57 : (subst > term > term)] : ((((X54 @ X56 @ X55)) = ((X57 @ X56 @ X55))) | ~ ! [X58 : term,X59 : subst,X60 : subst] : (((X57 @ (comp @ X59 @ X60) @ (sub @ X58 @ X60))) = ((sub @ (X57 @ X59 @ X58) @ X60))) | ~ ! [X61 : subst,X62 : term,X63 : subst] : (((sub @ (X54 @ X63 @ X62) @ X61)) = ((X54 @ (comp @ X63 @ X61) @ (sub @ X62 @ X61)))) | (((lam @ (X54 @ sh @ one))) != ((lam @ (X57 @ sh @ one)))))) & (pushprop_lem1_lthm <=> (! [X64 : term,X65 : subst] : (((sub @ one @ (push @ X64 @ X65))) = X64) => (! [X66 : term,X67 : subst] : (((comp @ sh @ (push @ X66 @ X67))) = X67) => ! [X68 : (term > $o),X69 : term,X70 : term,X71 : (term > $o),X72 : subst] : ((X71 @ (sub @ X70 @ (push @ X69 @ X72))) | ~(X68 @ X70))))) & (hoasapinj1 <=> ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X74 = X76) | (((ap @ (sub @ X74 @ id) @ X75)) != ((ap @ (sub @ X76 @ id) @ X73))))) & (! [X77 : (subst > term > subst > $o),X78 : term,X79 : (term > $o)] : (~ ! [X80 : term] : (~(X79 @ X80) | (X79 @ (sub @ X78 @ (push @ X80 @ id)))) | (X79 @ (lam @ X78)) | ~ ! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : ((X77 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84) | ~(X77 @ X82 @ X81 @ (comp @ X83 @ X84))) | ~ ! [X85 : term] : (((X79 @ X85)) = ((X77 @ id @ X85 @ id))) | ~ ! [X86 : subst,X87 : subst,X88 : subst,X89 : term] : (~(X77 @ (comp @ X88 @ X86) @ (sub @ X89 @ X86) @ X87) | (X77 @ X88 @ X89 @ (comp @ X86 @ X87))) | ~ ! [X90 : (subst > term > term)] : (~ ! [X91 : term,X92 : subst,X93 : subst] : (((X90 @ (comp @ X92 @ X93) @ (sub @ X91 @ X93))) = ((sub @ (X90 @ X92 @ X91) @ X93))) | (X77 @ id @ (lam @ (X90 @ sh @ one)) @ id) | ~ ! [X94 : term] : ((X77 @ id @ (X90 @ id @ X94) @ id) | ~(X77 @ id @ X94 @ id)))) <=> hoasinduction_lem3v2) & ((! [X95 : (term > $o),X96 : term] : (~ ! [X97 : term] : (~(var @ X97) | (X95 @ X97)) | ~ ! [X98 : term,X99 : term] : (~(X95 @ X98) | ~(X95 @ X99) | (X95 @ (ap @ X99 @ X98))) | (X95 @ X96) | ~ ! [X100 : term] : (~ ! [X101 : term] : ((X95 @ (sub @ X100 @ (push @ X101 @ id))) | ~(X95 @ X101)) | (X95 @ (lam @ X100)))) => (! [X102 : term,X103 : term,X104 : (subst > term > subst > $o)] : (~(X104 @ id @ X102 @ id) | (X104 @ id @ (ap @ X102 @ X103) @ id) | ~ ! [X105 : subst,X106 : term,X107 : subst,X108 : subst] : (~(X104 @ X107 @ X106 @ (comp @ X105 @ X108)) | (X104 @ (comp @ X107 @ X105) @ (sub @ X106 @ X105) @ X108)) | ~ ! [X109 : term,X110 : term] : (~(X104 @ id @ X109 @ id) | (X104 @ id @ (ap @ (sub @ X110 @ id) @ X109) @ id) | ~(X104 @ id @ X110 @ id)) | ~ ! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (~(X104 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111) @ X114) | (X104 @ X113 @ X112 @ (comp @ X111 @ X114))) | ~(X104 @ id @ X103 @ id)) => (! [X115 : (subst > term > subst > $o),X116 : term] : (~ ! [X117 : (subst > term > term)] : ((X115 @ id @ (lam @ (X117 @ sh @ one)) @ id) | ~ ! [X118 : term] : (~(X115 @ id @ X118 @ id) | (X115 @ id @ (X117 @ id @ X118) @ id)) | ~ ! [X119 : term,X120 : subst,X121 : subst] : (((X117 @ (comp @ X121 @ X120) @ (sub @ X119 @ X120))) = ((sub @ (X117 @ X121 @ X119) @ X120)))) | ~ ! [X122 : term] : ((X115 @ id @ (sub @ X116 @ (push @ X122 @ id)) @ id) | ~(X115 @ id @ X122 @ id)) | (X115 @ id @ (lam @ X116) @ id) | ~ ! [X123 : subst,X124 : subst,X125 : subst,X126 : term] : (~(X115 @ (comp @ X123 @ X125) @ (sub @ X126 @ X125) @ X124) | (X115 @ X123 @ X126 @ (comp @ X125 @ X124))) | ~ ! [X127 : subst,X128 : subst,X129 : term,X130 : subst] : ((X115 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X130) | ~(X115 @ X127 @ X129 @ (comp @ X128 @ X130)))) => ! [X131 : (subst > term > subst > $o),X132 : term] : (~ ! [X133 : subst,X134 : subst,X135 : term,X136 : subst] : ((X131 @ (comp @ X134 @ X133) @ (sub @ X135 @ X133) @ X136) | ~(X131 @ X134 @ X135 @ (comp @ X133 @ X136))) | (X131 @ id @ X132 @ id) | ~ ! [X137 : subst,X138 : subst,X139 : subst,X140 : term] : ((X131 @ X137 @ X140 @ (comp @ X138 @ X139)) | ~(X131 @ (comp @ X137 @ X138) @ (sub @ X140 @ X138) @ X139)) | ~ ! [X141 : term] : (~(var @ (sub @ X141 @ id)) | (X131 @ id @ X141 @ id)) | ~ ! [X142 : term,X143 : term] : ((X131 @ id @ (ap @ (sub @ X142 @ id) @ X143) @ id) | ~(X131 @ id @ X142 @ id) | ~(X131 @ id @ X143 @ id)) | ~ ! [X144 : (subst > term > term)] : ((X131 @ id @ (lam @ (X144 @ sh @ one)) @ id) | ~ ! [X145 : term] : ((X131 @ id @ (X144 @ id @ X145) @ id) | ~(X131 @ id @ X145 @ id)) | ~ ! [X146 : subst,X147 : subst,X148 : term] : (((X144 @ (comp @ X147 @ X146) @ (sub @ X148 @ X146))) = ((sub @ (X144 @ X147 @ X148) @ X146)))))))) <=> hoasinduction_lthm) & (! [X149 : (subst > term > term),X150 : term,X151 : term] : ((((ap @ (sub @ X150 @ id) @ X151)) != ((lam @ (X149 @ sh @ one)))) | ~ ! [X152 : subst,X153 : term,X154 : subst] : (((X149 @ (comp @ X154 @ X152) @ (sub @ X153 @ X152))) = ((sub @ (X149 @ X154 @ X153) @ X152)))) <=> hoaslamnotap) & ~ulamvar1 & pushprop_gthm & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> axscons) & pushprop_lem1v2_gthm & ((! [X156 : (subst > term > subst > $o)] : ~ ! [X157 : (term > $o)] : ~ ! [X158 : term] : (((X156 @ id @ X158 @ id)) = ((X157 @ X158))) => (! [X159 : (term > $o),X160 : term] : (~ ! [X161 : term] : ((X159 @ X161) | ~(var @ X161)) | (X159 @ X160) | ~ ! [X162 : term] : ((X159 @ (lam @ X162)) | ~ ! [X163 : term] : ((X159 @ (sub @ X162 @ (push @ X163 @ id))) | ~(X159 @ X163))) | ~ ! [X164 : term,X165 : term] : (~(X159 @ X165) | (X159 @ (ap @ X164 @ X165)) | ~(X159 @ X164))) => (! [X166 : term] : (((sub @ X166 @ id)) = X166) => (! [X167 : (subst > term > subst > $o),X168 : (term > $o),X169 : term] : (~ ! [X170 : term] : (~(X168 @ X170) | (X168 @ (sub @ X169 @ (push @ X170 @ id)))) | ~ ! [X171 : (subst > term > term)] : (~ ! [X172 : term] : ((X167 @ id @ (X171 @ id @ X172) @ id) | ~(X167 @ id @ X172 @ id)) | ~ ! [X173 : subst,X174 : subst,X175 : term] : (((X171 @ (comp @ X174 @ X173) @ (sub @ X175 @ X173))) = ((sub @ (X171 @ X174 @ X175) @ X173))) | (X167 @ id @ (lam @ (X171 @ sh @ one)) @ id)) | (X168 @ (lam @ X169)) | ~ ! [X176 : term] : (((X168 @ X176)) = ((X167 @ id @ X176 @ id)))) => ! [X177 : (subst > term > subst > $o),X178 : term] : (~ ! [X179 : (subst > term > term)] : (~ ! [X180 : subst,X181 : subst,X182 : term] : (((X179 @ (comp @ X180 @ X181) @ (sub @ X182 @ X181))) = ((sub @ (X179 @ X180 @ X182) @ X181))) | (X177 @ id @ (lam @ (X179 @ sh @ one)) @ id) | ~ ! [X183 : term] : ((X177 @ id @ (X179 @ id @ X183) @ id) | ~(X177 @ id @ X183 @ id))) | ~ ! [X184 : term] : ((X177 @ id @ X184 @ id) | ~(var @ (sub @ X184 @ id))) | ~ ! [X185 : subst,X186 : subst,X187 : subst,X188 : term] : (~(X177 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X185) | (X177 @ X186 @ X188 @ (comp @ X187 @ X185))) | ~ ! [X189 : term,X190 : term] : (~(X177 @ id @ X190 @ id) | ~(X177 @ id @ X189 @ id) | (X177 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id)) | (X177 @ id @ X178 @ id) | ~ ! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : ((X177 @ (comp @ X192 @ X193) @ (sub @ X191 @ X193) @ X194) | ~(X177 @ X192 @ X191 @ (comp @ X193 @ X194)))))))) <=> hoasinduction_lthm_3) & (! [X195 : (term > $o),X196 : term,X197 : subst] : ((X195 @ (sub @ X196 @ X197)) | ~ ! [X198 : term] : ((X195 @ (lam @ X198)) | ~ ! [X199 : term] : ((X195 @ (sub @ X198 @ (push @ X199 @ id))) | ~(X195 @ X199))) | ~ ! [X200 : term,X201 : term] : (~(X195 @ X201) | (X195 @ (ap @ X200 @ X201)) | ~(X195 @ X200)) | ~ ! [X202 : term] : ((X195 @ (sub @ X202 @ X197)) | ~(var @ X202))) <=> induction2lem) & (! [X203 : term] : (((sub @ X203 @ id)) = X203) <=> termmset) & (hoasinduction_lem3v2a <=> ! [X204 : (subst > term > subst > $o),X205 : term,X206 : (term > $o)] : (~ ! [X207 : (subst > term > term)] : (~ ! [X208 : term,X209 : subst,X210 : subst] : (((X207 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209))) = ((sub @ (X207 @ X210 @ X208) @ X209))) | (X204 @ id @ (lam @ (X207 @ sh @ one)) @ id) | ~ ! [X211 : term] : (~(X204 @ id @ X211 @ id) | (X204 @ id @ (X207 @ id @ X211) @ id))) | ~ ! [X212 : term] : ((X206 @ (sub @ X205 @ (push @ X212 @ id))) | ~(X206 @ X212)) | ~ ! [X213 : term] : (((X206 @ X213)) = ((X204 @ id @ X213 @ id))) | (X206 @ (lam @ X205)))) & hoasinduction_lem3b_gthm & (hoasapinj2 <=> ! [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 = X216) | (((ap @ (sub @ X217 @ id) @ X216)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ~lamnotap & induction2lem_gthm & ((^[X218 : (subst > term > subst > $o), X219 : (term > $o)] : (! [X220 : term] : (((X219 @ X220)) = ((X218 @ id @ X220 @ id))))) = hoasinduction_p_and_p_prime) & (apinj1 <=> ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X222 = X224) | (((ap @ X224 @ X223)) != ((ap @ X222 @ X221))))) & (pushprop_p_and_p_prime = (^[X225 : term, X226 : subst, X227 : (term > $o), X228 : (term > $o)] : (! [X229 : term] : (((X228 @ X229)) = ((X227 @ (sub @ X229 @ (push @ X225 @ X226)))))))) & (! [X230 : (subst > term > subst > $o),X231 : term] : ((X230 @ id @ (lam @ (sub @ X231 @ (push @ one @ sh))) @ id) | ~ ! [X232 : term] : (~(X230 @ id @ X232 @ id) | (X230 @ id @ (sub @ X231 @ (push @ X232 @ id)) @ id)) | ~ ! [X233 : (subst > term > term)] : (~ ! [X234 : term] : ((X230 @ id @ (X233 @ id @ X234) @ id) | ~(X230 @ id @ X234 @ id)) | (X230 @ id @ (lam @ (X233 @ sh @ one)) @ id) | ~ ! [X235 : subst,X236 : subst,X237 : term] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))))) <=> hoasinduction_lem3aa_lthm) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoaslamnotvar & ! [X238 : d_subst,X239 : d_subst] : ((((d2subst @ X239)) = ((d2subst @ X238))) => (X238 = X239)) & ((! [X240 : term,X241 : subst] : (((sub @ one @ (push @ X240 @ X241))) = X240) => ! [X242 : (term > $o),X243 : subst,X244 : (term > $o),X245 : term] : (~ ! [X246 : term] : (((X242 @ X246)) = ((X244 @ (sub @ X246 @ (push @ X245 @ X243))))) | (X242 @ one) | ~(X244 @ X245))) <=> pushprop_lem1v2_lthm) & (hoasinduction_lem3 <=> ! [X247 : term,X248 : (subst > term > subst > $o)] : (~ ! [X249 : term] : (~(X248 @ id @ X249 @ id) | (X248 @ id @ (sub @ X247 @ (push @ X249 @ id)) @ id)) | (X248 @ id @ (lam @ X247) @ id) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~(X248 @ X250 @ X251 @ (comp @ X252 @ X253)) | (X248 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) | ~ ! [X254 : (subst > term > term)] : (~ ! [X255 : subst,X256 : term,X257 : subst] : (((sub @ (X254 @ X255 @ X256) @ X257)) = ((X254 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257)))) | (X248 @ id @ (lam @ (X254 @ sh @ one)) @ id) | ~ ! [X258 : term] : ((X248 @ id @ (X254 @ id @ X258) @ id) | ~(X248 @ id @ X258 @ id))) | ~ ! [X259 : subst,X260 : term,X261 : subst,X262 : subst] : (~(X248 @ (comp @ X262 @ X259) @ (sub @ X260 @ X259) @ X261) | (X248 @ X262 @ X260 @ (comp @ X259 @ X261))))) & hoasinduction_lem3v2_gthm & (! [X263 : term,X264 : subst,X265 : (term > $o)] : ~ ! [X266 : (term > $o)] : ~ ! [X267 : term] : (((X266 @ X267)) = ((X265 @ (sub @ X267 @ (push @ X263 @ X264))))) <=> pushprop_lem0) & ((! [X268 : term] : ~ ! [X269 : (subst > term > term)] : ~ ! [X270 : term,X271 : subst] : (((sub @ X268 @ (push @ X270 @ X271))) = ((X269 @ X271 @ X270))) => (! [X272 : term] : (((sub @ X272 @ id)) = X272) => ! [X273 : term,X274 : (term > $o),X275 : (subst > term > subst > $o)] : ((X274 @ (lam @ X273)) | ~ ! [X276 : term] : ((X274 @ (sub @ X273 @ (push @ X276 @ id))) | ~(X274 @ X276)) | ~ ! [X277 : (subst > term > term)] : (~ ! [X278 : term] : (~(X275 @ id @ X278 @ id) | (X275 @ id @ (X277 @ id @ X278) @ id)) | (X275 @ id @ (lam @ (X277 @ sh @ one)) @ id) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((X277 @ (comp @ X281 @ X279) @ (sub @ X280 @ X279))) = ((sub @ (X277 @ X281 @ X280) @ X279)))) | ~ ! [X282 : term] : (((X275 @ id @ X282 @ id)) = ((X274 @ X282)))))) <=> hoasinduction_lem3v2a_lthm) & hoasinduction_lem2_lthm & (! [X283 : (subst > term > subst > $o),X284 : term] : (~ ! [X285 : (subst > term > term),X286 : term] : (~ ! [X287 : subst,X288 : subst,X289 : term] : (((sub @ (sub @ X286 @ (push @ X289 @ X287)) @ X288)) = ((sub @ (X285 @ X287 @ X289) @ X288))) | (X283 @ id @ (lam @ (X285 @ sh @ one)) @ id) | ~ ! [X290 : term] : ((X283 @ id @ (X285 @ id @ X290) @ id) | ~(X283 @ id @ X290 @ id)) | ~ ! [X291 : subst,X292 : subst,X293 : term] : (((X285 @ (comp @ X292 @ X291) @ (sub @ X293 @ X291))) = ((sub @ X286 @ (push @ (sub @ X293 @ X291) @ (comp @ X292 @ X291)))))) | ~ ! [X294 : term] : (~(X283 @ id @ X294 @ id) | (X283 @ id @ (sub @ X284 @ (push @ X294 @ id)) @ id)) | (X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & (hoasinduction_lem2v2 <=> ! [X295 : term,X296 : term,X297 : (subst > term > subst > $o),X298 : (term > $o)] : ((X298 @ (ap @ X296 @ X295)) | ~(X298 @ X296) | ~(X298 @ X295) | ~ ! [X299 : term,X300 : term] : (~(X297 @ id @ X300 @ id) | ~(X297 @ id @ X299 @ id) | (X297 @ id @ (ap @ (sub @ X300 @ id) @ X299) @ id)) | ~ ! [X301 : term] : (((X297 @ id @ X301 @ id)) = ((X298 @ X301))) | ~ ! [X302 : subst,X303 : subst,X304 : term,X305 : subst] : ((X297 @ X303 @ X304 @ (comp @ X302 @ X305)) | ~(X297 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302) @ X305)) | ~ ! [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (~(X297 @ X307 @ X306 @ (comp @ X308 @ X309)) | (X297 @ (comp @ X307 @ X308) @ (sub @ X306 @ X308) @ X309)))) & pushprop_lem1_gthm & (induction2_lthm <=> (! [X310 : term] : (((sub @ X310 @ id)) = X310) => (! [X311 : term,X312 : (term > $o),X313 : subst] : (~ ! [X314 : term] : ((X312 @ (lam @ X314)) | ~ ! [X315 : term] : (~(X312 @ X315) | (X312 @ (sub @ X314 @ (push @ X315 @ id))))) | ~ ! [X316 : term] : (~(var @ X316) | (X312 @ (sub @ X316 @ X313))) | ~ ! [X317 : term,X318 : term] : ((X312 @ (ap @ X318 @ X317)) | ~(X312 @ X317) | ~(X312 @ X318)) | (X312 @ (sub @ X311 @ X313))) => ! [X319 : term,X320 : (term > $o)] : (~ ! [X321 : term] : (~ ! [X322 : term] : (~(X320 @ X322) | (X320 @ (sub @ X321 @ (push @ X322 @ id)))) | (X320 @ (lam @ X321))) | ~ ! [X323 : term] : (~(var @ X323) | (X320 @ X323)) | (X320 @ X319) | ~ ! [X324 : term,X325 : term] : (~(X320 @ X325) | (X320 @ (ap @ X324 @ X325)) | ~(X320 @ X324)))))) & (! [X326 : subst] : (((comp @ id @ X326)) = X326) <=> axidl) & termmset_gthm & hoaslamnotap_lthm & pushprop_lem3v2 & (! [X327 : subst] : (((comp @ X327 @ id)) = X327) <=> axidr) & (axshiftcons <=> ! [X328 : subst,X329 : term] : (((comp @ sh @ (push @ X329 @ X328))) = X328)) & hoasapnotvar & ((! [X330 : subst,X331 : term] : (((sub @ one @ (push @ X331 @ X330))) = X331) => (! [X332 : subst,X333 : term] : (((comp @ sh @ (push @ X333 @ X332))) = X332) => (! [X334 : subst] : (((comp @ X334 @ id)) = X334) => (! [X335 : (term > $o),X336 : term] : (~ ! [X337 : term] : ((X335 @ X337) | ~(var @ X337)) | ~ ! [X338 : term] : ((X335 @ (lam @ X338)) | ~(X335 @ X338)) | (X335 @ X336) | ~ ! [X339 : term,X340 : term] : (~(X335 @ X340) | ~(X335 @ X339) | (X335 @ (ap @ X340 @ X339)))) => ! [X341 : (term > $o),X342 : term,X343 : subst] : ((X341 @ (sub @ X342 @ X343)) | ~ ! [X344 : term] : ((X341 @ (sub @ X344 @ X343)) | ~(var @ X344)) | ~ ! [X345 : term] : (~ ! [X346 : term] : ((X341 @ (sub @ X345 @ (push @ X346 @ id))) | ~(X341 @ X346)) | (X341 @ (lam @ X345))) | ~ ! [X347 : term,X348 : term] : (~(X341 @ X347) | ~(X341 @ X348) | (X341 @ (ap @ X347 @ X348)))))))) <=> induction2lem_lthm) & hoasinduction_lem1v2_gthm & (! [X349 : term] : (((sub @ X349 @ id)) = X349) <=> axvarid) & (! [X350 : (subst > term > subst > $o)] : ~ ! [X351 : (term > $o)] : ~ ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) <=> hoasinduction_lem0) & (laminj <=> ! [X353 : term,X354 : term] : ((((lam @ X354)) != ((lam @ X353))) | (X353 = X354))) & axmap & (! [X355 : term,X356 : term,X357 : term,X358 : term] : ((X355 = X358) | (((ap @ X356 @ X355)) != ((ap @ X357 @ X358)))) <=> apinj2) & (hoasinduction <=> ! [X359 : term,X360 : (subst > term > subst > $o)] : (~ ! [X361 : (subst > term > term)] : ((X360 @ id @ (lam @ (X361 @ sh @ one)) @ id) | ~ ! [X362 : term] : (~(X360 @ id @ X362 @ id) | (X360 @ id @ (X361 @ id @ X362) @ id)) | ~ ! [X363 : subst,X364 : term,X365 : subst] : (((X361 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365))) = ((sub @ (X361 @ X363 @ X364) @ X365)))) | ~ ! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : ((X360 @ (comp @ X367 @ X369) @ (sub @ X368 @ X369) @ X366) | ~(X360 @ X367 @ X368 @ (comp @ X369 @ X366))) | (X360 @ id @ X359 @ id) | ~ ! [X370 : term] : (~(var @ (sub @ X370 @ id)) | (X360 @ id @ X370 @ id)) | ~ ! [X371 : subst,X372 : subst,X373 : subst,X374 : term] : ((X360 @ X372 @ X374 @ (comp @ X373 @ X371)) | ~(X360 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373) @ X371)) | ~ ! [X375 : term,X376 : term] : (~(X360 @ id @ X375 @ id) | (X360 @ id @ (ap @ (sub @ X375 @ id) @ X376) @ id) | ~(X360 @ id @ X376 @ id)))) & ((! [X377 : term] : (((sub @ X377 @ id)) = X377) => ! [X378 : term,X379 : (term > $o),X380 : (subst > term > subst > $o)] : (~ ! [X381 : term] : (~(X379 @ X381) | (X379 @ (sub @ X378 @ (push @ X381 @ id)))) | ~ ! [X382 : subst,X383 : subst,X384 : subst,X385 : term] : (~(X380 @ X384 @ X385 @ (comp @ X383 @ X382)) | (X380 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383) @ X382)) | ~ ! [X386 : term,X387 : subst,X388 : subst,X389 : subst] : ((X380 @ X389 @ X386 @ (comp @ X388 @ X387)) | ~(X380 @ (comp @ X389 @ X388) @ (sub @ X386 @ X388) @ X387)) | ~ ! [X390 : term] : (((X380 @ id @ X390 @ id)) = ((X379 @ X390))) | (X379 @ (lam @ X378)) | ~ ! [X391 : (subst > term > term)] : (~ ! [X392 : term] : ((X380 @ id @ (X391 @ id @ X392) @ id) | ~(X380 @ id @ X392 @ id)) | (X380 @ id @ (lam @ (X391 @ sh @ one)) @ id) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X391 @ X393 @ X394) @ X395)) = ((X391 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))))) <=> hoasinduction_lem3v2_lthm) & hoasinduction_lem1 & pushprop_lem2v2_gthm & ! [X396 : term] : ? [X397 : d_term] : (((d2term @ X397)) = X396) & pushprop_lem3v2_lthm & ulamvarsh & (! [X398 : term] : ~ ! [X399 : (subst > term > term)] : ~ ! [X400 : subst,X401 : term] : (((sub @ X398 @ (push @ X401 @ X400))) = ((X399 @ X400 @ X401))) <=> hoasinduction_lem3v2_f) & pushprop_lem2v2 & axabs & (sh = ((d2subst @ d_id))) & pushprop_lthm & hoasinduction_lem2v2_gthm & axclos & ! [X402 : d_term] : (d_one = X402) & (! [X403 : term,X404 : (subst > term > subst > $o)] : (~ ! [X405 : term] : ((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id) | ~(X404 @ id @ X405 @ id)) | (X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id) | ~ ! [X406 : (subst > term > term)] : (~ ! [X407 : term] : (~(X404 @ id @ X407 @ id) | (X404 @ id @ (X406 @ id @ X407) @ id)) | ~ ! [X408 : subst,X409 : term,X410 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X406 @ X408 @ X409) @ X410))) | (X404 @ id @ (lam @ (X406 @ sh @ one)) @ id))) <=> hoasinduction_lem3aa) & hoasapnotvar_gthm & (induction <=> ! [X411 : term,X412 : (term > $o)] : ((X412 @ X411) | ~ ! [X413 : term,X414 : term] : (~(X412 @ X414) | ~(X412 @ X413) | (X412 @ (ap @ X413 @ X414))) | ~ ! [X415 : term] : (~(var @ X415) | (X412 @ X415)) | ~ ! [X416 : term] : ((X412 @ (lam @ X416)) | ~(X412 @ X416)))) & hoasapnotvar_lthm & (! [X417 : term,X418 : term,X419 : (subst > term > subst > $o)] : (~ ! [X420 : term,X421 : term] : ((X419 @ id @ (ap @ (sub @ X421 @ id) @ X420) @ id) | ~(X419 @ id @ X421 @ id) | ~(X419 @ id @ X420 @ id)) | ~ ! [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((X419 @ X422 @ X425 @ (comp @ X424 @ X423)) | ~(X419 @ (comp @ X422 @ X424) @ (sub @ X425 @ X424) @ X423)) | ~ ! [X426 : subst,X427 : term,X428 : subst,X429 : subst] : (~(X419 @ X426 @ X427 @ (comp @ X429 @ X428)) | (X419 @ (comp @ X426 @ X429) @ (sub @ X427 @ X429) @ X428)) | ~(X419 @ id @ X418 @ id) | ~(X419 @ id @ X417 @ id) | (X419 @ id @ (ap @ X417 @ X418) @ id)) <=> hoasinduction_lem2) & axapp & apnotvar & ((! [X430 : term] : (((sub @ X430 @ id)) = X430) => (! [X431 : (subst > term > subst > $o),X432 : term] : (~ ! [X433 : term] : (~(X431 @ id @ X433 @ id) | (X431 @ id @ (sub @ X432 @ (push @ X433 @ id)) @ id)) | ~ ! [X434 : (subst > term > term)] : (~ ! [X435 : subst,X436 : subst,X437 : term] : (((sub @ (X434 @ X435 @ X437) @ X436)) = ((X434 @ (comp @ X435 @ X436) @ (sub @ X437 @ X436)))) | ~ ! [X438 : term] : (~(X431 @ id @ X438 @ id) | (X431 @ id @ (X434 @ id @ X438) @ id)) | (X431 @ id @ (lam @ (X434 @ sh @ one)) @ id)) | (X431 @ id @ (lam @ (sub @ X432 @ (push @ one @ sh))) @ id)) => ! [X439 : term,X440 : (subst > term > subst > $o)] : (~ ! [X441 : term] : (~(X440 @ id @ X441 @ id) | (X440 @ id @ (sub @ X439 @ (push @ X441 @ id)) @ id)) | ~ ! [X442 : (subst > term > term)] : (~ ! [X443 : subst,X444 : term,X445 : subst] : (((X442 @ (comp @ X445 @ X443) @ (sub @ X444 @ X443))) = ((sub @ (X442 @ X445 @ X444) @ X443))) | ~ ! [X446 : term] : (~(X440 @ id @ X446 @ id) | (X440 @ id @ (X442 @ id @ X446) @ id)) | (X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) | (X440 @ id @ (lam @ X439) @ id)))) <=> hoasinduction_lem3a_lthm) & axassoc & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ! [X447 : d_subst] : (d_id = X447) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X448 : d_term,X449 : d_term] : ((((d2term @ X449)) = ((d2term @ X448))) => (X448 = X449)) & (termmset_lthm <=> (! [X450 : term] : (((sub @ X450 @ id)) = X450) => ! [X451 : term] : (((sub @ X451 @ id)) = X451))) & (shinj <=> ! [X452 : term,X453 : term] : ((X452 = X453) | (((sub @ X453 @ sh)) != ((sub @ X452 @ sh))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X454 : (subst > term > subst > $o),X455 : term] : (~ ! [X456 : term,X457 : term] : (~(X454 @ id @ X457 @ id) | (X454 @ id @ (ap @ (sub @ X456 @ id) @ X457) @ id) | ~(X454 @ id @ X456 @ id)) | ~ ! [X458 : (subst > term > term)] : ((X454 @ id @ (lam @ (X458 @ sh @ one)) @ id) | ~ ! [X459 : subst,X460 : term,X461 : subst] : (((sub @ (X458 @ X461 @ X460) @ X459)) = ((X458 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459)))) | ~ ! [X462 : term] : ((X454 @ id @ (X458 @ id @ X462) @ id) | ~(X454 @ id @ X462 @ id))) | (X454 @ id @ X455 @ id)) <=> hoasinduction_no_psi_cond) & induction2_gthm & (! [X463 : term,X464 : subst] : (((sub @ one @ (push @ X463 @ X464))) = X463) <=> axvarcons) & hoasinduction_lem1v2 & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotvar_gthm & hoasinduction_gthm & hoasinduction_lem3_gthm & (hoasapinj2_lthm <=> (! [X465 : term,X466 : term,X467 : term,X468 : term] : ((((ap @ X467 @ X466)) != ((ap @ X468 @ X465))) | (X465 = X466)) => ! [X469 : term,X470 : term,X471 : term,X472 : term] : ((((ap @ (sub @ X472 @ id) @ X470)) != ((ap @ (sub @ X471 @ id) @ X469))) | (X469 = X470)))) & pushprop_lem2v2_lthm & ((! [X473 : term] : (((sub @ X473 @ id)) = X473) => (! [X474 : term,X475 : (subst > term > subst > $o)] : (~ ! [X476 : (subst > term > term)] : ((X475 @ id @ (lam @ (X476 @ sh @ one)) @ id) | ~ ! [X477 : term,X478 : subst,X479 : subst] : (((X476 @ (comp @ X478 @ X479) @ (sub @ X477 @ X479))) = ((sub @ (X476 @ X478 @ X477) @ X479))) | ~ ! [X480 : term] : (~(X475 @ id @ X480 @ id) | (X475 @ id @ (X476 @ id @ X480) @ id))) | ~ ! [X481 : term] : ((X475 @ id @ (sub @ X474 @ (push @ X481 @ id)) @ id) | ~(X475 @ id @ X481 @ id)) | (X475 @ id @ (lam @ (sub @ X474 @ (push @ one @ sh))) @ id)) => ! [X482 : (subst > term > subst > $o),X483 : term] : (~ ! [X484 : subst,X485 : term,X486 : subst,X487 : subst] : (~(X482 @ X487 @ X485 @ (comp @ X486 @ X484)) | (X482 @ (comp @ X487 @ X486) @ (sub @ X485 @ X486) @ X484)) | (X482 @ id @ (lam @ X483) @ id) | ~ ! [X488 : (subst > term > term)] : ((X482 @ id @ (lam @ (X488 @ sh @ one)) @ id) | ~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X491 @ X489) @ X490)) = ((X488 @ (comp @ X491 @ X490) @ (sub @ X489 @ X490)))) | ~ ! [X492 : term] : ((X482 @ id @ (X488 @ id @ X492) @ id) | ~(X482 @ id @ X492 @ id))) | ~ ! [X493 : term] : (~(X482 @ id @ X493 @ id) | (X482 @ id @ (sub @ X483 @ (push @ X493 @ id)) @ id)) | ~ ! [X494 : subst,X495 : term,X496 : subst,X497 : subst] : (~(X482 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497) @ X494) | (X482 @ X496 @ X495 @ (comp @ X497 @ X494)))))) <=> hoasinduction_lem3_lthm) & (hoasapinj1_lthm <=> (! [X498 : term] : (((sub @ X498 @ id)) = X498) => (! [X499 : term,X500 : term,X501 : term,X502 : term] : ((((ap @ X499 @ X502)) != ((ap @ X500 @ X501))) | (X499 = X500)) => ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X505 = X506) | (((ap @ (sub @ X505 @ id) @ X504)) != ((ap @ (sub @ X506 @ id) @ X503))))))) & ((! [X507 : term,X508 : subst] : (((sub @ one @ (push @ X507 @ X508))) = X507) => (! [X509 : term,X510 : subst] : (((comp @ sh @ (push @ X509 @ X510))) = X510) => (! [X511 : term,X512 : term] : ((X511 = X512) | (((lam @ X512)) != ((lam @ X511)))) => ! [X513 : (subst > term > term),X514 : (subst > term > term),X515 : term,X516 : subst] : (~ ! [X517 : subst,X518 : subst,X519 : term] : (((X514 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X514 @ X518 @ X519) @ X517))) | (((X514 @ X516 @ X515)) = ((X513 @ X516 @ X515))) | ~ ! [X520 : subst,X521 : subst,X522 : term] : (((X513 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520))) = ((sub @ (X513 @ X521 @ X522) @ X520))) | (((lam @ (X514 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))))))) <=> hoaslaminj_lthm) & (! [X523 : (term > $o),X524 : subst,X525 : (term > $o),X526 : term,X527 : term] : ((X525 @ (sub @ X527 @ (push @ X526 @ X524))) | ~(X523 @ X527)) <=> pushprop_lem1) & lamnotvar & hoaslamnotvar_lthm & (! [X528 : term,X529 : (term > $o)] : (~ ! [X530 : term] : ((X529 @ (lam @ X530)) | ~ ! [X531 : term] : ((X529 @ (sub @ X530 @ (push @ X531 @ id))) | ~(X529 @ X531))) | ~ ! [X532 : term,X533 : term] : (~(X529 @ X532) | (X529 @ (ap @ X532 @ X533)) | ~(X529 @ X533)) | ~ ! [X534 : term] : ((X529 @ X534) | ~(var @ X534)) | (X529 @ X528)) <=> induction2) & (! [X535 : term,X536 : (subst > term > subst > $o)] : ((X536 @ id @ (lam @ X535) @ id) | ~ ! [X537 : (subst > term > term)] : (~ ! [X538 : term,X539 : subst,X540 : subst] : (((sub @ (X537 @ X539 @ X538) @ X540)) = ((X537 @ (comp @ X539 @ X540) @ (sub @ X538 @ X540)))) | ~ ! [X541 : term] : ((X536 @ id @ (X537 @ id @ X541) @ id) | ~(X536 @ id @ X541 @ id)) | (X536 @ id @ (lam @ (X537 @ sh @ one)) @ id)) | ~ ! [X542 : term] : (~(X536 @ id @ X542 @ id) | (X536 @ id @ (sub @ X535 @ (push @ X542 @ id)) @ id))) <=> hoasinduction_lem3a) & (one = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & (! [X543 : subst,X544 : (term > $o),X545 : term] : ~ ! [X546 : (term > $o)] : ~ ! [X547 : term] : (((X544 @ (sub @ X547 @ (push @ X545 @ X543)))) = ((X546 @ X547))) <=> pushprop_lem0_lthm) & hoaslamnotap_gthm & (hoasinduction_lem3b <=> ! [X548 : term] : ~ ! [X549 : (subst > term > term)] : (((X549 @ sh @ one)) != ((sub @ X548 @ (push @ one @ sh)))))),
% 37.84/5.79 inference(rectify,[],[f1])).
% 37.84/5.79 thf(f5,plain,(
% 37.84/5.79 ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ X5)) = $true) | ~ (((var @ X5)) = $true)) | ~ ! [X6 : term] : (~ ! [X7 : term] : (~ (((X3 @ X7)) = $true) | (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true)) | (((X3 @ (lam @ X6))) = $true)) | ~ ! [X8 : term,X9 : term] : ((((X3 @ (ap @ X8 @ X9))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (term > $o),X13 : (subst > term > subst > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : (~ (((X13 @ id @ X15 @ id)) = $true) | (((X13 @ id @ (X14 @ id @ X15) @ id)) = $true)) | ~ ! [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) = ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | (((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true)) | ~ ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) | ~ ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | ~ (((X12 @ X20)) = $true)) | (((X12 @ (lam @ X11))) = $true)) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25))))) | ~ ! [X28 : term,X29 : term] : (~ (((X21 @ id @ X28 @ id)) = $true) | ~ ($true = ((X21 @ id @ X29 @ id))) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true)))))))) & (! [X30 : term] : ~ ! [X31 : (subst > term > term)] : ~ ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop = $true) & (ulamvarind = $true) & (! [X36 : term] : ~ ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (substmonoid_gthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X38 : (term > $o),X39 : (term > $o),X40 : subst,X41 : term] : ((((X39 @ one)) = $true) | ~ ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) | ~ (((X38 @ X41)) = $true)) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ~ ! [X44 : (term > $o)] : ~ ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lthm_orig = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ((! [X48 : subst] : (((comp @ id @ X48)) = X48) => (! [X49 : subst] : (((comp @ X49 @ id)) = X49) => (! [X50 : subst] : (((comp @ id @ X50)) = X50) & ! [X51 : subst] : (((comp @ X51 @ id)) = X51)))) <=> (substmonoid_lthm = $true)) & ((substmonoid = $true) <=> (! [X52 : subst] : (((comp @ id @ X52)) = X52) & ! [X53 : subst] : (((comp @ X53 @ id)) = X53))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem0_gthm = $true) & ((hoaslaminj = $true) <=> ! [X54 : (subst > term > term),X55 : term,X56 : subst,X57 : (subst > term > term)] : ((((X54 @ X56 @ X55)) = ((X57 @ X56 @ X55))) | ~ ! [X58 : term,X59 : subst,X60 : subst] : (((X57 @ (comp @ X59 @ X60) @ (sub @ X58 @ X60))) = ((sub @ (X57 @ X59 @ X58) @ X60))) | ~ ! [X61 : subst,X62 : term,X63 : subst] : (((sub @ (X54 @ X63 @ X62) @ X61)) = ((X54 @ (comp @ X63 @ X61) @ (sub @ X62 @ X61)))) | (((lam @ (X54 @ sh @ one))) != ((lam @ (X57 @ sh @ one)))))) & ((pushprop_lem1_lthm = $true) <=> (! [X64 : term,X65 : subst] : (((sub @ one @ (push @ X64 @ X65))) = X64) => (! [X66 : term,X67 : subst] : (((comp @ sh @ (push @ X66 @ X67))) = X67) => ! [X68 : (term > $o),X69 : term,X70 : term,X71 : (term > $o),X72 : subst] : ((((X71 @ (sub @ X70 @ (push @ X69 @ X72)))) = $true) | ~ (((X68 @ X70)) = $true))))) & ((hoasapinj1 = $true) <=> ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X74 = X76) | (((ap @ (sub @ X74 @ id) @ X75)) != ((ap @ (sub @ X76 @ id) @ X73))))) & (! [X77 : (subst > term > subst > $o),X78 : term,X79 : (term > $o)] : (~ ! [X80 : term] : (~ (((X79 @ X80)) = $true) | (((X79 @ (sub @ X78 @ (push @ X80 @ id)))) = $true)) | (((X79 @ (lam @ X78))) = $true) | ~ ! [X81 : term,X82 : subst,X83 : subst,X84 : subst] : ((((X77 @ (comp @ X82 @ X83) @ (sub @ X81 @ X83) @ X84)) = $true) | ~ (((X77 @ X82 @ X81 @ (comp @ X83 @ X84))) = $true)) | ~ ! [X85 : term] : (((X79 @ X85)) = ((X77 @ id @ X85 @ id))) | ~ ! [X86 : subst,X87 : subst,X88 : subst,X89 : term] : (~ (((X77 @ (comp @ X88 @ X86) @ (sub @ X89 @ X86) @ X87)) = $true) | ($true = ((X77 @ X88 @ X89 @ (comp @ X86 @ X87))))) | ~ ! [X90 : (subst > term > term)] : (~ ! [X91 : term,X92 : subst,X93 : subst] : (((X90 @ (comp @ X92 @ X93) @ (sub @ X91 @ X93))) = ((sub @ (X90 @ X92 @ X91) @ X93))) | (((X77 @ id @ (lam @ (X90 @ sh @ one)) @ id)) = $true) | ~ ! [X94 : term] : ((((X77 @ id @ (X90 @ id @ X94) @ id)) = $true) | ~ (((X77 @ id @ X94 @ id)) = $true)))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X95 : (term > $o),X96 : term] : (~ ! [X97 : term] : (~ (((var @ X97)) = $true) | (((X95 @ X97)) = $true)) | ~ ! [X98 : term,X99 : term] : (~ (((X95 @ X98)) = $true) | ~ (((X95 @ X99)) = $true) | (((X95 @ (ap @ X99 @ X98))) = $true)) | (((X95 @ X96)) = $true) | ~ ! [X100 : term] : (~ ! [X101 : term] : ((((X95 @ (sub @ X100 @ (push @ X101 @ id)))) = $true) | ~ (((X95 @ X101)) = $true)) | ($true = ((X95 @ (lam @ X100)))))) => (! [X102 : term,X103 : term,X104 : (subst > term > subst > $o)] : (~ (((X104 @ id @ X102 @ id)) = $true) | (((X104 @ id @ (ap @ X102 @ X103) @ id)) = $true) | ~ ! [X105 : subst,X106 : term,X107 : subst,X108 : subst] : (~ (((X104 @ X107 @ X106 @ (comp @ X105 @ X108))) = $true) | (((X104 @ (comp @ X107 @ X105) @ (sub @ X106 @ X105) @ X108)) = $true)) | ~ ! [X109 : term,X110 : term] : (~ ($true = ((X104 @ id @ X109 @ id))) | (((X104 @ id @ (ap @ (sub @ X110 @ id) @ X109) @ id)) = $true) | ~ (((X104 @ id @ X110 @ id)) = $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (~ (((X104 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111) @ X114)) = $true) | (((X104 @ X113 @ X112 @ (comp @ X111 @ X114))) = $true)) | ~ (((X104 @ id @ X103 @ id)) = $true)) => (! [X115 : (subst > term > subst > $o),X116 : term] : (~ ! [X117 : (subst > term > term)] : ((((X115 @ id @ (lam @ (X117 @ sh @ one)) @ id)) = $true) | ~ ! [X118 : term] : (~ (((X115 @ id @ X118 @ id)) = $true) | (((X115 @ id @ (X117 @ id @ X118) @ id)) = $true)) | ~ ! [X119 : term,X120 : subst,X121 : subst] : (((X117 @ (comp @ X121 @ X120) @ (sub @ X119 @ X120))) = ((sub @ (X117 @ X121 @ X119) @ X120)))) | ~ ! [X122 : term] : ((((X115 @ id @ (sub @ X116 @ (push @ X122 @ id)) @ id)) = $true) | ~ (((X115 @ id @ X122 @ id)) = $true)) | (((X115 @ id @ (lam @ X116) @ id)) = $true) | ~ ! [X123 : subst,X124 : subst,X125 : subst,X126 : term] : (~ (((X115 @ (comp @ X123 @ X125) @ (sub @ X126 @ X125) @ X124)) = $true) | (((X115 @ X123 @ X126 @ (comp @ X125 @ X124))) = $true)) | ~ ! [X127 : subst,X128 : subst,X129 : term,X130 : subst] : ((((X115 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X130)) = $true) | ~ ($true = ((X115 @ X127 @ X129 @ (comp @ X128 @ X130)))))) => ! [X131 : (subst > term > subst > $o),X132 : term] : (~ ! [X133 : subst,X134 : subst,X135 : term,X136 : subst] : (($true = ((X131 @ (comp @ X134 @ X133) @ (sub @ X135 @ X133) @ X136))) | ~ (((X131 @ X134 @ X135 @ (comp @ X133 @ X136))) = $true)) | (((X131 @ id @ X132 @ id)) = $true) | ~ ! [X137 : subst,X138 : subst,X139 : subst,X140 : term] : ((((X131 @ X137 @ X140 @ (comp @ X138 @ X139))) = $true) | ~ (((X131 @ (comp @ X137 @ X138) @ (sub @ X140 @ X138) @ X139)) = $true)) | ~ ! [X141 : term] : (~ (((var @ (sub @ X141 @ id))) = $true) | (((X131 @ id @ X141 @ id)) = $true)) | ~ ! [X142 : term,X143 : term] : ((((X131 @ id @ (ap @ (sub @ X142 @ id) @ X143) @ id)) = $true) | ~ (((X131 @ id @ X142 @ id)) = $true) | ~ (((X131 @ id @ X143 @ id)) = $true)) | ~ ! [X144 : (subst > term > term)] : ((((X131 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ~ ! [X145 : term] : ((((X131 @ id @ (X144 @ id @ X145) @ id)) = $true) | ~ (((X131 @ id @ X145 @ id)) = $true)) | ~ ! [X146 : subst,X147 : subst,X148 : term] : (((X144 @ (comp @ X147 @ X146) @ (sub @ X148 @ X146))) = ((sub @ (X144 @ X147 @ X148) @ X146)))))))) <=> (hoasinduction_lthm = $true)) & (! [X149 : (subst > term > term),X150 : term,X151 : term] : ((((ap @ (sub @ X150 @ id) @ X151)) != ((lam @ (X149 @ sh @ one)))) | ~ ! [X152 : subst,X153 : term,X154 : subst] : (((X149 @ (comp @ X154 @ X152) @ (sub @ X153 @ X152))) = ((sub @ (X149 @ X154 @ X153) @ X152)))) <=> (hoaslamnotap = $true)) & ~ (ulamvar1 = $true) & (pushprop_gthm = $true) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & (pushprop_lem1v2_gthm = $true) & ((! [X156 : (subst > term > subst > $o)] : ~ ! [X157 : (term > $o)] : ~ ! [X158 : term] : (((X156 @ id @ X158 @ id)) = ((X157 @ X158))) => (! [X159 : (term > $o),X160 : term] : (~ ! [X161 : term] : ((((X159 @ X161)) = $true) | ~ (((var @ X161)) = $true)) | (((X159 @ X160)) = $true) | ~ ! [X162 : term] : ((((X159 @ (lam @ X162))) = $true) | ~ ! [X163 : term] : (($true = ((X159 @ (sub @ X162 @ (push @ X163 @ id))))) | ~ (((X159 @ X163)) = $true))) | ~ ! [X164 : term,X165 : term] : (~ (((X159 @ X165)) = $true) | (((X159 @ (ap @ X164 @ X165))) = $true) | ~ (((X159 @ X164)) = $true))) => (! [X166 : term] : (((sub @ X166 @ id)) = X166) => (! [X167 : (subst > term > subst > $o),X168 : (term > $o),X169 : term] : (~ ! [X170 : term] : (~ (((X168 @ X170)) = $true) | ($true = ((X168 @ (sub @ X169 @ (push @ X170 @ id)))))) | ~ ! [X171 : (subst > term > term)] : (~ ! [X172 : term] : ((((X167 @ id @ (X171 @ id @ X172) @ id)) = $true) | ~ (((X167 @ id @ X172 @ id)) = $true)) | ~ ! [X173 : subst,X174 : subst,X175 : term] : (((X171 @ (comp @ X174 @ X173) @ (sub @ X175 @ X173))) = ((sub @ (X171 @ X174 @ X175) @ X173))) | (((X167 @ id @ (lam @ (X171 @ sh @ one)) @ id)) = $true)) | (((X168 @ (lam @ X169))) = $true) | ~ ! [X176 : term] : (((X168 @ X176)) = ((X167 @ id @ X176 @ id)))) => ! [X177 : (subst > term > subst > $o),X178 : term] : (~ ! [X179 : (subst > term > term)] : (~ ! [X180 : subst,X181 : subst,X182 : term] : (((X179 @ (comp @ X180 @ X181) @ (sub @ X182 @ X181))) = ((sub @ (X179 @ X180 @ X182) @ X181))) | (((X177 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ~ ! [X183 : term] : ((((X177 @ id @ (X179 @ id @ X183) @ id)) = $true) | ~ (((X177 @ id @ X183 @ id)) = $true))) | ~ ! [X184 : term] : ((((X177 @ id @ X184 @ id)) = $true) | ~ (((var @ (sub @ X184 @ id))) = $true)) | ~ ! [X185 : subst,X186 : subst,X187 : subst,X188 : term] : (~ (((X177 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X185)) = $true) | (((X177 @ X186 @ X188 @ (comp @ X187 @ X185))) = $true)) | ~ ! [X189 : term,X190 : term] : (~ (((X177 @ id @ X190 @ id)) = $true) | ~ (((X177 @ id @ X189 @ id)) = $true) | (((X177 @ id @ (ap @ (sub @ X189 @ id) @ X190) @ id)) = $true)) | (((X177 @ id @ X178 @ id)) = $true) | ~ ! [X191 : term,X192 : subst,X193 : subst,X194 : subst] : ((((X177 @ (comp @ X192 @ X193) @ (sub @ X191 @ X193) @ X194)) = $true) | ~ (((X177 @ X192 @ X191 @ (comp @ X193 @ X194))) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X195 : (term > $o),X196 : term,X197 : subst] : ((((X195 @ (sub @ X196 @ X197))) = $true) | ~ ! [X198 : term] : ((((X195 @ (lam @ X198))) = $true) | ~ ! [X199 : term] : (($true = ((X195 @ (sub @ X198 @ (push @ X199 @ id))))) | ~ ($true = ((X195 @ X199))))) | ~ ! [X200 : term,X201 : term] : (~ (((X195 @ X201)) = $true) | (((X195 @ (ap @ X200 @ X201))) = $true) | ~ (((X195 @ X200)) = $true)) | ~ ! [X202 : term] : ((((X195 @ (sub @ X202 @ X197))) = $true) | ~ (((var @ X202)) = $true))) <=> (induction2lem = $true)) & (! [X203 : term] : (((sub @ X203 @ id)) = X203) <=> (termmset = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X204 : (subst > term > subst > $o),X205 : term,X206 : (term > $o)] : (~ ! [X207 : (subst > term > term)] : (~ ! [X208 : term,X209 : subst,X210 : subst] : (((X207 @ (comp @ X210 @ X209) @ (sub @ X208 @ X209))) = ((sub @ (X207 @ X210 @ X208) @ X209))) | (((X204 @ id @ (lam @ (X207 @ sh @ one)) @ id)) = $true) | ~ ! [X211 : term] : (~ (((X204 @ id @ X211 @ id)) = $true) | ($true = ((X204 @ id @ (X207 @ id @ X211) @ id))))) | ~ ! [X212 : term] : ((((X206 @ (sub @ X205 @ (push @ X212 @ id)))) = $true) | ~ (((X206 @ X212)) = $true)) | ~ ! [X213 : term] : (((X206 @ X213)) = ((X204 @ id @ X213 @ id))) | (((X206 @ (lam @ X205))) = $true))) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 = X216) | (((ap @ (sub @ X217 @ id) @ X216)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ~ (lamnotap = $true) & (induction2lem_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((apinj1 = $true) <=> ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X222 = X224) | (((ap @ X224 @ X223)) != ((ap @ X222 @ X221))))) & (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)))))))))))))) & (! [X230 : (subst > term > subst > $o),X231 : term] : ((((X230 @ id @ (lam @ (sub @ X231 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X232 : term] : (~ (((X230 @ id @ X232 @ id)) = $true) | (((X230 @ id @ (sub @ X231 @ (push @ X232 @ id)) @ id)) = $true)) | ~ ! [X233 : (subst > term > term)] : (~ ! [X234 : term] : (($true = ((X230 @ id @ (X233 @ id @ X234) @ id))) | ~ (((X230 @ id @ X234 @ id)) = $true)) | (((X230 @ id @ (lam @ (X233 @ sh @ one)) @ id)) = $true) | ~ ! [X235 : subst,X236 : subst,X237 : term] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoaslamnotvar = $true) & ! [X238 : d_subst,X239 : d_subst] : ((((d2subst @ X239)) = ((d2subst @ X238))) => (X238 = X239)) & ((! [X240 : term,X241 : subst] : (((sub @ one @ (push @ X240 @ X241))) = X240) => ! [X242 : (term > $o),X243 : subst,X244 : (term > $o),X245 : term] : (~ ! [X246 : term] : (((X242 @ X246)) = ((X244 @ (sub @ X246 @ (push @ X245 @ X243))))) | (((X242 @ one)) = $true) | ~ (((X244 @ X245)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X247 : term,X248 : (subst > term > subst > $o)] : (~ ! [X249 : term] : (~ (((X248 @ id @ X249 @ id)) = $true) | (((X248 @ id @ (sub @ X247 @ (push @ X249 @ id)) @ id)) = $true)) | (((X248 @ id @ (lam @ X247) @ id)) = $true) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~ ($true = ((X248 @ X250 @ X251 @ (comp @ X252 @ X253)))) | (((X248 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true)) | ~ ! [X254 : (subst > term > term)] : (~ ! [X255 : subst,X256 : term,X257 : subst] : (((sub @ (X254 @ X255 @ X256) @ X257)) = ((X254 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257)))) | (((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true) | ~ ! [X258 : term] : ((((X248 @ id @ (X254 @ id @ X258) @ id)) = $true) | ~ (((X248 @ id @ X258 @ id)) = $true))) | ~ ! [X259 : subst,X260 : term,X261 : subst,X262 : subst] : (~ (((X248 @ (comp @ X262 @ X259) @ (sub @ X260 @ X259) @ X261)) = $true) | (((X248 @ X262 @ X260 @ (comp @ X259 @ X261))) = $true)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X263 : term,X264 : subst,X265 : (term > $o)] : ~ ! [X266 : (term > $o)] : ~ ! [X267 : term] : (((X266 @ X267)) = ((X265 @ (sub @ X267 @ (push @ X263 @ X264))))) <=> (pushprop_lem0 = $true)) & ((! [X268 : term] : ~ ! [X269 : (subst > term > term)] : ~ ! [X270 : term,X271 : subst] : (((sub @ X268 @ (push @ X270 @ X271))) = ((X269 @ X271 @ X270))) => (! [X272 : term] : (((sub @ X272 @ id)) = X272) => ! [X273 : term,X274 : (term > $o),X275 : (subst > term > subst > $o)] : ((((X274 @ (lam @ X273))) = $true) | ~ ! [X276 : term] : ((((X274 @ (sub @ X273 @ (push @ X276 @ id)))) = $true) | ~ (((X274 @ X276)) = $true)) | ~ ! [X277 : (subst > term > term)] : (~ ! [X278 : term] : (~ (((X275 @ id @ X278 @ id)) = $true) | (((X275 @ id @ (X277 @ id @ X278) @ id)) = $true)) | (((X275 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((X277 @ (comp @ X281 @ X279) @ (sub @ X280 @ X279))) = ((sub @ (X277 @ X281 @ X280) @ X279)))) | ~ ! [X282 : term] : (((X275 @ id @ X282 @ id)) = ((X274 @ X282)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X283 : (subst > term > subst > $o),X284 : term] : (~ ! [X285 : (subst > term > term),X286 : term] : (~ ! [X287 : subst,X288 : subst,X289 : term] : (((sub @ (sub @ X286 @ (push @ X289 @ X287)) @ X288)) = ((sub @ (X285 @ X287 @ X289) @ X288))) | (((X283 @ id @ (lam @ (X285 @ sh @ one)) @ id)) = $true) | ~ ! [X290 : term] : ((((X283 @ id @ (X285 @ id @ X290) @ id)) = $true) | ~ (((X283 @ id @ X290 @ id)) = $true)) | ~ ! [X291 : subst,X292 : subst,X293 : term] : (((X285 @ (comp @ X292 @ X291) @ (sub @ X293 @ X291))) = ((sub @ X286 @ (push @ (sub @ X293 @ X291) @ (comp @ X292 @ X291)))))) | ~ ! [X294 : term] : (~ (((X283 @ id @ X294 @ id)) = $true) | (((X283 @ id @ (sub @ X284 @ (push @ X294 @ id)) @ id)) = $true)) | (((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X295 : term,X296 : term,X297 : (subst > term > subst > $o),X298 : (term > $o)] : ((((X298 @ (ap @ X296 @ X295))) = $true) | ~ (((X298 @ X296)) = $true) | ~ (((X298 @ X295)) = $true) | ~ ! [X299 : term,X300 : term] : (~ ($true = ((X297 @ id @ X300 @ id))) | ~ (((X297 @ id @ X299 @ id)) = $true) | (((X297 @ id @ (ap @ (sub @ X300 @ id) @ X299) @ id)) = $true)) | ~ ! [X301 : term] : (((X297 @ id @ X301 @ id)) = ((X298 @ X301))) | ~ ! [X302 : subst,X303 : subst,X304 : term,X305 : subst] : ((((X297 @ X303 @ X304 @ (comp @ X302 @ X305))) = $true) | ~ ($true = ((X297 @ (comp @ X303 @ X302) @ (sub @ X304 @ X302) @ X305)))) | ~ ! [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (~ (((X297 @ X307 @ X306 @ (comp @ X308 @ X309))) = $true) | (((X297 @ (comp @ X307 @ X308) @ (sub @ X306 @ X308) @ X309)) = $true)))) & (pushprop_lem1_gthm = $true) & ((induction2_lthm = $true) <=> (! [X310 : term] : (((sub @ X310 @ id)) = X310) => (! [X311 : term,X312 : (term > $o),X313 : subst] : (~ ! [X314 : term] : ((((X312 @ (lam @ X314))) = $true) | ~ ! [X315 : term] : (~ (((X312 @ X315)) = $true) | (((X312 @ (sub @ X314 @ (push @ X315 @ id)))) = $true))) | ~ ! [X316 : term] : (~ (((var @ X316)) = $true) | (((X312 @ (sub @ X316 @ X313))) = $true)) | ~ ! [X317 : term,X318 : term] : ((((X312 @ (ap @ X318 @ X317))) = $true) | ~ (((X312 @ X317)) = $true) | ~ (((X312 @ X318)) = $true)) | (((X312 @ (sub @ X311 @ X313))) = $true)) => ! [X319 : term,X320 : (term > $o)] : (~ ! [X321 : term] : (~ ! [X322 : term] : (~ (((X320 @ X322)) = $true) | (((X320 @ (sub @ X321 @ (push @ X322 @ id)))) = $true)) | (((X320 @ (lam @ X321))) = $true)) | ~ ! [X323 : term] : (~ ($true = ((var @ X323))) | (((X320 @ X323)) = $true)) | (((X320 @ X319)) = $true) | ~ ! [X324 : term,X325 : term] : (~ (((X320 @ X325)) = $true) | (((X320 @ (ap @ X324 @ X325))) = $true) | ~ (((X320 @ X324)) = $true)))))) & (! [X326 : subst] : (((comp @ id @ X326)) = X326) <=> (axidl = $true)) & (termmset_gthm = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (! [X327 : subst] : (((comp @ X327 @ id)) = X327) <=> (axidr = $true)) & ((axshiftcons = $true) <=> ! [X328 : subst,X329 : term] : (((comp @ sh @ (push @ X329 @ X328))) = X328)) & (hoasapnotvar = $true) & ((! [X330 : subst,X331 : term] : (((sub @ one @ (push @ X331 @ X330))) = X331) => (! [X332 : subst,X333 : term] : (((comp @ sh @ (push @ X333 @ X332))) = X332) => (! [X334 : subst] : (((comp @ X334 @ id)) = X334) => (! [X335 : (term > $o),X336 : term] : (~ ! [X337 : term] : ((((X335 @ X337)) = $true) | ~ (((var @ X337)) = $true)) | ~ ! [X338 : term] : (($true = ((X335 @ (lam @ X338)))) | ~ (((X335 @ X338)) = $true)) | (((X335 @ X336)) = $true) | ~ ! [X339 : term,X340 : term] : (~ (((X335 @ X340)) = $true) | ~ (((X335 @ X339)) = $true) | (((X335 @ (ap @ X340 @ X339))) = $true))) => ! [X341 : (term > $o),X342 : term,X343 : subst] : ((((X341 @ (sub @ X342 @ X343))) = $true) | ~ ! [X344 : term] : ((((X341 @ (sub @ X344 @ X343))) = $true) | ~ (((var @ X344)) = $true)) | ~ ! [X345 : term] : (~ ! [X346 : term] : ((((X341 @ (sub @ X345 @ (push @ X346 @ id)))) = $true) | ~ (((X341 @ X346)) = $true)) | (((X341 @ (lam @ X345))) = $true)) | ~ ! [X347 : term,X348 : term] : (~ (((X341 @ X347)) = $true) | ~ (((X341 @ X348)) = $true) | (((X341 @ (ap @ X347 @ X348))) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (! [X349 : term] : (((sub @ X349 @ id)) = X349) <=> (axvarid = $true)) & (! [X350 : (subst > term > subst > $o)] : ~ ! [X351 : (term > $o)] : ~ ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) <=> (hoasinduction_lem0 = $true)) & ((laminj = $true) <=> ! [X353 : term,X354 : term] : ((((lam @ X354)) != ((lam @ X353))) | (X353 = X354))) & (axmap = $true) & (! [X355 : term,X356 : term,X357 : term,X358 : term] : ((X355 = X358) | (((ap @ X356 @ X355)) != ((ap @ X357 @ X358)))) <=> (apinj2 = $true)) & ((hoasinduction = $true) <=> ! [X359 : term,X360 : (subst > term > subst > $o)] : (~ ! [X361 : (subst > term > term)] : ((((X360 @ id @ (lam @ (X361 @ sh @ one)) @ id)) = $true) | ~ ! [X362 : term] : (~ (((X360 @ id @ X362 @ id)) = $true) | (((X360 @ id @ (X361 @ id @ X362) @ id)) = $true)) | ~ ! [X363 : subst,X364 : term,X365 : subst] : (((X361 @ (comp @ X363 @ X365) @ (sub @ X364 @ X365))) = ((sub @ (X361 @ X363 @ X364) @ X365)))) | ~ ! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : ((((X360 @ (comp @ X367 @ X369) @ (sub @ X368 @ X369) @ X366)) = $true) | ~ (((X360 @ X367 @ X368 @ (comp @ X369 @ X366))) = $true)) | (((X360 @ id @ X359 @ id)) = $true) | ~ ! [X370 : term] : (~ ($true = ((var @ (sub @ X370 @ id)))) | (((X360 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : subst,X372 : subst,X373 : subst,X374 : term] : ((((X360 @ X372 @ X374 @ (comp @ X373 @ X371))) = $true) | ~ (((X360 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373) @ X371)) = $true)) | ~ ! [X375 : term,X376 : term] : (~ (((X360 @ id @ X375 @ id)) = $true) | (((X360 @ id @ (ap @ (sub @ X375 @ id) @ X376) @ id)) = $true) | ~ (((X360 @ id @ X376 @ id)) = $true)))) & ((! [X377 : term] : (((sub @ X377 @ id)) = X377) => ! [X378 : term,X379 : (term > $o),X380 : (subst > term > subst > $o)] : (~ ! [X381 : term] : (~ (((X379 @ X381)) = $true) | (((X379 @ (sub @ X378 @ (push @ X381 @ id)))) = $true)) | ~ ! [X382 : subst,X383 : subst,X384 : subst,X385 : term] : (~ (((X380 @ X384 @ X385 @ (comp @ X383 @ X382))) = $true) | (((X380 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383) @ X382)) = $true)) | ~ ! [X386 : term,X387 : subst,X388 : subst,X389 : subst] : ((((X380 @ X389 @ X386 @ (comp @ X388 @ X387))) = $true) | ~ (((X380 @ (comp @ X389 @ X388) @ (sub @ X386 @ X388) @ X387)) = $true)) | ~ ! [X390 : term] : (((X380 @ id @ X390 @ id)) = ((X379 @ X390))) | (((X379 @ (lam @ X378))) = $true) | ~ ! [X391 : (subst > term > term)] : (~ ! [X392 : term] : ((((X380 @ id @ (X391 @ id @ X392) @ id)) = $true) | ~ (((X380 @ id @ X392 @ id)) = $true)) | (((X380 @ id @ (lam @ (X391 @ sh @ one)) @ id)) = $true) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X391 @ X393 @ X394) @ X395)) = ((X391 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X396 : term] : ? [X397 : d_term] : (((d2term @ X397)) = X396) & (pushprop_lem3v2_lthm = $true) & (ulamvarsh = $true) & (! [X398 : term] : ~ ! [X399 : (subst > term > term)] : ~ ! [X400 : subst,X401 : term] : (((sub @ X398 @ (push @ X401 @ X400))) = ((X399 @ X400 @ X401))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem2v2 = $true) & (axabs = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (axclos = $true) & ! [X402 : d_term] : (d_one = X402) & (! [X403 : term,X404 : (subst > term > subst > $o)] : (~ ! [X405 : term] : ((((X404 @ id @ (sub @ X403 @ (push @ X405 @ id)) @ id)) = $true) | ~ (((X404 @ id @ X405 @ id)) = $true)) | (((X404 @ id @ (lam @ (sub @ X403 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X406 : (subst > term > term)] : (~ ! [X407 : term] : (~ (((X404 @ id @ X407 @ id)) = $true) | ($true = ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ~ ! [X408 : subst,X409 : term,X410 : subst] : (((X406 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X406 @ X408 @ X409) @ X410))) | (((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasapnotvar_gthm = $true) & ((induction = $true) <=> ! [X411 : term,X412 : (term > $o)] : ((((X412 @ X411)) = $true) | ~ ! [X413 : term,X414 : term] : (~ (((X412 @ X414)) = $true) | ~ (((X412 @ X413)) = $true) | (((X412 @ (ap @ X413 @ X414))) = $true)) | ~ ! [X415 : term] : (~ (((var @ X415)) = $true) | (((X412 @ X415)) = $true)) | ~ ! [X416 : term] : ((((X412 @ (lam @ X416))) = $true) | ~ (((X412 @ X416)) = $true)))) & (hoasapnotvar_lthm = $true) & (! [X417 : term,X418 : term,X419 : (subst > term > subst > $o)] : (~ ! [X420 : term,X421 : term] : (($true = ((X419 @ id @ (ap @ (sub @ X421 @ id) @ X420) @ id))) | ~ (((X419 @ id @ X421 @ id)) = $true) | ~ (((X419 @ id @ X420 @ id)) = $true)) | ~ ! [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((((X419 @ X422 @ X425 @ (comp @ X424 @ X423))) = $true) | ~ (((X419 @ (comp @ X422 @ X424) @ (sub @ X425 @ X424) @ X423)) = $true)) | ~ ! [X426 : subst,X427 : term,X428 : subst,X429 : subst] : (~ (((X419 @ X426 @ X427 @ (comp @ X429 @ X428))) = $true) | (((X419 @ (comp @ X426 @ X429) @ (sub @ X427 @ X429) @ X428)) = $true)) | ~ (((X419 @ id @ X418 @ id)) = $true) | ~ (((X419 @ id @ X417 @ id)) = $true) | (((X419 @ id @ (ap @ X417 @ X418) @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (axapp = $true) & (apnotvar = $true) & ((! [X430 : term] : (((sub @ X430 @ id)) = X430) => (! [X431 : (subst > term > subst > $o),X432 : term] : (~ ! [X433 : term] : (~ (((X431 @ id @ X433 @ id)) = $true) | (((X431 @ id @ (sub @ X432 @ (push @ X433 @ id)) @ id)) = $true)) | ~ ! [X434 : (subst > term > term)] : (~ ! [X435 : subst,X436 : subst,X437 : term] : (((sub @ (X434 @ X435 @ X437) @ X436)) = ((X434 @ (comp @ X435 @ X436) @ (sub @ X437 @ X436)))) | ~ ! [X438 : term] : (~ (((X431 @ id @ X438 @ id)) = $true) | (((X431 @ id @ (X434 @ id @ X438) @ id)) = $true)) | (((X431 @ id @ (lam @ (X434 @ sh @ one)) @ id)) = $true)) | (((X431 @ id @ (lam @ (sub @ X432 @ (push @ one @ sh))) @ id)) = $true)) => ! [X439 : term,X440 : (subst > term > subst > $o)] : (~ ! [X441 : term] : (~ (((X440 @ id @ X441 @ id)) = $true) | (((X440 @ id @ (sub @ X439 @ (push @ X441 @ id)) @ id)) = $true)) | ~ ! [X442 : (subst > term > term)] : (~ ! [X443 : subst,X444 : term,X445 : subst] : (((X442 @ (comp @ X445 @ X443) @ (sub @ X444 @ X443))) = ((sub @ (X442 @ X445 @ X444) @ X443))) | ~ ! [X446 : term] : (~ (((X440 @ id @ X446 @ id)) = $true) | (((X440 @ id @ (X442 @ id @ X446) @ id)) = $true)) | (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) = $true)) | (((X440 @ id @ (lam @ X439) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (axassoc = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X447 : d_subst] : (d_id = X447) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X448 : d_term,X449 : d_term] : ((((d2term @ X449)) = ((d2term @ X448))) => (X448 = X449)) & ((termmset_lthm = $true) <=> (! [X450 : term] : (((sub @ X450 @ id)) = X450) => ! [X451 : term] : (((sub @ X451 @ id)) = X451))) & ((shinj = $true) <=> ! [X452 : term,X453 : term] : ((X452 = X453) | (((sub @ X453 @ sh)) != ((sub @ X452 @ sh))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X454 : (subst > term > subst > $o),X455 : term] : (~ ! [X456 : term,X457 : term] : (~ (((X454 @ id @ X457 @ id)) = $true) | (((X454 @ id @ (ap @ (sub @ X456 @ id) @ X457) @ id)) = $true) | ~ (((X454 @ id @ X456 @ id)) = $true)) | ~ ! [X458 : (subst > term > term)] : ((((X454 @ id @ (lam @ (X458 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : subst,X460 : term,X461 : subst] : (((sub @ (X458 @ X461 @ X460) @ X459)) = ((X458 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459)))) | ~ ! [X462 : term] : ((((X454 @ id @ (X458 @ id @ X462) @ id)) = $true) | ~ (((X454 @ id @ X462 @ id)) = $true))) | (((X454 @ id @ X455 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (induction2_gthm = $true) & (! [X463 : term,X464 : subst] : (((sub @ one @ (push @ X463 @ X464))) = X463) <=> (axvarcons = $true)) & (hoasinduction_lem1v2 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X465 : term,X466 : term,X467 : term,X468 : term] : ((((ap @ X467 @ X466)) != ((ap @ X468 @ X465))) | (X465 = X466)) => ! [X469 : term,X470 : term,X471 : term,X472 : term] : ((((ap @ (sub @ X472 @ id) @ X470)) != ((ap @ (sub @ X471 @ id) @ X469))) | (X469 = X470)))) & (pushprop_lem2v2_lthm = $true) & ((! [X473 : term] : (((sub @ X473 @ id)) = X473) => (! [X474 : term,X475 : (subst > term > subst > $o)] : (~ ! [X476 : (subst > term > term)] : ((((X475 @ id @ (lam @ (X476 @ sh @ one)) @ id)) = $true) | ~ ! [X477 : term,X478 : subst,X479 : subst] : (((X476 @ (comp @ X478 @ X479) @ (sub @ X477 @ X479))) = ((sub @ (X476 @ X478 @ X477) @ X479))) | ~ ! [X480 : term] : (~ (((X475 @ id @ X480 @ id)) = $true) | (((X475 @ id @ (X476 @ id @ X480) @ id)) = $true))) | ~ ! [X481 : term] : ((((X475 @ id @ (sub @ X474 @ (push @ X481 @ id)) @ id)) = $true) | ~ (((X475 @ id @ X481 @ id)) = $true)) | (((X475 @ id @ (lam @ (sub @ X474 @ (push @ one @ sh))) @ id)) = $true)) => ! [X482 : (subst > term > subst > $o),X483 : term] : (~ ! [X484 : subst,X485 : term,X486 : subst,X487 : subst] : (~ (((X482 @ X487 @ X485 @ (comp @ X486 @ X484))) = $true) | (((X482 @ (comp @ X487 @ X486) @ (sub @ X485 @ X486) @ X484)) = $true)) | (((X482 @ id @ (lam @ X483) @ id)) = $true) | ~ ! [X488 : (subst > term > term)] : ((((X482 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X491 @ X489) @ X490)) = ((X488 @ (comp @ X491 @ X490) @ (sub @ X489 @ X490)))) | ~ ! [X492 : term] : ((((X482 @ id @ (X488 @ id @ X492) @ id)) = $true) | ~ (((X482 @ id @ X492 @ id)) = $true))) | ~ ! [X493 : term] : (~ (((X482 @ id @ X493 @ id)) = $true) | ($true = ((X482 @ id @ (sub @ X483 @ (push @ X493 @ id)) @ id)))) | ~ ! [X494 : subst,X495 : term,X496 : subst,X497 : subst] : (~ (((X482 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497) @ X494)) = $true) | (((X482 @ X496 @ X495 @ (comp @ X497 @ X494))) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X498 : term] : (((sub @ X498 @ id)) = X498) => (! [X499 : term,X500 : term,X501 : term,X502 : term] : ((((ap @ X499 @ X502)) != ((ap @ X500 @ X501))) | (X499 = X500)) => ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X505 = X506) | (((ap @ (sub @ X505 @ id) @ X504)) != ((ap @ (sub @ X506 @ id) @ X503))))))) & ((! [X507 : term,X508 : subst] : (((sub @ one @ (push @ X507 @ X508))) = X507) => (! [X509 : term,X510 : subst] : (((comp @ sh @ (push @ X509 @ X510))) = X510) => (! [X511 : term,X512 : term] : ((X511 = X512) | (((lam @ X512)) != ((lam @ X511)))) => ! [X513 : (subst > term > term),X514 : (subst > term > term),X515 : term,X516 : subst] : (~ ! [X517 : subst,X518 : subst,X519 : term] : (((X514 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X514 @ X518 @ X519) @ X517))) | (((X514 @ X516 @ X515)) = ((X513 @ X516 @ X515))) | ~ ! [X520 : subst,X521 : subst,X522 : term] : (((X513 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520))) = ((sub @ (X513 @ X521 @ X522) @ X520))) | (((lam @ (X514 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (! [X523 : (term > $o),X524 : subst,X525 : (term > $o),X526 : term,X527 : term] : ((((X525 @ (sub @ X527 @ (push @ X526 @ X524)))) = $true) | ~ (((X523 @ X527)) = $true)) <=> (pushprop_lem1 = $true)) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X528 : term,X529 : (term > $o)] : (~ ! [X530 : term] : ((((X529 @ (lam @ X530))) = $true) | ~ ! [X531 : term] : ((((X529 @ (sub @ X530 @ (push @ X531 @ id)))) = $true) | ~ (((X529 @ X531)) = $true))) | ~ ! [X532 : term,X533 : term] : (~ (((X529 @ X532)) = $true) | ($true = ((X529 @ (ap @ X532 @ X533)))) | ~ (((X529 @ X533)) = $true)) | ~ ! [X534 : term] : ((((X529 @ X534)) = $true) | ~ (((var @ X534)) = $true)) | (((X529 @ X528)) = $true)) <=> (induction2 = $true)) & (! [X535 : term,X536 : (subst > term > subst > $o)] : ((((X536 @ id @ (lam @ X535) @ id)) = $true) | ~ ! [X537 : (subst > term > term)] : (~ ! [X538 : term,X539 : subst,X540 : subst] : (((sub @ (X537 @ X539 @ X538) @ X540)) = ((X537 @ (comp @ X539 @ X540) @ (sub @ X538 @ X540)))) | ~ ! [X541 : term] : ((((X536 @ id @ (X537 @ id @ X541) @ id)) = $true) | ~ (((X536 @ id @ X541 @ id)) = $true)) | (((X536 @ id @ (lam @ (X537 @ sh @ one)) @ id)) = $true)) | ~ ! [X542 : term] : (~ (((X536 @ id @ X542 @ id)) = $true) | (((X536 @ id @ (sub @ X535 @ (push @ X542 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3a = $true)) & (one = ((d2term @ d_one))) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X543 : subst,X544 : (term > $o),X545 : term] : ~ ! [X546 : (term > $o)] : ~ ! [X547 : term] : (((X544 @ (sub @ X547 @ (push @ X545 @ X543)))) = ((X546 @ X547))) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X548 : term] : ~ ! [X549 : (subst > term > term)] : (((X549 @ sh @ one)) != ((sub @ X548 @ (push @ one @ sh)))))),
% 37.84/5.79 inference(fool_elimination,[],[f4])).
% 37.84/5.79 thf(f6,plain,(
% 37.84/5.79 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X3 @ X4 @ (comp @ X2 @ X1)) => (X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) => (! [X5 : term,X6 : subst,X7 : subst,X8 : subst] : ((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6) => (X0 @ X7 @ X5 @ (comp @ X8 @ X6))) => (! [X9 : (subst > term > term)] : (! [X10 : subst,X11 : term,X12 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) => (! [X13 : term] : ((X0 @ id @ X13 @ id) => (X0 @ id @ (X9 @ id @ X13) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X14 : subst, X15 : term] : ((X9 @ X14 @ X15)))) @ id))) => ! [X16 : term] : (! [X17 : term] : ((X0 @ id @ X17 @ id) => (X0 @ id @ (sub @ X16 @ (push @ X17 @ id)) @ id)) => (X0 @ id @ (lam @ X16) @ id))))) = hoasinduction_lem3)),
% 37.84/5.79 inference(rectify,[],[f3])).
% 37.84/5.79 thf(f7,plain,(
% 37.84/5.79 ~(! [X0 : (subst > term > subst > $o)] : (! [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) => (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) = $true)) => (! [X7 : subst,X5 : term,X8 : subst,X6 : subst] : ((((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true) => (((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) = $true)) => (! [X9 : (subst > term > term)] : (! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) => (! [X13 : term] : ((((X0 @ id @ X13 @ id)) = $true) => (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X16 : term] : (! [X17 : term] : ((((X0 @ id @ X17 @ id)) = $true) => (((X0 @ id @ (sub @ X16 @ (push @ X17 @ id)) @ id)) = $true)) => (((X0 @ id @ (lam @ X16) @ id)) = $true))))) <=> (hoasinduction_lem3 = $true))),
% 37.84/5.79 inference(fool_elimination,[],[f6])).
% 37.84/5.79 thf(f8,plain,(
% 37.84/5.79 ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ X5)) = $true) | ~ (((var @ X5)) = $true)) | ~ ! [X6 : term] : (~ ! [X7 : term] : (~ (((X3 @ X7)) = $true) | (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true)) | (((X3 @ (lam @ X6))) = $true)) | ~ ! [X8 : term,X9 : term] : ((((X3 @ (ap @ X8 @ X9))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (term > $o),X13 : (subst > term > subst > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : (~ (((X13 @ id @ X15 @ id)) = $true) | (((X13 @ id @ (X14 @ id @ X15) @ id)) = $true)) | ~ ! [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) = ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | (((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true)) | ~ ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) | ~ ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | ~ (((X12 @ X20)) = $true)) | (((X12 @ (lam @ X11))) = $true)) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25))))) | ~ ! [X28 : term,X29 : term] : (~ (((X21 @ id @ X28 @ id)) = $true) | ~ ($true = ((X21 @ id @ X29 @ id))) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true)))))))) & (! [X30 : term] : ~ ! [X31 : (subst > term > term)] : ~ ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop = $true) & (ulamvarind = $true) & (! [X36 : term] : ~ ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (substmonoid_gthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X38 : (term > $o),X39 : (term > $o),X40 : subst,X41 : term] : ((((X39 @ one)) = $true) | ~ ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) | ~ (((X38 @ X41)) = $true)) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ~ ! [X44 : (term > $o)] : ~ ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lthm_orig = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X46 : subst] : (((comp @ id @ X46)) = X46) => (! [X47 : subst] : (((comp @ X47 @ id)) = X47) => (! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49))))) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) <=> (substmonoid = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem0_gthm = $true) & (! [X53 : term,X55 : (subst > term > term),X52 : (subst > term > term),X54 : subst] : ((((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one)))) | ~ ! [X56 : term,X57 : subst,X58 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) = ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | ~ ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) = ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59))))) <=> (hoaslaminj = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) => (! [X64 : term,X65 : subst] : (((comp @ sh @ (push @ X64 @ X65))) = X65) => ! [X66 : (term > $o),X67 : term,X68 : term,X69 : (term > $o),X70 : subst] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | ~ (((X66 @ X68)) = $true))))) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) <=> (hoasapinj1 = $true)) & (! [X75 : (subst > term > subst > $o),X76 : term,X77 : (term > $o)] : (~ ! [X78 : term] : (~ (((X77 @ X78)) = $true) | (((X77 @ (sub @ X76 @ (push @ X78 @ id)))) = $true)) | (((X77 @ (lam @ X76))) = $true) | ~ ! [X79 : term,X80 : subst,X81 : subst,X82 : subst] : ((((X75 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81) @ X82)) = $true) | ~ (((X75 @ X80 @ X79 @ (comp @ X81 @ X82))) = $true)) | ~ ! [X83 : term] : (((X75 @ id @ X83 @ id)) = ((X77 @ X83))) | ~ ! [X84 : subst,X85 : subst,X86 : subst,X87 : term] : (~ (((X75 @ (comp @ X86 @ X84) @ (sub @ X87 @ X84) @ X85)) = $true) | (((X75 @ X86 @ X87 @ (comp @ X84 @ X85))) = $true)) | ~ ! [X88 : (subst > term > term)] : (~ ! [X89 : term,X90 : subst,X91 : subst] : (((X88 @ (comp @ X90 @ X91) @ (sub @ X89 @ X91))) = ((sub @ (X88 @ X90 @ X89) @ X91))) | (((X75 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true) | ~ ! [X92 : term] : ((((X75 @ id @ (X88 @ id @ X92) @ id)) = $true) | ~ (((X75 @ id @ X92 @ id)) = $true)))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X93 : (term > $o),X94 : term] : (~ ! [X95 : term] : (~ (((var @ X95)) = $true) | (((X93 @ X95)) = $true)) | ~ ! [X96 : term,X97 : term] : (~ (((X93 @ X96)) = $true) | ~ (((X93 @ X97)) = $true) | (((X93 @ (ap @ X97 @ X96))) = $true)) | (((X93 @ X94)) = $true) | ~ ! [X98 : term] : (~ ! [X99 : term] : ((((X93 @ (sub @ X98 @ (push @ X99 @ id)))) = $true) | ~ (((X93 @ X99)) = $true)) | ($true = ((X93 @ (lam @ X98)))))) => (! [X100 : term,X101 : term,X102 : (subst > term > subst > $o)] : (~ (((X102 @ id @ X100 @ id)) = $true) | (((X102 @ id @ (ap @ X100 @ X101) @ id)) = $true) | ~ ! [X103 : subst,X104 : term,X105 : subst,X106 : subst] : (~ (((X102 @ X105 @ X104 @ (comp @ X103 @ X106))) = $true) | (((X102 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103) @ X106)) = $true)) | ~ ! [X107 : term,X108 : term] : (~ (((X102 @ id @ X107 @ id)) = $true) | (((X102 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id)) = $true) | ~ (((X102 @ id @ X108 @ id)) = $true)) | ~ ! [X109 : subst,X110 : term,X111 : subst,X112 : subst] : (~ (((X102 @ (comp @ X111 @ X109) @ (sub @ X110 @ X109) @ X112)) = $true) | (((X102 @ X111 @ X110 @ (comp @ X109 @ X112))) = $true)) | ~ (((X102 @ id @ X101 @ id)) = $true)) => (! [X113 : (subst > term > subst > $o),X114 : term] : (~ ! [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ~ ! [X116 : term] : (~ (((X113 @ id @ X116 @ id)) = $true) | (((X113 @ id @ (X115 @ id @ X116) @ id)) = $true)) | ~ ! [X117 : term,X118 : subst,X119 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) = ((sub @ (X115 @ X119 @ X117) @ X118)))) | ~ ! [X120 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X120 @ id)) @ id)) = $true) | ~ (((X113 @ id @ X120 @ id)) = $true)) | (((X113 @ id @ (lam @ X114) @ id)) = $true) | ~ ! [X121 : subst,X122 : subst,X123 : subst,X124 : term] : (~ (((X113 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) = $true) | (((X113 @ X121 @ X124 @ (comp @ X123 @ X122))) = $true)) | ~ ! [X125 : subst,X126 : subst,X127 : term,X128 : subst] : ((((X113 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126) @ X128)) = $true) | ~ ($true = ((X113 @ X125 @ X127 @ (comp @ X126 @ X128)))))) => ! [X129 : (subst > term > subst > $o),X130 : term] : (~ ! [X131 : subst,X132 : subst,X133 : term,X134 : subst] : ((((X129 @ (comp @ X132 @ X131) @ (sub @ X133 @ X131) @ X134)) = $true) | ~ (((X129 @ X132 @ X133 @ (comp @ X131 @ X134))) = $true)) | (((X129 @ id @ X130 @ id)) = $true) | ~ ! [X135 : subst,X136 : subst,X137 : subst,X138 : term] : ((((X129 @ X135 @ X138 @ (comp @ X136 @ X137))) = $true) | ~ (((X129 @ (comp @ X135 @ X136) @ (sub @ X138 @ X136) @ X137)) = $true)) | ~ ! [X139 : term] : (~ (((var @ (sub @ X139 @ id))) = $true) | (((X129 @ id @ X139 @ id)) = $true)) | ~ ! [X140 : term,X141 : term] : ((((X129 @ id @ (ap @ (sub @ X140 @ id) @ X141) @ id)) = $true) | ~ (((X129 @ id @ X140 @ id)) = $true) | ~ (((X129 @ id @ X141 @ id)) = $true)) | ~ ! [X142 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X142 @ sh @ one)) @ id)) = $true) | ~ ! [X143 : term] : ((((X129 @ id @ (X142 @ id @ X143) @ id)) = $true) | ~ (((X129 @ id @ X143 @ id)) = $true)) | ~ ! [X144 : subst,X146 : term,X145 : subst] : (((X142 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))) = ((sub @ (X142 @ X145 @ X146) @ X144)))))))) <=> (hoasinduction_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X147 : (subst > term > term),X149 : term,X148 : term] : (~ ! [X151 : term,X152 : subst,X150 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) = ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149))))) & ~ (ulamvar1 = $true) & (pushprop_gthm = $true) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) <=> (axscons = $true)) & (pushprop_lem1v2_gthm = $true) & ((! [X154 : (subst > term > subst > $o)] : ~ ! [X155 : (term > $o)] : ~ ! [X156 : term] : (((X154 @ id @ X156 @ id)) = ((X155 @ X156))) => (! [X157 : (term > $o),X158 : term] : (~ ! [X159 : term] : ((((X157 @ X159)) = $true) | ~ (((var @ X159)) = $true)) | (((X157 @ X158)) = $true) | ~ ! [X160 : term] : ((((X157 @ (lam @ X160))) = $true) | ~ ! [X161 : term] : ((((X157 @ (sub @ X160 @ (push @ X161 @ id)))) = $true) | ~ (((X157 @ X161)) = $true))) | ~ ! [X162 : term,X163 : term] : (~ (((X157 @ X163)) = $true) | (((X157 @ (ap @ X162 @ X163))) = $true) | ~ (((X157 @ X162)) = $true))) => (! [X164 : term] : (((sub @ X164 @ id)) = X164) => (! [X165 : (subst > term > subst > $o),X166 : (term > $o),X167 : term] : (~ ! [X168 : term] : (~ (((X166 @ X168)) = $true) | ($true = ((X166 @ (sub @ X167 @ (push @ X168 @ id)))))) | ~ ! [X169 : (subst > term > term)] : (~ ! [X170 : term] : ((((X165 @ id @ (X169 @ id @ X170) @ id)) = $true) | ~ (((X165 @ id @ X170 @ id)) = $true)) | ~ ! [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171)))) | (((X165 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true)) | (((X166 @ (lam @ X167))) = $true) | ~ ! [X174 : term] : (((X165 @ id @ X174 @ id)) = ((X166 @ X174)))) => ! [X175 : (subst > term > subst > $o),X176 : term] : (~ ! [X177 : (subst > term > term)] : (~ ! [X179 : subst,X178 : subst,X180 : term] : (((X177 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) = ((sub @ (X177 @ X178 @ X180) @ X179))) | (((X175 @ id @ (lam @ (X177 @ sh @ one)) @ id)) = $true) | ~ ! [X181 : term] : ((((X175 @ id @ (X177 @ id @ X181) @ id)) = $true) | ~ (((X175 @ id @ X181 @ id)) = $true))) | ~ ! [X182 : term] : ((((X175 @ id @ X182 @ id)) = $true) | ~ (((var @ (sub @ X182 @ id))) = $true)) | ~ ! [X183 : subst,X184 : subst,X185 : subst,X186 : term] : (~ ($true = ((X175 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185) @ X183))) | (((X175 @ X184 @ X186 @ (comp @ X185 @ X183))) = $true)) | ~ ! [X187 : term,X188 : term] : (~ (((X175 @ id @ X188 @ id)) = $true) | ~ (((X175 @ id @ X187 @ id)) = $true) | (((X175 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)) = $true)) | (((X175 @ id @ X176 @ id)) = $true) | ~ ! [X189 : term,X190 : subst,X191 : subst,X192 : subst] : ((((X175 @ (comp @ X190 @ X191) @ (sub @ X189 @ X191) @ X192)) = $true) | ~ (((X175 @ X190 @ X189 @ (comp @ X191 @ X192))) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X193 : (term > $o),X194 : term,X195 : subst] : ((((X193 @ (sub @ X194 @ X195))) = $true) | ~ ! [X196 : term] : ((((X193 @ (lam @ X196))) = $true) | ~ ! [X197 : term] : ((((X193 @ (sub @ X196 @ (push @ X197 @ id)))) = $true) | ~ (((X193 @ X197)) = $true))) | ~ ! [X198 : term,X199 : term] : (~ (((X193 @ X199)) = $true) | (((X193 @ (ap @ X198 @ X199))) = $true) | ~ (((X193 @ X198)) = $true)) | ~ ! [X200 : term] : ((((X193 @ (sub @ X200 @ X195))) = $true) | ~ (((var @ X200)) = $true))) <=> (induction2lem = $true)) & ((termmset = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & ((hoasinduction_lem3v2a = $true) <=> ! [X202 : (subst > term > subst > $o),X203 : term,X204 : (term > $o)] : (~ ! [X205 : (subst > term > term)] : (~ ! [X208 : subst,X206 : term,X207 : subst] : (((sub @ (X205 @ X208 @ X206) @ X207)) = ((X205 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207)))) | (((X202 @ id @ (lam @ (X205 @ sh @ one)) @ id)) = $true) | ~ ! [X209 : term] : (~ (((X202 @ id @ X209 @ id)) = $true) | (((X202 @ id @ (X205 @ id @ X209) @ id)) = $true))) | ~ ! [X210 : term] : ((((X204 @ (sub @ X203 @ (push @ X210 @ id)))) = $true) | ~ ($true = ((X204 @ X210)))) | ~ ! [X211 : term] : (((X204 @ X211)) = ((X202 @ id @ X211 @ id))) | ($true = ((X204 @ (lam @ X203)))))) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ~ (lamnotap = $true) & (induction2lem_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((apinj1 = $true) <=> ! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219))) & (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)))))))))))))) & (! [X220 : (subst > term > subst > $o),X221 : term] : ((((X220 @ id @ (lam @ (sub @ X221 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X222 : term] : (~ ($true = ((X220 @ id @ X222 @ id))) | (((X220 @ id @ (sub @ X221 @ (push @ X222 @ id)) @ id)) = $true)) | ~ ! [X223 : (subst > term > term)] : (~ ! [X224 : term] : ((((X220 @ id @ (X223 @ id @ X224) @ id)) = $true) | ~ (((X220 @ id @ X224 @ id)) = $true)) | ($true = ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id))) | ~ ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X226 @ X225) @ (sub @ X227 @ X225))) = ((sub @ (X223 @ X226 @ X227) @ X225))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoaslamnotvar = $true) & ! [X228 : d_subst,X229 : d_subst] : ((((d2subst @ X228)) = ((d2subst @ X229))) => (X228 = X229)) & ((! [X230 : term,X231 : subst] : (((sub @ one @ (push @ X230 @ X231))) = X230) => ! [X232 : (term > $o),X233 : subst,X234 : (term > $o),X235 : term] : (~ ! [X236 : term] : (((X232 @ X236)) = ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true) | ~ (((X234 @ X235)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X237 : term,X238 : (subst > term > subst > $o)] : (~ ! [X239 : term] : (~ (((X238 @ id @ X239 @ id)) = $true) | (((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) = $true)) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ~ ! [X240 : subst,X241 : term,X242 : subst,X243 : subst] : (~ (((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) = $true) | (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) = $true)) | ~ ! [X244 : (subst > term > term)] : (~ ! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) | (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) = $true) | ~ ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | ~ (((X238 @ id @ X248 @ id)) = $true))) | ~ ! [X249 : subst,X250 : term,X251 : subst,X252 : subst] : (~ (((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) | (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) = $true)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X255 : (term > $o),X254 : subst,X253 : term] : ~ ! [X256 : (term > $o)] : ~ ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) <=> (pushprop_lem0 = $true)) & ((! [X258 : term] : ~ ! [X259 : (subst > term > term)] : ~ ! [X261 : subst,X260 : term] : (((sub @ X258 @ (push @ X260 @ X261))) = ((X259 @ X261 @ X260))) => (! [X262 : term] : (((sub @ X262 @ id)) = X262) => ! [X263 : term,X264 : (term > $o),X265 : (subst > term > subst > $o)] : ((((X264 @ (lam @ X263))) = $true) | ~ ! [X266 : term] : ((((X264 @ (sub @ X263 @ (push @ X266 @ id)))) = $true) | ~ (((X264 @ X266)) = $true)) | ~ ! [X267 : (subst > term > term)] : (~ ! [X268 : term] : (~ (((X265 @ id @ X268 @ id)) = $true) | (((X265 @ id @ (X267 @ id @ X268) @ id)) = $true)) | (((X265 @ id @ (lam @ (X267 @ sh @ one)) @ id)) = $true) | ~ ! [X269 : subst,X270 : term,X271 : subst] : (((sub @ (X267 @ X271 @ X270) @ X269)) = ((X267 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269))))) | ~ ! [X272 : term] : (((X265 @ id @ X272 @ id)) = ((X264 @ X272)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X273 : (subst > term > subst > $o),X274 : term] : (~ ! [X275 : (subst > term > term),X276 : term] : (~ ! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sub @ X276 @ (push @ X279 @ X277)) @ X278)) = ((sub @ (X275 @ X277 @ X279) @ X278))) | (((X273 @ id @ (lam @ (X275 @ sh @ one)) @ id)) = $true) | ~ ! [X280 : term] : ((((X273 @ id @ (X275 @ id @ X280) @ id)) = $true) | ~ (((X273 @ id @ X280 @ id)) = $true)) | ~ ! [X283 : term,X282 : subst,X281 : subst] : (((sub @ X276 @ (push @ (sub @ X283 @ X281) @ (comp @ X282 @ X281)))) = ((X275 @ (comp @ X282 @ X281) @ (sub @ X283 @ X281))))) | ~ ! [X284 : term] : (~ (((X273 @ id @ X284 @ id)) = $true) | (((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)) = $true)) | (((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X285 : term,X286 : term,X287 : (subst > term > subst > $o),X288 : (term > $o)] : ((((X288 @ (ap @ X286 @ X285))) = $true) | ~ (((X288 @ X286)) = $true) | ~ (((X288 @ X285)) = $true) | ~ ! [X289 : term,X290 : term] : (~ (((X287 @ id @ X290 @ id)) = $true) | ~ (((X287 @ id @ X289 @ id)) = $true) | ($true = ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id)))) | ~ ! [X291 : term] : (((X287 @ id @ X291 @ id)) = ((X288 @ X291))) | ~ ! [X292 : subst,X293 : subst,X294 : term,X295 : subst] : ((((X287 @ X293 @ X294 @ (comp @ X292 @ X295))) = $true) | ~ (((X287 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) = $true)) | ~ ! [X296 : term,X297 : subst,X298 : subst,X299 : subst] : (~ (((X287 @ X297 @ X296 @ (comp @ X298 @ X299))) = $true) | ($true = ((X287 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298) @ X299)))))) & (pushprop_lem1_gthm = $true) & ((induction2_lthm = $true) <=> (! [X300 : term] : (((sub @ X300 @ id)) = X300) => (! [X301 : term,X302 : (term > $o),X303 : subst] : (~ ! [X304 : term] : ((((X302 @ (lam @ X304))) = $true) | ~ ! [X305 : term] : (~ (((X302 @ X305)) = $true) | (((X302 @ (sub @ X304 @ (push @ X305 @ id)))) = $true))) | ~ ! [X306 : term] : (~ (((var @ X306)) = $true) | (((X302 @ (sub @ X306 @ X303))) = $true)) | ~ ! [X307 : term,X308 : term] : ((((X302 @ (ap @ X308 @ X307))) = $true) | ~ (((X302 @ X307)) = $true) | ~ (((X302 @ X308)) = $true)) | (((X302 @ (sub @ X301 @ X303))) = $true)) => ! [X309 : term,X310 : (term > $o)] : (~ ! [X311 : term] : (~ ! [X312 : term] : (~ (((X310 @ X312)) = $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) | (((X310 @ (lam @ X311))) = $true)) | ~ ! [X313 : term] : (~ ($true = ((var @ X313))) | (((X310 @ X313)) = $true)) | (((X310 @ X309)) = $true) | ~ ! [X314 : term,X315 : term] : (~ (((X310 @ X315)) = $true) | (((X310 @ (ap @ X314 @ X315))) = $true) | ~ (((X310 @ X314)) = $true)))))) & ((axidl = $true) <=> ! [X316 : subst] : (((comp @ id @ X316)) = X316)) & (termmset_gthm = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) <=> (axidr = $true)) & ((axshiftcons = $true) <=> ! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318)) & (hoasapnotvar = $true) & ((! [X320 : subst,X321 : term] : (((sub @ one @ (push @ X321 @ X320))) = X321) => (! [X323 : term,X322 : subst] : (((comp @ sh @ (push @ X323 @ X322))) = X322) => (! [X324 : subst] : (((comp @ X324 @ id)) = X324) => (! [X325 : (term > $o),X326 : term] : (~ ! [X327 : term] : ((((X325 @ X327)) = $true) | ~ ($true = ((var @ X327)))) | ~ ! [X328 : term] : ((((X325 @ (lam @ X328))) = $true) | ~ (((X325 @ X328)) = $true)) | (((X325 @ X326)) = $true) | ~ ! [X329 : term,X330 : term] : (~ (((X325 @ X330)) = $true) | ~ (((X325 @ X329)) = $true) | (((X325 @ (ap @ X330 @ X329))) = $true))) => ! [X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ (sub @ X332 @ X333))) = $true) | ~ ! [X334 : term] : ((((X331 @ (sub @ X334 @ X333))) = $true) | ~ (((var @ X334)) = $true)) | ~ ! [X335 : term] : (~ ! [X336 : term] : (($true = ((X331 @ (sub @ X335 @ (push @ X336 @ id))))) | ~ ($true = ((X331 @ X336)))) | (((X331 @ (lam @ X335))) = $true)) | ~ ! [X337 : term,X338 : term] : (~ (((X331 @ X337)) = $true) | ~ (((X331 @ X338)) = $true) | (((X331 @ (ap @ X337 @ X338))) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) <=> (axvarid = $true)) & (! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0 = $true)) & ((laminj = $true) <=> ! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343))))) & (axmap = $true) & ((apinj2 = $true) <=> ! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348))) & ((hoasinduction = $true) <=> ! [X349 : term,X350 : (subst > term > subst > $o)] : (~ ! [X351 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id)) = $true) | ~ ! [X352 : term] : (~ (((X350 @ id @ X352 @ id)) = $true) | (((X350 @ id @ (X351 @ id @ X352) @ id)) = $true)) | ~ ! [X355 : subst,X353 : subst,X354 : term] : (((X351 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X351 @ X353 @ X354) @ X355)))) | ~ ! [X356 : subst,X357 : subst,X358 : term,X359 : subst] : ((((X350 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359) @ X356)) = $true) | ~ (((X350 @ X357 @ X358 @ (comp @ X359 @ X356))) = $true)) | (((X350 @ id @ X349 @ id)) = $true) | ~ ! [X360 : term] : (~ (((var @ (sub @ X360 @ id))) = $true) | (((X350 @ id @ X360 @ id)) = $true)) | ~ ! [X361 : subst,X362 : subst,X363 : subst,X364 : term] : ((((X350 @ X362 @ X364 @ (comp @ X363 @ X361))) = $true) | ~ (((X350 @ (comp @ X362 @ X363) @ (sub @ X364 @ X363) @ X361)) = $true)) | ~ ! [X365 : term,X366 : term] : (~ (((X350 @ id @ X365 @ id)) = $true) | (((X350 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id)) = $true) | ~ (((X350 @ id @ X366 @ id)) = $true)))) & ((! [X367 : term] : (((sub @ X367 @ id)) = X367) => ! [X368 : term,X369 : (term > $o),X370 : (subst > term > subst > $o)] : (~ ! [X371 : term] : (~ (((X369 @ X371)) = $true) | (((X369 @ (sub @ X368 @ (push @ X371 @ id)))) = $true)) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (~ ($true = ((X370 @ X374 @ X375 @ (comp @ X373 @ X372)))) | (((X370 @ (comp @ X374 @ X373) @ (sub @ X375 @ X373) @ X372)) = $true)) | ~ ! [X376 : term,X377 : subst,X378 : subst,X379 : subst] : ((((X370 @ X379 @ X376 @ (comp @ X378 @ X377))) = $true) | ~ (((X370 @ (comp @ X379 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true)) | ~ ! [X380 : term] : (((X369 @ X380)) = ((X370 @ id @ X380 @ id))) | (((X369 @ (lam @ X368))) = $true) | ~ ! [X381 : (subst > term > term)] : (~ ! [X382 : term] : ((((X370 @ id @ (X381 @ id @ X382) @ id)) = $true) | ~ (((X370 @ id @ X382 @ id)) = $true)) | ($true = ((X370 @ id @ (lam @ (X381 @ sh @ one)) @ id))) | ~ ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X381 @ X383 @ X384) @ X385)) = ((X381 @ (comp @ X383 @ X385) @ (sub @ X384 @ X385))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & (pushprop_lem3v2_lthm = $true) & (ulamvarsh = $true) & (! [X388 : term] : ~ ! [X389 : (subst > term > term)] : ~ ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem2v2 = $true) & (axabs = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (axclos = $true) & ! [X392 : d_term] : (d_one = X392) & (! [X393 : term,X394 : (subst > term > subst > $o)] : (~ ! [X395 : term] : ((((X394 @ id @ (sub @ X393 @ (push @ X395 @ id)) @ id)) = $true) | ~ (((X394 @ id @ X395 @ id)) = $true)) | (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X396 : (subst > term > term)] : (~ ! [X397 : term] : (~ (((X394 @ id @ X397 @ id)) = $true) | (((X394 @ id @ (X396 @ id @ X397) @ id)) = $true)) | ~ ! [X398 : subst,X399 : term,X400 : subst] : (((X396 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X396 @ X398 @ X399) @ X400))) | (((X394 @ id @ (lam @ (X396 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasapnotvar_gthm = $true) & ((induction = $true) <=> ! [X401 : term,X402 : (term > $o)] : ((((X402 @ X401)) = $true) | ~ ! [X403 : term,X404 : term] : (~ (((X402 @ X404)) = $true) | ~ (((X402 @ X403)) = $true) | (((X402 @ (ap @ X403 @ X404))) = $true)) | ~ ! [X405 : term] : (~ (((var @ X405)) = $true) | (((X402 @ X405)) = $true)) | ~ ! [X406 : term] : ((((X402 @ (lam @ X406))) = $true) | ~ (((X402 @ X406)) = $true)))) & (hoasapnotvar_lthm = $true) & (! [X407 : term,X408 : term,X409 : (subst > term > subst > $o)] : (~ ! [X410 : term,X411 : term] : ((((X409 @ id @ (ap @ (sub @ X411 @ id) @ X410) @ id)) = $true) | ~ (((X409 @ id @ X411 @ id)) = $true) | ~ (((X409 @ id @ X410 @ id)) = $true)) | ~ ! [X412 : subst,X413 : subst,X414 : subst,X415 : term] : ((((X409 @ X412 @ X415 @ (comp @ X414 @ X413))) = $true) | ~ (((X409 @ (comp @ X412 @ X414) @ (sub @ X415 @ X414) @ X413)) = $true)) | ~ ! [X416 : subst,X417 : term,X418 : subst,X419 : subst] : (~ (((X409 @ X416 @ X417 @ (comp @ X419 @ X418))) = $true) | ($true = ((X409 @ (comp @ X416 @ X419) @ (sub @ X417 @ X419) @ X418)))) | ~ (((X409 @ id @ X408 @ id)) = $true) | ~ (((X409 @ id @ X407 @ id)) = $true) | (((X409 @ id @ (ap @ X407 @ X408) @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (axapp = $true) & (apnotvar = $true) & ((! [X420 : term] : (((sub @ X420 @ id)) = X420) => (! [X421 : (subst > term > subst > $o),X422 : term] : (~ ! [X423 : term] : (~ (((X421 @ id @ X423 @ id)) = $true) | (((X421 @ id @ (sub @ X422 @ (push @ X423 @ id)) @ id)) = $true)) | ~ ! [X424 : (subst > term > term)] : (~ ! [X425 : subst,X426 : subst,X427 : term] : (((sub @ (X424 @ X425 @ X427) @ X426)) = ((X424 @ (comp @ X425 @ X426) @ (sub @ X427 @ X426)))) | ~ ! [X428 : term] : (~ (((X421 @ id @ X428 @ id)) = $true) | (((X421 @ id @ (X424 @ id @ X428) @ id)) = $true)) | (((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true)) | (((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id)) = $true)) => ! [X429 : term,X430 : (subst > term > subst > $o)] : (~ ! [X431 : term] : (~ (((X430 @ id @ X431 @ id)) = $true) | (((X430 @ id @ (sub @ X429 @ (push @ X431 @ id)) @ id)) = $true)) | ~ ! [X432 : (subst > term > term)] : (~ ! [X434 : term,X435 : subst,X433 : subst] : (((sub @ (X432 @ X435 @ X434) @ X433)) = ((X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433)))) | ~ ! [X436 : term] : (~ (((X430 @ id @ X436 @ id)) = $true) | (((X430 @ id @ (X432 @ id @ X436) @ id)) = $true)) | (((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id)) = $true)) | (((X430 @ id @ (lam @ X429) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (axassoc = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X437 : d_subst] : (d_id = X437) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) = ((d2term @ X439))) => (X438 = X439)) & ((termmset_lthm = $true) <=> (! [X440 : term] : (((sub @ X440 @ id)) = X440) => ! [X441 : term] : (((sub @ X441 @ id)) = X441))) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) <=> (shinj = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X444 : (subst > term > subst > $o),X445 : term] : (~ ! [X446 : term,X447 : term] : (~ (((X444 @ id @ X447 @ id)) = $true) | (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) = $true) | ~ (((X444 @ id @ X446 @ id)) = $true)) | ~ ! [X448 : (subst > term > term)] : ((((X444 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term,X449 : subst,X451 : subst] : (((sub @ (X448 @ X451 @ X450) @ X449)) = ((X448 @ (comp @ X451 @ X449) @ (sub @ X450 @ X449)))) | ~ ! [X452 : term] : ((((X444 @ id @ (X448 @ id @ X452) @ id)) = $true) | ~ (((X444 @ id @ X452 @ id)) = $true))) | (((X444 @ id @ X445 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (induction2_gthm = $true) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) <=> (axvarcons = $true)) & (hoasinduction_lem1v2 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X455 : term,X456 : term,X457 : term,X458 : term] : ((((ap @ X458 @ X455)) != ((ap @ X457 @ X456))) | (X455 = X456)) => ! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))))) & (pushprop_lem2v2_lthm = $true) & ((! [X463 : term] : (((sub @ X463 @ id)) = X463) => (! [X464 : term,X465 : (subst > term > subst > $o)] : (~ ! [X466 : (subst > term > term)] : ((((X465 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ~ ! [X467 : term,X468 : subst,X469 : subst] : (((X466 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469))) = ((sub @ (X466 @ X468 @ X467) @ X469))) | ~ ! [X470 : term] : (~ (((X465 @ id @ X470 @ id)) = $true) | (((X465 @ id @ (X466 @ id @ X470) @ id)) = $true))) | ~ ! [X471 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X471 @ id)) @ id)) = $true) | ~ (((X465 @ id @ X471 @ id)) = $true)) | (((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true)) => ! [X472 : (subst > term > subst > $o),X473 : term] : (~ ! [X474 : subst,X475 : term,X476 : subst,X477 : subst] : (~ (((X472 @ X477 @ X475 @ (comp @ X476 @ X474))) = $true) | (((X472 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476) @ X474)) = $true)) | (((X472 @ id @ (lam @ X473) @ id)) = $true) | ~ ! [X478 : (subst > term > term)] : ((((X472 @ id @ (lam @ (X478 @ sh @ one)) @ id)) = $true) | ~ ! [X481 : subst,X480 : subst,X479 : term] : (((X478 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))) = ((sub @ (X478 @ X481 @ X479) @ X480))) | ~ ! [X482 : term] : ((((X472 @ id @ (X478 @ id @ X482) @ id)) = $true) | ~ (((X472 @ id @ X482 @ id)) = $true))) | ~ ! [X483 : term] : (~ (((X472 @ id @ X483 @ id)) = $true) | (((X472 @ id @ (sub @ X473 @ (push @ X483 @ id)) @ id)) = $true)) | ~ ! [X484 : subst,X485 : term,X486 : subst,X487 : subst] : (~ (((X472 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487) @ X484)) = $true) | (((X472 @ X486 @ X485 @ (comp @ X487 @ X484))) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & ((! [X488 : term] : (((sub @ X488 @ id)) = X488) => (! [X489 : term,X492 : term,X490 : term,X491 : term] : ((X489 = X490) | (((ap @ X490 @ X491)) != ((ap @ X489 @ X492)))) => ! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))))) <=> (hoasapinj1_lthm = $true)) & ((! [X498 : subst,X497 : term] : (((sub @ one @ (push @ X497 @ X498))) = X497) => (! [X499 : term,X500 : subst] : (((comp @ sh @ (push @ X499 @ X500))) = X500) => (! [X502 : term,X501 : term] : ((((lam @ X502)) != ((lam @ X501))) | (X501 = X502)) => ! [X504 : (subst > term > term),X506 : subst,X505 : term,X503 : (subst > term > term)] : ((((X504 @ X506 @ X505)) = ((X503 @ X506 @ X505))) | (((lam @ (X504 @ sh @ one))) != ((lam @ (X503 @ sh @ one)))) | ~ ! [X511 : subst,X512 : term,X510 : subst] : (((X503 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510))) = ((sub @ (X503 @ X511 @ X512) @ X510))) | ~ ! [X509 : term,X508 : subst,X507 : subst] : (((X504 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X504 @ X508 @ X509) @ X507))))))) <=> (hoaslaminj_lthm = $true)) & (! [X513 : (term > $o),X514 : subst,X515 : (term > $o),X516 : term,X517 : term] : ((((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true) | ~ (((X513 @ X517)) = $true)) <=> (pushprop_lem1 = $true)) & (lamnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X518 : term,X519 : (term > $o)] : (~ ! [X520 : term] : ((((X519 @ (lam @ X520))) = $true) | ~ ! [X521 : term] : ((((X519 @ (sub @ X520 @ (push @ X521 @ id)))) = $true) | ~ (((X519 @ X521)) = $true))) | ~ ! [X522 : term,X523 : term] : (~ (((X519 @ X522)) = $true) | (((X519 @ (ap @ X522 @ X523))) = $true) | ~ (((X519 @ X523)) = $true)) | ~ ! [X524 : term] : ((((X519 @ X524)) = $true) | ~ (((var @ X524)) = $true)) | (((X519 @ X518)) = $true)) <=> (induction2 = $true)) & (! [X525 : term,X526 : (subst > term > subst > $o)] : ((((X526 @ id @ (lam @ X525) @ id)) = $true) | ~ ! [X527 : (subst > term > term)] : (~ ! [X530 : subst,X529 : subst,X528 : term] : (((X527 @ (comp @ X529 @ X530) @ (sub @ X528 @ X530))) = ((sub @ (X527 @ X529 @ X528) @ X530))) | ~ ! [X531 : term] : ((((X526 @ id @ (X527 @ id @ X531) @ id)) = $true) | ~ (((X526 @ id @ X531 @ id)) = $true)) | (((X526 @ id @ (lam @ (X527 @ sh @ one)) @ id)) = $true)) | ~ ! [X532 : term] : (~ (((X526 @ id @ X532 @ id)) = $true) | (((X526 @ id @ (sub @ X525 @ (push @ X532 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3a = $true)) & (one = ((d2term @ d_one))) & ~ (((var @ (d2term @ d_one))) = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X533 : subst,X534 : (term > $o),X535 : term] : ~ ! [X536 : (term > $o)] : ~ ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537)))) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ~ ! [X539 : (subst > term > term)] : (((X539 @ sh @ one)) != ((sub @ X538 @ (push @ one @ sh)))))),
% 37.84/5.79 inference(rectify,[],[f5])).
% 37.84/5.79 thf(f9,plain,(
% 37.84/5.79 (! [X444 : (subst > term > subst > $o),X445 : term] : (~ ! [X448 : (subst > term > term)] : (~ ! [X450 : term,X449 : subst,X451 : subst] : (((sub @ (X448 @ X451 @ X450) @ X449)) = ((X448 @ (comp @ X451 @ X449) @ (sub @ X450 @ X449)))) | ~ ! [X452 : term] : ((((X444 @ id @ (X448 @ id @ X452) @ id)) = $true) | (((X444 @ id @ X452 @ id)) != $true)) | (((X444 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true)) | ~ ! [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) != $true) | (((X444 @ id @ X446 @ id)) != $true) | (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343))))) & ((hoaslamnotap = $true) <=> ! [X147 : (subst > term > term),X149 : term,X148 : term] : (~ ! [X151 : term,X152 : subst,X150 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) = ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149))))) & ((hoasinduction_lthm = $true) <=> (! [X93 : (term > $o),X94 : term] : ((((X93 @ X94)) = $true) | ~ ! [X96 : term,X97 : term] : ((((X93 @ X96)) != $true) | (((X93 @ (ap @ X97 @ X96))) = $true) | (((X93 @ X97)) != $true)) | ~ ! [X95 : term] : ((((var @ X95)) != $true) | (((X93 @ X95)) = $true)) | ~ ! [X98 : term] : (~ ! [X99 : term] : ((((X93 @ X99)) != $true) | (((X93 @ (sub @ X98 @ (push @ X99 @ id)))) = $true)) | ($true = ((X93 @ (lam @ X98)))))) => (! [X102 : (subst > term > subst > $o),X100 : term,X101 : term] : (~ ! [X104 : term,X106 : subst,X103 : subst,X105 : subst] : ((((X102 @ X105 @ X104 @ (comp @ X103 @ X106))) != $true) | (((X102 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103) @ X106)) = $true)) | (((X102 @ id @ X101 @ id)) != $true) | (((X102 @ id @ (ap @ X100 @ X101) @ id)) = $true) | ~ ! [X112 : subst,X111 : subst,X109 : subst,X110 : term] : ((((X102 @ X111 @ X110 @ (comp @ X109 @ X112))) = $true) | (((X102 @ (comp @ X111 @ X109) @ (sub @ X110 @ X109) @ X112)) != $true)) | ~ ! [X107 : term,X108 : term] : ((((X102 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id)) = $true) | (((X102 @ id @ X108 @ id)) != $true) | (((X102 @ id @ X107 @ id)) != $true)) | (((X102 @ id @ X100 @ id)) != $true)) => (! [X114 : term,X113 : (subst > term > subst > $o)] : (~ ! [X125 : subst,X127 : term,X128 : subst,X126 : subst] : ((((X113 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126) @ X128)) = $true) | ($true != ((X113 @ X125 @ X127 @ (comp @ X126 @ X128))))) | (((X113 @ id @ (lam @ X114) @ id)) = $true) | ~ ! [X124 : term,X122 : subst,X121 : subst,X123 : subst] : ((((X113 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) != $true) | (((X113 @ X121 @ X124 @ (comp @ X123 @ X122))) = $true)) | ~ ! [X115 : (subst > term > term)] : (~ ! [X117 : term,X118 : subst,X119 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) = ((sub @ (X115 @ X119 @ X117) @ X118))) | (((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ~ ! [X116 : term] : ((((X113 @ id @ X116 @ id)) != $true) | (((X113 @ id @ (X115 @ id @ X116) @ id)) = $true))) | ~ ! [X120 : term] : ((((X113 @ id @ X120 @ id)) != $true) | (((X113 @ id @ (sub @ X114 @ (push @ X120 @ id)) @ id)) = $true))) => ! [X130 : term,X129 : (subst > term > subst > $o)] : (~ ! [X133 : term,X134 : subst,X131 : subst,X132 : subst] : ((((X129 @ (comp @ X132 @ X131) @ (sub @ X133 @ X131) @ X134)) = $true) | (((X129 @ X132 @ X133 @ (comp @ X131 @ X134))) != $true)) | ~ ! [X139 : term] : ((((var @ (sub @ X139 @ id))) != $true) | (((X129 @ id @ X139 @ id)) = $true)) | ~ ! [X142 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X142 @ sh @ one)) @ id)) = $true) | ~ ! [X144 : subst,X146 : term,X145 : subst] : (((X142 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))) = ((sub @ (X142 @ X145 @ X146) @ X144))) | ~ ! [X143 : term] : ((((X129 @ id @ X143 @ id)) != $true) | (((X129 @ id @ (X142 @ id @ X143) @ id)) = $true))) | ~ ! [X141 : term,X140 : term] : ((((X129 @ id @ X141 @ id)) != $true) | (((X129 @ id @ (ap @ (sub @ X140 @ id) @ X141) @ id)) = $true) | (((X129 @ id @ X140 @ id)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ~ ! [X137 : subst,X138 : term,X135 : subst,X136 : subst] : ((((X129 @ X135 @ X138 @ (comp @ X136 @ X137))) = $true) | (((X129 @ (comp @ X135 @ X136) @ (sub @ X138 @ X136) @ X137)) != $true))))))) & ((axshiftcons = $true) <=> ! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318)) & ((pushprop_lem0_lthm = $true) <=> ! [X533 : subst,X534 : (term > $o),X535 : term] : ~ ! [X536 : (term > $o)] : ~ ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537)))) & ((hoasinduction_lem3 = $true) <=> ! [X237 : term,X238 : (subst > term > subst > $o)] : (~ ! [X244 : (subst > term > term)] : ((((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) = $true) | ~ ! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) | ~ ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | (((X238 @ id @ X248 @ id)) != $true))) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ~ ! [X250 : term,X251 : subst,X249 : subst,X252 : subst] : ((((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) = $true) | (((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) != $true)) | ~ ! [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) = $true) | (((X238 @ id @ X239 @ id)) != $true)) | ~ ! [X243 : subst,X241 : term,X240 : subst,X242 : subst] : ((((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) = $true) | (((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) != $true)))) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar_gthm = $true) & (axassoc = $true) & ((termmset = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (termmset_gthm = $true) & (hoasapnotvar = $true) & ((! [X463 : term] : (((sub @ X463 @ id)) = X463) => (! [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X471 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X471 @ id)) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) | ~ ! [X466 : (subst > term > term)] : (~ ! [X467 : term,X468 : subst,X469 : subst] : (((X466 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469))) = ((sub @ (X466 @ X468 @ X467) @ X469))) | (((X465 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ~ ! [X470 : term] : ((((X465 @ id @ X470 @ id)) != $true) | (((X465 @ id @ (X466 @ id @ X470) @ id)) = $true)))) => ! [X472 : (subst > term > subst > $o),X473 : term] : (~ ! [X486 : subst,X484 : subst,X487 : subst,X485 : term] : ((((X472 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487) @ X484)) != $true) | (((X472 @ X486 @ X485 @ (comp @ X487 @ X484))) = $true)) | (((X472 @ id @ (lam @ X473) @ id)) = $true) | ~ ! [X478 : (subst > term > term)] : ((((X472 @ id @ (lam @ (X478 @ sh @ one)) @ id)) = $true) | ~ ! [X481 : subst,X480 : subst,X479 : term] : (((X478 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))) = ((sub @ (X478 @ X481 @ X479) @ X480))) | ~ ! [X482 : term] : ((((X472 @ id @ (X478 @ id @ X482) @ id)) = $true) | (((X472 @ id @ X482 @ id)) != $true))) | ~ ! [X483 : term] : ((((X472 @ id @ X483 @ id)) != $true) | (((X472 @ id @ (sub @ X473 @ (push @ X483 @ id)) @ id)) = $true)) | ~ ! [X475 : term,X476 : subst,X474 : subst,X477 : subst] : ((((X472 @ X477 @ X475 @ (comp @ X476 @ X474))) != $true) | (((X472 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476) @ X474)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (((d2subst @ d_id)) = id) & ! [X437 : d_subst] : (d_id = X437) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (induction2_gthm = $true) & ((! [X420 : term] : (((sub @ X420 @ id)) = X420) => (! [X422 : term,X421 : (subst > term > subst > $o)] : (~ ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ~ ! [X425 : subst,X426 : subst,X427 : term] : (((sub @ (X424 @ X425 @ X427) @ X426)) = ((X424 @ (comp @ X425 @ X426) @ (sub @ X427 @ X426)))) | ~ ! [X428 : term] : ((((X421 @ id @ X428 @ id)) != $true) | (((X421 @ id @ (X424 @ id @ X428) @ id)) = $true))) | ~ ! [X423 : term] : ((((X421 @ id @ X423 @ id)) != $true) | (((X421 @ id @ (sub @ X422 @ (push @ X423 @ id)) @ id)) = $true)) | (((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id)) = $true)) => ! [X430 : (subst > term > subst > $o),X429 : term] : (~ ! [X431 : term] : ((((X430 @ id @ X431 @ id)) != $true) | (((X430 @ id @ (sub @ X429 @ (push @ X431 @ id)) @ id)) = $true)) | ~ ! [X432 : (subst > term > term)] : (~ ! [X436 : term] : ((((X430 @ id @ (X432 @ id @ X436) @ id)) = $true) | (((X430 @ id @ X436 @ id)) != $true)) | (((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id)) = $true) | ~ ! [X434 : term,X435 : subst,X433 : subst] : (((sub @ (X432 @ X435 @ X434) @ X433)) = ((X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433))))) | (((X430 @ id @ (lam @ X429) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : (~ ! [X6 : term] : ((((X3 @ (lam @ X6))) = $true) | ~ ! [X7 : term] : ((((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | (((X3 @ X7)) != $true))) | ~ ! [X8 : term,X9 : term] : ((((X3 @ X8)) != $true) | (((X3 @ (ap @ X8 @ X9))) = $true) | (((X3 @ X9)) != $true)) | ~ ! [X5 : term] : ((((var @ X5)) != $true) | (((X3 @ X5)) = $true)) | (((X3 @ X4)) = $true)) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X12 : (term > $o),X11 : term,X13 : (subst > term > subst > $o)] : ((((X12 @ (lam @ X11))) = $true) | ~ ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) | ~ ! [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ~ ! [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) = ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | ~ ! [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) = $true) | (((X13 @ id @ X15 @ id)) != $true))) | ~ ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | (((X12 @ X20)) != $true))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25))))) | ~ ! [X29 : term,X28 : term] : (($true != ((X21 @ id @ X29 @ id))) | (((X21 @ id @ X28 @ id)) != $true) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true)))))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (! [X30 : term] : ~ ! [X31 : (subst > term > term)] : ~ ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X77 : (term > $o),X75 : (subst > term > subst > $o),X76 : term] : (~ ! [X84 : subst,X87 : term,X85 : subst,X86 : subst] : ((((X75 @ (comp @ X86 @ X84) @ (sub @ X87 @ X84) @ X85)) != $true) | (((X75 @ X86 @ X87 @ (comp @ X84 @ X85))) = $true)) | ~ ! [X78 : term] : ((((X77 @ (sub @ X76 @ (push @ X78 @ id)))) = $true) | (((X77 @ X78)) != $true)) | ~ ! [X88 : (subst > term > term)] : (~ ! [X92 : term] : ((((X75 @ id @ X92 @ id)) != $true) | (((X75 @ id @ (X88 @ id @ X92) @ id)) = $true)) | ~ ! [X89 : term,X90 : subst,X91 : subst] : (((X88 @ (comp @ X90 @ X91) @ (sub @ X89 @ X91))) = ((sub @ (X88 @ X90 @ X89) @ X91))) | (((X75 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true)) | (((X77 @ (lam @ X76))) = $true) | ~ ! [X83 : term] : (((X75 @ id @ X83 @ id)) = ((X77 @ X83))) | ~ ! [X81 : subst,X79 : term,X82 : subst,X80 : subst] : ((((X75 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81) @ X82)) = $true) | (((X75 @ X80 @ X79 @ (comp @ X81 @ X82))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X230 : term,X231 : subst] : (((sub @ one @ (push @ X230 @ X231))) = X230) => ! [X232 : (term > $o),X235 : term,X234 : (term > $o),X233 : subst] : (~ ! [X236 : term] : (((X232 @ X236)) = ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X234 @ X235)) != $true) | (((X232 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X255 : (term > $o),X254 : subst,X253 : term] : ~ ! [X256 : (term > $o)] : ~ ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X154 : (subst > term > subst > $o)] : ~ ! [X155 : (term > $o)] : ~ ! [X156 : term] : (((X154 @ id @ X156 @ id)) = ((X155 @ X156))) => (! [X157 : (term > $o),X158 : term] : (~ ! [X160 : term] : (~ ! [X161 : term] : ((((X157 @ X161)) != $true) | (((X157 @ (sub @ X160 @ (push @ X161 @ id)))) = $true)) | (((X157 @ (lam @ X160))) = $true)) | ~ ! [X159 : term] : ((((var @ X159)) != $true) | (((X157 @ X159)) = $true)) | ~ ! [X163 : term,X162 : term] : ((((X157 @ X162)) != $true) | (((X157 @ X163)) != $true) | (((X157 @ (ap @ X162 @ X163))) = $true)) | (((X157 @ X158)) = $true)) => (! [X164 : term] : (((sub @ X164 @ id)) = X164) => (! [X167 : term,X165 : (subst > term > subst > $o),X166 : (term > $o)] : ((((X166 @ (lam @ X167))) = $true) | ~ ! [X174 : term] : (((X165 @ id @ X174 @ id)) = ((X166 @ X174))) | ~ ! [X168 : term] : (($true = ((X166 @ (sub @ X167 @ (push @ X168 @ id))))) | (((X166 @ X168)) != $true)) | ~ ! [X169 : (subst > term > term)] : ((((X165 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ~ ! [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171)))) | ~ ! [X170 : term] : ((((X165 @ id @ (X169 @ id @ X170) @ id)) = $true) | (((X165 @ id @ X170 @ id)) != $true)))) => ! [X175 : (subst > term > subst > $o),X176 : term] : (~ ! [X187 : term,X188 : term] : ((((X175 @ id @ X188 @ id)) != $true) | (((X175 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)) = $true) | (((X175 @ id @ X187 @ id)) != $true)) | ~ ! [X177 : (subst > term > term)] : (~ ! [X181 : term] : ((((X175 @ id @ (X177 @ id @ X181) @ id)) = $true) | (((X175 @ id @ X181 @ id)) != $true)) | (((X175 @ id @ (lam @ (X177 @ sh @ one)) @ id)) = $true) | ~ ! [X179 : subst,X178 : subst,X180 : term] : (((X177 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) = ((sub @ (X177 @ X178 @ X180) @ X179)))) | ~ ! [X182 : term] : ((((X175 @ id @ X182 @ id)) = $true) | (((var @ (sub @ X182 @ id))) != $true)) | ~ ! [X184 : subst,X183 : subst,X185 : subst,X186 : term] : (($true != ((X175 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185) @ X183))) | (((X175 @ X184 @ X186 @ (comp @ X185 @ X183))) = $true)) | (((X175 @ id @ X176 @ id)) = $true) | ~ ! [X190 : subst,X191 : subst,X189 : term,X192 : subst] : ((((X175 @ X190 @ X189 @ (comp @ X191 @ X192))) != $true) | (((X175 @ (comp @ X190 @ X191) @ (sub @ X189 @ X191) @ X192)) = $true)))))))) & (axmap = $true) & ((! [X498 : subst,X497 : term] : (((sub @ one @ (push @ X497 @ X498))) = X497) => (! [X499 : term,X500 : subst] : (((comp @ sh @ (push @ X499 @ X500))) = X500) => (! [X502 : term,X501 : term] : ((((lam @ X502)) != ((lam @ X501))) | (X501 = X502)) => ! [X504 : (subst > term > term),X506 : subst,X505 : term,X503 : (subst > term > term)] : ((((X504 @ X506 @ X505)) = ((X503 @ X506 @ X505))) | (((lam @ (X504 @ sh @ one))) != ((lam @ (X503 @ sh @ one)))) | ~ ! [X511 : subst,X512 : term,X510 : subst] : (((X503 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510))) = ((sub @ (X503 @ X511 @ X512) @ X510))) | ~ ! [X509 : term,X508 : subst,X507 : subst] : (((X504 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X504 @ X508 @ X509) @ X507))))))) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X202 : (subst > term > subst > $o),X203 : term,X204 : (term > $o)] : (~ ! [X211 : term] : (((X204 @ X211)) = ((X202 @ id @ X211 @ id))) | ($true = ((X204 @ (lam @ X203)))) | ~ ! [X205 : (subst > term > term)] : (~ ! [X209 : term] : ((((X202 @ id @ X209 @ id)) != $true) | (((X202 @ id @ (X205 @ id @ X209) @ id)) = $true)) | ~ ! [X208 : subst,X206 : term,X207 : subst] : (((sub @ (X205 @ X208 @ X206) @ X207)) = ((X205 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207)))) | (((X202 @ id @ (lam @ (X205 @ sh @ one)) @ id)) = $true)) | ~ ! [X210 : term] : (($true != ((X204 @ X210))) | (((X204 @ (sub @ X203 @ (push @ X210 @ id)))) = $true)))) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) <=> (shinj = $true)) & (hoaslamnotvar = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) => (! [X64 : term,X65 : subst] : (((comp @ sh @ (push @ X64 @ X65))) = X65) => ! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true))))) & (lamnotap != $true) & (hoasinduction_lem3_gthm = $true) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) <=> (substmonoid = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X394 : (subst > term > subst > $o),X393 : term] : (~ ! [X395 : term] : ((((X394 @ id @ (sub @ X393 @ (push @ X395 @ id)) @ id)) = $true) | (((X394 @ id @ X395 @ id)) != $true)) | ~ ! [X396 : (subst > term > term)] : ((((X394 @ id @ (lam @ (X396 @ sh @ one)) @ id)) = $true) | ~ ! [X397 : term] : ((((X394 @ id @ (X396 @ id @ X397) @ id)) = $true) | (((X394 @ id @ X397 @ id)) != $true)) | ~ ! [X398 : subst,X399 : term,X400 : subst] : (((X396 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X396 @ X398 @ X399) @ X400)))) | (((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X40 : subst,X41 : term,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ~ ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) | (((X38 @ X41)) != $true)) <=> (pushprop_lem1v2 = $true)) & (hoasinduction_lem1 = $true) & ((! [X258 : term] : ~ ! [X259 : (subst > term > term)] : ~ ! [X261 : subst,X260 : term] : (((sub @ X258 @ (push @ X260 @ X261))) = ((X259 @ X261 @ X260))) => (! [X262 : term] : (((sub @ X262 @ id)) = X262) => ! [X264 : (term > $o),X265 : (subst > term > subst > $o),X263 : term] : (~ ! [X272 : term] : (((X265 @ id @ X272 @ id)) = ((X264 @ X272))) | (((X264 @ (lam @ X263))) = $true) | ~ ! [X266 : term] : ((((X264 @ (sub @ X263 @ (push @ X266 @ id)))) = $true) | (((X264 @ X266)) != $true)) | ~ ! [X267 : (subst > term > term)] : ((((X265 @ id @ (lam @ (X267 @ sh @ one)) @ id)) = $true) | ~ ! [X268 : term] : ((((X265 @ id @ (X267 @ id @ X268) @ id)) = $true) | (((X265 @ id @ X268 @ id)) != $true)) | ~ ! [X269 : subst,X270 : term,X271 : subst] : (((sub @ (X267 @ X271 @ X270) @ X269)) = ((X267 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvarind = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2 = $true) <=> ! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ((apinj1 = $true) <=> ! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219))) & (induction2lem_gthm = $true) & (hoaslaminj_gthm = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) <=> (axscons = $true)) & (! [X288 : (term > $o),X287 : (subst > term > subst > $o),X286 : term,X285 : term] : (~ ! [X291 : term] : (((X287 @ id @ X291 @ id)) = ((X288 @ X291))) | ~ ! [X297 : subst,X296 : term,X298 : subst,X299 : subst] : (($true = ((X287 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298) @ X299))) | (((X287 @ X297 @ X296 @ (comp @ X298 @ X299))) != $true)) | ~ ! [X295 : subst,X293 : subst,X292 : subst,X294 : term] : ((((X287 @ X293 @ X294 @ (comp @ X292 @ X295))) = $true) | (((X287 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) != $true)) | (((X288 @ X285)) != $true) | ~ ! [X290 : term,X289 : term] : ((((X287 @ id @ X289 @ id)) != $true) | (((X287 @ id @ X290 @ id)) != $true) | ($true = ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id)))) | (((X288 @ (ap @ X286 @ X285))) = $true) | (((X288 @ X286)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) <=> (axidr = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ~ ! [X44 : (term > $o)] : ~ ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) = ((d2term @ X439))) => (X438 = X439)) & (axapp = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X53 : term,X55 : (subst > term > term),X52 : (subst > term > term),X54 : subst] : ((((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one)))) | ~ ! [X56 : term,X57 : subst,X58 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) = ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | ~ ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) = ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59))))) <=> (hoaslaminj = $true)) & (pushprop = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) <=> (axvarid = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X455 : term,X456 : term,X457 : term,X458 : term] : ((((ap @ X458 @ X455)) != ((ap @ X457 @ X456))) | (X455 = X456)) => ! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3a = $true) <=> ! [X525 : term,X526 : (subst > term > subst > $o)] : (~ ! [X527 : (subst > term > term)] : (~ ! [X531 : term] : ((((X526 @ id @ X531 @ id)) != $true) | (((X526 @ id @ (X527 @ id @ X531) @ id)) = $true)) | ~ ! [X530 : subst,X529 : subst,X528 : term] : (((X527 @ (comp @ X529 @ X530) @ (sub @ X528 @ X530))) = ((sub @ (X527 @ X529 @ X528) @ X530))) | (((X526 @ id @ (lam @ (X527 @ sh @ one)) @ id)) = $true)) | ~ ! [X532 : term] : ((((X526 @ id @ (sub @ X525 @ (push @ X532 @ id)) @ id)) = $true) | (((X526 @ id @ X532 @ id)) != $true)) | (((X526 @ id @ (lam @ X525) @ id)) = $true))) & ((! [X488 : term] : (((sub @ X488 @ id)) = X488) => (! [X489 : term,X492 : term,X490 : term,X491 : term] : ((X489 = X490) | (((ap @ X490 @ X491)) != ((ap @ X489 @ X492)))) => ! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X388 : term] : ~ ! [X389 : (subst > term > term)] : ~ ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X36 : term] : ~ ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> ! [X195 : subst,X194 : term,X193 : (term > $o)] : ((((X193 @ (sub @ X194 @ X195))) = $true) | ~ ! [X199 : term,X198 : term] : ((((X193 @ X199)) != $true) | (((X193 @ (ap @ X198 @ X199))) = $true) | (((X193 @ X198)) != $true)) | ~ ! [X200 : term] : ((((var @ X200)) != $true) | (((X193 @ (sub @ X200 @ X195))) = $true)) | ~ ! [X196 : term] : ((((X193 @ (lam @ X196))) = $true) | ~ ! [X197 : term] : ((((X193 @ X197)) != $true) | (((X193 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))))) & (axvarshift = $true) & ((induction = $true) <=> ! [X401 : term,X402 : (term > $o)] : ((((X402 @ X401)) = $true) | ~ ! [X406 : term] : ((((X402 @ X406)) != $true) | (((X402 @ (lam @ X406))) = $true)) | ~ ! [X404 : term,X403 : term] : ((((X402 @ X404)) != $true) | (((X402 @ X403)) != $true) | (((X402 @ (ap @ X403 @ X404))) = $true)) | ~ ! [X405 : term] : ((((var @ X405)) != $true) | (((X402 @ X405)) = $true)))) & (ulamvar1 != $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem0_gthm = $true) & (apnotvar = $true) & (pushprop_lem2v2_lthm = $true) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (! [X273 : (subst > term > subst > $o),X274 : term] : (~ ! [X284 : term] : ((((X273 @ id @ X284 @ id)) != $true) | (((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)) = $true)) | (((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X275 : (subst > term > term),X276 : term] : (~ ! [X280 : term] : ((((X273 @ id @ X280 @ id)) != $true) | (((X273 @ id @ (X275 @ id @ X280) @ id)) = $true)) | ~ ! [X283 : term,X282 : subst,X281 : subst] : (((sub @ X276 @ (push @ (sub @ X283 @ X281) @ (comp @ X282 @ X281)))) = ((X275 @ (comp @ X282 @ X281) @ (sub @ X283 @ X281)))) | ~ ! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sub @ X276 @ (push @ X279 @ X277)) @ X278)) = ((sub @ (X275 @ X277 @ X279) @ X278))) | (((X273 @ id @ (lam @ (X275 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & (pushprop_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true))) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) <=> (axvarcons = $true)) & ((substmonoid_lthm = $true) <=> (! [X46 : subst] : (((comp @ id @ X46)) = X46) => (! [X47 : subst] : (((comp @ X47 @ id)) = X47) => (! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49))))) & ((hoasinduction = $true) <=> ! [X350 : (subst > term > subst > $o),X349 : term] : ((((X350 @ id @ X349 @ id)) = $true) | ~ ! [X357 : subst,X356 : subst,X358 : term,X359 : subst] : ((((X350 @ X357 @ X358 @ (comp @ X359 @ X356))) != $true) | (((X350 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359) @ X356)) = $true)) | ~ ! [X366 : term,X365 : term] : ((((X350 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id)) = $true) | (((X350 @ id @ X366 @ id)) != $true) | (((X350 @ id @ X365 @ id)) != $true)) | ~ ! [X360 : term] : ((((X350 @ id @ X360 @ id)) = $true) | (((var @ (sub @ X360 @ id))) != $true)) | ~ ! [X351 : (subst > term > term)] : (~ ! [X355 : subst,X353 : subst,X354 : term] : (((X351 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X351 @ X353 @ X354) @ X355))) | ~ ! [X352 : term] : ((((X350 @ id @ X352 @ id)) != $true) | (((X350 @ id @ (X351 @ id @ X352) @ id)) = $true)) | (((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id)) = $true)) | ~ ! [X363 : subst,X361 : subst,X362 : subst,X364 : term] : ((((X350 @ X362 @ X364 @ (comp @ X363 @ X361))) = $true) | (((X350 @ (comp @ X362 @ X363) @ (sub @ X364 @ X363) @ X361)) != $true)))) & (axabs = $true) & ((! [X300 : term] : (((sub @ X300 @ id)) = X300) => (! [X301 : term,X302 : (term > $o),X303 : subst] : (~ ! [X307 : term,X308 : term] : ((((X302 @ X307)) != $true) | (((X302 @ (ap @ X308 @ X307))) = $true) | (((X302 @ X308)) != $true)) | ~ ! [X306 : term] : ((((var @ X306)) != $true) | (((X302 @ (sub @ X306 @ X303))) = $true)) | (((X302 @ (sub @ X301 @ X303))) = $true) | ~ ! [X304 : term] : ((((X302 @ (lam @ X304))) = $true) | ~ ! [X305 : term] : ((((X302 @ (sub @ X304 @ (push @ X305 @ id)))) = $true) | (((X302 @ X305)) != $true)))) => ! [X309 : term,X310 : (term > $o)] : (~ ! [X311 : term] : (~ ! [X312 : term] : ((((X310 @ X312)) != $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) | (((X310 @ (lam @ X311))) = $true)) | ~ ! [X314 : term,X315 : term] : ((((X310 @ (ap @ X314 @ X315))) = $true) | (((X310 @ X314)) != $true) | (((X310 @ X315)) != $true)) | (((X310 @ X309)) = $true) | ~ ! [X313 : term] : (($true != ((var @ X313))) | (((X310 @ X313)) = $true))))) <=> (induction2_lthm = $true)) & (one = ((d2term @ d_one))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X367 : term] : (((sub @ X367 @ id)) = X367) => ! [X368 : term,X369 : (term > $o),X370 : (subst > term > subst > $o)] : (~ ! [X376 : term,X379 : subst,X378 : subst,X377 : subst] : ((((X370 @ (comp @ X379 @ X378) @ (sub @ X376 @ X378) @ X377)) != $true) | (((X370 @ X379 @ X376 @ (comp @ X378 @ X377))) = $true)) | (((X369 @ (lam @ X368))) = $true) | ~ ! [X380 : term] : (((X369 @ X380)) = ((X370 @ id @ X380 @ id))) | ~ ! [X381 : (subst > term > term)] : (($true = ((X370 @ id @ (lam @ (X381 @ sh @ one)) @ id))) | ~ ! [X382 : term] : ((((X370 @ id @ X382 @ id)) != $true) | (((X370 @ id @ (X381 @ id @ X382) @ id)) = $true)) | ~ ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X381 @ X383 @ X384) @ X385)) = ((X381 @ (comp @ X383 @ X385) @ (sub @ X384 @ X385))))) | ~ ! [X373 : subst,X374 : subst,X372 : subst,X375 : term] : ((((X370 @ (comp @ X374 @ X373) @ (sub @ X375 @ X373) @ X372)) = $true) | ($true != ((X370 @ X374 @ X375 @ (comp @ X373 @ X372))))) | ~ ! [X371 : term] : ((((X369 @ X371)) != $true) | (((X369 @ (sub @ X368 @ (push @ X371 @ id)))) = $true))))) & (hoasapinj1_gthm = $true) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & (! [X518 : term,X519 : (term > $o)] : (~ ! [X520 : term] : ((((X519 @ (lam @ X520))) = $true) | ~ ! [X521 : term] : ((((X519 @ X521)) != $true) | (((X519 @ (sub @ X520 @ (push @ X521 @ id)))) = $true))) | (((X519 @ X518)) = $true) | ~ ! [X524 : term] : ((((X519 @ X524)) = $true) | (((var @ X524)) != $true)) | ~ ! [X522 : term,X523 : term] : ((((X519 @ X523)) != $true) | (((X519 @ (ap @ X522 @ X523))) = $true) | (((X519 @ X522)) != $true))) <=> (induction2 = $true)) & (((d2subst @ d_id)) = sh) & (! [X407 : term,X408 : term,X409 : (subst > term > subst > $o)] : ((((X409 @ id @ X407 @ id)) != $true) | (((X409 @ id @ X408 @ id)) != $true) | ~ ! [X418 : subst,X417 : term,X416 : subst,X419 : subst] : (($true = ((X409 @ (comp @ X416 @ X419) @ (sub @ X417 @ X419) @ X418))) | (((X409 @ X416 @ X417 @ (comp @ X419 @ X418))) != $true)) | ~ ! [X415 : term,X414 : subst,X412 : subst,X413 : subst] : ((((X409 @ X412 @ X415 @ (comp @ X414 @ X413))) = $true) | (((X409 @ (comp @ X412 @ X414) @ (sub @ X415 @ X414) @ X413)) != $true)) | ~ ! [X411 : term,X410 : term] : ((((X409 @ id @ (ap @ (sub @ X411 @ id) @ X410) @ id)) = $true) | (((X409 @ id @ X411 @ id)) != $true) | (((X409 @ id @ X410 @ id)) != $true)) | (((X409 @ id @ (ap @ X407 @ X408) @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & ((axidl = $true) <=> ! [X316 : subst] : (((comp @ id @ X316)) = X316)) & ((termmset_lthm = $true) <=> (! [X440 : term] : (((sub @ X440 @ id)) = X440) => ! [X441 : term] : (((sub @ X441 @ id)) = X441))) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ! [X228 : d_subst,X229 : d_subst] : ((((d2subst @ X228)) = ((d2subst @ X229))) => (X228 = X229)) & ((apinj2 = $true) <=> ! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348))) & (! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0 = $true)) & (((var @ (d2term @ d_one))) != $true) & (! [X221 : term,X220 : (subst > term > subst > $o)] : (~ ! [X222 : term] : (($true != ((X220 @ id @ X222 @ id))) | (((X220 @ id @ (sub @ X221 @ (push @ X222 @ id)) @ id)) = $true)) | (((X220 @ id @ (lam @ (sub @ X221 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X223 : (subst > term > term)] : (~ ! [X224 : term] : ((((X220 @ id @ (X223 @ id @ X224) @ id)) = $true) | (((X220 @ id @ X224 @ id)) != $true)) | ~ ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X226 @ X225) @ (sub @ X227 @ X225))) = ((sub @ (X223 @ X226 @ X227) @ X225))) | ($true = ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (axclos = $true) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ~ ! [X539 : (subst > term > term)] : (((X539 @ sh @ one)) != ((sub @ X538 @ (push @ one @ sh))))) & ((induction2lem_lthm = $true) <=> (! [X320 : subst,X321 : term] : (((sub @ one @ (push @ X321 @ X320))) = X321) => (! [X323 : term,X322 : subst] : (((comp @ sh @ (push @ X323 @ X322))) = X322) => (! [X324 : subst] : (((comp @ X324 @ id)) = X324) => (! [X326 : term,X325 : (term > $o)] : ((((X325 @ X326)) = $true) | ~ ! [X328 : term] : ((((X325 @ X328)) != $true) | (((X325 @ (lam @ X328))) = $true)) | ~ ! [X327 : term] : ((((X325 @ X327)) = $true) | ($true != ((var @ X327)))) | ~ ! [X329 : term,X330 : term] : ((((X325 @ X329)) != $true) | (((X325 @ (ap @ X330 @ X329))) = $true) | (((X325 @ X330)) != $true))) => ! [X332 : term,X333 : subst,X331 : (term > $o)] : ((((X331 @ (sub @ X332 @ X333))) = $true) | ~ ! [X335 : term] : (~ ! [X336 : term] : (($true = ((X331 @ (sub @ X335 @ (push @ X336 @ id))))) | ($true != ((X331 @ X336)))) | (((X331 @ (lam @ X335))) = $true)) | ~ ! [X338 : term,X337 : term] : ((((X331 @ X338)) != $true) | (((X331 @ X337)) != $true) | (((X331 @ (ap @ X337 @ X338))) = $true)) | ~ ! [X334 : term] : ((((var @ X334)) != $true) | (((X331 @ (sub @ X334 @ X333))) = $true))))))))),
% 37.84/5.79 inference(flattening,[],[f8])).
% 37.84/5.79 thf(f10,plain,(
% 37.84/5.79 ~((hoasinduction_lem3 = $true) <=> ! [X0 : (subst > term > subst > $o)] : (! [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) => (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) = $true)) => (! [X7 : subst,X5 : term,X8 : subst,X6 : subst] : ((((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true) => (((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) = $true)) => (! [X9 : (subst > term > term)] : (! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) => (! [X13 : term] : ((((X0 @ id @ X13 @ id)) = $true) => (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X14 : term] : (! [X15 : term] : ((((X0 @ id @ X15 @ id)) = $true) => (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) = $true)) => (((X0 @ id @ (lam @ X14) @ id)) = $true))))))),
% 37.84/5.79 inference(rectify,[],[f7])).
% 37.84/5.79 thf(f11,plain,(
% 37.84/5.79 (hoasinduction_lem3 = $true) <~> ! [X0 : (subst > term > subst > $o)] : (((! [X14 : term] : (? [X15 : term] : ((((X0 @ id @ X15 @ id)) = $true) & (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) != $true)) | (((X0 @ id @ (lam @ X14) @ id)) = $true)) | ? [X9 : (subst > term > term)] : (((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) != $true) & ! [X13 : term] : ((((X0 @ id @ X13 @ id)) != $true) | (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true))) & ! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))))) | ? [X6 : subst,X8 : subst,X5 : term,X7 : subst] : ((((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) != $true) & (((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true))) | ? [X1 : subst,X4 : term,X2 : subst,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) != $true)))),
% 37.84/5.79 inference(ennf_transformation,[],[f10])).
% 37.84/5.79 thf(f12,plain,(
% 37.84/5.79 (hoasinduction_lem3 = $true) <~> ! [X0 : (subst > term > subst > $o)] : (? [X6 : subst,X8 : subst,X5 : term,X7 : subst] : ((((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) != $true) & (((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true)) | ! [X14 : term] : (? [X15 : term] : ((((X0 @ id @ X15 @ id)) = $true) & (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) != $true)) | (((X0 @ id @ (lam @ X14) @ id)) = $true)) | ? [X9 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) != $true) & ! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) & ! [X13 : term] : ((((X0 @ id @ X13 @ id)) != $true) | (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true))) | ? [X1 : subst,X4 : term,X2 : subst,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) != $true)))),
% 37.84/5.79 inference(flattening,[],[f11])).
% 37.84/5.79 thf(f13,plain,(
% 37.84/5.79 ((hoasinduction_no_psi_cond = $true) <=> ! [X444 : (subst > term > subst > $o),X445 : term] : (? [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) = $true) & (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) != $true) & (((X444 @ id @ X446 @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true) | ? [X448 : (subst > term > term)] : (! [X452 : term] : ((((X444 @ id @ (X448 @ id @ X452) @ id)) = $true) | (((X444 @ id @ X452 @ id)) != $true)) & ! [X450 : term,X449 : subst,X451 : subst] : (((sub @ (X448 @ X451 @ X450) @ X449)) = ((X448 @ (comp @ X451 @ X449) @ (sub @ X450 @ X449)))) & (((X444 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)))) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343))))) & (! [X149 : term,X148 : term,X147 : (subst > term > term)] : (? [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) != ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149)))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lthm = $true) <=> (((! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X135 : subst,X136 : subst,X137 : subst,X138 : term] : ((((X129 @ (comp @ X135 @ X136) @ (sub @ X138 @ X136) @ X137)) = $true) & (((X129 @ X135 @ X138 @ (comp @ X136 @ X137))) != $true)) | ? [X133 : term,X131 : subst,X134 : subst,X132 : subst] : ((((X129 @ (comp @ X132 @ X131) @ (sub @ X133 @ X131) @ X134)) != $true) & (((X129 @ X132 @ X133 @ (comp @ X131 @ X134))) = $true)) | ? [X142 : (subst > term > term)] : (! [X144 : subst,X146 : term,X145 : subst] : (((X142 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))) = ((sub @ (X142 @ X145 @ X146) @ X144))) & ! [X143 : term] : ((((X129 @ id @ X143 @ id)) != $true) | (((X129 @ id @ (X142 @ id @ X143) @ id)) = $true)) & (((X129 @ id @ (lam @ (X142 @ sh @ one)) @ id)) != $true)) | ? [X139 : term] : ((((var @ (sub @ X139 @ id))) = $true) & (((X129 @ id @ X139 @ id)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ? [X141 : term,X140 : term] : ((((X129 @ id @ (ap @ (sub @ X140 @ id) @ X141) @ id)) != $true) & (((X129 @ id @ X140 @ id)) = $true) & (((X129 @ id @ X141 @ id)) = $true))) | ? [X113 : (subst > term > subst > $o),X114 : term] : (! [X125 : subst,X127 : term,X128 : subst,X126 : subst] : ((((X113 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126) @ X128)) = $true) | ($true != ((X113 @ X125 @ X127 @ (comp @ X126 @ X128))))) & ! [X124 : term,X122 : subst,X121 : subst,X123 : subst] : ((((X113 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) != $true) | (((X113 @ X121 @ X124 @ (comp @ X123 @ X122))) = $true)) & ! [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ? [X116 : term] : ((((X113 @ id @ (X115 @ id @ X116) @ id)) != $true) & (((X113 @ id @ X116 @ id)) = $true)) | ? [X117 : term,X119 : subst,X118 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) != ((sub @ (X115 @ X119 @ X117) @ X118)))) & ! [X120 : term] : ((((X113 @ id @ X120 @ id)) != $true) | (((X113 @ id @ (sub @ X114 @ (push @ X120 @ id)) @ id)) = $true)) & (((X113 @ id @ (lam @ X114) @ id)) != $true))) | ? [X100 : term,X101 : term,X102 : (subst > term > subst > $o)] : ((((X102 @ id @ X101 @ id)) = $true) & (((X102 @ id @ X100 @ id)) = $true) & (((X102 @ id @ (ap @ X100 @ X101) @ id)) != $true) & ! [X104 : term,X106 : subst,X103 : subst,X105 : subst] : ((((X102 @ X105 @ X104 @ (comp @ X103 @ X106))) != $true) | (((X102 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103) @ X106)) = $true)) & ! [X107 : term,X108 : term] : ((((X102 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id)) = $true) | (((X102 @ id @ X108 @ id)) != $true) | (((X102 @ id @ X107 @ id)) != $true)) & ! [X112 : subst,X111 : subst,X109 : subst,X110 : term] : ((((X102 @ X111 @ X110 @ (comp @ X109 @ X112))) = $true) | (((X102 @ (comp @ X111 @ X109) @ (sub @ X110 @ X109) @ X112)) != $true)))) | ? [X94 : term,X93 : (term > $o)] : (! [X95 : term] : ((((var @ X95)) != $true) | (((X93 @ X95)) = $true)) & ! [X96 : term,X97 : term] : ((((X93 @ X96)) != $true) | (((X93 @ (ap @ X97 @ X96))) = $true) | (((X93 @ X97)) != $true)) & ! [X98 : term] : (($true = ((X93 @ (lam @ X98)))) | ? [X99 : term] : ((((X93 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & (((X93 @ X99)) = $true))) & (((X93 @ X94)) != $true)))) & ((axshiftcons = $true) <=> ! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318)) & ((pushprop_lem0_lthm = $true) <=> ! [X534 : (term > $o),X533 : subst,X535 : term] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537)))) & ((hoasinduction_lem3 = $true) <=> ! [X237 : term,X238 : (subst > term > subst > $o)] : (? [X244 : (subst > term > term)] : (! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) & ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | (((X238 @ id @ X248 @ id)) != $true)) & (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) != $true)) | ? [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) != $true) & (((X238 @ id @ X239 @ id)) = $true)) | ? [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) = $true) & (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) != $true)) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ? [X249 : subst,X250 : term,X252 : subst,X251 : subst] : ((((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) & (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) != $true)))) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar_gthm = $true) & (axassoc = $true) & ((termmset = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (termmset_gthm = $true) & (hoasapnotvar = $true) & (((! [X473 : term,X472 : (subst > term > subst > $o)] : (? [X478 : (subst > term > term)] : (! [X482 : term] : ((((X472 @ id @ (X478 @ id @ X482) @ id)) = $true) | (((X472 @ id @ X482 @ id)) != $true)) & ! [X481 : subst,X480 : subst,X479 : term] : (((X478 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))) = ((sub @ (X478 @ X481 @ X479) @ X480))) & (((X472 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true)) | (((X472 @ id @ (lam @ X473) @ id)) = $true) | ? [X485 : term,X484 : subst,X486 : subst,X487 : subst] : ((((X472 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487) @ X484)) = $true) & (((X472 @ X486 @ X485 @ (comp @ X487 @ X484))) != $true)) | ? [X483 : term] : ((((X472 @ id @ (sub @ X473 @ (push @ X483 @ id)) @ id)) != $true) & (((X472 @ id @ X483 @ id)) = $true)) | ? [X474 : subst,X475 : term,X476 : subst,X477 : subst] : ((((X472 @ X477 @ X475 @ (comp @ X476 @ X474))) = $true) & (((X472 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476) @ X474)) != $true))) | ? [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) != $true) & ! [X471 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X471 @ id)) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X466 : (subst > term > term)] : (? [X469 : subst,X467 : term,X468 : subst] : (((X466 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469))) != ((sub @ (X466 @ X468 @ X467) @ X469))) | (((X465 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ? [X470 : term] : ((((X465 @ id @ (X466 @ id @ X470) @ id)) != $true) & (((X465 @ id @ X470 @ id)) = $true))))) | ? [X463 : term] : (((sub @ X463 @ id)) != X463)) <=> (hoasinduction_lem3_lthm = $true)) & (((d2subst @ d_id)) = id) & ! [X437 : d_subst] : (d_id = X437) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (induction2_gthm = $true) & (((! [X430 : (subst > term > subst > $o),X429 : term] : (? [X431 : term] : ((((X430 @ id @ X431 @ id)) = $true) & (((X430 @ id @ (sub @ X429 @ (push @ X431 @ id)) @ id)) != $true)) | (((X430 @ id @ (lam @ X429) @ id)) = $true) | ? [X432 : (subst > term > term)] : (! [X434 : term,X435 : subst,X433 : subst] : (((sub @ (X432 @ X435 @ X434) @ X433)) = ((X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433)))) & (((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id)) != $true) & ! [X436 : term] : ((((X430 @ id @ (X432 @ id @ X436) @ id)) = $true) | (((X430 @ id @ X436 @ id)) != $true)))) | ? [X421 : (subst > term > subst > $o),X422 : term] : ((((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id)) != $true) & ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X426 : subst,X427 : term,X425 : subst] : (((sub @ (X424 @ X425 @ X427) @ X426)) != ((X424 @ (comp @ X425 @ X426) @ (sub @ X427 @ X426)))) | ? [X428 : term] : ((((X421 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X421 @ id @ X428 @ id)) = $true))) & ! [X423 : term] : ((((X421 @ id @ X423 @ id)) != $true) | (((X421 @ id @ (sub @ X422 @ (push @ X423 @ id)) @ id)) = $true)))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420)) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true))) | ? [X12 : (term > $o),X13 : (subst > term > subst > $o),X11 : term] : (! [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) != ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | ? [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) != $true) & (((X13 @ id @ X15 @ id)) = $true))) & ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) & (((X12 @ (lam @ X11))) != $true) & ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | (((X12 @ X20)) != $true)))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X3 : (term > $o),X4 : term] : (! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & ! [X8 : term,X9 : term] : ((((X3 @ X8)) != $true) | (((X3 @ (ap @ X8 @ X9))) = $true) | (((X3 @ X9)) != $true)) & ! [X5 : term] : ((((var @ X5)) != $true) | (((X3 @ X5)) = $true)) & (((X3 @ X4)) != $true))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X30 : term] : ? [X31 : (subst > term > term)] : ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X75 : (subst > term > subst > $o),X77 : (term > $o),X76 : term] : (? [X85 : subst,X84 : subst,X86 : subst,X87 : term] : ((((X75 @ (comp @ X86 @ X84) @ (sub @ X87 @ X84) @ X85)) = $true) & (((X75 @ X86 @ X87 @ (comp @ X84 @ X85))) != $true)) | (((X77 @ (lam @ X76))) = $true) | ? [X88 : (subst > term > term)] : (! [X92 : term] : ((((X75 @ id @ X92 @ id)) != $true) | (((X75 @ id @ (X88 @ id @ X92) @ id)) = $true)) & (((X75 @ id @ (lam @ (X88 @ sh @ one)) @ id)) != $true) & ! [X89 : term,X90 : subst,X91 : subst] : (((X88 @ (comp @ X90 @ X91) @ (sub @ X89 @ X91))) = ((sub @ (X88 @ X90 @ X89) @ X91)))) | ? [X83 : term] : (((X75 @ id @ X83 @ id)) != ((X77 @ X83))) | ? [X81 : subst,X79 : term,X82 : subst,X80 : subst] : ((((X75 @ X80 @ X79 @ (comp @ X81 @ X82))) = $true) & (((X75 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81) @ X82)) != $true)) | ? [X78 : term] : ((((X77 @ X78)) = $true) & (((X77 @ (sub @ X76 @ (push @ X78 @ id)))) != $true)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) != $true) | ? [X236 : term] : (((X232 @ X236)) != ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true)) | ? [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) != X230))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X255 : (term > $o),X253 : term,X254 : subst] : ? [X256 : (term > $o)] : ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X176 : term,X175 : (subst > term > subst > $o)] : (? [X188 : term,X187 : term] : ((((X175 @ id @ X187 @ id)) = $true) & (((X175 @ id @ X188 @ id)) = $true) & (((X175 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)) != $true)) | (((X175 @ id @ X176 @ id)) = $true) | ? [X190 : subst,X192 : subst,X191 : subst,X189 : term] : ((((X175 @ X190 @ X189 @ (comp @ X191 @ X192))) = $true) & (((X175 @ (comp @ X190 @ X191) @ (sub @ X189 @ X191) @ X192)) != $true)) | ? [X182 : term] : ((((var @ (sub @ X182 @ id))) = $true) & (((X175 @ id @ X182 @ id)) != $true)) | ? [X185 : subst,X184 : subst,X183 : subst,X186 : term] : (($true = ((X175 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185) @ X183))) & (((X175 @ X184 @ X186 @ (comp @ X185 @ X183))) != $true)) | ? [X177 : (subst > term > term)] : (! [X179 : subst,X178 : subst,X180 : term] : (((X177 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) = ((sub @ (X177 @ X178 @ X180) @ X179))) & ! [X181 : term] : ((((X175 @ id @ (X177 @ id @ X181) @ id)) = $true) | (((X175 @ id @ X181 @ id)) != $true)) & (((X175 @ id @ (lam @ (X177 @ sh @ one)) @ id)) != $true))) | ? [X167 : term,X166 : (term > $o),X165 : (subst > term > subst > $o)] : (! [X174 : term] : (((X165 @ id @ X174 @ id)) = ((X166 @ X174))) & ! [X168 : term] : (($true = ((X166 @ (sub @ X167 @ (push @ X168 @ id))))) | (((X166 @ X168)) != $true)) & (((X166 @ (lam @ X167))) != $true) & ! [X169 : (subst > term > term)] : (? [X170 : term] : ((((X165 @ id @ (X169 @ id @ X170) @ id)) != $true) & (((X165 @ id @ X170 @ id)) = $true)) | (((X165 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))))) | ? [X164 : term] : (((sub @ X164 @ id)) != X164)) | ? [X157 : (term > $o),X158 : term] : (! [X160 : term] : (? [X161 : term] : ((((X157 @ (sub @ X160 @ (push @ X161 @ id)))) != $true) & (((X157 @ X161)) = $true)) | (((X157 @ (lam @ X160))) = $true)) & ! [X163 : term,X162 : term] : ((((X157 @ X162)) != $true) | (((X157 @ X163)) != $true) | (((X157 @ (ap @ X162 @ X163))) = $true)) & (((X157 @ X158)) != $true) & ! [X159 : term] : ((((var @ X159)) != $true) | (((X157 @ X159)) = $true)))) | ? [X154 : (subst > term > subst > $o)] : ! [X155 : (term > $o)] : ? [X156 : term] : (((X154 @ id @ X156 @ id)) != ((X155 @ X156))))) & (axmap = $true) & ((((! [X506 : subst,X503 : (subst > term > term),X505 : term,X504 : (subst > term > term)] : ((((X504 @ X506 @ X505)) = ((X503 @ X506 @ X505))) | (((lam @ (X504 @ sh @ one))) != ((lam @ (X503 @ sh @ one)))) | ? [X511 : subst,X510 : subst,X512 : term] : (((X503 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510))) != ((sub @ (X503 @ X511 @ X512) @ X510))) | ? [X509 : term,X508 : subst,X507 : subst] : (((X504 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) != ((sub @ (X504 @ X508 @ X509) @ X507)))) | ? [X501 : term,X502 : term] : ((X501 != X502) & (((lam @ X502)) = ((lam @ X501))))) | ? [X499 : term,X500 : subst] : (((comp @ sh @ (push @ X499 @ X500))) != X500)) | ? [X497 : term,X498 : subst] : (((sub @ one @ (push @ X497 @ X498))) != X497)) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X202 : (subst > term > subst > $o),X203 : term,X204 : (term > $o)] : (? [X211 : term] : (((X204 @ X211)) != ((X202 @ id @ X211 @ id))) | ? [X210 : term] : (($true = ((X204 @ X210))) & (((X204 @ (sub @ X203 @ (push @ X210 @ id)))) != $true)) | ($true = ((X204 @ (lam @ X203)))) | ? [X205 : (subst > term > term)] : (! [X208 : subst,X206 : term,X207 : subst] : (((sub @ (X205 @ X208 @ X206) @ X207)) = ((X205 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207)))) & (((X202 @ id @ (lam @ (X205 @ sh @ one)) @ id)) != $true) & ! [X209 : term] : ((((X202 @ id @ X209 @ id)) != $true) | (((X202 @ id @ (X205 @ id @ X209) @ id)) = $true)))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) <=> (shinj = $true)) & (hoaslamnotvar = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true)) | ? [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) != X65)) | ? [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) != X62))) & (lamnotap != $true) & (hoasinduction_lem3_gthm = $true) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) <=> (substmonoid = $true)) & (! [X393 : term,X394 : (subst > term > subst > $o)] : ((((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true) | ? [X395 : term] : ((((X394 @ id @ (sub @ X393 @ (push @ X395 @ id)) @ id)) != $true) & (((X394 @ id @ X395 @ id)) = $true)) | ? [X396 : (subst > term > term)] : (! [X397 : term] : ((((X394 @ id @ (X396 @ id @ X397) @ id)) = $true) | (((X394 @ id @ X397 @ id)) != $true)) & (((X394 @ id @ (lam @ (X396 @ sh @ one)) @ id)) != $true) & ! [X398 : subst,X399 : term,X400 : subst] : (((X396 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X396 @ X398 @ X399) @ X400))))) <=> (hoasinduction_lem3aa = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((pushprop_lem1v2 = $true) <=> ! [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ? [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) != ((X39 @ X42))) | (((X38 @ X41)) != $true))) & (hoasinduction_lem1 = $true) & (((! [X263 : term,X264 : (term > $o),X265 : (subst > term > subst > $o)] : (? [X267 : (subst > term > term)] : ((((X265 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true) & ! [X269 : subst,X270 : term,X271 : subst] : (((sub @ (X267 @ X271 @ X270) @ X269)) = ((X267 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)))) & ! [X268 : term] : ((((X265 @ id @ (X267 @ id @ X268) @ id)) = $true) | (((X265 @ id @ X268 @ id)) != $true))) | ? [X266 : term] : ((((X264 @ (sub @ X263 @ (push @ X266 @ id)))) != $true) & (((X264 @ X266)) = $true)) | (((X264 @ (lam @ X263))) = $true) | ? [X272 : term] : (((X265 @ id @ X272 @ id)) != ((X264 @ X272)))) | ? [X262 : term] : (((sub @ X262 @ id)) != X262)) | ? [X258 : term] : ! [X259 : (subst > term > term)] : ? [X261 : subst,X260 : term] : (((sub @ X258 @ (push @ X260 @ X261))) != ((X259 @ X261 @ X260)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvarind = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2 = $true) <=> ! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ((apinj1 = $true) <=> ! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219))) & (induction2lem_gthm = $true) & (hoaslaminj_gthm = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) <=> (axscons = $true)) & (! [X288 : (term > $o),X287 : (subst > term > subst > $o),X285 : term,X286 : term] : ((((X288 @ (ap @ X286 @ X285))) = $true) | ? [X297 : subst,X296 : term,X298 : subst,X299 : subst] : (($true != ((X287 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298) @ X299))) & (((X287 @ X297 @ X296 @ (comp @ X298 @ X299))) = $true)) | ? [X293 : subst,X294 : term,X295 : subst,X292 : subst] : ((((X287 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) = $true) & (((X287 @ X293 @ X294 @ (comp @ X292 @ X295))) != $true)) | ? [X291 : term] : (((X287 @ id @ X291 @ id)) != ((X288 @ X291))) | (((X288 @ X286)) != $true) | (((X288 @ X285)) != $true) | ? [X289 : term,X290 : term] : ((((X287 @ id @ X289 @ id)) = $true) & (((X287 @ id @ X290 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) <=> (axidr = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ? [X44 : (term > $o)] : ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) != ((d2term @ X439))) | (X438 = X439)) & (axapp = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoaslaminj = $true) <=> ! [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (? [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) != ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | ? [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) != ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | (((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one)))))) & (pushprop = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) <=> (axvarid = $true)) & ((! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))) | ? [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) = ((ap @ X457 @ X456))) & (X455 != X456))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3a = $true) <=> ! [X526 : (subst > term > subst > $o),X525 : term] : (? [X527 : (subst > term > term)] : (! [X531 : term] : ((((X526 @ id @ X531 @ id)) != $true) | (((X526 @ id @ (X527 @ id @ X531) @ id)) = $true)) & ! [X530 : subst,X529 : subst,X528 : term] : (((X527 @ (comp @ X529 @ X530) @ (sub @ X528 @ X530))) = ((sub @ (X527 @ X529 @ X528) @ X530))) & (((X526 @ id @ (lam @ (X527 @ sh @ one)) @ id)) != $true)) | ? [X532 : term] : ((((X526 @ id @ X532 @ id)) = $true) & (((X526 @ id @ (sub @ X525 @ (push @ X532 @ id)) @ id)) != $true)) | (((X526 @ id @ (lam @ X525) @ id)) = $true))) & (((! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))) | ? [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) = ((ap @ X489 @ X492))) & (X489 != X490))) | ? [X488 : term] : (((sub @ X488 @ id)) != X488)) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X388 : term] : ? [X389 : (subst > term > term)] : ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X36 : term] : ? [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) = ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((induction2lem = $true) <=> ! [X195 : subst,X193 : (term > $o),X194 : term] : (? [X199 : term,X198 : term] : ((((X193 @ X198)) = $true) & (((X193 @ (ap @ X198 @ X199))) != $true) & (((X193 @ X199)) = $true)) | ? [X196 : term] : ((((X193 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X193 @ X197)) != $true) | (((X193 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | ? [X200 : term] : ((((X193 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | (((X193 @ (sub @ X194 @ X195))) = $true))) & (axvarshift = $true) & (! [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) = $true) | ? [X406 : term] : ((((X402 @ X406)) = $true) & (((X402 @ (lam @ X406))) != $true)) | ? [X403 : term,X404 : term] : ((((X402 @ X403)) = $true) & (((X402 @ X404)) = $true) & (((X402 @ (ap @ X403 @ X404))) != $true)) | ? [X405 : term] : ((((X402 @ X405)) != $true) & (((var @ X405)) = $true))) <=> (induction = $true)) & (ulamvar1 != $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem0_gthm = $true) & (apnotvar = $true) & (pushprop_lem2v2_lthm = $true) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (! [X274 : term,X273 : (subst > term > subst > $o)] : (? [X284 : term] : ((((X273 @ id @ X284 @ id)) = $true) & (((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)) != $true)) | (((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id)) = $true) | ? [X275 : (subst > term > term),X276 : term] : (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sub @ X276 @ (push @ X279 @ X277)) @ X278)) = ((sub @ (X275 @ X277 @ X279) @ X278))) & (((X273 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true) & ! [X280 : term] : ((((X273 @ id @ X280 @ id)) != $true) | (((X273 @ id @ (X275 @ id @ X280) @ id)) = $true)) & ! [X283 : term,X282 : subst,X281 : subst] : (((sub @ X276 @ (push @ (sub @ X283 @ X281) @ (comp @ X282 @ X281)))) = ((X275 @ (comp @ X282 @ X281) @ (sub @ X283 @ X281)))))) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & (pushprop_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true))) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) <=> (axvarcons = $true)) & ((substmonoid_lthm = $true) <=> (((! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49)) | ? [X47 : subst] : (((comp @ X47 @ id)) != X47)) | ? [X46 : subst] : (((comp @ id @ X46)) != X46))) & ((hoasinduction = $true) <=> ! [X350 : (subst > term > subst > $o),X349 : term] : (? [X364 : term,X363 : subst,X362 : subst,X361 : subst] : ((((X350 @ X362 @ X364 @ (comp @ X363 @ X361))) != $true) & (((X350 @ (comp @ X362 @ X363) @ (sub @ X364 @ X363) @ X361)) = $true)) | ? [X351 : (subst > term > term)] : (! [X352 : term] : ((((X350 @ id @ X352 @ id)) != $true) | (((X350 @ id @ (X351 @ id @ X352) @ id)) = $true)) & (((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : subst,X353 : subst,X354 : term] : (((X351 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X351 @ X353 @ X354) @ X355)))) | (((X350 @ id @ X349 @ id)) = $true) | ? [X360 : term] : ((((X350 @ id @ X360 @ id)) != $true) & (((var @ (sub @ X360 @ id))) = $true)) | ? [X359 : subst,X358 : term,X357 : subst,X356 : subst] : ((((X350 @ X357 @ X358 @ (comp @ X359 @ X356))) = $true) & (((X350 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359) @ X356)) != $true)) | ? [X366 : term,X365 : term] : ((((X350 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id)) != $true) & (((X350 @ id @ X365 @ id)) = $true) & (((X350 @ id @ X366 @ id)) = $true)))) & (axabs = $true) & (((! [X309 : term,X310 : (term > $o)] : (? [X313 : term] : (($true = ((var @ X313))) & (((X310 @ X313)) != $true)) | ? [X311 : term] : (! [X312 : term] : ((((X310 @ X312)) != $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) & (((X310 @ (lam @ X311))) != $true)) | ? [X314 : term,X315 : term] : ((((X310 @ X314)) = $true) & (((X310 @ X315)) = $true) & (((X310 @ (ap @ X314 @ X315))) != $true)) | (((X310 @ X309)) = $true)) | ? [X303 : subst,X301 : term,X302 : (term > $o)] : (! [X304 : term] : (? [X305 : term] : ((((X302 @ X305)) = $true) & (((X302 @ (sub @ X304 @ (push @ X305 @ id)))) != $true)) | (((X302 @ (lam @ X304))) = $true)) & ! [X306 : term] : ((((var @ X306)) != $true) | (((X302 @ (sub @ X306 @ X303))) = $true)) & ! [X307 : term,X308 : term] : ((((X302 @ X307)) != $true) | (((X302 @ (ap @ X308 @ X307))) = $true) | (((X302 @ X308)) != $true)) & (((X302 @ (sub @ X301 @ X303))) != $true))) | ? [X300 : term] : (((sub @ X300 @ id)) != X300)) <=> (induction2_lthm = $true)) & (one = ((d2term @ d_one))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X367 : term] : (((sub @ X367 @ id)) != X367) | ! [X369 : (term > $o),X368 : term,X370 : (subst > term > subst > $o)] : (? [X371 : term] : ((((X369 @ (sub @ X368 @ (push @ X371 @ id)))) != $true) & (((X369 @ X371)) = $true)) | ? [X373 : subst,X372 : subst,X375 : term,X374 : subst] : ((((X370 @ (comp @ X374 @ X373) @ (sub @ X375 @ X373) @ X372)) != $true) & ($true = ((X370 @ X374 @ X375 @ (comp @ X373 @ X372))))) | ? [X381 : (subst > term > term)] : (! [X382 : term] : ((((X370 @ id @ X382 @ id)) != $true) | (((X370 @ id @ (X381 @ id @ X382) @ id)) = $true)) & ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X381 @ X383 @ X384) @ X385)) = ((X381 @ (comp @ X383 @ X385) @ (sub @ X384 @ X385)))) & ($true != ((X370 @ id @ (lam @ (X381 @ sh @ one)) @ id)))) | ? [X380 : term] : (((X369 @ X380)) != ((X370 @ id @ X380 @ id))) | (((X369 @ (lam @ X368))) = $true) | ? [X377 : subst,X379 : subst,X376 : term,X378 : subst] : ((((X370 @ (comp @ X379 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true) & (((X370 @ X379 @ X376 @ (comp @ X378 @ X377))) != $true))))) & (hoasapinj1_gthm = $true) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & (! [X518 : term,X519 : (term > $o)] : (? [X520 : term] : ((((X519 @ (lam @ X520))) != $true) & ! [X521 : term] : ((((X519 @ X521)) != $true) | (((X519 @ (sub @ X520 @ (push @ X521 @ id)))) = $true))) | (((X519 @ X518)) = $true) | ? [X523 : term,X522 : term] : ((((X519 @ (ap @ X522 @ X523))) != $true) & (((X519 @ X523)) = $true) & (((X519 @ X522)) = $true)) | ? [X524 : term] : ((((X519 @ X524)) != $true) & (((var @ X524)) = $true))) <=> (induction2 = $true)) & (((d2subst @ d_id)) = sh) & (! [X408 : term,X407 : term,X409 : (subst > term > subst > $o)] : ((((X409 @ id @ (ap @ X407 @ X408) @ id)) = $true) | ? [X411 : term,X410 : term] : ((((X409 @ id @ X411 @ id)) = $true) & (((X409 @ id @ X410 @ id)) = $true) & (((X409 @ id @ (ap @ (sub @ X411 @ id) @ X410) @ id)) != $true)) | (((X409 @ id @ X408 @ id)) != $true) | ? [X417 : term,X419 : subst,X418 : subst,X416 : subst] : ((((X409 @ X416 @ X417 @ (comp @ X419 @ X418))) = $true) & ($true != ((X409 @ (comp @ X416 @ X419) @ (sub @ X417 @ X419) @ X418)))) | ? [X412 : subst,X414 : subst,X413 : subst,X415 : term] : ((((X409 @ X412 @ X415 @ (comp @ X414 @ X413))) != $true) & (((X409 @ (comp @ X412 @ X414) @ (sub @ X415 @ X414) @ X413)) = $true)) | (((X409 @ id @ X407 @ id)) != $true)) <=> (hoasinduction_lem2 = $true)) & ((axidl = $true) <=> ! [X316 : subst] : (((comp @ id @ X316)) = X316)) & ((! [X441 : term] : (((sub @ X441 @ id)) = X441) | ? [X440 : term] : (((sub @ X440 @ id)) != X440)) <=> (termmset_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ! [X229 : d_subst,X228 : d_subst] : ((X228 = X229) | (((d2subst @ X228)) != ((d2subst @ X229)))) & ((apinj2 = $true) <=> ! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348))) & (! [X340 : (subst > term > subst > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0 = $true)) & (((var @ (d2term @ d_one))) != $true) & (! [X221 : term,X220 : (subst > term > subst > $o)] : (? [X223 : (subst > term > term)] : (($true != ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id))) & ! [X224 : term] : ((((X220 @ id @ (X223 @ id @ X224) @ id)) = $true) | (((X220 @ id @ X224 @ id)) != $true)) & ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X226 @ X225) @ (sub @ X227 @ X225))) = ((sub @ (X223 @ X226 @ X227) @ X225)))) | (((X220 @ id @ (lam @ (sub @ X221 @ (push @ one @ sh))) @ id)) = $true) | ? [X222 : term] : (($true = ((X220 @ id @ X222 @ id))) & (((X220 @ id @ (sub @ X221 @ (push @ X222 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (axclos = $true) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((X539 @ sh @ one)) = ((sub @ X538 @ (push @ one @ sh))))) & ((induction2lem_lthm = $true) <=> ((((! [X331 : (term > $o),X333 : subst,X332 : term] : (? [X334 : term] : ((((var @ X334)) = $true) & (((X331 @ (sub @ X334 @ X333))) != $true)) | ? [X335 : term] : ((((X331 @ (lam @ X335))) != $true) & ! [X336 : term] : (($true = ((X331 @ (sub @ X335 @ (push @ X336 @ id))))) | ($true != ((X331 @ X336))))) | (((X331 @ (sub @ X332 @ X333))) = $true) | ? [X337 : term,X338 : term] : ((((X331 @ (ap @ X337 @ X338))) != $true) & (((X331 @ X337)) = $true) & (((X331 @ X338)) = $true))) | ? [X325 : (term > $o),X326 : term] : (! [X328 : term] : ((((X325 @ X328)) != $true) | (((X325 @ (lam @ X328))) = $true)) & ! [X327 : term] : ((((X325 @ X327)) = $true) | ($true != ((var @ X327)))) & (((X325 @ X326)) != $true) & ! [X329 : term,X330 : term] : ((((X325 @ X329)) != $true) | (((X325 @ (ap @ X330 @ X329))) = $true) | (((X325 @ X330)) != $true)))) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324)) | ? [X322 : subst,X323 : term] : (((comp @ sh @ (push @ X323 @ X322))) != X322)) | ? [X320 : subst,X321 : term] : (((sub @ one @ (push @ X321 @ X320))) != X321)))),
% 37.84/5.79 inference(ennf_transformation,[],[f9])).
% 37.84/5.79 thf(f14,plain,(
% 37.84/5.79 ((apinj2 = $true) <=> ! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348))) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ((laminj = $true) <=> ! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X444 : (subst > term > subst > $o),X445 : term] : (? [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) = $true) & (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) != $true) & (((X444 @ id @ X446 @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true) | ? [X448 : (subst > term > term)] : (! [X452 : term] : ((((X444 @ id @ (X448 @ id @ X452) @ id)) = $true) | (((X444 @ id @ X452 @ id)) != $true)) & ! [X450 : term,X449 : subst,X451 : subst] : (((sub @ (X448 @ X451 @ X450) @ X449)) = ((X448 @ (comp @ X451 @ X449) @ (sub @ X450 @ X449)))) & (((X444 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)))) & (! [X393 : term,X394 : (subst > term > subst > $o)] : ((((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true) | ? [X395 : term] : ((((X394 @ id @ (sub @ X393 @ (push @ X395 @ id)) @ id)) != $true) & (((X394 @ id @ X395 @ id)) = $true)) | ? [X396 : (subst > term > term)] : (! [X397 : term] : ((((X394 @ id @ (X396 @ id @ X397) @ id)) = $true) | (((X394 @ id @ X397 @ id)) != $true)) & (((X394 @ id @ (lam @ (X396 @ sh @ one)) @ id)) != $true) & ! [X398 : subst,X399 : term,X400 : subst] : (((X396 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X396 @ X398 @ X399) @ X400))))) <=> (hoasinduction_lem3aa = $true)) & ((axshiftcons = $true) <=> ! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318)) & ((induction2lem_lthm = $true) <=> (! [X331 : (term > $o),X333 : subst,X332 : term] : (? [X334 : term] : ((((var @ X334)) = $true) & (((X331 @ (sub @ X334 @ X333))) != $true)) | ? [X335 : term] : ((((X331 @ (lam @ X335))) != $true) & ! [X336 : term] : (($true = ((X331 @ (sub @ X335 @ (push @ X336 @ id))))) | ($true != ((X331 @ X336))))) | (((X331 @ (sub @ X332 @ X333))) = $true) | ? [X337 : term,X338 : term] : ((((X331 @ (ap @ X337 @ X338))) != $true) & (((X331 @ X337)) = $true) & (((X331 @ X338)) = $true))) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324) | ? [X325 : (term > $o),X326 : term] : (! [X328 : term] : ((((X325 @ X328)) != $true) | (((X325 @ (lam @ X328))) = $true)) & ! [X327 : term] : ((((X325 @ X327)) = $true) | ($true != ((var @ X327)))) & (((X325 @ X326)) != $true) & ! [X329 : term,X330 : term] : ((((X325 @ X329)) != $true) | (((X325 @ (ap @ X330 @ X329))) = $true) | (((X325 @ X330)) != $true))) | ? [X322 : subst,X323 : term] : (((comp @ sh @ (push @ X323 @ X322))) != X322) | ? [X320 : subst,X321 : term] : (((sub @ one @ (push @ X321 @ X320))) != X321))) & ((pushprop_lem1v2 = $true) <=> ! [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ? [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) != ((X39 @ X42))) | (((X38 @ X41)) != $true))) & ((apinj1 = $true) <=> ! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219))) & (! [X288 : (term > $o),X287 : (subst > term > subst > $o),X285 : term,X286 : term] : ((((X288 @ (ap @ X286 @ X285))) = $true) | ? [X297 : subst,X296 : term,X298 : subst,X299 : subst] : (($true != ((X287 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298) @ X299))) & (((X287 @ X297 @ X296 @ (comp @ X298 @ X299))) = $true)) | ? [X293 : subst,X294 : term,X295 : subst,X292 : subst] : ((((X287 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) = $true) & (((X287 @ X293 @ X294 @ (comp @ X292 @ X295))) != $true)) | ? [X291 : term] : (((X287 @ id @ X291 @ id)) != ((X288 @ X291))) | (((X288 @ X286)) != $true) | (((X288 @ X285)) != $true) | ? [X289 : term,X290 : term] : ((((X287 @ id @ X289 @ id)) = $true) & (((X287 @ id @ X290 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) <=> (axvarcons = $true)) & ((? [X154 : (subst > term > subst > $o)] : ! [X155 : (term > $o)] : ? [X156 : term] : (((X154 @ id @ X156 @ id)) != ((X155 @ X156))) | ? [X167 : term,X166 : (term > $o),X165 : (subst > term > subst > $o)] : (! [X174 : term] : (((X165 @ id @ X174 @ id)) = ((X166 @ X174))) & ! [X168 : term] : (($true = ((X166 @ (sub @ X167 @ (push @ X168 @ id))))) | (((X166 @ X168)) != $true)) & (((X166 @ (lam @ X167))) != $true) & ! [X169 : (subst > term > term)] : (? [X170 : term] : ((((X165 @ id @ (X169 @ id @ X170) @ id)) != $true) & (((X165 @ id @ X170 @ id)) = $true)) | (((X165 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171)))))) | ! [X176 : term,X175 : (subst > term > subst > $o)] : (? [X188 : term,X187 : term] : ((((X175 @ id @ X187 @ id)) = $true) & (((X175 @ id @ X188 @ id)) = $true) & (((X175 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)) != $true)) | (((X175 @ id @ X176 @ id)) = $true) | ? [X190 : subst,X192 : subst,X191 : subst,X189 : term] : ((((X175 @ X190 @ X189 @ (comp @ X191 @ X192))) = $true) & (((X175 @ (comp @ X190 @ X191) @ (sub @ X189 @ X191) @ X192)) != $true)) | ? [X182 : term] : ((((var @ (sub @ X182 @ id))) = $true) & (((X175 @ id @ X182 @ id)) != $true)) | ? [X185 : subst,X184 : subst,X183 : subst,X186 : term] : (($true = ((X175 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185) @ X183))) & (((X175 @ X184 @ X186 @ (comp @ X185 @ X183))) != $true)) | ? [X177 : (subst > term > term)] : (! [X179 : subst,X178 : subst,X180 : term] : (((X177 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) = ((sub @ (X177 @ X178 @ X180) @ X179))) & ! [X181 : term] : ((((X175 @ id @ (X177 @ id @ X181) @ id)) = $true) | (((X175 @ id @ X181 @ id)) != $true)) & (((X175 @ id @ (lam @ (X177 @ sh @ one)) @ id)) != $true))) | ? [X164 : term] : (((sub @ X164 @ id)) != X164) | ? [X157 : (term > $o),X158 : term] : (! [X160 : term] : (? [X161 : term] : ((((X157 @ (sub @ X160 @ (push @ X161 @ id)))) != $true) & (((X157 @ X161)) = $true)) | (((X157 @ (lam @ X160))) = $true)) & ! [X163 : term,X162 : term] : ((((X157 @ X162)) != $true) | (((X157 @ X163)) != $true) | (((X157 @ (ap @ X162 @ X163))) = $true)) & (((X157 @ X158)) != $true) & ! [X159 : term] : ((((var @ X159)) != $true) | (((X157 @ X159)) = $true)))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X421 : (subst > term > subst > $o),X422 : term] : ((((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id)) != $true) & ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X426 : subst,X427 : term,X425 : subst] : (((sub @ (X424 @ X425 @ X427) @ X426)) != ((X424 @ (comp @ X425 @ X426) @ (sub @ X427 @ X426)))) | ? [X428 : term] : ((((X421 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X421 @ id @ X428 @ id)) = $true))) & ! [X423 : term] : ((((X421 @ id @ X423 @ id)) != $true) | (((X421 @ id @ (sub @ X422 @ (push @ X423 @ id)) @ id)) = $true))) | ! [X430 : (subst > term > subst > $o),X429 : term] : (? [X431 : term] : ((((X430 @ id @ X431 @ id)) = $true) & (((X430 @ id @ (sub @ X429 @ (push @ X431 @ id)) @ id)) != $true)) | (((X430 @ id @ (lam @ X429) @ id)) = $true) | ? [X432 : (subst > term > term)] : (! [X434 : term,X435 : subst,X433 : subst] : (((sub @ (X432 @ X435 @ X434) @ X433)) = ((X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433)))) & (((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id)) != $true) & ! [X436 : term] : ((((X430 @ id @ (X432 @ id @ X436) @ id)) = $true) | (((X430 @ id @ X436 @ id)) != $true)))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420))) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X229 : d_subst,X228 : d_subst] : ((X228 = X229) | (((d2subst @ X228)) != ((d2subst @ X229)))) & (! [X255 : (term > $o),X253 : term,X254 : subst] : ? [X256 : (term > $o)] : ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) <=> (pushprop_lem0 = $true)) & (pushprop_lem2v2_lthm = $true) & (! [X149 : term,X148 : term,X147 : (subst > term > term)] : (? [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) != ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149)))) <=> (hoaslamnotap = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & ((! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))) | ? [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) = ((ap @ X457 @ X456))) & (X455 != X456))) <=> (hoasapinj2_lthm = $true)) & ((! [X506 : subst,X503 : (subst > term > term),X505 : term,X504 : (subst > term > term)] : ((((X504 @ X506 @ X505)) = ((X503 @ X506 @ X505))) | (((lam @ (X504 @ sh @ one))) != ((lam @ (X503 @ sh @ one)))) | ? [X511 : subst,X510 : subst,X512 : term] : (((X503 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510))) != ((sub @ (X503 @ X511 @ X512) @ X510))) | ? [X509 : term,X508 : subst,X507 : subst] : (((X504 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) != ((sub @ (X504 @ X508 @ X509) @ X507)))) | ? [X497 : term,X498 : subst] : (((sub @ one @ (push @ X497 @ X498))) != X497) | ? [X501 : term,X502 : term] : ((X501 != X502) & (((lam @ X502)) = ((lam @ X501)))) | ? [X499 : term,X500 : subst] : (((comp @ sh @ (push @ X499 @ X500))) != X500)) <=> (hoaslaminj_lthm = $true)) & (((d2subst @ d_id)) = id) & (! [X340 : (subst > term > subst > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & (! [X202 : (subst > term > subst > $o),X203 : term,X204 : (term > $o)] : (? [X211 : term] : (((X204 @ X211)) != ((X202 @ id @ X211 @ id))) | ? [X210 : term] : (($true = ((X204 @ X210))) & (((X204 @ (sub @ X203 @ (push @ X210 @ id)))) != $true)) | ($true = ((X204 @ (lam @ X203)))) | ? [X205 : (subst > term > term)] : (! [X208 : subst,X206 : term,X207 : subst] : (((sub @ (X205 @ X208 @ X206) @ X207)) = ((X205 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207)))) & (((X202 @ id @ (lam @ (X205 @ sh @ one)) @ id)) != $true) & ! [X209 : term] : ((((X202 @ id @ X209 @ id)) != $true) | (((X202 @ id @ (X205 @ id @ X209) @ id)) = $true)))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj2 = $true) <=> ! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214))))) & (! [X408 : term,X407 : term,X409 : (subst > term > subst > $o)] : ((((X409 @ id @ (ap @ X407 @ X408) @ id)) = $true) | ? [X411 : term,X410 : term] : ((((X409 @ id @ X411 @ id)) = $true) & (((X409 @ id @ X410 @ id)) = $true) & (((X409 @ id @ (ap @ (sub @ X411 @ id) @ X410) @ id)) != $true)) | (((X409 @ id @ X408 @ id)) != $true) | ? [X417 : term,X419 : subst,X418 : subst,X416 : subst] : ((((X409 @ X416 @ X417 @ (comp @ X419 @ X418))) = $true) & ($true != ((X409 @ (comp @ X416 @ X419) @ (sub @ X417 @ X419) @ X418)))) | ? [X412 : subst,X414 : subst,X413 : subst,X415 : term] : ((((X409 @ X412 @ X415 @ (comp @ X414 @ X413))) != $true) & (((X409 @ (comp @ X412 @ X414) @ (sub @ X415 @ X414) @ X413)) = $true)) | (((X409 @ id @ X407 @ id)) != $true)) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) <=> (axvarid = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) <=> (substmonoid = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ? [X44 : (term > $o)] : ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) <=> ((! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49)) | ? [X47 : subst] : (((comp @ X47 @ id)) != X47) | ? [X46 : subst] : (((comp @ id @ X46)) != X46))) & ((induction2lem = $true) <=> ! [X195 : subst,X193 : (term > $o),X194 : term] : (? [X199 : term,X198 : term] : ((((X193 @ X198)) = $true) & (((X193 @ (ap @ X198 @ X199))) != $true) & (((X193 @ X199)) = $true)) | ? [X196 : term] : ((((X193 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X193 @ X197)) != $true) | (((X193 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | ? [X200 : term] : ((((X193 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | (((X193 @ (sub @ X194 @ X195))) = $true))) & (! [X388 : term] : ? [X389 : (subst > term > term)] : ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) <=> (hoasinduction_lem3v2_f = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X367 : term] : (((sub @ X367 @ id)) != X367) | ! [X369 : (term > $o),X368 : term,X370 : (subst > term > subst > $o)] : (? [X371 : term] : ((((X369 @ (sub @ X368 @ (push @ X371 @ id)))) != $true) & (((X369 @ X371)) = $true)) | ? [X373 : subst,X372 : subst,X375 : term,X374 : subst] : ((((X370 @ (comp @ X374 @ X373) @ (sub @ X375 @ X373) @ X372)) != $true) & ($true = ((X370 @ X374 @ X375 @ (comp @ X373 @ X372))))) | ? [X381 : (subst > term > term)] : (! [X382 : term] : ((((X370 @ id @ X382 @ id)) != $true) | (((X370 @ id @ (X381 @ id @ X382) @ id)) = $true)) & ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X381 @ X383 @ X384) @ X385)) = ((X381 @ (comp @ X383 @ X385) @ (sub @ X384 @ X385)))) & ($true != ((X370 @ id @ (lam @ (X381 @ sh @ one)) @ id)))) | ? [X380 : term] : (((X369 @ X380)) != ((X370 @ id @ X380 @ id))) | (((X369 @ (lam @ X368))) = $true) | ? [X377 : subst,X379 : subst,X376 : term,X378 : subst] : ((((X370 @ (comp @ X379 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true) & (((X370 @ X379 @ X376 @ (comp @ X378 @ X377))) != $true))))) & (! [X518 : term,X519 : (term > $o)] : (? [X520 : term] : ((((X519 @ (lam @ X520))) != $true) & ! [X521 : term] : ((((X519 @ X521)) != $true) | (((X519 @ (sub @ X520 @ (push @ X521 @ id)))) = $true))) | (((X519 @ X518)) = $true) | ? [X523 : term,X522 : term] : ((((X519 @ (ap @ X522 @ X523))) != $true) & (((X519 @ X523)) = $true) & (((X519 @ X522)) = $true)) | ? [X524 : term] : ((((X519 @ X524)) != $true) & (((var @ X524)) = $true))) <=> (induction2 = $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X237 : term,X238 : (subst > term > subst > $o)] : (? [X244 : (subst > term > term)] : (! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) & ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | (((X238 @ id @ X248 @ id)) != $true)) & (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) != $true)) | ? [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) != $true) & (((X238 @ id @ X239 @ id)) = $true)) | ? [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) = $true) & (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) != $true)) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ? [X249 : subst,X250 : term,X252 : subst,X251 : subst] : ((((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) & (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) != $true)))) & ((? [X113 : (subst > term > subst > $o),X114 : term] : (! [X125 : subst,X127 : term,X128 : subst,X126 : subst] : ((((X113 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126) @ X128)) = $true) | ($true != ((X113 @ X125 @ X127 @ (comp @ X126 @ X128))))) & ! [X124 : term,X122 : subst,X121 : subst,X123 : subst] : ((((X113 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) != $true) | (((X113 @ X121 @ X124 @ (comp @ X123 @ X122))) = $true)) & ! [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ? [X116 : term] : ((((X113 @ id @ (X115 @ id @ X116) @ id)) != $true) & (((X113 @ id @ X116 @ id)) = $true)) | ? [X117 : term,X119 : subst,X118 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) != ((sub @ (X115 @ X119 @ X117) @ X118)))) & ! [X120 : term] : ((((X113 @ id @ X120 @ id)) != $true) | (((X113 @ id @ (sub @ X114 @ (push @ X120 @ id)) @ id)) = $true)) & (((X113 @ id @ (lam @ X114) @ id)) != $true)) | ? [X94 : term,X93 : (term > $o)] : (! [X95 : term] : ((((var @ X95)) != $true) | (((X93 @ X95)) = $true)) & ! [X96 : term,X97 : term] : ((((X93 @ X96)) != $true) | (((X93 @ (ap @ X97 @ X96))) = $true) | (((X93 @ X97)) != $true)) & ! [X98 : term] : (($true = ((X93 @ (lam @ X98)))) | ? [X99 : term] : ((((X93 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & (((X93 @ X99)) = $true))) & (((X93 @ X94)) != $true)) | ? [X100 : term,X101 : term,X102 : (subst > term > subst > $o)] : ((((X102 @ id @ X101 @ id)) = $true) & (((X102 @ id @ X100 @ id)) = $true) & (((X102 @ id @ (ap @ X100 @ X101) @ id)) != $true) & ! [X104 : term,X106 : subst,X103 : subst,X105 : subst] : ((((X102 @ X105 @ X104 @ (comp @ X103 @ X106))) != $true) | (((X102 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103) @ X106)) = $true)) & ! [X107 : term,X108 : term] : ((((X102 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id)) = $true) | (((X102 @ id @ X108 @ id)) != $true) | (((X102 @ id @ X107 @ id)) != $true)) & ! [X112 : subst,X111 : subst,X109 : subst,X110 : term] : ((((X102 @ X111 @ X110 @ (comp @ X109 @ X112))) = $true) | (((X102 @ (comp @ X111 @ X109) @ (sub @ X110 @ X109) @ X112)) != $true))) | ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X135 : subst,X136 : subst,X137 : subst,X138 : term] : ((((X129 @ (comp @ X135 @ X136) @ (sub @ X138 @ X136) @ X137)) = $true) & (((X129 @ X135 @ X138 @ (comp @ X136 @ X137))) != $true)) | ? [X133 : term,X131 : subst,X134 : subst,X132 : subst] : ((((X129 @ (comp @ X132 @ X131) @ (sub @ X133 @ X131) @ X134)) != $true) & (((X129 @ X132 @ X133 @ (comp @ X131 @ X134))) = $true)) | ? [X142 : (subst > term > term)] : (! [X144 : subst,X146 : term,X145 : subst] : (((X142 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))) = ((sub @ (X142 @ X145 @ X146) @ X144))) & ! [X143 : term] : ((((X129 @ id @ X143 @ id)) != $true) | (((X129 @ id @ (X142 @ id @ X143) @ id)) = $true)) & (((X129 @ id @ (lam @ (X142 @ sh @ one)) @ id)) != $true)) | ? [X139 : term] : ((((var @ (sub @ X139 @ id))) = $true) & (((X129 @ id @ X139 @ id)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ? [X141 : term,X140 : term] : ((((X129 @ id @ (ap @ (sub @ X140 @ id) @ X141) @ id)) != $true) & (((X129 @ id @ X140 @ id)) = $true) & (((X129 @ id @ X141 @ id)) = $true)))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X221 : term,X220 : (subst > term > subst > $o)] : (? [X223 : (subst > term > term)] : (($true != ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id))) & ! [X224 : term] : ((((X220 @ id @ (X223 @ id @ X224) @ id)) = $true) | (((X220 @ id @ X224 @ id)) != $true)) & ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X226 @ X225) @ (sub @ X227 @ X225))) = ((sub @ (X223 @ X226 @ X227) @ X225)))) | (((X220 @ id @ (lam @ (sub @ X221 @ (push @ one @ sh))) @ id)) = $true) | ? [X222 : term] : (($true = ((X220 @ id @ X222 @ id))) & (((X220 @ id @ (sub @ X221 @ (push @ X222 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) <=> (axidr = $true)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) = $true) | ? [X406 : term] : ((((X402 @ X406)) = $true) & (((X402 @ (lam @ X406))) != $true)) | ? [X403 : term,X404 : term] : ((((X402 @ X403)) = $true) & (((X402 @ X404)) = $true) & (((X402 @ (ap @ X403 @ X404))) != $true)) | ? [X405 : term] : ((((X402 @ X405)) != $true) & (((var @ X405)) = $true))) <=> (induction = $true)) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X437 : d_subst] : (d_id = X437) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & ((pushprop_lem1 = $true) <=> ! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true))) & ((! [X309 : term,X310 : (term > $o)] : (? [X313 : term] : (($true = ((var @ X313))) & (((X310 @ X313)) != $true)) | ? [X311 : term] : (! [X312 : term] : ((((X310 @ X312)) != $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) & (((X310 @ (lam @ X311))) != $true)) | ? [X314 : term,X315 : term] : ((((X310 @ X314)) = $true) & (((X310 @ X315)) = $true) & (((X310 @ (ap @ X314 @ X315))) != $true)) | (((X310 @ X309)) = $true)) | ? [X300 : term] : (((sub @ X300 @ id)) != X300) | ? [X303 : subst,X301 : term,X302 : (term > $o)] : (! [X304 : term] : (? [X305 : term] : ((((X302 @ X305)) = $true) & (((X302 @ (sub @ X304 @ (push @ X305 @ id)))) != $true)) | (((X302 @ (lam @ X304))) = $true)) & ! [X306 : term] : ((((var @ X306)) != $true) | (((X302 @ (sub @ X306 @ X303))) = $true)) & ! [X307 : term,X308 : term] : ((((X302 @ X307)) != $true) | (((X302 @ (ap @ X308 @ X307))) = $true) | (((X302 @ X308)) != $true)) & (((X302 @ (sub @ X301 @ X303))) != $true))) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & ((! [X441 : term] : (((sub @ X441 @ id)) = X441) | ? [X440 : term] : (((sub @ X440 @ id)) != X440)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X75 : (subst > term > subst > $o),X77 : (term > $o),X76 : term] : (? [X85 : subst,X84 : subst,X86 : subst,X87 : term] : ((((X75 @ (comp @ X86 @ X84) @ (sub @ X87 @ X84) @ X85)) = $true) & (((X75 @ X86 @ X87 @ (comp @ X84 @ X85))) != $true)) | (((X77 @ (lam @ X76))) = $true) | ? [X88 : (subst > term > term)] : (! [X92 : term] : ((((X75 @ id @ X92 @ id)) != $true) | (((X75 @ id @ (X88 @ id @ X92) @ id)) = $true)) & (((X75 @ id @ (lam @ (X88 @ sh @ one)) @ id)) != $true) & ! [X89 : term,X90 : subst,X91 : subst] : (((X88 @ (comp @ X90 @ X91) @ (sub @ X89 @ X91))) = ((sub @ (X88 @ X90 @ X89) @ X91)))) | ? [X83 : term] : (((X75 @ id @ X83 @ id)) != ((X77 @ X83))) | ? [X81 : subst,X79 : term,X82 : subst,X80 : subst] : ((((X75 @ X80 @ X79 @ (comp @ X81 @ X82))) = $true) & (((X75 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81) @ X82)) != $true)) | ? [X78 : term] : ((((X77 @ X78)) = $true) & (((X77 @ (sub @ X76 @ (push @ X78 @ id)))) != $true)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) != $true) | ? [X236 : term] : (((X232 @ X236)) != ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true)) | ? [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) != X230))) & (! [X274 : term,X273 : (subst > term > subst > $o)] : (? [X284 : term] : ((((X273 @ id @ X284 @ id)) = $true) & (((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)) != $true)) | (((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id)) = $true) | ? [X275 : (subst > term > term),X276 : term] : (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sub @ X276 @ (push @ X279 @ X277)) @ X278)) = ((sub @ (X275 @ X277 @ X279) @ X278))) & (((X273 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true) & ! [X280 : term] : ((((X273 @ id @ X280 @ id)) != $true) | (((X273 @ id @ (X275 @ id @ X280) @ id)) = $true)) & ! [X283 : term,X282 : subst,X281 : subst] : (((sub @ X276 @ (push @ (sub @ X283 @ X281) @ (comp @ X282 @ X281)))) = ((X275 @ (comp @ X282 @ X281) @ (sub @ X283 @ X281)))))) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((termmset = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (ulamvarsh = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X534 : (term > $o),X533 : subst,X535 : term] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537)))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((X539 @ sh @ one)) = ((sub @ X538 @ (push @ one @ sh))))) & (hoaslamnotap_gthm = $true) & ((! [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X12 : (term > $o),X13 : (subst > term > subst > $o),X11 : term] : (! [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) != ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | ? [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) != $true) & (((X13 @ id @ X15 @ id)) = $true))) & ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) & (((X12 @ (lam @ X11))) != $true) & ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | (((X12 @ X20)) != $true))) | ? [X3 : (term > $o),X4 : term] : (! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & ! [X8 : term,X9 : term] : ((((X3 @ X8)) != $true) | (((X3 @ (ap @ X8 @ X9))) = $true) | (((X3 @ X9)) != $true)) & ! [X5 : term] : ((((var @ X5)) != $true) | (((X3 @ X5)) = $true)) & (((X3 @ X4)) != $true)) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X36 : term] : ? [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) = ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (lamnotvar = $true) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) != ((d2term @ X439))) | (X438 = X439)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) <=> (axscons = $true)) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))) | ? [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) = ((ap @ X489 @ X492))) & (X489 != X490)) | ? [X488 : term] : (((sub @ X488 @ id)) != X488))) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & ((hoaslaminj = $true) <=> ! [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (? [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) != ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | ? [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) != ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | (((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one)))))) & ((hoasinduction = $true) <=> ! [X350 : (subst > term > subst > $o),X349 : term] : (? [X364 : term,X363 : subst,X362 : subst,X361 : subst] : ((((X350 @ X362 @ X364 @ (comp @ X363 @ X361))) != $true) & (((X350 @ (comp @ X362 @ X363) @ (sub @ X364 @ X363) @ X361)) = $true)) | ? [X351 : (subst > term > term)] : (! [X352 : term] : ((((X350 @ id @ X352 @ id)) != $true) | (((X350 @ id @ (X351 @ id @ X352) @ id)) = $true)) & (((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : subst,X353 : subst,X354 : term] : (((X351 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X351 @ X353 @ X354) @ X355)))) | (((X350 @ id @ X349 @ id)) = $true) | ? [X360 : term] : ((((X350 @ id @ X360 @ id)) != $true) & (((var @ (sub @ X360 @ id))) = $true)) | ? [X359 : subst,X358 : term,X357 : subst,X356 : subst] : ((((X350 @ X357 @ X358 @ (comp @ X359 @ X356))) = $true) & (((X350 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359) @ X356)) != $true)) | ? [X366 : term,X365 : term] : ((((X350 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id)) != $true) & (((X350 @ id @ X365 @ id)) = $true) & (((X350 @ id @ X366 @ id)) = $true)))) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & ((? [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) != X62) | ? [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) != X65) | ! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X258 : term] : ! [X259 : (subst > term > term)] : ? [X261 : subst,X260 : term] : (((sub @ X258 @ (push @ X260 @ X261))) != ((X259 @ X261 @ X260))) | ? [X262 : term] : (((sub @ X262 @ id)) != X262) | ! [X263 : term,X264 : (term > $o),X265 : (subst > term > subst > $o)] : (? [X267 : (subst > term > term)] : ((((X265 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true) & ! [X269 : subst,X270 : term,X271 : subst] : (((sub @ (X267 @ X271 @ X270) @ X269)) = ((X267 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)))) & ! [X268 : term] : ((((X265 @ id @ (X267 @ id @ X268) @ id)) = $true) | (((X265 @ id @ X268 @ id)) != $true))) | ? [X266 : term] : ((((X264 @ (sub @ X263 @ (push @ X266 @ id)))) != $true) & (((X264 @ X266)) = $true)) | (((X264 @ (lam @ X263))) = $true) | ? [X272 : term] : (((X265 @ id @ X272 @ id)) != ((X264 @ X272)))))) & ((hoasinduction_lem3a = $true) <=> ! [X526 : (subst > term > subst > $o),X525 : term] : (? [X527 : (subst > term > term)] : (! [X531 : term] : ((((X526 @ id @ X531 @ id)) != $true) | (((X526 @ id @ (X527 @ id @ X531) @ id)) = $true)) & ! [X530 : subst,X529 : subst,X528 : term] : (((X527 @ (comp @ X529 @ X530) @ (sub @ X528 @ X530))) = ((sub @ (X527 @ X529 @ X528) @ X530))) & (((X526 @ id @ (lam @ (X527 @ sh @ one)) @ id)) != $true)) | ? [X532 : term] : ((((X526 @ id @ X532 @ id)) = $true) & (((X526 @ id @ (sub @ X525 @ (push @ X532 @ id)) @ id)) != $true)) | (((X526 @ id @ (lam @ X525) @ id)) = $true))) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) <=> (hoasapinj1 = $true)) & ((axidl = $true) <=> ! [X316 : subst] : (((comp @ id @ X316)) = X316)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X30 : term] : ? [X31 : (subst > term > term)] : ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33))))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) != $true) & ! [X471 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X471 @ id)) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X466 : (subst > term > term)] : (? [X469 : subst,X467 : term,X468 : subst] : (((X466 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469))) != ((sub @ (X466 @ X468 @ X467) @ X469))) | (((X465 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ? [X470 : term] : ((((X465 @ id @ (X466 @ id @ X470) @ id)) != $true) & (((X465 @ id @ X470 @ id)) = $true)))) | ? [X463 : term] : (((sub @ X463 @ id)) != X463) | ! [X473 : term,X472 : (subst > term > subst > $o)] : (? [X478 : (subst > term > term)] : (! [X482 : term] : ((((X472 @ id @ (X478 @ id @ X482) @ id)) = $true) | (((X472 @ id @ X482 @ id)) != $true)) & ! [X481 : subst,X480 : subst,X479 : term] : (((X478 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))) = ((sub @ (X478 @ X481 @ X479) @ X480))) & (((X472 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true)) | (((X472 @ id @ (lam @ X473) @ id)) = $true) | ? [X485 : term,X484 : subst,X486 : subst,X487 : subst] : ((((X472 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487) @ X484)) = $true) & (((X472 @ X486 @ X485 @ (comp @ X487 @ X484))) != $true)) | ? [X483 : term] : ((((X472 @ id @ (sub @ X473 @ (push @ X483 @ id)) @ id)) != $true) & (((X472 @ id @ X483 @ id)) = $true)) | ? [X474 : subst,X475 : term,X476 : subst,X477 : subst] : ((((X472 @ X477 @ X475 @ (comp @ X476 @ X474))) = $true) & (((X472 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476) @ X474)) != $true))))) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) <=> (shinj = $true)) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.79 inference(flattening,[],[f13])).
% 37.84/5.79 thf(f15,definition,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : ((((sP0 @ X0)) = $true) <=> ? [X9 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) != $true) & ! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) & ! [X13 : term] : ((((X0 @ id @ X13 @ id)) != $true) | (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f16,definition,(
% 37.84/5.79 (sP1 = $true) <=> ! [X0 : (subst > term > subst > $o)] : (? [X6 : subst,X8 : subst,X5 : term,X7 : subst] : ((((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) != $true) & (((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true)) | ! [X14 : term] : (? [X15 : term] : ((((X0 @ id @ X15 @ id)) = $true) & (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) != $true)) | (((X0 @ id @ (lam @ X14) @ id)) = $true)) | (((sP0 @ X0)) = $true) | ? [X1 : subst,X4 : term,X2 : subst,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f17,plain,(
% 37.84/5.79 (hoasinduction_lem3 = $true) <~> (sP1 = $true)),
% 37.84/5.79 inference(definition_folding,[],[f12,f16,f15])).
% 37.84/5.79 thf(f18,definition,(
% 37.84/5.79 ! [X472 : (subst > term > subst > $o)] : ((((sP2 @ X472)) = $true) <=> ? [X478 : (subst > term > term)] : (! [X482 : term] : ((((X472 @ id @ (X478 @ id @ X482) @ id)) = $true) | (((X472 @ id @ X482 @ id)) != $true)) & ! [X481 : subst,X480 : subst,X479 : term] : (((X478 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))) = ((sub @ (X478 @ X481 @ X479) @ X480))) & (((X472 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f19,definition,(
% 37.84/5.79 (sP3 = $true) <=> ? [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) != $true) & ! [X471 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X471 @ id)) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X466 : (subst > term > term)] : (? [X469 : subst,X467 : term,X468 : subst] : (((X466 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469))) != ((sub @ (X466 @ X468 @ X467) @ X469))) | (((X465 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ? [X470 : term] : ((((X465 @ id @ (X466 @ id @ X470) @ id)) != $true) & (((X465 @ id @ X470 @ id)) = $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f20,definition,(
% 37.84/5.79 (sP4 = $true) <=> ((sP3 = $true) | ? [X463 : term] : (((sub @ X463 @ id)) != X463) | ! [X473 : term,X472 : (subst > term > subst > $o)] : ((((sP2 @ X472)) = $true) | (((X472 @ id @ (lam @ X473) @ id)) = $true) | ? [X485 : term,X484 : subst,X486 : subst,X487 : subst] : ((((X472 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487) @ X484)) = $true) & (((X472 @ X486 @ X485 @ (comp @ X487 @ X484))) != $true)) | ? [X483 : term] : ((((X472 @ id @ (sub @ X473 @ (push @ X483 @ id)) @ id)) != $true) & (((X472 @ id @ X483 @ id)) = $true)) | ? [X474 : subst,X475 : term,X476 : subst,X477 : subst] : ((((X472 @ X477 @ X475 @ (comp @ X476 @ X474))) = $true) & (((X472 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476) @ X474)) != $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f21,definition,(
% 37.84/5.79 (sP5 = $true) <=> ! [X526 : (subst > term > subst > $o),X525 : term] : (? [X527 : (subst > term > term)] : (! [X531 : term] : ((((X526 @ id @ X531 @ id)) != $true) | (((X526 @ id @ (X527 @ id @ X531) @ id)) = $true)) & ! [X530 : subst,X529 : subst,X528 : term] : (((X527 @ (comp @ X529 @ X530) @ (sub @ X528 @ X530))) = ((sub @ (X527 @ X529 @ X528) @ X530))) & (((X526 @ id @ (lam @ (X527 @ sh @ one)) @ id)) != $true)) | ? [X532 : term] : ((((X526 @ id @ X532 @ id)) = $true) & (((X526 @ id @ (sub @ X525 @ (push @ X532 @ id)) @ id)) != $true)) | (((X526 @ id @ (lam @ X525) @ id)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f22,definition,(
% 37.84/5.79 (sP6 = $true) <=> (? [X258 : term] : ! [X259 : (subst > term > term)] : ? [X261 : subst,X260 : term] : (((sub @ X258 @ (push @ X260 @ X261))) != ((X259 @ X261 @ X260))) | ? [X262 : term] : (((sub @ X262 @ id)) != X262) | ! [X263 : term,X264 : (term > $o),X265 : (subst > term > subst > $o)] : (? [X267 : (subst > term > term)] : ((((X265 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true) & ! [X269 : subst,X270 : term,X271 : subst] : (((sub @ (X267 @ X271 @ X270) @ X269)) = ((X267 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269)))) & ! [X268 : term] : ((((X265 @ id @ (X267 @ id @ X268) @ id)) = $true) | (((X265 @ id @ X268 @ id)) != $true))) | ? [X266 : term] : ((((X264 @ (sub @ X263 @ (push @ X266 @ id)))) != $true) & (((X264 @ X266)) = $true)) | (((X264 @ (lam @ X263))) = $true) | ? [X272 : term] : (((X265 @ id @ X272 @ id)) != ((X264 @ X272)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f23,definition,(
% 37.84/5.79 ! [X350 : (subst > term > subst > $o)] : ((((sP7 @ X350)) = $true) <=> ? [X366 : term,X365 : term] : ((((X350 @ id @ (ap @ (sub @ X365 @ id) @ X366) @ id)) != $true) & (((X350 @ id @ X365 @ id)) = $true) & (((X350 @ id @ X366 @ id)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f24,definition,(
% 37.84/5.79 ! [X350 : (subst > term > subst > $o)] : ((((sP8 @ X350)) = $true) <=> ? [X351 : (subst > term > term)] : (! [X352 : term] : ((((X350 @ id @ X352 @ id)) != $true) | (((X350 @ id @ (X351 @ id @ X352) @ id)) = $true)) & (((X350 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : subst,X353 : subst,X354 : term] : (((X351 @ (comp @ X353 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X351 @ X353 @ X354) @ X355)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f25,definition,(
% 37.84/5.79 (sP9 = $true) <=> ! [X350 : (subst > term > subst > $o),X349 : term] : (? [X364 : term,X363 : subst,X362 : subst,X361 : subst] : ((((X350 @ X362 @ X364 @ (comp @ X363 @ X361))) != $true) & (((X350 @ (comp @ X362 @ X363) @ (sub @ X364 @ X363) @ X361)) = $true)) | (((sP8 @ X350)) = $true) | (((X350 @ id @ X349 @ id)) = $true) | ? [X360 : term] : ((((X350 @ id @ X360 @ id)) != $true) & (((var @ (sub @ X360 @ id))) = $true)) | ? [X359 : subst,X358 : term,X357 : subst,X356 : subst] : ((((X350 @ X357 @ X358 @ (comp @ X359 @ X356))) = $true) & (((X350 @ (comp @ X357 @ X359) @ (sub @ X358 @ X359) @ X356)) != $true)) | (((sP7 @ X350)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f26,definition,(
% 37.84/5.79 ! [X3 : (term > $o)] : ((((sP10 @ X3)) = $true) <=> ! [X8 : term,X9 : term] : ((((X3 @ X8)) != $true) | (((X3 @ (ap @ X8 @ X9))) = $true) | (((X3 @ X9)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f27,definition,(
% 37.84/5.79 ! [X21 : (subst > term > subst > $o)] : ((((sP11 @ X21)) = $true) <=> ? [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f28,definition,(
% 37.84/5.79 (sP12 = $true) <=> ? [X12 : (term > $o),X13 : (subst > term > subst > $o),X11 : term] : (! [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) != ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | ? [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) != $true) & (((X13 @ id @ X15 @ id)) = $true))) & ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) & (((X12 @ (lam @ X11))) != $true) & ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | (((X12 @ X20)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f29,definition,(
% 37.84/5.79 (sP13 = $true) <=> ? [X3 : (term > $o),X4 : term] : (! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & (((sP10 @ X3)) = $true) & ! [X5 : term] : ((((var @ X5)) != $true) | (((X3 @ X5)) = $true)) & (((X3 @ X4)) != $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f30,definition,(
% 37.84/5.79 (sP14 = $true) <=> (! [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | (((sP11 @ X21)) = $true)) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | (sP12 = $true) | (sP13 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f31,definition,(
% 37.84/5.79 (sP15 = $true) <=> ! [X274 : term,X273 : (subst > term > subst > $o)] : (? [X284 : term] : ((((X273 @ id @ X284 @ id)) = $true) & (((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)) != $true)) | (((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id)) = $true) | ? [X275 : (subst > term > term),X276 : term] : (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sub @ X276 @ (push @ X279 @ X277)) @ X278)) = ((sub @ (X275 @ X277 @ X279) @ X278))) & (((X273 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true) & ! [X280 : term] : ((((X273 @ id @ X280 @ id)) != $true) | (((X273 @ id @ (X275 @ id @ X280) @ id)) = $true)) & ! [X283 : term,X282 : subst,X281 : subst] : (((sub @ X276 @ (push @ (sub @ X283 @ X281) @ (comp @ X282 @ X281)))) = ((X275 @ (comp @ X282 @ X281) @ (sub @ X283 @ X281))))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f32,definition,(
% 37.84/5.79 ! [X75 : (subst > term > subst > $o)] : ((((sP16 @ X75)) = $true) <=> ? [X88 : (subst > term > term)] : (! [X92 : term] : ((((X75 @ id @ X92 @ id)) != $true) | (((X75 @ id @ (X88 @ id @ X92) @ id)) = $true)) & (((X75 @ id @ (lam @ (X88 @ sh @ one)) @ id)) != $true) & ! [X89 : term,X90 : subst,X91 : subst] : (((X88 @ (comp @ X90 @ X91) @ (sub @ X89 @ X91))) = ((sub @ (X88 @ X90 @ X89) @ X91)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f33,definition,(
% 37.84/5.79 (sP17 = $true) <=> ! [X75 : (subst > term > subst > $o),X77 : (term > $o),X76 : term] : (? [X85 : subst,X84 : subst,X86 : subst,X87 : term] : ((((X75 @ (comp @ X86 @ X84) @ (sub @ X87 @ X84) @ X85)) = $true) & (((X75 @ X86 @ X87 @ (comp @ X84 @ X85))) != $true)) | (((X77 @ (lam @ X76))) = $true) | (((sP16 @ X75)) = $true) | ? [X83 : term] : (((X75 @ id @ X83 @ id)) != ((X77 @ X83))) | ? [X81 : subst,X79 : term,X82 : subst,X80 : subst] : ((((X75 @ X80 @ X79 @ (comp @ X81 @ X82))) = $true) & (((X75 @ (comp @ X80 @ X81) @ (sub @ X79 @ X81) @ X82)) != $true)) | ? [X78 : term] : ((((X77 @ X78)) = $true) & (((X77 @ (sub @ X76 @ (push @ X78 @ id)))) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f34,definition,(
% 37.84/5.79 ! [X302 : (term > $o)] : ((((sP18 @ X302)) = $true) <=> ! [X307 : term,X308 : term] : ((((X302 @ X307)) != $true) | (((X302 @ (ap @ X308 @ X307))) = $true) | (((X302 @ X308)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f35,definition,(
% 37.84/5.79 ! [X310 : (term > $o)] : ((((sP19 @ X310)) = $true) <=> ? [X314 : term,X315 : term] : ((((X310 @ X314)) = $true) & (((X310 @ X315)) = $true) & (((X310 @ (ap @ X314 @ X315))) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f36,definition,(
% 37.84/5.79 (sP20 = $true) <=> ! [X309 : term,X310 : (term > $o)] : (? [X313 : term] : (($true = ((var @ X313))) & (((X310 @ X313)) != $true)) | ? [X311 : term] : (! [X312 : term] : ((((X310 @ X312)) != $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) & (((X310 @ (lam @ X311))) != $true)) | (((sP19 @ X310)) = $true) | (((X310 @ X309)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f37,definition,(
% 37.84/5.79 (sP21 = $true) <=> ((sP20 = $true) | ? [X300 : term] : (((sub @ X300 @ id)) != X300) | ? [X303 : subst,X301 : term,X302 : (term > $o)] : (! [X304 : term] : (? [X305 : term] : ((((X302 @ X305)) = $true) & (((X302 @ (sub @ X304 @ (push @ X305 @ id)))) != $true)) | (((X302 @ (lam @ X304))) = $true)) & ! [X306 : term] : ((((var @ X306)) != $true) | (((X302 @ (sub @ X306 @ X303))) = $true)) & (((sP18 @ X302)) = $true) & (((X302 @ (sub @ X301 @ X303))) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f38,definition,(
% 37.84/5.79 ! [X402 : (term > $o)] : ((((sP22 @ X402)) = $true) <=> ? [X403 : term,X404 : term] : ((((X402 @ X403)) = $true) & (((X402 @ X404)) = $true) & (((X402 @ (ap @ X403 @ X404))) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f39,definition,(
% 37.84/5.79 (sP23 = $true) <=> ! [X221 : term,X220 : (subst > term > subst > $o)] : (? [X223 : (subst > term > term)] : (($true != ((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id))) & ! [X224 : term] : ((((X220 @ id @ (X223 @ id @ X224) @ id)) = $true) | (((X220 @ id @ X224 @ id)) != $true)) & ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X226 @ X225) @ (sub @ X227 @ X225))) = ((sub @ (X223 @ X226 @ X227) @ X225)))) | (((X220 @ id @ (lam @ (sub @ X221 @ (push @ one @ sh))) @ id)) = $true) | ? [X222 : term] : (($true = ((X220 @ id @ X222 @ id))) & (((X220 @ id @ (sub @ X221 @ (push @ X222 @ id)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f40,definition,(
% 37.84/5.79 ! [X129 : (subst > term > subst > $o)] : ((((sP24 @ X129)) = $true) <=> ? [X141 : term,X140 : term] : ((((X129 @ id @ (ap @ (sub @ X140 @ id) @ X141) @ id)) != $true) & (((X129 @ id @ X140 @ id)) = $true) & (((X129 @ id @ X141 @ id)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f41,definition,(
% 37.84/5.79 ! [X129 : (subst > term > subst > $o)] : ((((sP25 @ X129)) = $true) <=> ? [X142 : (subst > term > term)] : (! [X144 : subst,X146 : term,X145 : subst] : (((X142 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))) = ((sub @ (X142 @ X145 @ X146) @ X144))) & ! [X143 : term] : ((((X129 @ id @ X143 @ id)) != $true) | (((X129 @ id @ (X142 @ id @ X143) @ id)) = $true)) & (((X129 @ id @ (lam @ (X142 @ sh @ one)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f42,definition,(
% 37.84/5.79 ! [X102 : (subst > term > subst > $o)] : ((((sP26 @ X102)) = $true) <=> ! [X107 : term,X108 : term] : ((((X102 @ id @ (ap @ (sub @ X108 @ id) @ X107) @ id)) = $true) | (((X102 @ id @ X108 @ id)) != $true) | (((X102 @ id @ X107 @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f43,definition,(
% 37.84/5.79 ! [X93 : (term > $o)] : ((((sP27 @ X93)) = $true) <=> ! [X96 : term,X97 : term] : ((((X93 @ X96)) != $true) | (((X93 @ (ap @ X97 @ X96))) = $true) | (((X93 @ X97)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f44,definition,(
% 37.84/5.79 ! [X113 : (subst > term > subst > $o)] : ((((sP28 @ X113)) = $true) <=> ! [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ? [X116 : term] : ((((X113 @ id @ (X115 @ id @ X116) @ id)) != $true) & (((X113 @ id @ X116 @ id)) = $true)) | ? [X117 : term,X119 : subst,X118 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) != ((sub @ (X115 @ X119 @ X117) @ X118)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f45,definition,(
% 37.84/5.79 (sP29 = $true) <=> ? [X113 : (subst > term > subst > $o),X114 : term] : (! [X125 : subst,X127 : term,X128 : subst,X126 : subst] : ((((X113 @ (comp @ X125 @ X126) @ (sub @ X127 @ X126) @ X128)) = $true) | ($true != ((X113 @ X125 @ X127 @ (comp @ X126 @ X128))))) & ! [X124 : term,X122 : subst,X121 : subst,X123 : subst] : ((((X113 @ (comp @ X121 @ X123) @ (sub @ X124 @ X123) @ X122)) != $true) | (((X113 @ X121 @ X124 @ (comp @ X123 @ X122))) = $true)) & (((sP28 @ X113)) = $true) & ! [X120 : term] : ((((X113 @ id @ X120 @ id)) != $true) | (((X113 @ id @ (sub @ X114 @ (push @ X120 @ id)) @ id)) = $true)) & (((X113 @ id @ (lam @ X114) @ id)) != $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f46,definition,(
% 37.84/5.79 (sP30 = $true) <=> ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X135 : subst,X136 : subst,X137 : subst,X138 : term] : ((((X129 @ (comp @ X135 @ X136) @ (sub @ X138 @ X136) @ X137)) = $true) & (((X129 @ X135 @ X138 @ (comp @ X136 @ X137))) != $true)) | ? [X133 : term,X131 : subst,X134 : subst,X132 : subst] : ((((X129 @ (comp @ X132 @ X131) @ (sub @ X133 @ X131) @ X134)) != $true) & (((X129 @ X132 @ X133 @ (comp @ X131 @ X134))) = $true)) | (((sP25 @ X129)) = $true) | ? [X139 : term] : ((((var @ (sub @ X139 @ id))) = $true) & (((X129 @ id @ X139 @ id)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | (((sP24 @ X129)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f47,definition,(
% 37.84/5.79 (sP31 = $true) <=> ? [X100 : term,X101 : term,X102 : (subst > term > subst > $o)] : ((((X102 @ id @ X101 @ id)) = $true) & (((X102 @ id @ X100 @ id)) = $true) & (((X102 @ id @ (ap @ X100 @ X101) @ id)) != $true) & ! [X104 : term,X106 : subst,X103 : subst,X105 : subst] : ((((X102 @ X105 @ X104 @ (comp @ X103 @ X106))) != $true) | (((X102 @ (comp @ X105 @ X103) @ (sub @ X104 @ X103) @ X106)) = $true)) & (((sP26 @ X102)) = $true) & ! [X112 : subst,X111 : subst,X109 : subst,X110 : term] : ((((X102 @ X111 @ X110 @ (comp @ X109 @ X112))) = $true) | (((X102 @ (comp @ X111 @ X109) @ (sub @ X110 @ X109) @ X112)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f48,definition,(
% 37.84/5.79 (sP32 = $true) <=> ((sP29 = $true) | ? [X94 : term,X93 : (term > $o)] : (! [X95 : term] : ((((var @ X95)) != $true) | (((X93 @ X95)) = $true)) & (((sP27 @ X93)) = $true) & ! [X98 : term] : (($true = ((X93 @ (lam @ X98)))) | ? [X99 : term] : ((((X93 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & (((X93 @ X99)) = $true))) & (((X93 @ X94)) != $true)) | (sP31 = $true) | (sP30 = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f49,definition,(
% 37.84/5.79 ! [X238 : (subst > term > subst > $o)] : ((((sP33 @ X238)) = $true) <=> ? [X244 : (subst > term > term)] : (! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) & ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | (((X238 @ id @ X248 @ id)) != $true)) & (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f50,definition,(
% 37.84/5.79 (sP34 = $true) <=> ! [X237 : term,X238 : (subst > term > subst > $o)] : ((((sP33 @ X238)) = $true) | ? [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) != $true) & (((X238 @ id @ X239 @ id)) = $true)) | ? [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) = $true) & (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) != $true)) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ? [X249 : subst,X250 : term,X252 : subst,X251 : subst] : ((((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) & (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f51,definition,(
% 37.84/5.79 ! [X519 : (term > $o)] : ((((sP35 @ X519)) = $true) <=> ? [X523 : term,X522 : term] : ((((X519 @ (ap @ X522 @ X523))) != $true) & (((X519 @ X523)) = $true) & (((X519 @ X522)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f52,definition,(
% 37.84/5.79 (sP36 = $true) <=> ! [X518 : term,X519 : (term > $o)] : (? [X520 : term] : ((((X519 @ (lam @ X520))) != $true) & ! [X521 : term] : ((((X519 @ X521)) != $true) | (((X519 @ (sub @ X520 @ (push @ X521 @ id)))) = $true))) | (((X519 @ X518)) = $true) | (((sP35 @ X519)) = $true) | ? [X524 : term] : ((((X519 @ X524)) != $true) & (((var @ X524)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f53,definition,(
% 37.84/5.79 ! [X370 : (subst > term > subst > $o)] : ((((sP37 @ X370)) = $true) <=> ? [X381 : (subst > term > term)] : (! [X382 : term] : ((((X370 @ id @ X382 @ id)) != $true) | (((X370 @ id @ (X381 @ id @ X382) @ id)) = $true)) & ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X381 @ X383 @ X384) @ X385)) = ((X381 @ (comp @ X383 @ X385) @ (sub @ X384 @ X385)))) & ($true != ((X370 @ id @ (lam @ (X381 @ sh @ one)) @ id)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f54,definition,(
% 37.84/5.79 (sP38 = $true) <=> (? [X367 : term] : (((sub @ X367 @ id)) != X367) | ! [X369 : (term > $o),X368 : term,X370 : (subst > term > subst > $o)] : (? [X371 : term] : ((((X369 @ (sub @ X368 @ (push @ X371 @ id)))) != $true) & (((X369 @ X371)) = $true)) | ? [X373 : subst,X372 : subst,X375 : term,X374 : subst] : ((((X370 @ (comp @ X374 @ X373) @ (sub @ X375 @ X373) @ X372)) != $true) & ($true = ((X370 @ X374 @ X375 @ (comp @ X373 @ X372))))) | (((sP37 @ X370)) = $true) | ? [X380 : term] : (((X369 @ X380)) != ((X370 @ id @ X380 @ id))) | (((X369 @ (lam @ X368))) = $true) | ? [X377 : subst,X379 : subst,X376 : term,X378 : subst] : ((((X370 @ (comp @ X379 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true) & (((X370 @ X379 @ X376 @ (comp @ X378 @ X377))) != $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f55,definition,(
% 37.84/5.79 ! [X193 : (term > $o)] : ((((sP39 @ X193)) = $true) <=> ? [X199 : term,X198 : term] : ((((X193 @ X198)) = $true) & (((X193 @ (ap @ X198 @ X199))) != $true) & (((X193 @ X199)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f56,definition,(
% 37.84/5.79 (sP40 = $true) <=> ! [X195 : subst,X193 : (term > $o),X194 : term] : ((((sP39 @ X193)) = $true) | ? [X196 : term] : ((((X193 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X193 @ X197)) != $true) | (((X193 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | ? [X200 : term] : ((((X193 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | (((X193 @ (sub @ X194 @ X195))) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f57,definition,(
% 37.84/5.79 ! [X409 : (subst > term > subst > $o)] : ((((sP41 @ X409)) = $true) <=> ? [X411 : term,X410 : term] : ((((X409 @ id @ X411 @ id)) = $true) & (((X409 @ id @ X410 @ id)) = $true) & (((X409 @ id @ (ap @ (sub @ X411 @ id) @ X410) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f58,definition,(
% 37.84/5.79 (sP42 = $true) <=> ! [X408 : term,X407 : term,X409 : (subst > term > subst > $o)] : ((((X409 @ id @ (ap @ X407 @ X408) @ id)) = $true) | (((sP41 @ X409)) = $true) | (((X409 @ id @ X408 @ id)) != $true) | ? [X417 : term,X419 : subst,X418 : subst,X416 : subst] : ((((X409 @ X416 @ X417 @ (comp @ X419 @ X418))) = $true) & ($true != ((X409 @ (comp @ X416 @ X419) @ (sub @ X417 @ X419) @ X418)))) | ? [X412 : subst,X414 : subst,X413 : subst,X415 : term] : ((((X409 @ X412 @ X415 @ (comp @ X414 @ X413))) != $true) & (((X409 @ (comp @ X412 @ X414) @ (sub @ X415 @ X414) @ X413)) = $true)) | (((X409 @ id @ X407 @ id)) != $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f59,definition,(
% 37.84/5.79 (sP43 = $true) <=> ! [X202 : (subst > term > subst > $o),X203 : term,X204 : (term > $o)] : (? [X211 : term] : (((X204 @ X211)) != ((X202 @ id @ X211 @ id))) | ? [X210 : term] : (($true = ((X204 @ X210))) & (((X204 @ (sub @ X203 @ (push @ X210 @ id)))) != $true)) | ($true = ((X204 @ (lam @ X203)))) | ? [X205 : (subst > term > term)] : (! [X208 : subst,X206 : term,X207 : subst] : (((sub @ (X205 @ X208 @ X206) @ X207)) = ((X205 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207)))) & (((X202 @ id @ (lam @ (X205 @ sh @ one)) @ id)) != $true) & ! [X209 : term] : ((((X202 @ id @ X209 @ id)) != $true) | (((X202 @ id @ (X205 @ id @ X209) @ id)) = $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f60,definition,(
% 37.84/5.79 (sP44 = $true) <=> (! [X506 : subst,X503 : (subst > term > term),X505 : term,X504 : (subst > term > term)] : ((((X504 @ X506 @ X505)) = ((X503 @ X506 @ X505))) | (((lam @ (X504 @ sh @ one))) != ((lam @ (X503 @ sh @ one)))) | ? [X511 : subst,X510 : subst,X512 : term] : (((X503 @ (comp @ X511 @ X510) @ (sub @ X512 @ X510))) != ((sub @ (X503 @ X511 @ X512) @ X510))) | ? [X509 : term,X508 : subst,X507 : subst] : (((X504 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) != ((sub @ (X504 @ X508 @ X509) @ X507)))) | ? [X497 : term,X498 : subst] : (((sub @ one @ (push @ X497 @ X498))) != X497) | ? [X501 : term,X502 : term] : ((X501 != X502) & (((lam @ X502)) = ((lam @ X501)))) | ? [X499 : term,X500 : subst] : (((comp @ sh @ (push @ X499 @ X500))) != X500))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f61,definition,(
% 37.84/5.79 (sP45 = $true) <=> ? [X421 : (subst > term > subst > $o),X422 : term] : ((((X421 @ id @ (lam @ (sub @ X422 @ (push @ one @ sh))) @ id)) != $true) & ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X426 : subst,X427 : term,X425 : subst] : (((sub @ (X424 @ X425 @ X427) @ X426)) != ((X424 @ (comp @ X425 @ X426) @ (sub @ X427 @ X426)))) | ? [X428 : term] : ((((X421 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X421 @ id @ X428 @ id)) = $true))) & ! [X423 : term] : ((((X421 @ id @ X423 @ id)) != $true) | (((X421 @ id @ (sub @ X422 @ (push @ X423 @ id)) @ id)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f62,definition,(
% 37.84/5.79 (sP46 = $true) <=> ((sP45 = $true) | ! [X430 : (subst > term > subst > $o),X429 : term] : (? [X431 : term] : ((((X430 @ id @ X431 @ id)) = $true) & (((X430 @ id @ (sub @ X429 @ (push @ X431 @ id)) @ id)) != $true)) | (((X430 @ id @ (lam @ X429) @ id)) = $true) | ? [X432 : (subst > term > term)] : (! [X434 : term,X435 : subst,X433 : subst] : (((sub @ (X432 @ X435 @ X434) @ X433)) = ((X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433)))) & (((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id)) != $true) & ! [X436 : term] : ((((X430 @ id @ (X432 @ id @ X436) @ id)) = $true) | (((X430 @ id @ X436 @ id)) != $true)))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f63,definition,(
% 37.84/5.79 ! [X157 : (term > $o)] : ((((sP47 @ X157)) = $true) <=> ! [X163 : term,X162 : term] : ((((X157 @ X162)) != $true) | (((X157 @ X163)) != $true) | (((X157 @ (ap @ X162 @ X163))) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f64,definition,(
% 37.84/5.79 ! [X175 : (subst > term > subst > $o)] : ((((sP48 @ X175)) = $true) <=> ? [X177 : (subst > term > term)] : (! [X179 : subst,X178 : subst,X180 : term] : (((X177 @ (comp @ X178 @ X179) @ (sub @ X180 @ X179))) = ((sub @ (X177 @ X178 @ X180) @ X179))) & ! [X181 : term] : ((((X175 @ id @ (X177 @ id @ X181) @ id)) = $true) | (((X175 @ id @ X181 @ id)) != $true)) & (((X175 @ id @ (lam @ (X177 @ sh @ one)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f65,definition,(
% 37.84/5.79 ! [X175 : (subst > term > subst > $o)] : ((((sP49 @ X175)) = $true) <=> ? [X188 : term,X187 : term] : ((((X175 @ id @ X187 @ id)) = $true) & (((X175 @ id @ X188 @ id)) = $true) & (((X175 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f66,definition,(
% 37.84/5.79 (sP50 = $true) <=> ! [X176 : term,X175 : (subst > term > subst > $o)] : ((((sP49 @ X175)) = $true) | (((X175 @ id @ X176 @ id)) = $true) | ? [X190 : subst,X192 : subst,X191 : subst,X189 : term] : ((((X175 @ X190 @ X189 @ (comp @ X191 @ X192))) = $true) & (((X175 @ (comp @ X190 @ X191) @ (sub @ X189 @ X191) @ X192)) != $true)) | ? [X182 : term] : ((((var @ (sub @ X182 @ id))) = $true) & (((X175 @ id @ X182 @ id)) != $true)) | ? [X185 : subst,X184 : subst,X183 : subst,X186 : term] : (($true = ((X175 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185) @ X183))) & (((X175 @ X184 @ X186 @ (comp @ X185 @ X183))) != $true)) | (((sP48 @ X175)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f67,definition,(
% 37.84/5.79 (sP51 = $true) <=> ? [X167 : term,X166 : (term > $o),X165 : (subst > term > subst > $o)] : (! [X174 : term] : (((X165 @ id @ X174 @ id)) = ((X166 @ X174))) & ! [X168 : term] : (($true = ((X166 @ (sub @ X167 @ (push @ X168 @ id))))) | (((X166 @ X168)) != $true)) & (((X166 @ (lam @ X167))) != $true) & ! [X169 : (subst > term > term)] : (? [X170 : term] : ((((X165 @ id @ (X169 @ id @ X170) @ id)) != $true) & (((X165 @ id @ X170 @ id)) = $true)) | (((X165 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f68,definition,(
% 37.84/5.79 (sP52 = $true) <=> (? [X154 : (subst > term > subst > $o)] : ! [X155 : (term > $o)] : ? [X156 : term] : (((X154 @ id @ X156 @ id)) != ((X155 @ X156))) | (sP51 = $true) | (sP50 = $true) | ? [X164 : term] : (((sub @ X164 @ id)) != X164) | ? [X157 : (term > $o),X158 : term] : (! [X160 : term] : (? [X161 : term] : ((((X157 @ (sub @ X160 @ (push @ X161 @ id)))) != $true) & (((X157 @ X161)) = $true)) | (((X157 @ (lam @ X160))) = $true)) & (((sP47 @ X157)) = $true) & (((X157 @ X158)) != $true) & ! [X159 : term] : ((((var @ X159)) != $true) | (((X157 @ X159)) = $true))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f69,definition,(
% 37.84/5.79 ! [X287 : (subst > term > subst > $o)] : ((((sP53 @ X287)) = $true) <=> ? [X289 : term,X290 : term] : ((((X287 @ id @ X289 @ id)) = $true) & (((X287 @ id @ X290 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f70,definition,(
% 37.84/5.79 (sP54 = $true) <=> ! [X288 : (term > $o),X287 : (subst > term > subst > $o),X285 : term,X286 : term] : ((((X288 @ (ap @ X286 @ X285))) = $true) | ? [X297 : subst,X296 : term,X298 : subst,X299 : subst] : (($true != ((X287 @ (comp @ X297 @ X298) @ (sub @ X296 @ X298) @ X299))) & (((X287 @ X297 @ X296 @ (comp @ X298 @ X299))) = $true)) | ? [X293 : subst,X294 : term,X295 : subst,X292 : subst] : ((((X287 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X295)) = $true) & (((X287 @ X293 @ X294 @ (comp @ X292 @ X295))) != $true)) | ? [X291 : term] : (((X287 @ id @ X291 @ id)) != ((X288 @ X291))) | (((X288 @ X286)) != $true) | (((X288 @ X285)) != $true) | (((sP53 @ X287)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f71,definition,(
% 37.84/5.79 ! [X325 : (term > $o)] : ((((sP55 @ X325)) = $true) <=> ! [X329 : term,X330 : term] : ((((X325 @ X329)) != $true) | (((X325 @ (ap @ X330 @ X329))) = $true) | (((X325 @ X330)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f72,definition,(
% 37.84/5.79 ! [X331 : (term > $o)] : ((((sP56 @ X331)) = $true) <=> ? [X337 : term,X338 : term] : ((((X331 @ (ap @ X337 @ X338))) != $true) & (((X331 @ X337)) = $true) & (((X331 @ X338)) = $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f73,definition,(
% 37.84/5.79 (sP57 = $true) <=> ! [X331 : (term > $o),X333 : subst,X332 : term] : (? [X334 : term] : ((((var @ X334)) = $true) & (((X331 @ (sub @ X334 @ X333))) != $true)) | ? [X335 : term] : ((((X331 @ (lam @ X335))) != $true) & ! [X336 : term] : (($true = ((X331 @ (sub @ X335 @ (push @ X336 @ id))))) | ($true != ((X331 @ X336))))) | (((X331 @ (sub @ X332 @ X333))) = $true) | (((sP56 @ X331)) = $true))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f74,definition,(
% 37.84/5.79 (sP58 = $true) <=> ((sP57 = $true) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324) | ? [X325 : (term > $o),X326 : term] : (! [X328 : term] : ((((X325 @ X328)) != $true) | (((X325 @ (lam @ X328))) = $true)) & ! [X327 : term] : ((((X325 @ X327)) = $true) | ($true != ((var @ X327)))) & (((X325 @ X326)) != $true) & (((sP55 @ X325)) = $true)) | ? [X322 : subst,X323 : term] : (((comp @ sh @ (push @ X323 @ X322))) != X322) | ? [X320 : subst,X321 : term] : (((sub @ one @ (push @ X321 @ X320))) != X321))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f75,definition,(
% 37.84/5.79 (sP59 = $true) <=> ! [X393 : term,X394 : (subst > term > subst > $o)] : ((((X394 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true) | ? [X395 : term] : ((((X394 @ id @ (sub @ X393 @ (push @ X395 @ id)) @ id)) != $true) & (((X394 @ id @ X395 @ id)) = $true)) | ? [X396 : (subst > term > term)] : (! [X397 : term] : ((((X394 @ id @ (X396 @ id @ X397) @ id)) = $true) | (((X394 @ id @ X397 @ id)) != $true)) & (((X394 @ id @ (lam @ (X396 @ sh @ one)) @ id)) != $true) & ! [X398 : subst,X399 : term,X400 : subst] : (((X396 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X396 @ X398 @ X399) @ X400)))))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f76,definition,(
% 37.84/5.79 ! [X444 : (subst > term > subst > $o)] : (($true = ((sP60 @ X444))) <=> ? [X448 : (subst > term > term)] : (! [X452 : term] : ((((X444 @ id @ (X448 @ id @ X452) @ id)) = $true) | (((X444 @ id @ X452 @ id)) != $true)) & ! [X450 : term,X449 : subst,X451 : subst] : (((sub @ (X448 @ X451 @ X450) @ X449)) = ((X448 @ (comp @ X451 @ X449) @ (sub @ X450 @ X449)))) & (((X444 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)))),
% 37.84/5.79 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 37.84/5.79 thf(f77,plain,(
% 37.84/5.79 ((apinj2 = $true) <=> ! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348))) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ((laminj = $true) <=> ! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X444 : (subst > term > subst > $o),X445 : term] : (? [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) = $true) & (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) != $true) & (((X444 @ id @ X446 @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true) | ($true = ((sP60 @ X444))))) & ((sP59 = $true) <=> (hoasinduction_lem3aa = $true)) & ((axshiftcons = $true) <=> ! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318)) & ((induction2lem_lthm = $true) <=> (sP58 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ? [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) != ((X39 @ X42))) | (((X38 @ X41)) != $true))) & ((apinj1 = $true) <=> ! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219))) & ((sP54 = $true) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) <=> (axvarcons = $true)) & ((sP52 = $true) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP46 = $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X229 : d_subst,X228 : d_subst] : ((X228 = X229) | (((d2subst @ X228)) != ((d2subst @ X229)))) & (! [X255 : (term > $o),X253 : term,X254 : subst] : ? [X256 : (term > $o)] : ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) <=> (pushprop_lem0 = $true)) & (pushprop_lem2v2_lthm = $true) & (! [X149 : term,X148 : term,X147 : (subst > term > term)] : (? [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) != ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149)))) <=> (hoaslamnotap = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & ((! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))) | ? [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) = ((ap @ X457 @ X456))) & (X455 != X456))) <=> (hoasapinj2_lthm = $true)) & ((sP44 = $true) <=> (hoaslaminj_lthm = $true)) & (((d2subst @ d_id)) = id) & (! [X340 : (subst > term > subst > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & ((sP43 = $true) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj2 = $true) <=> ! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214))))) & ((sP42 = $true) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) <=> (axvarid = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) <=> (substmonoid = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X43 : (subst > term > subst > $o)] : ? [X44 : (term > $o)] : ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) <=> ((! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49)) | ? [X47 : subst] : (((comp @ X47 @ id)) != X47) | ? [X46 : subst] : (((comp @ id @ X46)) != X46))) & ((induction2lem = $true) <=> (sP40 = $true)) & (! [X388 : term] : ? [X389 : (subst > term > term)] : ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) <=> (hoasinduction_lem3v2_f = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP38 = $true)) & ((sP36 = $true) <=> (induction2 = $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) <=> (sP34 = $true)) & ((sP32 = $true) <=> (hoasinduction_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & ((sP23 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) <=> (axidr = $true)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) = $true) | ? [X406 : term] : ((((X402 @ X406)) = $true) & (((X402 @ (lam @ X406))) != $true)) | (((sP22 @ X402)) = $true) | ? [X405 : term] : ((((X402 @ X405)) != $true) & (((var @ X405)) = $true))) <=> (induction = $true)) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X437 : d_subst] : (d_id = X437) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & ((pushprop_lem1 = $true) <=> ! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true))) & ((sP21 = $true) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & ((! [X441 : term] : (((sub @ X441 @ id)) = X441) | ? [X440 : term] : (((sub @ X440 @ id)) != X440)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> (sP17 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) != $true) | ? [X236 : term] : (((X232 @ X236)) != ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true)) | ? [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) != X230))) & ((sP15 = $true) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((termmset = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (ulamvarsh = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X534 : (term > $o),X533 : subst,X535 : term] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537)))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((X539 @ sh @ one)) = ((sub @ X538 @ (push @ one @ sh))))) & (hoaslamnotap_gthm = $true) & ((sP14 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X36 : term] : ? [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) = ((X37 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (lamnotvar = $true) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) != ((d2term @ X439))) | (X438 = X439)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) <=> (axscons = $true)) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))) | ? [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) = ((ap @ X489 @ X492))) & (X489 != X490)) | ? [X488 : term] : (((sub @ X488 @ id)) != X488))) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & ((hoaslaminj = $true) <=> ! [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (? [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) != ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | ? [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) != ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | (((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one)))))) & ((hoasinduction = $true) <=> (sP9 = $true)) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & ((? [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) != X62) | ? [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) != X65) | ! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (sP6 = $true)) & ((hoasinduction_lem3a = $true) <=> (sP5 = $true)) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) <=> (hoasapinj1 = $true)) & ((axidl = $true) <=> ! [X316 : subst] : (((comp @ id @ X316)) = X316)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X30 : term] : ? [X31 : (subst > term > term)] : ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33))))) & ((hoasinduction_lem3_lthm = $true) <=> (sP4 = $true)) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) <=> (shinj = $true)) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.79 inference(definition_folding,[],[f14,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18])).
% 37.84/5.79 thf(f78,plain,(
% 37.84/5.79 ((sP1 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X6 : subst,X8 : subst,X5 : term,X7 : subst] : ((((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) = $true) | (((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) != $true)) & ? [X14 : term] : (! [X15 : term] : ((((X0 @ id @ X15 @ id)) != $true) | (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) = $true)) & (((X0 @ id @ (lam @ X14) @ id)) != $true)) & (((sP0 @ X0)) != $true) & ! [X1 : subst,X4 : term,X2 : subst,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) != $true) | (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) = $true)))) & (! [X0 : (subst > term > subst > $o)] : (? [X6 : subst,X8 : subst,X5 : term,X7 : subst] : ((((X0 @ X7 @ X5 @ (comp @ X8 @ X6))) != $true) & (((X0 @ (comp @ X7 @ X8) @ (sub @ X5 @ X8) @ X6)) = $true)) | ! [X14 : term] : (? [X15 : term] : ((((X0 @ id @ X15 @ id)) = $true) & (((X0 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id)) != $true)) | (((X0 @ id @ (lam @ X14) @ id)) = $true)) | (((sP0 @ X0)) = $true) | ? [X1 : subst,X4 : term,X2 : subst,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) != $true))) | (sP1 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f16])).
% 37.84/5.79 thf(f79,plain,(
% 37.84/5.79 ((sP1 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : term,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) | (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)) & ? [X5 : term] : (! [X6 : term] : ((((X0 @ id @ X6 @ id)) != $true) | (((X0 @ id @ (sub @ X5 @ (push @ X6 @ id)) @ id)) = $true)) & (((X0 @ id @ (lam @ X5) @ id)) != $true)) & (((sP0 @ X0)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((X0 @ X10 @ X8 @ (comp @ X9 @ X7))) != $true) | (((X0 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9) @ X7)) = $true)))) & (! [X11 : (subst > term > subst > $o)] : (? [X12 : subst,X13 : subst,X14 : term,X15 : subst] : ((((X11 @ X15 @ X14 @ (comp @ X13 @ X12))) != $true) & (((X11 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13) @ X12)) = $true)) | ! [X16 : term] : (? [X17 : term] : ((((X11 @ id @ X17 @ id)) = $true) & (((X11 @ id @ (sub @ X16 @ (push @ X17 @ id)) @ id)) != $true)) | ($true = ((X11 @ id @ (lam @ X16) @ id)))) | (((sP0 @ X11)) = $true) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : ((((X11 @ X21 @ X19 @ (comp @ X20 @ X18))) = $true) & (((X11 @ (comp @ X21 @ X20) @ (sub @ X19 @ X20) @ X18)) != $true))) | (sP1 != $true))),
% 37.84/5.79 inference(rectify,[],[f78])).
% 37.84/5.79 thf(f80,plain,(
% 37.84/5.79 ((sP1 = $true) | (! [X1 : subst,X2 : subst,X3 : term,X4 : subst] : ((((sK61 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) | (((sK61 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)) & (! [X6 : term] : ((((sK61 @ id @ X6 @ id)) != $true) | (((sK61 @ id @ (sub @ sK62 @ (push @ X6 @ id)) @ id)) = $true)) & (((sK61 @ id @ (lam @ sK62) @ id)) != $true)) & (((sP0 @ sK61)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((sK61 @ X10 @ X8 @ (comp @ X9 @ X7))) != $true) | (((sK61 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9) @ X7)) = $true)))) & (! [X11 : (subst > term > subst > $o)] : (((((X11 @ (sK66 @ X11) @ (sK65 @ X11) @ (comp @ (sK64 @ X11) @ (sK63 @ X11)))) != $true) & (((X11 @ (comp @ (sK66 @ X11) @ (sK64 @ X11)) @ (sub @ (sK65 @ X11) @ (sK64 @ X11)) @ (sK63 @ X11))) = $true)) | ! [X16 : term] : (((((X11 @ id @ (sK67 @ X16 @ X11) @ id)) = $true) & (((X11 @ id @ (sub @ X16 @ (push @ (sK67 @ X16 @ X11) @ id)) @ id)) != $true)) | ($true = ((X11 @ id @ (lam @ X16) @ id)))) | (((sP0 @ X11)) = $true) | ((((X11 @ (sK71 @ X11) @ (sK69 @ X11) @ (comp @ (sK70 @ X11) @ (sK68 @ X11)))) = $true) & ($true != ((X11 @ (comp @ (sK71 @ X11) @ (sK70 @ X11)) @ (sub @ (sK69 @ X11) @ (sK70 @ X11)) @ (sK68 @ X11)))))) | (sP1 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK61,sK62,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK61),skolemize(X5,sK62),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f79])).
% 37.84/5.79 thf(f81,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X9 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) = $true) | ? [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) != ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) | ? [X13 : term] : ((((X0 @ id @ X13 @ id)) = $true) & (((X0 @ id @ (X9 @ id @ X13) @ id)) != $true)))) & (? [X9 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) != $true) & ! [X11 : term,X12 : subst,X10 : subst] : (((sub @ (X9 @ X12 @ X11) @ X10)) = ((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10)))) & ! [X13 : term] : ((((X0 @ id @ X13 @ id)) != $true) | (((X0 @ id @ (X9 @ id @ X13) @ id)) = $true))) | (((sP0 @ X0)) != $true)))),
% 37.84/5.79 inference(nnf_transformation,[],[f15])).
% 37.84/5.79 thf(f82,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | ? [X2 : term,X3 : subst,X4 : subst] : (((sub @ (X1 @ X3 @ X2) @ X4)) != ((X1 @ (comp @ X3 @ X4) @ (sub @ X2 @ X4)))) | ? [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) & (((X0 @ id @ (X1 @ id @ X5) @ id)) != $true)))) & (? [X6 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X6 @ Y0 @ Y1))))) @ id)) != $true) & ! [X7 : term,X8 : subst,X9 : subst] : (((X6 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9))) = ((sub @ (X6 @ X8 @ X7) @ X9))) & ! [X10 : term] : ((((X0 @ id @ X10 @ id)) != $true) | (((X0 @ id @ (X6 @ id @ X10) @ id)) = $true))) | (((sP0 @ X0)) != $true)))),
% 37.84/5.79 inference(rectify,[],[f81])).
% 37.84/5.79 thf(f83,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | (((sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) != ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))))) | ((((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true) & (((X0 @ id @ (X1 @ id @ (sK75 @ X1 @ X0)) @ id)) != $true)))) & (((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK76 @ X0 @ Y0 @ Y1))))) @ id)) != $true) & ! [X7 : term,X8 : subst,X9 : subst] : (((sub @ (sK76 @ X0 @ X8 @ X7) @ X9)) = ((sK76 @ X0 @ (comp @ X8 @ X9) @ (sub @ X7 @ X9)))) & ! [X10 : term] : ((((X0 @ id @ X10 @ id)) != $true) | (((X0 @ id @ (sK76 @ X0 @ id @ X10) @ id)) = $true))) | (((sP0 @ X0)) != $true)))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f82])).
% 37.84/5.79 thf(f84,plain,(
% 37.84/5.79 ((sP1 != $true) | (hoasinduction_lem3 != $true)) & ((sP1 = $true) | (hoasinduction_lem3 = $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f17])).
% 37.84/5.79 thf(f168,plain,(
% 37.84/5.79 ((sP34 = $true) | ? [X237 : term,X238 : (subst > term > subst > $o)] : ((((sP33 @ X238)) != $true) & ! [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) = $true) | (((X238 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) != $true) | (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) = $true)) & (((X238 @ id @ (lam @ X237) @ id)) != $true) & ! [X249 : subst,X250 : term,X252 : subst,X251 : subst] : ((((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) != $true) | (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) = $true)))) & (! [X237 : term,X238 : (subst > term > subst > $o)] : ((((sP33 @ X238)) = $true) | ? [X239 : term] : ((((X238 @ id @ (sub @ X237 @ (push @ X239 @ id)) @ id)) != $true) & (((X238 @ id @ X239 @ id)) = $true)) | ? [X240 : subst,X241 : term,X242 : subst,X243 : subst] : ((((X238 @ X240 @ X241 @ (comp @ X242 @ X243))) = $true) & (((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X243)) != $true)) | (((X238 @ id @ (lam @ X237) @ id)) = $true) | ? [X249 : subst,X250 : term,X252 : subst,X251 : subst] : ((((X238 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) & (((X238 @ X252 @ X250 @ (comp @ X249 @ X251))) != $true))) | (sP34 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f50])).
% 37.84/5.79 thf(f169,plain,(
% 37.84/5.79 ((sP34 = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : ((((sP33 @ X1)) != $true) & ! [X2 : term] : (($true = ((X1 @ id @ (sub @ X0 @ (push @ X2 @ id)) @ id))) | (((X1 @ id @ X2 @ id)) != $true)) & ! [X3 : subst,X4 : term,X5 : subst,X6 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X5 @ X6))) != $true) | (((X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X6)) = $true)) & (((X1 @ id @ (lam @ X0) @ id)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((X1 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7) @ X10)) != $true) | (((X1 @ X9 @ X8 @ (comp @ X7 @ X10))) = $true)))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : ((((sP33 @ X12)) = $true) | ? [X13 : term] : ((((X12 @ id @ (sub @ X11 @ (push @ X13 @ id)) @ id)) != $true) & (((X12 @ id @ X13 @ id)) = $true)) | ? [X14 : subst,X15 : term,X16 : subst,X17 : subst] : ((((X12 @ X14 @ X15 @ (comp @ X16 @ X17))) = $true) & (((X12 @ (comp @ X14 @ X16) @ (sub @ X15 @ X16) @ X17)) != $true)) | (((X12 @ id @ (lam @ X11) @ id)) = $true) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : ((((X12 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18) @ X21)) = $true) & (((X12 @ X20 @ X19 @ (comp @ X18 @ X21))) != $true))) | (sP34 != $true))),
% 37.84/5.79 inference(rectify,[],[f168])).
% 37.84/5.79 thf(f170,plain,(
% 37.84/5.79 ((sP34 = $true) | ((((sP33 @ sK254)) != $true) & ! [X2 : term] : ((((sK254 @ id @ (sub @ sK253 @ (push @ X2 @ id)) @ id)) = $true) | (((sK254 @ id @ X2 @ id)) != $true)) & ! [X3 : subst,X4 : term,X5 : subst,X6 : subst] : ((((sK254 @ X3 @ X4 @ (comp @ X5 @ X6))) != $true) | (((sK254 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X6)) = $true)) & (((sK254 @ id @ (lam @ sK253) @ id)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((sK254 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7) @ X10)) != $true) | (((sK254 @ X9 @ X8 @ (comp @ X7 @ X10))) = $true)))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : ((((sP33 @ X12)) = $true) | ((((X12 @ id @ (sub @ X11 @ (push @ (sK255 @ X12 @ X11) @ id)) @ id)) != $true) & (((X12 @ id @ (sK255 @ X12 @ X11) @ id)) = $true)) | (($true = ((X12 @ (sK256 @ X12) @ (sK257 @ X12) @ (comp @ (sK258 @ X12) @ (sK259 @ X12))))) & (((X12 @ (comp @ (sK256 @ X12) @ (sK258 @ X12)) @ (sub @ (sK257 @ X12) @ (sK258 @ X12)) @ (sK259 @ X12))) != $true)) | (((X12 @ id @ (lam @ X11) @ id)) = $true) | ((((X12 @ (comp @ (sK262 @ X12) @ (sK260 @ X12)) @ (sub @ (sK261 @ X12) @ (sK260 @ X12)) @ (sK263 @ X12))) = $true) & (((X12 @ (sK262 @ X12) @ (sK261 @ X12) @ (comp @ (sK260 @ X12) @ (sK263 @ X12)))) != $true))) | (sP34 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK253,sK254,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK253),skolemize(X1,sK254),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f169])).
% 37.84/5.79 thf(f171,plain,(
% 37.84/5.79 ! [X238 : (subst > term > subst > $o)] : (((((sP33 @ X238)) = $true) | ! [X244 : (subst > term > term)] : (? [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) != ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) | ? [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) != $true) & (((X238 @ id @ X248 @ id)) = $true)) | (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) = $true))) & (? [X244 : (subst > term > term)] : (! [X245 : subst,X247 : subst,X246 : term] : (((sub @ (X244 @ X245 @ X246) @ X247)) = ((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247)))) & ! [X248 : term] : ((((X238 @ id @ (X244 @ id @ X248) @ id)) = $true) | (((X238 @ id @ X248 @ id)) != $true)) & (((X238 @ id @ (lam @ (X244 @ sh @ one)) @ id)) != $true)) | (((sP33 @ X238)) != $true)))),
% 37.84/5.79 inference(nnf_transformation,[],[f49])).
% 37.84/5.79 thf(f172,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP33 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (? [X2 : subst,X3 : subst,X4 : term] : (((X1 @ (comp @ X2 @ X3) @ (sub @ X4 @ X3))) != ((sub @ (X1 @ X2 @ X4) @ X3))) | ? [X5 : term] : ((((X0 @ id @ (X1 @ id @ X5) @ id)) != $true) & (((X0 @ id @ X5 @ id)) = $true)) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true))) & (? [X6 : (subst > term > term)] : (! [X7 : subst,X8 : subst,X9 : term] : (((X6 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8))) = ((sub @ (X6 @ X7 @ X9) @ X8))) & ! [X10 : term] : ((((X0 @ id @ (X6 @ id @ X10) @ id)) = $true) | (((X0 @ id @ X10 @ id)) != $true)) & ($true != ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)))) | (((sP33 @ X0)) != $true)))),
% 37.84/5.79 inference(rectify,[],[f171])).
% 37.84/5.79 thf(f173,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP33 @ X0)) = $true) | ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK264 @ X1) @ (sK266 @ X1)) @ (sK265 @ X1))) != ((X1 @ (comp @ (sK264 @ X1) @ (sK265 @ X1)) @ (sub @ (sK266 @ X1) @ (sK265 @ X1))))) | ((((X0 @ id @ (X1 @ id @ (sK267 @ X1 @ X0)) @ id)) != $true) & (((X0 @ id @ (sK267 @ X1 @ X0) @ id)) = $true)) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true))) & ((! [X7 : subst,X8 : subst,X9 : term] : (((sK268 @ X0 @ (comp @ X7 @ X8) @ (sub @ X9 @ X8))) = ((sub @ (sK268 @ X0 @ X7 @ X9) @ X8))) & ! [X10 : term] : ((((X0 @ id @ (sK268 @ X0 @ id @ X10) @ id)) = $true) | (((X0 @ id @ X10 @ id)) != $true)) & (((X0 @ id @ (lam @ (sK268 @ X0 @ sh @ one)) @ id)) != $true)) | (((sP33 @ X0)) != $true)))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f172])).
% 37.84/5.79 thf(f187,plain,(
% 37.84/5.79 ! [X113 : (subst > term > subst > $o)] : (((((sP28 @ X113)) = $true) | ? [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) != $true) & ! [X116 : term] : ((((X113 @ id @ (X115 @ id @ X116) @ id)) = $true) | (((X113 @ id @ X116 @ id)) != $true)) & ! [X117 : term,X119 : subst,X118 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) = ((sub @ (X115 @ X119 @ X117) @ X118))))) & (! [X115 : (subst > term > term)] : ((((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ? [X116 : term] : ((((X113 @ id @ (X115 @ id @ X116) @ id)) != $true) & (((X113 @ id @ X116 @ id)) = $true)) | ? [X117 : term,X119 : subst,X118 : subst] : (((X115 @ (comp @ X119 @ X118) @ (sub @ X117 @ X118))) != ((sub @ (X115 @ X119 @ X117) @ X118)))) | (((sP28 @ X113)) != $true)))),
% 37.84/5.79 inference(nnf_transformation,[],[f44])).
% 37.84/5.79 thf(f188,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP28 @ X0)) = $true) | ? [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) != $true) & ! [X2 : term] : ((((X0 @ id @ (X1 @ id @ X2) @ id)) = $true) | (((X0 @ id @ X2 @ id)) != $true)) & ! [X3 : term,X4 : subst,X5 : subst] : (((X1 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5))) = ((sub @ (X1 @ X4 @ X3) @ X5))))) & (! [X6 : (subst > term > term)] : (($true = ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id))) | ? [X7 : term] : ((((X0 @ id @ (X6 @ id @ X7) @ id)) != $true) & (((X0 @ id @ X7 @ id)) = $true)) | ? [X8 : term,X9 : subst,X10 : subst] : (((sub @ (X6 @ X9 @ X8) @ X10)) != ((X6 @ (comp @ X9 @ X10) @ (sub @ X8 @ X10))))) | (((sP28 @ X0)) != $true)))),
% 37.84/5.79 inference(rectify,[],[f187])).
% 37.84/5.79 thf(f189,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP28 @ X0)) = $true) | ((((X0 @ id @ (lam @ (sK307 @ X0 @ sh @ one)) @ id)) != $true) & ! [X2 : term] : ((((X0 @ id @ (sK307 @ X0 @ id @ X2) @ id)) = $true) | (((X0 @ id @ X2 @ id)) != $true)) & ! [X3 : term,X4 : subst,X5 : subst] : (((sub @ (sK307 @ X0 @ X4 @ X3) @ X5)) = ((sK307 @ X0 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5)))))) & (! [X6 : (subst > term > term)] : (($true = ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id))) | ((((X0 @ id @ (X6 @ id @ (sK308 @ X6 @ X0)) @ id)) != $true) & (((X0 @ id @ (sK308 @ X6 @ X0) @ id)) = $true)) | (((sub @ (X6 @ (sK310 @ X6) @ (sK309 @ X6)) @ (sK311 @ X6))) != ((X6 @ (comp @ (sK310 @ X6) @ (sK311 @ X6)) @ (sub @ (sK309 @ X6) @ (sK311 @ X6)))))) | (((sP28 @ X0)) != $true)))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f188])).
% 37.84/5.79 thf(f212,plain,(
% 37.84/5.79 ((sP20 = $true) | ? [X309 : term,X310 : (term > $o)] : (! [X313 : term] : (($true != ((var @ X313))) | (((X310 @ X313)) = $true)) & ! [X311 : term] : (? [X312 : term] : ((((X310 @ X312)) = $true) & (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) != $true)) | (((X310 @ (lam @ X311))) = $true)) & (((sP19 @ X310)) != $true) & (((X310 @ X309)) != $true))) & (! [X309 : term,X310 : (term > $o)] : (? [X313 : term] : (($true = ((var @ X313))) & (((X310 @ X313)) != $true)) | ? [X311 : term] : (! [X312 : term] : ((((X310 @ X312)) != $true) | (((X310 @ (sub @ X311 @ (push @ X312 @ id)))) = $true)) & (((X310 @ (lam @ X311))) != $true)) | (((sP19 @ X310)) = $true) | (((X310 @ X309)) = $true)) | (sP20 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f36])).
% 37.84/5.79 thf(f213,plain,(
% 37.84/5.79 ((sP20 = $true) | ? [X0 : term,X1 : (term > $o)] : (! [X2 : term] : ((((var @ X2)) != $true) | (((X1 @ X2)) = $true)) & ! [X3 : term] : (? [X4 : term] : ((((X1 @ X4)) = $true) & (((X1 @ (sub @ X3 @ (push @ X4 @ id)))) != $true)) | (((X1 @ (lam @ X3))) = $true)) & (((sP19 @ X1)) != $true) & (((X1 @ X0)) != $true))) & (! [X5 : term,X6 : (term > $o)] : (? [X7 : term] : ((((var @ X7)) = $true) & (((X6 @ X7)) != $true)) | ? [X8 : term] : (! [X9 : term] : ((((X6 @ X9)) != $true) | (((X6 @ (sub @ X8 @ (push @ X9 @ id)))) = $true)) & (((X6 @ (lam @ X8))) != $true)) | (((sP19 @ X6)) = $true) | (((X6 @ X5)) = $true)) | (sP20 != $true))),
% 37.84/5.79 inference(rectify,[],[f212])).
% 37.84/5.79 thf(f214,plain,(
% 37.84/5.79 ((sP20 = $true) | (! [X2 : term] : ((((var @ X2)) != $true) | (((sK341 @ X2)) = $true)) & ! [X3 : term] : (((((sK341 @ (sK342 @ X3))) = $true) & (((sK341 @ (sub @ X3 @ (push @ (sK342 @ X3) @ id)))) != $true)) | (((sK341 @ (lam @ X3))) = $true)) & ($true != ((sP19 @ sK341))) & (((sK341 @ sK340)) != $true))) & (! [X5 : term,X6 : (term > $o)] : (((((var @ (sK343 @ X6))) = $true) & (((X6 @ (sK343 @ X6))) != $true)) | (! [X9 : term] : ((((X6 @ X9)) != $true) | (((X6 @ (sub @ (sK344 @ X6) @ (push @ X9 @ id)))) = $true)) & (((X6 @ (lam @ (sK344 @ X6)))) != $true)) | (((sP19 @ X6)) = $true) | (((X6 @ X5)) = $true)) | (sP20 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK340,sK341,vAPP,vAPP,vAPP]),skolemize(X0,sK340),skolemize(X1,sK341),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f213])).
% 37.84/5.79 thf(f215,plain,(
% 37.84/5.79 ! [X310 : (term > $o)] : (((((sP19 @ X310)) = $true) | ! [X314 : term,X315 : term] : ((((X310 @ X314)) != $true) | (((X310 @ X315)) != $true) | (((X310 @ (ap @ X314 @ X315))) = $true))) & (? [X314 : term,X315 : term] : ((((X310 @ X314)) = $true) & (((X310 @ X315)) = $true) & (((X310 @ (ap @ X314 @ X315))) != $true)) | (((sP19 @ X310)) != $true)))),
% 37.84/5.79 inference(nnf_transformation,[],[f35])).
% 37.84/5.79 thf(f216,plain,(
% 37.84/5.79 ! [X0 : (term > $o)] : (((((sP19 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ X1)) != $true) | (((X0 @ X2)) != $true) | (((X0 @ (ap @ X1 @ X2))) = $true))) & (? [X3 : term,X4 : term] : ((((X0 @ X3)) = $true) & (((X0 @ X4)) = $true) & (((X0 @ (ap @ X3 @ X4))) != $true)) | (((sP19 @ X0)) != $true)))),
% 37.84/5.79 inference(rectify,[],[f215])).
% 37.84/5.79 thf(f217,plain,(
% 37.84/5.79 ! [X0 : (term > $o)] : (((((sP19 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ X1)) != $true) | (((X0 @ X2)) != $true) | (((X0 @ (ap @ X1 @ X2))) = $true))) & (((((X0 @ (sK345 @ X0))) = $true) & (((X0 @ (sK346 @ X0))) = $true) & (((X0 @ (ap @ (sK345 @ X0) @ (sK346 @ X0)))) != $true)) | (((sP19 @ X0)) != $true)))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f216])).
% 37.84/5.79 thf(f230,plain,(
% 37.84/5.79 ((sP14 = $true) | (? [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) != $true) & ! [X23 : (subst > term > term)] : (? [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) != ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) | ? [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) != $true) & (((X21 @ id @ X24 @ id)) = $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true)) & (((sP11 @ X21)) != $true)) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) & (sP12 != $true) & (sP13 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & ((! [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | (((sP11 @ X21)) = $true)) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | (sP12 = $true) | (sP13 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | (sP14 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f30])).
% 37.84/5.79 thf(f231,plain,(
% 37.84/5.79 ((sP14 = $true) | (? [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) != $true) & ! [X23 : (subst > term > term)] : (? [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) != ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) | ? [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) != $true) & (((X21 @ id @ X24 @ id)) = $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true)) & (((sP11 @ X21)) != $true)) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) & (sP12 != $true) & (sP13 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & (! [X22 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X27) @ X25)) = ((X23 @ (comp @ X26 @ X25) @ (sub @ X27 @ X25)))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | (((sP11 @ X21)) = $true)) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | (sP12 = $true) | (sP13 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | (sP14 != $true))),
% 37.84/5.79 inference(flattening,[],[f230])).
% 37.84/5.79 thf(f232,plain,(
% 37.84/5.79 ((sP14 = $true) | (? [X0 : term,X1 : (subst > term > subst > $o)] : (($true != ((X1 @ id @ X0 @ id))) & ! [X2 : (subst > term > term)] : (? [X3 : subst,X4 : term,X5 : subst] : (((sub @ (X2 @ X5 @ X4) @ X3)) != ((X2 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3)))) | ? [X6 : term] : ((((X1 @ id @ (X2 @ id @ X6) @ id)) != $true) & (((X1 @ id @ X6 @ id)) = $true)) | (((X1 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) & (((sP11 @ X1)) != $true)) & ! [X7 : (subst > term > subst > $o)] : ? [X8 : (term > $o)] : ! [X9 : term] : (((X8 @ X9)) = ((X7 @ id @ X9 @ id))) & (sP12 != $true) & (sP13 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : ((((X12 @ id @ X11 @ id)) = $true) | ? [X13 : (subst > term > term)] : (! [X14 : subst,X15 : term,X16 : subst] : (((X13 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) = ((sub @ (X13 @ X16 @ X15) @ X14))) & ! [X17 : term] : ((((X12 @ id @ (X13 @ id @ X17) @ id)) = $true) | (((X12 @ id @ X17 @ id)) != $true)) & (((X12 @ id @ (lam @ (X13 @ sh @ one)) @ id)) != $true)) | (((sP11 @ X12)) = $true)) | ? [X18 : (subst > term > subst > $o)] : ! [X19 : (term > $o)] : ? [X20 : term] : (((X19 @ X20)) != ((X18 @ id @ X20 @ id))) | (sP12 = $true) | (sP13 = $true) | ? [X21 : term] : (((sub @ X21 @ id)) != X21) | (sP14 != $true))),
% 37.84/5.79 inference(rectify,[],[f231])).
% 37.84/5.79 thf(f233,plain,(
% 37.84/5.79 ((sP14 = $true) | (((((sK380 @ id @ sK379 @ id)) != $true) & ! [X2 : (subst > term > term)] : ((((X2 @ (comp @ (sK383 @ X2) @ (sK381 @ X2)) @ (sub @ (sK382 @ X2) @ (sK381 @ X2)))) != ((sub @ (X2 @ (sK383 @ X2) @ (sK382 @ X2)) @ (sK381 @ X2)))) | ((((sK380 @ id @ (X2 @ id @ (sK384 @ X2)) @ id)) != $true) & ($true = ((sK380 @ id @ (sK384 @ X2) @ id)))) | (((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) & (((sP11 @ sK380)) != $true)) & ! [X7 : (subst > term > subst > $o)] : ! [X9 : term] : (((X7 @ id @ X9 @ id)) = ((sK385 @ X7 @ X9))) & (sP12 != $true) & (sP13 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : ((((X12 @ id @ X11 @ id)) = $true) | (! [X14 : subst,X15 : term,X16 : subst] : (((sub @ (sK386 @ X12 @ X16 @ X15) @ X14)) = ((sK386 @ X12 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14)))) & ! [X17 : term] : ((((X12 @ id @ (sK386 @ X12 @ id @ X17) @ id)) = $true) | (((X12 @ id @ X17 @ id)) != $true)) & (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true)) | (((sP11 @ X12)) = $true)) | ! [X19 : (term > $o)] : (((X19 @ (sK388 @ X19))) != ((sK387 @ id @ (sK388 @ X19) @ id))) | (sP12 = $true) | (sP13 = $true) | (sK389 != ((sub @ sK389 @ id))) | (sP14 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[sK379,sK380,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK387,vAPP,sK389]),skolemize(X0,sK379),skolemize(X1,sK380),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X18,sK387),skolemize(X21,sK71 @ X11),skolemize(X21,sK389)],[f232])).
% 37.84/5.79 thf(f234,plain,(
% 37.84/5.79 ((sP13 = $true) | ! [X3 : (term > $o),X4 : term] : (? [X6 : term] : (! [X7 : term] : ((((X3 @ X7)) != $true) | (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true)) & (((X3 @ (lam @ X6))) != $true)) | (((sP10 @ X3)) != $true) | ? [X5 : term] : ((((var @ X5)) = $true) & (((X3 @ X5)) != $true)) | (((X3 @ X4)) = $true))) & (? [X3 : (term > $o),X4 : term] : (! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & (((sP10 @ X3)) = $true) & ! [X5 : term] : ((((var @ X5)) != $true) | (((X3 @ X5)) = $true)) & (((X3 @ X4)) != $true)) | (sP13 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f29])).
% 37.84/5.79 thf(f235,plain,(
% 37.84/5.79 ((sP13 = $true) | ! [X0 : (term > $o),X1 : term] : (? [X2 : term] : (! [X3 : term] : ((((X0 @ X3)) != $true) | (((X0 @ (sub @ X2 @ (push @ X3 @ id)))) = $true)) & (((X0 @ (lam @ X2))) != $true)) | (((sP10 @ X0)) != $true) | ? [X4 : term] : ((((var @ X4)) = $true) & (((X0 @ X4)) != $true)) | (((X0 @ X1)) = $true))) & (? [X5 : (term > $o),X6 : term] : (! [X7 : term] : (? [X8 : term] : ((((X5 @ X8)) = $true) & (((X5 @ (sub @ X7 @ (push @ X8 @ id)))) != $true)) | (((X5 @ (lam @ X7))) = $true)) & (((sP10 @ X5)) = $true) & ! [X9 : term] : (($true != ((var @ X9))) | (((X5 @ X9)) = $true)) & (((X5 @ X6)) != $true)) | (sP13 != $true))),
% 37.84/5.79 inference(rectify,[],[f234])).
% 37.84/5.79 thf(f236,plain,(
% 37.84/5.79 ((sP13 = $true) | ! [X0 : (term > $o),X1 : term] : ((! [X3 : term] : ((((X0 @ X3)) != $true) | (((X0 @ (sub @ (sK390 @ X0) @ (push @ X3 @ id)))) = $true)) & (((X0 @ (lam @ (sK390 @ X0)))) != $true)) | (((sP10 @ X0)) != $true) | ((((var @ (sK391 @ X0))) = $true) & (((X0 @ (sK391 @ X0))) != $true)) | (((X0 @ X1)) = $true))) & ((! [X7 : term] : ((($true = ((sK392 @ (sK394 @ X7)))) & (((sK392 @ (sub @ X7 @ (push @ (sK394 @ X7) @ id)))) != $true)) | (((sK392 @ (lam @ X7))) = $true)) & (((sP10 @ sK392)) = $true) & ! [X9 : term] : (($true != ((var @ X9))) | (((sK392 @ X9)) = $true)) & (((sK392 @ sK393)) != $true)) | (sP13 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK392,sK393,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X5,sK392),skolemize(X6,sK393),skolemize(X21,sK71 @ X11)],[f235])).
% 37.84/5.79 thf(f237,plain,(
% 37.84/5.79 ((sP12 = $true) | ! [X12 : (term > $o),X13 : (subst > term > subst > $o),X11 : term] : (? [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) != $true) & ! [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) = ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) & ! [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) = $true) | (((X13 @ id @ X15 @ id)) != $true))) | ? [X19 : term] : (((X13 @ id @ X19 @ id)) != ((X12 @ X19))) | (((X12 @ (lam @ X11))) = $true) | ? [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) != $true) & (((X12 @ X20)) = $true)))) & (? [X12 : (term > $o),X13 : (subst > term > subst > $o),X11 : term] : (! [X14 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X16 : subst,X18 : term,X17 : subst] : (((sub @ (X14 @ X17 @ X18) @ X16)) != ((X14 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16)))) | ? [X15 : term] : ((((X13 @ id @ (X14 @ id @ X15) @ id)) != $true) & (((X13 @ id @ X15 @ id)) = $true))) & ! [X19 : term] : (((X13 @ id @ X19 @ id)) = ((X12 @ X19))) & (((X12 @ (lam @ X11))) != $true) & ! [X20 : term] : ((((X12 @ (sub @ X11 @ (push @ X20 @ id)))) = $true) | (((X12 @ X20)) != $true))) | (sP12 != $true))),
% 37.84/5.79 inference(nnf_transformation,[],[f28])).
% 37.84/5.79 thf(f238,plain,(
% 37.84/5.79 ((sP12 = $true) | ! [X0 : (term > $o),X1 : (subst > term > subst > $o),X2 : term] : (? [X3 : (subst > term > term)] : ((((X1 @ id @ (lam @ (X3 @ sh @ one)) @ id)) != $true) & ! [X4 : subst,X5 : term,X6 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) & ! [X7 : term] : ((((X1 @ id @ (X3 @ id @ X7) @ id)) = $true) | (((X1 @ id @ X7 @ id)) != $true))) | ? [X8 : term] : (((X0 @ X8)) != ((X1 @ id @ X8 @ id))) | (((X0 @ (lam @ X2))) = $true) | ? [X9 : term] : ((((X0 @ (sub @ X2 @ (push @ X9 @ id)))) != $true) & (((X0 @ X9)) = $true)))) & (? [X10 : (term > $o),X11 : (subst > term > subst > $o),X12 : term] : (! [X13 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true) | ? [X14 : subst,X15 : term,X16 : subst] : (((X13 @ (comp @ X16 @ X14) @ (sub @ X15 @ X14))) != ((sub @ (X13 @ X16 @ X15) @ X14))) | ? [X17 : term] : ((((X11 @ id @ (X13 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true))) & ! [X18 : term] : (((X10 @ X18)) = ((X11 @ id @ X18 @ id))) & ($true != ((X10 @ (lam @ X12)))) & ! [X19 : term] : ((((X10 @ (sub @ X12 @ (push @ X19 @ id)))) = $true) | (((X10 @ X19)) != $true))) | (sP12 != $true))),
% 37.84/5.79 inference(rectify,[],[f237])).
% 37.84/5.79 thf(f239,plain,(
% 37.84/5.79 ((sP12 = $true) | ! [X0 : (term > $o),X1 : (subst > term > subst > $o),X2 : term] : (((((X1 @ id @ (lam @ (sK395 @ X1 @ sh @ one)) @ id)) != $true) & ! [X4 : subst,X5 : term,X6 : subst] : (((sK395 @ X1 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (sK395 @ X1 @ X6 @ X5) @ X4))) & ! [X7 : term] : ((((X1 @ id @ (sK395 @ X1 @ id @ X7) @ id)) = $true) | (((X1 @ id @ X7 @ id)) != $true))) | (((X0 @ (sK396 @ X1 @ X0))) != ((X1 @ id @ (sK396 @ X1 @ X0) @ id))) | (((X0 @ (lam @ X2))) = $true) | ((((X0 @ (sub @ X2 @ (push @ (sK397 @ X2 @ X0) @ id)))) != $true) & (((X0 @ (sK397 @ X2 @ X0))) = $true)))) & ((! [X13 : (subst > term > term)] : ((((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true) | (((X13 @ (comp @ (sK403 @ X13) @ (sK401 @ X13)) @ (sub @ (sK402 @ X13) @ (sK401 @ X13)))) != ((sub @ (X13 @ (sK403 @ X13) @ (sK402 @ X13)) @ (sK401 @ X13)))) | ((((sK399 @ id @ (X13 @ id @ (sK404 @ X13)) @ id)) != $true) & (((sK399 @ id @ (sK404 @ X13) @ id)) = $true))) & ! [X18 : term] : (((sK399 @ id @ X18 @ id)) = ((sK398 @ X18))) & (((sK398 @ (lam @ sK400))) != $true) & ! [X19 : term] : ((((sK398 @ (sub @ sK400 @ (push @ X19 @ id)))) = $true) | (((sK398 @ X19)) != $true))) | (sP12 != $true))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,sK398,sK399,sK400,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X10,sK398),skolemize(X11,sK399),skolemize(X12,sK400),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f238])).
% 37.84/5.79 thf(f240,plain,(
% 37.84/5.79 ! [X21 : (subst > term > subst > $o)] : (((((sP11 @ X21)) = $true) | ! [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) != $true) | ($true != ((X21 @ id @ X29 @ id))) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true))) & (? [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true)) | (((sP11 @ X21)) != $true)))),
% 37.84/5.79 inference(nnf_transformation,[],[f27])).
% 37.84/5.79 thf(f241,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP11 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id)) = $true))) & (? [X3 : term,X4 : term] : ((((X0 @ id @ X4 @ id)) = $true) & (((X0 @ id @ X3 @ id)) = $true) & (((X0 @ id @ (ap @ (sub @ X4 @ id) @ X3) @ id)) != $true)) | (((sP11 @ X0)) != $true)))),
% 37.84/5.79 inference(rectify,[],[f240])).
% 37.84/5.79 thf(f242,plain,(
% 37.84/5.79 ! [X0 : (subst > term > subst > $o)] : (((((sP11 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id)) = $true))) & (((((X0 @ id @ (sK406 @ X0) @ id)) = $true) & (((X0 @ id @ (sK405 @ X0) @ id)) = $true) & (((X0 @ id @ (ap @ (sub @ (sK406 @ X0) @ id) @ (sK405 @ X0)) @ id)) != $true)) | (((sP11 @ X0)) != $true)))),
% 37.84/5.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11)],[f241])).
% 37.84/5.79 thf(f272,plain,(
% 37.84/5.79 (((apinj2 = $true) | ? [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) = ((ap @ X347 @ X348))) & (X345 != X348))) & (! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348)) | (apinj2 != $true))) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & (((laminj = $true) | ? [X343 : term,X344 : term] : ((X343 != X344) & (((lam @ X344)) = ((lam @ X343))))) & (! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343)))) | (laminj != $true))) & (((hoasinduction_no_psi_cond = $true) | ? [X444 : (subst > term > subst > $o),X445 : term] : (! [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) != $true) | (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) = $true) | (((X444 @ id @ X446 @ id)) != $true)) & (((X444 @ id @ X445 @ id)) != $true) & ($true != ((sP60 @ X444))))) & (! [X444 : (subst > term > subst > $o),X445 : term] : (? [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) = $true) & (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) != $true) & (((X444 @ id @ X446 @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true) | ($true = ((sP60 @ X444)))) | (hoasinduction_no_psi_cond != $true))) & (((sP59 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP59 != $true))) & (((axshiftcons = $true) | ? [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) != X318)) & (! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318) | (axshiftcons != $true))) & (((induction2lem_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (induction2lem_lthm != $true))) & (((pushprop_lem1v2 = $true) | ? [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) != $true) & ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) & (((X38 @ X41)) = $true))) & (! [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ? [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) != ((X39 @ X42))) | (((X38 @ X41)) != $true)) | (pushprop_lem1v2 != $true))) & (((apinj1 = $true) | ? [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) = ((ap @ X219 @ X218))) & (X217 != X219))) & (! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219)) | (apinj1 != $true))) & (((sP54 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP54 != $true))) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & ((! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) != X453))) & (((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP46 != $true)) & ((sP46 = $true) | (hoasinduction_lem3a_lthm != $true))) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X229 : d_subst,X228 : d_subst] : ((X228 = X229) | (((d2subst @ X228)) != ((d2subst @ X229)))) & ((! [X255 : (term > $o),X253 : term,X254 : subst] : ? [X256 : (term > $o)] : ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X255 : (term > $o),X253 : term,X254 : subst] : ! [X256 : (term > $o)] : ? [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) != ((X256 @ X257))))) & (pushprop_lem2v2_lthm = $true) & ((! [X149 : term,X148 : term,X147 : (subst > term > term)] : (? [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) != ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X149 : term,X148 : term,X147 : (subst > term > term)] : (! [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) = ((sub @ (X147 @ X152 @ X151) @ X150))) & (((lam @ (X147 @ sh @ one))) = ((ap @ (sub @ X148 @ id) @ X149)))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & (((! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))) | ? [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) = ((ap @ X457 @ X456))) & (X455 != X456))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 != X460) & (((ap @ (sub @ X461 @ id) @ X459)) = ((ap @ (sub @ X462 @ id) @ X460)))) & ! [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) != ((ap @ X457 @ X456))) | (X455 = X456))))) & (((sP44 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP44 != $true))) & (((d2subst @ d_id)) = id) & ((! [X340 : (subst > term > subst > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X340 : (subst > term > subst > $o)] : ! [X341 : (term > $o)] : ? [X342 : term] : (((X341 @ X342)) != ((X340 @ id @ X342 @ id))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & (((sP43 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP43 != $true))) & (((hoasapinj2 = $true) | ? [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 != X214) & (((ap @ (sub @ X213 @ id) @ X212)) = ((ap @ (sub @ X215 @ id) @ X214))))) & (! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214)))) | (hoasapinj2 != $true))) & (((sP42 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP42 != $true))) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & ((! [X339 : term] : (((sub @ X339 @ id)) = X339) | (axvarid != $true)) & ((axvarid = $true) | ? [X339 : term] : (((sub @ X339 @ id)) != X339))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X51 : subst] : (((comp @ X51 @ id)) != X51) | ? [X50 : subst] : (((comp @ id @ X50)) != X50)))) & (((hoasinduction_lem0_lthm = $true) | ? [X43 : (subst > term > subst > $o)] : ! [X44 : (term > $o)] : ? [X45 : term] : (((X44 @ X45)) != ((X43 @ id @ X45 @ id)))) & (! [X43 : (subst > term > subst > $o)] : ? [X44 : (term > $o)] : ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (((substmonoid_lthm = $true) | ((? [X48 : subst] : (((comp @ id @ X48)) != X48) | ? [X49 : subst] : (((comp @ X49 @ id)) != X49)) & ! [X47 : subst] : (((comp @ X47 @ id)) = X47) & ! [X46 : subst] : (((comp @ id @ X46)) = X46))) & (((! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49)) | ? [X47 : subst] : (((comp @ X47 @ id)) != X47) | ? [X46 : subst] : (((comp @ id @ X46)) != X46)) | (substmonoid_lthm != $true))) & (((induction2lem = $true) | (sP40 != $true)) & ((sP40 = $true) | (induction2lem != $true))) & ((! [X388 : term] : ? [X389 : (subst > term > term)] : ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X388 : term] : ! [X389 : (subst > term > term)] : ? [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) != ((X389 @ X390 @ X391))))) & (((hoasinduction_lem3v2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2_lthm != $true))) & (((sP36 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP36 != $true))) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasinduction_lem3 = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3 != $true))) & (((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (((sP23 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP23 != $true))) & (hoasinduction_lem1_gthm = $true) & ((! [X317 : subst] : (((comp @ X317 @ id)) = X317) | (axidr != $true)) & ((axidr = $true) | ? [X317 : subst] : (((comp @ X317 @ id)) != X317))) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & ((! [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) = $true) | ? [X406 : term] : ((((X402 @ X406)) = $true) & (((X402 @ (lam @ X406))) != $true)) | (((sP22 @ X402)) = $true) | ? [X405 : term] : ((((X402 @ X405)) != $true) & (((var @ X405)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) != $true) & ! [X406 : term] : ((((X402 @ X406)) != $true) | (((X402 @ (lam @ X406))) = $true)) & (((sP22 @ X402)) != $true) & ! [X405 : term] : ((((X402 @ X405)) = $true) | (((var @ X405)) != $true))))) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X437 : d_subst] : (d_id = X437) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & (((pushprop_lem1 = $true) | ? [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) = $true) & (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) != $true))) & (! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true)) | (pushprop_lem1 != $true))) & (((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true))) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (((! [X441 : term] : (((sub @ X441 @ id)) = X441) | ? [X440 : term] : (((sub @ X440 @ id)) != X440)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X441 : term] : (((sub @ X441 @ id)) != X441) & ! [X440 : term] : (((sub @ X440 @ id)) = X440)))) & (((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true))) & (((pushprop_lem1v2_lthm = $true) | (? [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) = $true) & ! [X236 : term] : (((X232 @ X236)) = ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) & (((X232 @ one)) != $true)) & ! [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) = X230))) & ((! [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) != $true) | ? [X236 : term] : (((X232 @ X236)) != ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true)) | ? [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) != X230)) | (pushprop_lem1v2_lthm != $true))) & (((sP15 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP15 != $true))) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (((termmset = $true) | ? [X201 : term] : (((sub @ X201 @ id)) != X201)) & (! [X201 : term] : (((sub @ X201 @ id)) = X201) | (termmset != $true))) & (ulamvarsh = $true) & (((pushprop_lem0_lthm = $true) | ? [X534 : (term > $o),X533 : subst,X535 : term] : ! [X536 : (term > $o)] : ? [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) != ((X536 @ X537)))) & (! [X534 : (term > $o),X533 : subst,X535 : term] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537))) | (pushprop_lem0_lthm != $true))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X538 : term] : ! [X539 : (subst > term > term)] : (((X539 @ sh @ one)) != ((sub @ X538 @ (push @ one @ sh))))) & (! [X538 : term] : ? [X539 : (subst > term > term)] : (((X539 @ sh @ one)) = ((sub @ X538 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (hoaslamnotap_gthm = $true) & (((sP14 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP14 != $true))) & (pushprop_lem2v2 = $true) & ((! [X36 : term] : ? [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) = ((X37 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X36 : term] : ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one))))) & (lamnotvar = $true) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) != ((d2term @ X439))) | (X438 = X439)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & ((! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) | (axscons != $true)) & ((axscons = $true) | ? [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) != X153))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & (((hoasapinj1_lthm = $true) | (? [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 != X496) & (((ap @ (sub @ X496 @ id) @ X493)) = ((ap @ (sub @ X495 @ id) @ X494)))) & ! [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) != ((ap @ X489 @ X492))) | (X489 = X490)) & ! [X488 : term] : (((sub @ X488 @ id)) = X488))) & ((! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))) | ? [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) = ((ap @ X489 @ X492))) & (X489 != X490)) | ? [X488 : term] : (((sub @ X488 @ id)) != X488)) | (hoasapinj1_lthm != $true))) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & (((hoaslaminj = $true) | ? [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (! [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) = ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) & ! [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) = ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) & (((X55 @ X54 @ X53)) != ((X52 @ X54 @ X53))) & (((lam @ (X55 @ sh @ one))) = ((lam @ (X52 @ sh @ one)))))) & (! [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (? [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) != ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | ? [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) != ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | (((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one))))) | (hoaslaminj != $true))) & (((hoasinduction = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction != $true))) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & (((? [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) != X62) | ? [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) != X65) | ! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) & ! [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) = X65) & ? [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) != $true) & (((X66 @ X68)) = $true))))) & (pushprop_lem2v2_gthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem3v2a_lthm != $true))) & (((hoasinduction_lem3a = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction_lem3a != $true))) & ((! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) = ((ap @ (sub @ X74 @ id) @ X71))) & (X72 != X74)))) & (((axidl = $true) | ? [X316 : subst] : (((comp @ id @ X316)) != X316)) & (! [X316 : subst] : (((comp @ id @ X316)) = X316) | (axidl != $true))) & (hoasinduction_lem1v2_gthm = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X30 : term] : ! [X31 : (subst > term > term)] : ? [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) != ((sub @ X30 @ (push @ X32 @ X33))))) & (! [X30 : term] : ? [X31 : (subst > term > term)] : ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (((hoasinduction_lem3_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3_lthm != $true))) & ((! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X442 : term,X443 : term] : ((X442 != X443) & (((sub @ X443 @ sh)) = ((sub @ X442 @ sh)))))) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.79 inference(nnf_transformation,[],[f77])).
% 37.84/5.79 thf(f273,plain,(
% 37.84/5.79 ((apinj2 = $true) | ? [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) = ((ap @ X347 @ X348))) & (X345 != X348))) & (! [X347 : term,X345 : term,X346 : term,X348 : term] : ((((ap @ X346 @ X345)) != ((ap @ X347 @ X348))) | (X345 = X348)) | (apinj2 != $true)) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ((laminj = $true) | ? [X343 : term,X344 : term] : ((X343 != X344) & (((lam @ X344)) = ((lam @ X343))))) & (! [X343 : term,X344 : term] : ((X343 = X344) | (((lam @ X344)) != ((lam @ X343)))) | (laminj != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X444 : (subst > term > subst > $o),X445 : term] : (! [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) != $true) | (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) = $true) | (((X444 @ id @ X446 @ id)) != $true)) & (((X444 @ id @ X445 @ id)) != $true) & ($true != ((sP60 @ X444))))) & (! [X444 : (subst > term > subst > $o),X445 : term] : (? [X446 : term,X447 : term] : ((((X444 @ id @ X447 @ id)) = $true) & (((X444 @ id @ (ap @ (sub @ X446 @ id) @ X447) @ id)) != $true) & (((X444 @ id @ X446 @ id)) = $true)) | (((X444 @ id @ X445 @ id)) = $true) | ($true = ((sP60 @ X444)))) | (hoasinduction_no_psi_cond != $true)) & ((sP59 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP59 != $true)) & ((axshiftcons = $true) | ? [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) != X318)) & (! [X319 : term,X318 : subst] : (((comp @ sh @ (push @ X319 @ X318))) = X318) | (axshiftcons != $true)) & ((induction2lem_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (induction2lem_lthm != $true)) & ((pushprop_lem1v2 = $true) | ? [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) != $true) & ! [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) = ((X39 @ X42))) & (((X38 @ X41)) = $true))) & (! [X41 : term,X40 : subst,X38 : (term > $o),X39 : (term > $o)] : ((((X39 @ one)) = $true) | ? [X42 : term] : (((X38 @ (sub @ X42 @ (push @ X41 @ X40)))) != ((X39 @ X42))) | (((X38 @ X41)) != $true)) | (pushprop_lem1v2 != $true)) & ((apinj1 = $true) | ? [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) = ((ap @ X219 @ X218))) & (X217 != X219))) & (! [X216 : term,X219 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X216)) != ((ap @ X219 @ X218))) | (X217 = X219)) | (apinj1 != $true)) & ((sP54 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP54 != $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X392 : d_term] : (d_one = X392) & (! [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) = X453) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X454 : subst,X453 : term] : (((sub @ one @ (push @ X453 @ X454))) != X453)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP46 != $true)) & ((sP46 = $true) | (hoasinduction_lem3a_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X229 : d_subst,X228 : d_subst] : ((X228 = X229) | (((d2subst @ X228)) != ((d2subst @ X229)))) & (! [X255 : (term > $o),X253 : term,X254 : subst] : ? [X256 : (term > $o)] : ! [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) = ((X256 @ X257))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X255 : (term > $o),X253 : term,X254 : subst] : ! [X256 : (term > $o)] : ? [X257 : term] : (((X255 @ (sub @ X257 @ (push @ X253 @ X254)))) != ((X256 @ X257)))) & (pushprop_lem2v2_lthm = $true) & (! [X149 : term,X148 : term,X147 : (subst > term > term)] : (? [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) != ((sub @ (X147 @ X152 @ X151) @ X150))) | (((lam @ (X147 @ sh @ one))) != ((ap @ (sub @ X148 @ id) @ X149)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X149 : term,X148 : term,X147 : (subst > term > term)] : (! [X151 : term,X150 : subst,X152 : subst] : (((X147 @ (comp @ X152 @ X150) @ (sub @ X151 @ X150))) = ((sub @ (X147 @ X152 @ X151) @ X150))) & (((lam @ (X147 @ sh @ one))) = ((ap @ (sub @ X148 @ id) @ X149))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & (! [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 = X460) | (((ap @ (sub @ X461 @ id) @ X459)) != ((ap @ (sub @ X462 @ id) @ X460)))) | ? [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) = ((ap @ X457 @ X456))) & (X455 != X456)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X459 : term,X461 : term,X460 : term,X462 : term] : ((X459 != X460) & (((ap @ (sub @ X461 @ id) @ X459)) = ((ap @ (sub @ X462 @ id) @ X460)))) & ! [X457 : term,X456 : term,X455 : term,X458 : term] : ((((ap @ X458 @ X455)) != ((ap @ X457 @ X456))) | (X455 = X456)))) & ((sP44 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP44 != $true)) & (((d2subst @ d_id)) = id) & (! [X340 : (subst > term > subst > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X340 : (subst > term > subst > $o)] : ! [X341 : (term > $o)] : ? [X342 : term] : (((X341 @ X342)) != ((X340 @ id @ X342 @ id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & ((sP43 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP43 != $true)) & ((hoasapinj2 = $true) | ? [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 != X214) & (((ap @ (sub @ X213 @ id) @ X212)) = ((ap @ (sub @ X215 @ id) @ X214))))) & (! [X213 : term,X214 : term,X212 : term,X215 : term] : ((X212 = X214) | (((ap @ (sub @ X213 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X214)))) | (hoasapinj2 != $true)) & ((sP42 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP42 != $true)) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X339 : term] : (((sub @ X339 @ id)) = X339) | (axvarid != $true)) & ((axvarid = $true) | ? [X339 : term] : (((sub @ X339 @ id)) != X339)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X50 : subst] : (((comp @ id @ X50)) = X50)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X51 : subst] : (((comp @ X51 @ id)) != X51) | ? [X50 : subst] : (((comp @ id @ X50)) != X50)) & ((hoasinduction_lem0_lthm = $true) | ? [X43 : (subst > term > subst > $o)] : ! [X44 : (term > $o)] : ? [X45 : term] : (((X44 @ X45)) != ((X43 @ id @ X45 @ id)))) & (! [X43 : (subst > term > subst > $o)] : ? [X44 : (term > $o)] : ! [X45 : term] : (((X44 @ X45)) = ((X43 @ id @ X45 @ id))) | (hoasinduction_lem0_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) | ((? [X48 : subst] : (((comp @ id @ X48)) != X48) | ? [X49 : subst] : (((comp @ X49 @ id)) != X49)) & ! [X47 : subst] : (((comp @ X47 @ id)) = X47) & ! [X46 : subst] : (((comp @ id @ X46)) = X46))) & ((! [X48 : subst] : (((comp @ id @ X48)) = X48) & ! [X49 : subst] : (((comp @ X49 @ id)) = X49)) | ? [X47 : subst] : (((comp @ X47 @ id)) != X47) | ? [X46 : subst] : (((comp @ id @ X46)) != X46) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | (sP40 != $true)) & ((sP40 = $true) | (induction2lem != $true)) & (! [X388 : term] : ? [X389 : (subst > term > term)] : ! [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) = ((X389 @ X390 @ X391))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X388 : term] : ! [X389 : (subst > term > term)] : ? [X391 : term,X390 : subst] : (((sub @ X388 @ (push @ X391 @ X390))) != ((X389 @ X390 @ X391)))) & ((hoasinduction_lem3v2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((sP36 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP36 != $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3 != $true)) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP23 != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X317 : subst] : (((comp @ X317 @ id)) = X317) | (axidr != $true)) & ((axidr = $true) | ? [X317 : subst] : (((comp @ X317 @ id)) != X317)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) = $true) | ? [X406 : term] : ((((X402 @ X406)) = $true) & (((X402 @ (lam @ X406))) != $true)) | (((sP22 @ X402)) = $true) | ? [X405 : term] : ((((X402 @ X405)) != $true) & (((var @ X405)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X402 : (term > $o),X401 : term] : ((((X402 @ X401)) != $true) & ! [X406 : term] : ((((X402 @ X406)) != $true) | (((X402 @ (lam @ X406))) = $true)) & (((sP22 @ X402)) != $true) & ! [X405 : term] : ((((X402 @ X405)) = $true) | (((var @ X405)) != $true)))) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X437 : d_subst] : (d_id = X437) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & ((pushprop_lem1 = $true) | ? [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) = $true) & (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) != $true))) & (! [X515 : (term > $o),X517 : term,X513 : (term > $o),X516 : term,X514 : subst] : ((((X513 @ X517)) != $true) | (((X515 @ (sub @ X517 @ (push @ X516 @ X514)))) = $true)) | (pushprop_lem1 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (! [X441 : term] : (((sub @ X441 @ id)) = X441) | ? [X440 : term] : (((sub @ X440 @ id)) != X440) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X441 : term] : (((sub @ X441 @ id)) != X441) & ! [X440 : term] : (((sub @ X440 @ id)) = X440))) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) = $true) & ! [X236 : term] : (((X232 @ X236)) = ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) & (((X232 @ one)) != $true)) & ! [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) = X230))) & (! [X234 : (term > $o),X235 : term,X233 : subst,X232 : (term > $o)] : ((((X234 @ X235)) != $true) | ? [X236 : term] : (((X232 @ X236)) != ((X234 @ (sub @ X236 @ (push @ X235 @ X233))))) | (((X232 @ one)) = $true)) | ? [X231 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X231))) != X230) | (pushprop_lem1v2_lthm != $true)) & ((sP15 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP15 != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((termmset = $true) | ? [X201 : term] : (((sub @ X201 @ id)) != X201)) & (! [X201 : term] : (((sub @ X201 @ id)) = X201) | (termmset != $true)) & (ulamvarsh = $true) & ((pushprop_lem0_lthm = $true) | ? [X534 : (term > $o),X533 : subst,X535 : term] : ! [X536 : (term > $o)] : ? [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) != ((X536 @ X537)))) & (! [X534 : (term > $o),X533 : subst,X535 : term] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X534 @ (sub @ X537 @ (push @ X535 @ X533)))) = ((X536 @ X537))) | (pushprop_lem0_lthm != $true)) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X538 : term] : ! [X539 : (subst > term > term)] : (((X539 @ sh @ one)) != ((sub @ X538 @ (push @ one @ sh))))) & (! [X538 : term] : ? [X539 : (subst > term > term)] : (((X539 @ sh @ one)) = ((sub @ X538 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoaslamnotap_gthm = $true) & ((sP14 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP14 != $true)) & (pushprop_lem2v2 = $true) & (! [X36 : term] : ? [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) = ((X37 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X36 : term] : ! [X37 : (subst > term > term)] : (((sub @ X36 @ (push @ one @ sh))) != ((X37 @ sh @ one)))) & (lamnotvar = $true) & ! [X439 : d_term,X438 : d_term] : ((((d2term @ X438)) != ((d2term @ X439))) | (X438 = X439)) & ! [X34 : subst] : ? [X35 : d_subst] : (((d2subst @ X35)) = X34) & (! [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) = X153) | (axscons != $true)) & ((axscons = $true) | ? [X153 : subst] : (((push @ (sub @ one @ X153) @ (comp @ sh @ X153))) != X153)) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 != X496) & (((ap @ (sub @ X496 @ id) @ X493)) = ((ap @ (sub @ X495 @ id) @ X494)))) & ! [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) != ((ap @ X489 @ X492))) | (X489 = X490)) & ! [X488 : term] : (((sub @ X488 @ id)) = X488))) & (! [X495 : term,X494 : term,X496 : term,X493 : term] : ((X495 = X496) | (((ap @ (sub @ X496 @ id) @ X493)) != ((ap @ (sub @ X495 @ id) @ X494)))) | ? [X491 : term,X489 : term,X492 : term,X490 : term] : ((((ap @ X490 @ X491)) = ((ap @ X489 @ X492))) & (X489 != X490)) | ? [X488 : term] : (((sub @ X488 @ id)) != X488) | (hoasapinj1_lthm != $true)) & ! [X386 : term] : ? [X387 : d_term] : (((d2term @ X387)) = X386) & ((hoaslaminj = $true) | ? [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (! [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) = ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) & ! [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) = ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) & (((X55 @ X54 @ X53)) != ((X52 @ X54 @ X53))) & (((lam @ (X55 @ sh @ one))) = ((lam @ (X52 @ sh @ one)))))) & (! [X54 : subst,X55 : (subst > term > term),X53 : term,X52 : (subst > term > term)] : (? [X56 : term,X58 : subst,X57 : subst] : (((sub @ (X55 @ X57 @ X56) @ X58)) != ((X55 @ (comp @ X57 @ X58) @ (sub @ X56 @ X58)))) | ? [X60 : term,X61 : subst,X59 : subst] : (((sub @ (X52 @ X61 @ X60) @ X59)) != ((X52 @ (comp @ X61 @ X59) @ (sub @ X60 @ X59)))) | (((X55 @ X54 @ X53)) = ((X52 @ X54 @ X53))) | (((lam @ (X55 @ sh @ one))) != ((lam @ (X52 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoasinduction = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction != $true)) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & (? [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) != X62) | ? [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) != X65) | ! [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) = $true) | (((X66 @ X68)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) & ! [X65 : subst,X64 : term] : (((comp @ sh @ (push @ X64 @ X65))) = X65) & ? [X66 : (term > $o),X68 : term,X67 : term,X70 : subst,X69 : (term > $o)] : ((((X69 @ (sub @ X68 @ (push @ X67 @ X70)))) != $true) & (((X66 @ X68)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction_lem3a != $true)) & (! [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) != ((ap @ (sub @ X74 @ id) @ X71))) | (X72 = X74)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X71 : term,X73 : term,X74 : term,X72 : term] : ((((ap @ (sub @ X72 @ id) @ X73)) = ((ap @ (sub @ X74 @ id) @ X71))) & (X72 != X74))) & ((axidl = $true) | ? [X316 : subst] : (((comp @ id @ X316)) != X316)) & (! [X316 : subst] : (((comp @ id @ X316)) = X316) | (axidl != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X30 : term] : ! [X31 : (subst > term > term)] : ? [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) != ((sub @ X30 @ (push @ X32 @ X33))))) & (! [X30 : term] : ? [X31 : (subst > term > term)] : ! [X32 : term,X33 : subst] : (((X31 @ X33 @ X32)) = ((sub @ X30 @ (push @ X32 @ X33)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X442 : term,X443 : term] : ((X442 = X443) | (((sub @ X443 @ sh)) != ((sub @ X442 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X442 : term,X443 : term] : ((X442 != X443) & (((sub @ X443 @ sh)) = ((sub @ X442 @ sh))))) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.79 inference(flattening,[],[f272])).
% 37.84/5.79 thf(f274,plain,(
% 37.84/5.79 ((apinj2 = $true) | ? [X0 : term,X1 : term,X2 : term,X3 : term] : ((((ap @ X0 @ X3)) = ((ap @ X2 @ X1))) & (X1 != X3))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((((ap @ X4 @ X7)) != ((ap @ X6 @ X5))) | (X5 = X7)) | (apinj2 != $true)) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ((laminj = $true) | ? [X8 : term,X9 : term] : ((X8 != X9) & (((lam @ X9)) = ((lam @ X8))))) & (! [X10 : term,X11 : term] : ((X10 = X11) | (((lam @ X11)) != ((lam @ X10)))) | (laminj != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X14 : term,X15 : term] : (($true != ((X12 @ id @ X15 @ id))) | (((X12 @ id @ (ap @ (sub @ X14 @ id) @ X15) @ id)) = $true) | (((X12 @ id @ X14 @ id)) != $true)) & (((X12 @ id @ X13 @ id)) != $true) & (((sP60 @ X12)) != $true))) & (! [X16 : (subst > term > subst > $o),X17 : term] : (? [X18 : term,X19 : term] : ((((X16 @ id @ X19 @ id)) = $true) & ($true != ((X16 @ id @ (ap @ (sub @ X18 @ id) @ X19) @ id))) & (((X16 @ id @ X18 @ id)) = $true)) | (((X16 @ id @ X17 @ id)) = $true) | (((sP60 @ X16)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((sP59 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP59 != $true)) & ((axshiftcons = $true) | ? [X20 : term,X21 : subst] : (((comp @ sh @ (push @ X20 @ X21))) != X21)) & (! [X22 : term,X23 : subst] : (((comp @ sh @ (push @ X22 @ X23))) = X23) | (axshiftcons != $true)) & ((induction2lem_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (induction2lem_lthm != $true)) & ((pushprop_lem1v2 = $true) | ? [X24 : term,X25 : subst,X26 : (term > $o),X27 : (term > $o)] : ((((X27 @ one)) != $true) & ! [X28 : term] : (((X27 @ X28)) = ((X26 @ (sub @ X28 @ (push @ X24 @ X25))))) & (((X26 @ X24)) = $true))) & (! [X29 : term,X30 : subst,X31 : (term > $o),X32 : (term > $o)] : ((((X32 @ one)) = $true) | ? [X33 : term] : (((X32 @ X33)) != ((X31 @ (sub @ X33 @ (push @ X29 @ X30))))) | (((X31 @ X29)) != $true)) | (pushprop_lem1v2 != $true)) & ((apinj1 = $true) | ? [X34 : term,X35 : term,X36 : term,X37 : term] : ((((ap @ X35 @ X37)) = ((ap @ X36 @ X34))) & (X35 != X36))) & (! [X38 : term,X39 : term,X40 : term,X41 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X39 = X40)) | (apinj1 != $true)) & ((sP54 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP54 != $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X42 : d_term] : (d_one = X42) & (! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X45 : subst,X46 : term] : (((sub @ one @ (push @ X46 @ X45))) != X46)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP46 != $true)) & ((sP46 = $true) | (hoasinduction_lem3a_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X47 : d_subst,X48 : d_subst] : ((X47 = X48) | (((d2subst @ X47)) != ((d2subst @ X48)))) & (! [X49 : (term > $o),X50 : term,X51 : subst] : ? [X52 : (term > $o)] : ! [X53 : term] : (((X49 @ (sub @ X53 @ (push @ X50 @ X51)))) = ((X52 @ X53))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X54 : (term > $o),X55 : term,X56 : subst] : ! [X57 : (term > $o)] : ? [X58 : term] : (((X57 @ X58)) != ((X54 @ (sub @ X58 @ (push @ X55 @ X56)))))) & (pushprop_lem2v2_lthm = $true) & (! [X59 : term,X60 : term,X61 : (subst > term > term)] : (? [X62 : term,X63 : subst,X64 : subst] : (((sub @ (X61 @ X64 @ X62) @ X63)) != ((X61 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63)))) | (((ap @ (sub @ X60 @ id) @ X59)) != ((lam @ (X61 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X65 : term,X66 : term,X67 : (subst > term > term)] : (! [X68 : term,X69 : subst,X70 : subst] : (((sub @ (X67 @ X70 @ X68) @ X69)) = ((X67 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69)))) & (((ap @ (sub @ X66 @ id) @ X65)) = ((lam @ (X67 @ sh @ one)))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((X71 = X73) | (((ap @ (sub @ X72 @ id) @ X71)) != ((ap @ (sub @ X74 @ id) @ X73)))) | ? [X75 : term,X76 : term,X77 : term,X78 : term] : ((((ap @ X75 @ X76)) = ((ap @ X78 @ X77))) & (X76 != X77)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X79 : term,X80 : term,X81 : term,X82 : term] : ((X79 != X81) & (((ap @ (sub @ X82 @ id) @ X81)) = ((ap @ (sub @ X80 @ id) @ X79)))) & ! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X83 @ X84)) != ((ap @ X86 @ X85))) | (X84 = X85)))) & ((sP44 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP44 != $true)) & (((d2subst @ d_id)) = id) & (! [X87 : (subst > term > subst > $o)] : ? [X88 : (term > $o)] : ! [X89 : term] : (((X87 @ id @ X89 @ id)) = ((X88 @ X89))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X90 : (subst > term > subst > $o)] : ! [X91 : (term > $o)] : ? [X92 : term] : (((X91 @ X92)) != ((X90 @ id @ X92 @ id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & ((sP43 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP43 != $true)) & ((hoasapinj2 = $true) | ? [X93 : term,X94 : term,X95 : term,X96 : term] : ((X94 != X95) & (((ap @ (sub @ X96 @ id) @ X94)) = ((ap @ (sub @ X93 @ id) @ X95))))) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X98 = X99) | (((ap @ (sub @ X97 @ id) @ X99)) != ((ap @ (sub @ X100 @ id) @ X98)))) | (hoasapinj2 != $true)) & ((sP42 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP42 != $true)) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X101 : term] : (((sub @ X101 @ id)) = X101) | (axvarid != $true)) & ((axvarid = $true) | ? [X102 : term] : (((sub @ X102 @ id)) != X102)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X103 : subst] : (((comp @ X103 @ id)) = X103) & ! [X104 : subst] : (((comp @ id @ X104)) = X104)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X105 : subst] : (((comp @ X105 @ id)) != X105) | ? [X106 : subst] : (((comp @ id @ X106)) != X106)) & ((hoasinduction_lem0_lthm = $true) | ? [X107 : (subst > term > subst > $o)] : ! [X108 : (term > $o)] : ? [X109 : term] : (((X107 @ id @ X109 @ id)) != ((X108 @ X109)))) & (! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X110 @ id @ X112 @ id)) = ((X111 @ X112))) | (hoasinduction_lem0_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) | ((? [X113 : subst] : (((comp @ id @ X113)) != X113) | ? [X114 : subst] : (((comp @ X114 @ id)) != X114)) & ! [X115 : subst] : (((comp @ X115 @ id)) = X115) & ! [X116 : subst] : (((comp @ id @ X116)) = X116))) & ((! [X117 : subst] : (((comp @ id @ X117)) = X117) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X119 : subst] : (((comp @ X119 @ id)) != X119) | ? [X120 : subst] : (((comp @ id @ X120)) != X120) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | (sP40 != $true)) & ((sP40 = $true) | (induction2lem != $true)) & (! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X125 : term] : ! [X126 : (subst > term > term)] : ? [X127 : term,X128 : subst] : (((X126 @ X128 @ X127)) != ((sub @ X125 @ (push @ X127 @ X128))))) & ((hoasinduction_lem3v2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((sP36 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP36 != $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3 != $true)) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP23 != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X129 : subst] : (((comp @ X129 @ id)) = X129) | (axidr != $true)) & ((axidr = $true) | ? [X130 : subst] : (((comp @ X130 @ id)) != X130)) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X131 : (term > $o),X132 : term] : ((((X131 @ X132)) = $true) | ? [X133 : term] : ((((X131 @ X133)) = $true) & (((X131 @ (lam @ X133))) != $true)) | (((sP22 @ X131)) = $true) | ? [X134 : term] : ((((X131 @ X134)) != $true) & (((var @ X134)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X135 : (term > $o),X136 : term] : ((((X135 @ X136)) != $true) & ! [X137 : term] : ((((X135 @ X137)) != $true) | ($true = ((X135 @ (lam @ X137))))) & (((sP22 @ X135)) != $true) & ! [X138 : term] : ((((X135 @ X138)) = $true) | (((var @ X138)) != $true)))) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X139 : d_subst] : (d_id = X139) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & ((pushprop_lem1 = $true) | ? [X140 : (term > $o),X141 : term,X142 : (term > $o),X143 : term,X144 : subst] : ((((X142 @ X141)) = $true) & (((X140 @ (sub @ X141 @ (push @ X143 @ X144)))) != $true))) & (! [X145 : (term > $o),X146 : term,X147 : (term > $o),X148 : term,X149 : subst] : ((((X147 @ X146)) != $true) | (((X145 @ (sub @ X146 @ (push @ X148 @ X149)))) = $true)) | (pushprop_lem1 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (! [X150 : term] : (((sub @ X150 @ id)) = X150) | ? [X151 : term] : (((sub @ X151 @ id)) != X151) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X152 : term] : (((sub @ X152 @ id)) != X152) & ! [X153 : term] : (((sub @ X153 @ id)) = X153))) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X154 : (term > $o),X155 : term,X156 : subst,X157 : (term > $o)] : ((((X154 @ X155)) = $true) & ! [X158 : term] : (((X154 @ (sub @ X158 @ (push @ X155 @ X156)))) = ((X157 @ X158))) & ($true != ((X157 @ one)))) & ! [X159 : subst,X160 : term] : (((sub @ one @ (push @ X160 @ X159))) = X160))) & (! [X161 : (term > $o),X162 : term,X163 : subst,X164 : (term > $o)] : ((((X161 @ X162)) != $true) | ? [X165 : term] : (((X164 @ X165)) != ((X161 @ (sub @ X165 @ (push @ X162 @ X163))))) | (((X164 @ one)) = $true)) | ? [X166 : subst,X167 : term] : (((sub @ one @ (push @ X167 @ X166))) != X167) | (pushprop_lem1v2_lthm != $true)) & ((sP15 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP15 != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((termmset = $true) | ? [X168 : term] : (((sub @ X168 @ id)) != X168)) & (! [X169 : term] : (((sub @ X169 @ id)) = X169) | (termmset != $true)) & (ulamvarsh = $true) & ((pushprop_lem0_lthm = $true) | ? [X170 : (term > $o),X171 : subst,X172 : term] : ! [X173 : (term > $o)] : ? [X174 : term] : (((X173 @ X174)) != ((X170 @ (sub @ X174 @ (push @ X172 @ X171)))))) & (! [X175 : (term > $o),X176 : subst,X177 : term] : ? [X178 : (term > $o)] : ! [X179 : term] : (((X175 @ (sub @ X179 @ (push @ X177 @ X176)))) = ((X178 @ X179))) | (pushprop_lem0_lthm != $true)) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X180 : term] : ! [X181 : (subst > term > term)] : (((sub @ X180 @ (push @ one @ sh))) != ((X181 @ sh @ one)))) & (! [X182 : term] : ? [X183 : (subst > term > term)] : (((sub @ X182 @ (push @ one @ sh))) = ((X183 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoaslamnotap_gthm = $true) & ((sP14 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP14 != $true)) & (pushprop_lem2v2 = $true) & (! [X184 : term] : ? [X185 : (subst > term > term)] : (((X185 @ sh @ one)) = ((sub @ X184 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X186 : term] : ! [X187 : (subst > term > term)] : (((sub @ X186 @ (push @ one @ sh))) != ((X187 @ sh @ one)))) & (lamnotvar = $true) & ! [X188 : d_term,X189 : d_term] : ((((d2term @ X189)) != ((d2term @ X188))) | (X188 = X189)) & ! [X190 : subst] : ? [X191 : d_subst] : (((d2subst @ X191)) = X190) & (! [X192 : subst] : (((push @ (sub @ one @ X192) @ (comp @ sh @ X192))) = X192) | (axscons != $true)) & ((axscons = $true) | ? [X193 : subst] : (((push @ (sub @ one @ X193) @ (comp @ sh @ X193))) != X193)) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X194 : term,X195 : term,X196 : term,X197 : term] : ((X194 != X196) & (((ap @ (sub @ X196 @ id) @ X197)) = ((ap @ (sub @ X194 @ id) @ X195)))) & ! [X198 : term,X199 : term,X200 : term,X201 : term] : ((((ap @ X201 @ X198)) != ((ap @ X199 @ X200))) | (X199 = X201)) & ! [X202 : term] : (((sub @ X202 @ id)) = X202))) & (! [X203 : term,X204 : term,X205 : term,X206 : term] : ((X203 = X205) | (((ap @ (sub @ X203 @ id) @ X204)) != ((ap @ (sub @ X205 @ id) @ X206)))) | ? [X207 : term,X208 : term,X209 : term,X210 : term] : ((((ap @ X208 @ X209)) = ((ap @ X210 @ X207))) & (X208 != X210)) | ? [X211 : term] : (((sub @ X211 @ id)) != X211) | (hoasapinj1_lthm != $true)) & ! [X212 : term] : ? [X213 : d_term] : (((d2term @ X213)) = X212) & ((hoaslaminj = $true) | ? [X214 : subst,X215 : (subst > term > term),X216 : term,X217 : (subst > term > term)] : (! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (X215 @ X220 @ X218) @ X219)) = ((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219)))) & ! [X221 : term,X222 : subst,X223 : subst] : (((sub @ (X217 @ X222 @ X221) @ X223)) = ((X217 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223)))) & (((X217 @ X214 @ X216)) != ((X215 @ X214 @ X216))) & (((lam @ (X217 @ sh @ one))) = ((lam @ (X215 @ sh @ one)))))) & (! [X224 : subst,X225 : (subst > term > term),X226 : term,X227 : (subst > term > term)] : (? [X228 : term,X229 : subst,X230 : subst] : (((X225 @ (comp @ X230 @ X229) @ (sub @ X228 @ X229))) != ((sub @ (X225 @ X230 @ X228) @ X229))) | ? [X231 : term,X232 : subst,X233 : subst] : (((X227 @ (comp @ X232 @ X233) @ (sub @ X231 @ X233))) != ((sub @ (X227 @ X232 @ X231) @ X233))) | (((X227 @ X224 @ X226)) = ((X225 @ X224 @ X226))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X227 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoasinduction = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction != $true)) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & (? [X234 : term,X235 : subst] : (((sub @ one @ (push @ X234 @ X235))) != X234) | ? [X236 : subst,X237 : term] : (((comp @ sh @ (push @ X237 @ X236))) != X236) | ! [X238 : (term > $o),X239 : term,X240 : term,X241 : subst,X242 : (term > $o)] : ((((X242 @ (sub @ X239 @ (push @ X240 @ X241)))) = $true) | (((X238 @ X239)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X243 : term,X244 : subst] : (((sub @ one @ (push @ X243 @ X244))) = X243) & ! [X245 : subst,X246 : term] : (((comp @ sh @ (push @ X246 @ X245))) = X245) & ? [X247 : (term > $o),X248 : term,X249 : term,X250 : subst,X251 : (term > $o)] : ((((X251 @ (sub @ X248 @ (push @ X249 @ X250)))) != $true) & (((X247 @ X248)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction_lem3a != $true)) & (! [X252 : term,X253 : term,X254 : term,X255 : term] : ((((ap @ (sub @ X255 @ id) @ X253)) != ((ap @ (sub @ X254 @ id) @ X252))) | (X254 = X255)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X256 : term,X257 : term,X258 : term,X259 : term] : ((((ap @ (sub @ X258 @ id) @ X256)) = ((ap @ (sub @ X259 @ id) @ X257))) & (X258 != X259))) & ((axidl = $true) | ? [X260 : subst] : (((comp @ id @ X260)) != X260)) & (! [X261 : subst] : (((comp @ id @ X261)) = X261) | (axidl != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X262 : term] : ! [X263 : (subst > term > term)] : ? [X264 : term,X265 : subst] : (((sub @ X262 @ (push @ X264 @ X265))) != ((X263 @ X265 @ X264)))) & (! [X266 : term] : ? [X267 : (subst > term > term)] : ! [X268 : term,X269 : subst] : (((sub @ X266 @ (push @ X268 @ X269))) = ((X267 @ X269 @ X268))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X270 : term,X271 : term] : ((X270 = X271) | (((sub @ X270 @ sh)) != ((sub @ X271 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X272 : term,X273 : term] : ((X272 != X273) & (((sub @ X272 @ sh)) = ((sub @ X273 @ sh))))) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.79 inference(rectify,[],[f273])).
% 37.84/5.79 thf(f275,plain,(
% 37.84/5.79 ((apinj2 = $true) | ((((ap @ sK477 @ sK476)) = ((ap @ sK475 @ sK478))) & (sK476 != sK478))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((((ap @ X4 @ X7)) != ((ap @ X6 @ X5))) | (X5 = X7)) | (apinj2 != $true)) & (ulamvar1 != $true) & (((var @ (d2term @ d_one))) != $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)))))))))))))) & (pushprop = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ((laminj = $true) | ((sK480 != sK479) & (((lam @ sK480)) = ((lam @ sK479))))) & (! [X10 : term,X11 : term] : ((X10 = X11) | (((lam @ X11)) != ((lam @ X10)))) | (laminj != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X14 : term,X15 : term] : ((((sK481 @ id @ X15 @ id)) != $true) | (((sK481 @ id @ (ap @ (sub @ X14 @ id) @ X15) @ id)) = $true) | ($true != ((sK481 @ id @ X14 @ id)))) & (((sK481 @ id @ sK482 @ id)) != $true) & (((sP60 @ sK481)) != $true))) & (! [X16 : (subst > term > subst > $o),X17 : term] : (((((X16 @ id @ (sK484 @ X16) @ id)) = $true) & (((X16 @ id @ (ap @ (sub @ (sK483 @ X16) @ id) @ (sK484 @ X16)) @ id)) != $true) & (((X16 @ id @ (sK483 @ X16) @ id)) = $true)) | (((X16 @ id @ X17 @ id)) = $true) | (((sP60 @ X16)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((sP59 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP59 != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK485 @ sK486))) != sK486)) & (! [X22 : term,X23 : subst] : (((comp @ sh @ (push @ X22 @ X23))) = X23) | (axshiftcons != $true)) & ((induction2lem_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (induction2lem_lthm != $true)) & ((pushprop_lem1v2 = $true) | ((((sK490 @ one)) != $true) & ! [X28 : term] : (((sK490 @ X28)) = ((sK489 @ (sub @ X28 @ (push @ sK487 @ sK488))))) & (((sK489 @ sK487)) = $true))) & (! [X29 : term,X30 : subst,X31 : (term > $o),X32 : (term > $o)] : ((((X32 @ one)) = $true) | (((X32 @ (sK491 @ X32 @ X31 @ X30 @ X29))) != ((X31 @ (sub @ (sK491 @ X32 @ X31 @ X30 @ X29) @ (push @ X29 @ X30))))) | (((X31 @ X29)) != $true)) | (pushprop_lem1v2 != $true)) & ((apinj1 = $true) | ((((ap @ sK493 @ sK495)) = ((ap @ sK494 @ sK492))) & (sK493 != sK494))) & (! [X38 : term,X39 : term,X40 : term,X41 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X39 = X40)) | (apinj1 != $true)) & ((sP54 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP54 != $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & ! [X42 : d_term] : (d_one = X42) & (! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44) | (axvarcons != $true)) & ((axvarcons = $true) | (((sub @ one @ (push @ sK497 @ sK496))) != sK497)) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP46 != $true)) & ((sP46 = $true) | (hoasinduction_lem3a_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & ! [X47 : d_subst,X48 : d_subst] : ((X47 = X48) | (((d2subst @ X47)) != ((d2subst @ X48)))) & (! [X49 : (term > $o),X50 : term,X51 : subst] : ! [X53 : term] : (((X49 @ (sub @ X53 @ (push @ X50 @ X51)))) = ((sK498 @ X51 @ X50 @ X49 @ X53))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X57 : (term > $o)] : (((sK499 @ (sub @ (sK502 @ X57) @ (push @ sK500 @ sK501)))) != ((X57 @ (sK502 @ X57))))) & (pushprop_lem2v2_lthm = $true) & (! [X59 : term,X60 : term,X61 : (subst > term > term)] : ((((X61 @ (comp @ (sK505 @ X61) @ (sK504 @ X61)) @ (sub @ (sK503 @ X61) @ (sK504 @ X61)))) != ((sub @ (X61 @ (sK505 @ X61) @ (sK503 @ X61)) @ (sK504 @ X61)))) | (((ap @ (sub @ X60 @ id) @ X59)) != ((lam @ (X61 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X68 : term,X69 : subst,X70 : subst] : (((sub @ (sK508 @ X70 @ X68) @ X69)) = ((sK508 @ (comp @ X70 @ X69) @ (sub @ X68 @ X69)))) & (((lam @ (sK508 @ sh @ one))) = ((ap @ (sub @ sK507 @ id) @ sK506))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2 = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((X71 = X73) | (((ap @ (sub @ X72 @ id) @ X71)) != ((ap @ (sub @ X74 @ id) @ X73)))) | ((((ap @ sK512 @ sK511)) = ((ap @ sK509 @ sK510))) & (sK511 != sK510)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((sK515 != sK513) & (((ap @ (sub @ sK514 @ id) @ sK513)) = ((ap @ (sub @ sK516 @ id) @ sK515)))) & ! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X83 @ X84)) != ((ap @ X86 @ X85))) | (X84 = X85)))) & ((sP44 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP44 != $true)) & (((d2subst @ d_id)) = id) & (! [X87 : (subst > term > subst > $o)] : ! [X89 : term] : (((X87 @ id @ X89 @ id)) = ((sK517 @ X87 @ X89))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X91 : (term > $o)] : (((X91 @ (sK519 @ X91))) != ((sK518 @ id @ (sK519 @ X91) @ id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (one = ((d2term @ d_one))) & ((sP43 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP43 != $true)) & ((hoasapinj2 = $true) | ((sK522 != sK521) & (((ap @ (sub @ sK520 @ id) @ sK522)) = ((ap @ (sub @ sK523 @ id) @ sK521))))) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X98 = X99) | (((ap @ (sub @ X97 @ id) @ X99)) != ((ap @ (sub @ X100 @ id) @ X98)))) | (hoasapinj2 != $true)) & ((sP42 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP42 != $true)) & (hoasinduction_lem3b_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X101 : term] : (((sub @ X101 @ id)) = X101) | (axvarid != $true)) & ((axvarid = $true) | (sK524 != ((sub @ sK524 @ id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X103 : subst] : (((comp @ X103 @ id)) = X103) & ! [X104 : subst] : (((comp @ id @ X104)) = X104)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK525 @ id)) != sK525) | (sK526 != ((comp @ id @ sK526)))) & ((hoasinduction_lem0_lthm = $true) | ! [X108 : (term > $o)] : (((sK527 @ id @ (sK528 @ X108) @ id)) != ((X108 @ (sK528 @ X108))))) & (! [X110 : (subst > term > subst > $o)] : ! [X112 : term] : (((X110 @ id @ X112 @ id)) = ((sK529 @ X110 @ X112))) | (hoasinduction_lem0_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) | (((((comp @ id @ sK530)) != sK530) | (((comp @ sK531 @ id)) != sK531)) & ! [X115 : subst] : (((comp @ X115 @ id)) = X115) & ! [X116 : subst] : (((comp @ id @ X116)) = X116))) & ((! [X117 : subst] : (((comp @ id @ X117)) = X117) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | (((comp @ sK532 @ id)) != sK532) | (((comp @ id @ sK533)) != sK533) | (substmonoid_lthm != $true)) & ((induction2lem = $true) | (sP40 != $true)) & ((sP40 = $true) | (induction2lem != $true)) & (! [X121 : term] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((sK534 @ X121 @ X124 @ X123))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X126 : (subst > term > term)] : (((X126 @ (sK537 @ X126) @ (sK536 @ X126))) != ((sub @ sK535 @ (push @ (sK536 @ X126) @ (sK537 @ X126)))))) & ((hoasinduction_lem3v2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((sP36 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP36 != $true)) & (axassoc = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP34 != $true)) & ((sP34 = $true) | (hoasinduction_lem3 != $true)) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP23 != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X129 : subst] : (((comp @ X129 @ id)) = X129) | (axidr != $true)) & ((axidr = $true) | (sK538 != ((comp @ sK538 @ id)))) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X131 : (term > $o),X132 : term] : ((((X131 @ X132)) = $true) | ((((X131 @ (sK539 @ X131))) = $true) & (((X131 @ (lam @ (sK539 @ X131)))) != $true)) | (((sP22 @ X131)) = $true) | ((((X131 @ (sK540 @ X131))) != $true) & (((var @ (sK540 @ X131))) = $true))) | (induction != $true)) & ((induction = $true) | ((((sK541 @ sK542)) != $true) & ! [X137 : term] : ((((sK541 @ X137)) != $true) | (((sK541 @ (lam @ X137))) = $true)) & (((sP22 @ sK541)) != $true) & ! [X138 : term] : ((((sK541 @ X138)) = $true) | (((var @ X138)) != $true)))) & (termmset_gthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ! [X139 : d_subst] : (d_id = X139) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axapp = $true) & ((pushprop_lem1 = $true) | ((((sK545 @ sK544)) = $true) & (((sK543 @ (sub @ sK544 @ (push @ sK546 @ sK547)))) != $true))) & (! [X145 : (term > $o),X146 : term,X147 : (term > $o),X148 : term,X149 : subst] : ((((X147 @ X146)) != $true) | (((X145 @ (sub @ X146 @ (push @ X148 @ X149)))) = $true)) | (pushprop_lem1 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & (hoasapnotvar = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (! [X150 : term] : (((sub @ X150 @ id)) = X150) | (sK548 != ((sub @ sK548 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((sK549 != ((sub @ sK549 @ id))) & ! [X153 : term] : (((sub @ X153 @ id)) = X153))) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1v2_lthm = $true) | (((((sK550 @ sK551)) = $true) & ! [X158 : term] : (((sK553 @ X158)) = ((sK550 @ (sub @ X158 @ (push @ sK551 @ sK552))))) & (((sK553 @ one)) != $true)) & ! [X159 : subst,X160 : term] : (((sub @ one @ (push @ X160 @ X159))) = X160))) & (! [X161 : (term > $o),X162 : term,X163 : subst,X164 : (term > $o)] : ((((X161 @ X162)) != $true) | (((X161 @ (sub @ (sK554 @ X164 @ X163 @ X162 @ X161) @ (push @ X162 @ X163)))) != ((X164 @ (sK554 @ X164 @ X163 @ X162 @ X161)))) | (((X164 @ one)) = $true)) | (((sub @ one @ (push @ sK556 @ sK555))) != sK556) | (pushprop_lem1v2_lthm != $true)) & ((sP15 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP15 != $true)) & (pushprop_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((termmset = $true) | (sK557 != ((sub @ sK557 @ id)))) & (! [X169 : term] : (((sub @ X169 @ id)) = X169) | (termmset != $true)) & (ulamvarsh = $true) & ((pushprop_lem0_lthm = $true) | ! [X173 : (term > $o)] : (((sK558 @ (sub @ (sK561 @ X173) @ (push @ sK560 @ sK559)))) != ((X173 @ (sK561 @ X173))))) & (! [X175 : (term > $o),X176 : subst,X177 : term] : ! [X179 : term] : (((sK562 @ X177 @ X176 @ X175 @ X179)) = ((X175 @ (sub @ X179 @ (push @ X177 @ X176))))) | (pushprop_lem0_lthm != $true)) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X181 : (subst > term > term)] : (((X181 @ sh @ one)) != ((sub @ sK563 @ (push @ one @ sh))))) & (! [X182 : term] : (((sK564 @ X182 @ sh @ one)) = ((sub @ X182 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoaslamnotap_gthm = $true) & ((sP14 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP14 != $true)) & (pushprop_lem2v2 = $true) & (! [X184 : term] : (((sK565 @ X184 @ sh @ one)) = ((sub @ X184 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X187 : (subst > term > term)] : (((sub @ sK566 @ (push @ one @ sh))) != ((X187 @ sh @ one)))) & (lamnotvar = $true) & ! [X188 : d_term,X189 : d_term] : ((((d2term @ X189)) != ((d2term @ X188))) | (X188 = X189)) & ! [X190 : subst] : (((d2subst @ (sK567 @ X190))) = X190) & (! [X192 : subst] : (((push @ (sub @ one @ X192) @ (comp @ sh @ X192))) = X192) | (axscons != $true)) & ((axscons = $true) | (sK568 != ((push @ (sub @ one @ sK568) @ (comp @ sh @ sK568))))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) | (((sK571 != sK569) & (((ap @ (sub @ sK569 @ id) @ sK570)) = ((ap @ (sub @ sK571 @ id) @ sK572)))) & ! [X198 : term,X199 : term,X200 : term,X201 : term] : ((((ap @ X201 @ X198)) != ((ap @ X199 @ X200))) | (X199 = X201)) & ! [X202 : term] : (((sub @ X202 @ id)) = X202))) & (! [X203 : term,X204 : term,X205 : term,X206 : term] : ((X203 = X205) | (((ap @ (sub @ X203 @ id) @ X204)) != ((ap @ (sub @ X205 @ id) @ X206)))) | ((((ap @ sK576 @ sK573)) = ((ap @ sK574 @ sK575))) & (sK576 != sK574)) | (((sub @ sK577 @ id)) != sK577) | (hoasapinj1_lthm != $true)) & ! [X212 : term] : (((d2term @ (sK578 @ X212))) = X212) & ((hoaslaminj = $true) | (! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (sK580 @ X220 @ X218) @ X219)) = ((sK580 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219)))) & ! [X221 : term,X222 : subst,X223 : subst] : (((sK582 @ (comp @ X222 @ X223) @ (sub @ X221 @ X223))) = ((sub @ (sK582 @ X222 @ X221) @ X223))) & (((sK582 @ sK579 @ sK581)) != ((sK580 @ sK579 @ sK581))) & (((lam @ (sK580 @ sh @ one))) = ((lam @ (sK582 @ sh @ one)))))) & (! [X224 : subst,X225 : (subst > term > term),X226 : term,X227 : (subst > term > term)] : ((((sub @ (X225 @ (sK585 @ X225) @ (sK583 @ X225)) @ (sK584 @ X225))) != ((X225 @ (comp @ (sK585 @ X225) @ (sK584 @ X225)) @ (sub @ (sK583 @ X225) @ (sK584 @ X225))))) | (((X227 @ (comp @ (sK587 @ X227) @ (sK588 @ X227)) @ (sub @ (sK586 @ X227) @ (sK588 @ X227)))) != ((sub @ (X227 @ (sK587 @ X227) @ (sK586 @ X227)) @ (sK588 @ X227)))) | (((X227 @ X224 @ X226)) = ((X225 @ X224 @ X226))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X227 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoasinduction = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction != $true)) & (axclos = $true) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_gthm = $true) & ((sK589 != ((sub @ one @ (push @ sK589 @ sK590)))) | (sK591 != ((comp @ sh @ (push @ sK592 @ sK591)))) | ! [X238 : (term > $o),X239 : term,X240 : term,X241 : subst,X242 : (term > $o)] : ((((X242 @ (sub @ X239 @ (push @ X240 @ X241)))) = $true) | (((X238 @ X239)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X243 : term,X244 : subst] : (((sub @ one @ (push @ X243 @ X244))) = X243) & ! [X245 : subst,X246 : term] : (((comp @ sh @ (push @ X246 @ X245))) = X245) & ((((sK597 @ (sub @ sK594 @ (push @ sK595 @ sK596)))) != $true) & (((sK593 @ sK594)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | (sP5 != $true)) & ((sP5 = $true) | (hoasinduction_lem3a != $true)) & (! [X252 : term,X253 : term,X254 : term,X255 : term] : ((((ap @ (sub @ X255 @ id) @ X253)) != ((ap @ (sub @ X254 @ id) @ X252))) | (X254 = X255)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK601 @ id) @ sK599)) = ((ap @ (sub @ sK600 @ id) @ sK598))) & (sK601 != sK600))) & ((axidl = $true) | (sK602 != ((comp @ id @ sK602)))) & (! [X261 : subst] : (((comp @ id @ X261)) = X261) | (axidl != $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X263 : (subst > term > term)] : (((X263 @ (sK605 @ X263) @ (sK604 @ X263))) != ((sub @ sK603 @ (push @ (sK604 @ X263) @ (sK605 @ X263)))))) & (! [X266 : term] : ! [X268 : term,X269 : subst] : (((sub @ X266 @ (push @ X268 @ X269))) = ((sK606 @ X266 @ X269 @ X268))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP4 != $true)) & ((sP4 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X270 : term,X271 : term] : ((X270 = X271) | (((sub @ X270 @ sh)) != ((sub @ X271 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ((sK607 != sK608) & (((sub @ sK608 @ sh)) = ((sub @ sK607 @ sh))))) & (apnotvar = $true) & (hoasinduction_lem2_gthm = $true)),
% 37.84/5.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,vAPP,vAPP,sK485,sK486,sK487,sK488,sK489,sK490,vAPP,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,sK499,sK500,sK501,vAPP,vAPP,vAPP,vAPP,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,vAPP,sK518,vAPP,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,vAPP,vAPP,sK530,sK531,sK532,sK533,vAPP,sK535,vAPP,vAPP,sK538,vAPP,vAPP,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,vAPP,sK555,sK556,sK557,sK558,sK559,sK560,vAPP,vAPP,sK563,vAPP,vAPP,sK566,vAPP,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,vAPP,sK579,sK580,sK581,sK582,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK589,sK590,sK591,sK592,sK593,sK594,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,sK603,vAPP,vAPP,vAPP,sK607,sK608]),skolemize(X0,sK475),skolemize(X1,sK476),skolemize(X2,sK477),skolemize(X3,sK478),skolemize(X8,sK479),skolemize(X9,sK480),skolemize(X12,sK481),skolemize(X13,sK482),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X20,sK485),skolemize(X21,sK486),skolemize(X24,sK487),skolemize(X25,sK488),skolemize(X26,sK489),skolemize(X27,sK490),skolemize(X21,sK71 @ X11),skolemize(X34,sK492),skolemize(X35,sK493),skolemize(X36,sK494),skolemize(X37,sK495),skolemize(X45,sK496),skolemize(X46,sK497),skolemize(X21,sK71 @ X11),skolemize(X54,sK499),skolemize(X55,sK500),skolemize(X56,sK501),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X65,sK506),skolemize(X66,sK507),skolemize(X67,sK508),skolemize(X75,sK509),skolemize(X76,sK510),skolemize(X77,sK511),skolemize(X78,sK512),skolemize(X79,sK513),skolemize(X80,sK514),skolemize(X81,sK515),skolemize(X82,sK516),skolemize(X21,sK71 @ X11),skolemize(X90,sK518),skolemize(X21,sK71 @ X11),skolemize(X93,sK520),skolemize(X94,sK521),skolemize(X95,sK522),skolemize(X96,sK523),skolemize(X102,sK524),skolemize(X105,sK525),skolemize(X106,sK526),skolemize(X107,sK527),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X113,sK530),skolemize(X114,sK531),skolemize(X119,sK532),skolemize(X120,sK533),skolemize(X21,sK71 @ X11),skolemize(X125,sK535),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X130,sK538),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X135,sK541),skolemize(X136,sK542),skolemize(X140,sK543),skolemize(X141,sK544),skolemize(X142,sK545),skolemize(X143,sK546),skolemize(X144,sK547),skolemize(X151,sK548),skolemize(X152,sK549),skolemize(X154,sK550),skolemize(X155,sK551),skolemize(X156,sK552),skolemize(X157,sK553),skolemize(X21,sK71 @ X11),skolemize(X166,sK555),skolemize(X167,sK556),skolemize(X168,sK557),skolemize(X170,sK558),skolemize(X171,sK559),skolemize(X172,sK560),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X180,sK563),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X186,sK566),skolemize(X21,sK71 @ X11),skolemize(X193,sK568),skolemize(X194,sK569),skolemize(X195,sK570),skolemize(X196,sK571),skolemize(X197,sK572),skolemize(X207,sK573),skolemize(X208,sK574),skolemize(X209,sK575),skolemize(X210,sK576),skolemize(X211,sK577),skolemize(X21,sK71 @ X11),skolemize(X214,sK579),skolemize(X215,sK580),skolemize(X216,sK581),skolemize(X217,sK582),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X234,sK589),skolemize(X235,sK590),skolemize(X236,sK591),skolemize(X237,sK592),skolemize(X247,sK593),skolemize(X248,sK594),skolemize(X249,sK595),skolemize(X250,sK596),skolemize(X251,sK597),skolemize(X256,sK598),skolemize(X257,sK599),skolemize(X258,sK600),skolemize(X259,sK601),skolemize(X260,sK602),skolemize(X262,sK603),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X21,sK71 @ X11),skolemize(X272,sK607),skolemize(X273,sK608)],[f274])).
% 37.84/5.80 thf(f285,plain,(
% 37.84/5.80 (sP1 = $true) | (((sP0 @ sK61)) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f80])).
% 37.84/5.80 thf(f286,plain,(
% 37.84/5.80 (sP1 = $true) | (((sK61 @ id @ (lam @ sK62) @ id)) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f80])).
% 37.84/5.80 thf(f293,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP0 @ X0)) = $true) | ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | (((sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) != ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))))) | (((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f83])).
% 37.84/5.80 thf(f295,plain,(
% 37.84/5.80 (hoasinduction_lem3 != $true) | (sP1 != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f84])).
% 37.84/5.80 thf(f517,plain,(
% 37.84/5.80 (sP34 = $true) | (((sK254 @ id @ (lam @ sK253) @ id)) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f170])).
% 37.84/5.80 thf(f520,plain,(
% 37.84/5.80 (((sP33 @ sK254)) != $true) | (sP34 = $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f170])).
% 37.84/5.80 thf(f524,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP33 @ X0)) = $true) | (((X0 @ id @ (sK267 @ X1 @ X0) @ id)) = $true) | (((sub @ (X1 @ (sK264 @ X1) @ (sK266 @ X1)) @ (sK265 @ X1))) != ((X1 @ (comp @ (sK264 @ X1) @ (sK265 @ X1)) @ (sub @ (sK266 @ X1) @ (sK265 @ X1))))) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f173])).
% 37.84/5.80 thf(f576,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((sub @ (X6 @ (sK310 @ X6) @ (sK309 @ X6)) @ (sK311 @ X6))) != ((X6 @ (comp @ (sK310 @ X6) @ (sK311 @ X6)) @ (sub @ (sK309 @ X6) @ (sK311 @ X6))))) | (((sP28 @ X0)) != $true) | (((X0 @ id @ (X6 @ id @ (sK308 @ X6 @ X0)) @ id)) != $true) | ($true = ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)))) )),
% 37.84/5.80 inference(cnf_transformation,[],[f189])).
% 37.84/5.80 thf(f579,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (lam @ (sK307 @ X0 @ sh @ one)) @ id)) != $true) | (((sP28 @ X0)) = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f189])).
% 37.84/5.80 thf(f624,plain,(
% 37.84/5.80 ( ! [X6 : (term > $o),X5 : term] : ((((X6 @ X5)) = $true) | (((X6 @ (lam @ (sK344 @ X6)))) != $true) | (((var @ (sK343 @ X6))) = $true) | (sP20 != $true) | (((sP19 @ X6)) = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f214])).
% 37.84/5.80 thf(f626,plain,(
% 37.84/5.80 (((sK341 @ sK340)) != $true) | (sP20 = $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f214])).
% 37.84/5.80 thf(f629,plain,(
% 37.84/5.80 ( ! [X3 : term] : ((((sK341 @ (sK342 @ X3))) = $true) | (((sK341 @ (lam @ X3))) = $true) | (sP20 = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f214])).
% 37.84/5.80 thf(f631,plain,(
% 37.84/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (ap @ (sK345 @ X0) @ (sK346 @ X0)))) != $true) | (((sP19 @ X0)) != $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f217])).
% 37.84/5.80 thf(f670,plain,(
% 37.84/5.80 ( ! [X11 : term,X19 : (term > $o),X12 : (subst > term > subst > $o)] : ((((X12 @ id @ X11 @ id)) = $true) | (sP12 = $true) | (sP13 = $true) | (((sP11 @ X12)) = $true) | (sP14 != $true) | (((X19 @ (sK388 @ X19))) != ((sK387 @ id @ (sK388 @ X19) @ id))) | (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true) | (sK389 != ((sub @ sK389 @ id)))) )),
% 37.84/5.80 inference(cnf_transformation,[],[f233])).
% 37.84/5.80 thf(f678,plain,(
% 37.84/5.80 ( ! [X2 : (subst > term > term)] : (($true = ((sK380 @ id @ (sK384 @ X2) @ id))) | (((X2 @ (comp @ (sK383 @ X2) @ (sK381 @ X2)) @ (sub @ (sK382 @ X2) @ (sK381 @ X2)))) != ((sub @ (X2 @ (sK383 @ X2) @ (sK382 @ X2)) @ (sK381 @ X2)))) | (((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (sP14 = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f233])).
% 37.84/5.80 thf(f680,plain,(
% 37.84/5.80 (sP14 = $true) | (((sK380 @ id @ sK379 @ id)) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f233])).
% 37.84/5.80 thf(f681,plain,(
% 37.84/5.80 (sP13 != $true) | (((sK392 @ sK393)) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f236])).
% 37.84/5.80 thf(f685,plain,(
% 37.84/5.80 ( ! [X7 : term] : ((sP13 != $true) | (((sK392 @ (lam @ X7))) = $true) | ($true = ((sK392 @ (sK394 @ X7))))) )),
% 37.84/5.80 inference(cnf_transformation,[],[f236])).
% 37.84/5.80 thf(f691,plain,(
% 37.84/5.80 (sP12 != $true) | (((sK398 @ (lam @ sK400))) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f239])).
% 37.84/5.80 thf(f692,plain,(
% 37.84/5.80 ( ! [X18 : term] : ((sP12 != $true) | (((sK399 @ id @ X18 @ id)) = ((sK398 @ X18)))) )),
% 37.84/5.80 inference(cnf_transformation,[],[f239])).
% 37.84/5.80 thf(f693,plain,(
% 37.84/5.80 ( ! [X13 : (subst > term > term)] : ((((sK399 @ id @ (sK404 @ X13) @ id)) = $true) | (sP12 != $true) | (((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true) | (((X13 @ (comp @ (sK403 @ X13) @ (sK401 @ X13)) @ (sub @ (sK402 @ X13) @ (sK401 @ X13)))) != ((sub @ (X13 @ (sK403 @ X13) @ (sK402 @ X13)) @ (sK401 @ X13))))) )),
% 37.84/5.80 inference(cnf_transformation,[],[f239])).
% 37.84/5.80 thf(f701,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (ap @ (sub @ (sK406 @ X0) @ id) @ (sK405 @ X0)) @ id)) != $true) | (((sP11 @ X0)) != $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f242])).
% 37.84/5.80 thf(f822,plain,(
% 37.84/5.80 ( ! [X212 : term] : ((((d2term @ (sK578 @ X212))) = X212)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f833,plain,(
% 37.84/5.80 ( ! [X190 : subst] : ((((d2subst @ (sK567 @ X190))) = X190)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f876,plain,(
% 37.84/5.80 ( ! [X139 : d_subst] : ((d_id = X139)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f902,plain,(
% 37.84/5.80 (hoasinduction_lem3 = $true) | (sP34 != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f921,plain,(
% 37.84/5.80 ( ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((X110 @ id @ X112 @ id)) = ((sK529 @ X110 @ X112))) | (hoasinduction_lem0_lthm != $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f922,plain,(
% 37.84/5.80 ( ! [X108 : (term > $o)] : ((((sK527 @ id @ (sK528 @ X108) @ id)) != ((X108 @ (sK528 @ X108)))) | (hoasinduction_lem0_lthm = $true)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f942,plain,(
% 37.84/5.80 (one = ((d2term @ d_one)))),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f947,plain,(
% 37.84/5.80 (((d2subst @ d_id)) = id)),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f956,plain,(
% 37.84/5.80 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f973,plain,(
% 37.84/5.80 ( ! [X42 : d_term] : ((d_one = X42)) )),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f1005,plain,(
% 37.84/5.80 (((var @ (d2term @ d_one))) != $true)),
% 37.84/5.80 inference(cnf_transformation,[],[f275])).
% 37.84/5.80 thf(f1012,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ ((^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true) | (((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true) | (((sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) != ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))))) | (((sP0 @ X0)) = $true)) )),
% 37.84/5.80 inference(definition_unfolding,[],[f293,f956])).
% 37.84/5.80 thf(f1045,plain,(
% 37.84/5.80 ( ! [X11 : term,X19 : (term > $o),X12 : (subst > term > subst > $o)] : ((((X12 @ id @ X11 @ id)) = $true) | (((X19 @ (sK388 @ X19))) = $true) | (sK389 != ((sub @ sK389 @ id))) | (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true) | (sP13 = $true) | (((sK387 @ id @ (sK388 @ X19) @ id)) = $true) | (((sP11 @ X12)) = $true) | (sP14 != $true) | (sP12 = $true)) )),
% 37.84/5.80 inference(xor_proxy_clausification,[],[f670])).
% 37.84/5.80 thf(f1046,plain,(
% 37.84/5.80 ( ! [X11 : term,X19 : (term > $o),X12 : (subst > term > subst > $o)] : ((sK389 != ((sub @ sK389 @ id))) | (((X12 @ id @ X11 @ id)) = $true) | (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true) | ($false = ((X19 @ (sK388 @ X19)))) | (sP12 = $true) | ($false = ((sK387 @ id @ (sK388 @ X19) @ id))) | (sP14 != $true) | (((sP11 @ X12)) = $true) | (sP13 = $true)) )),
% 37.84/5.80 inference(xor_proxy_clausification,[],[f670])).
% 37.84/5.80 thf(f1081,plain,(
% 37.84/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) != ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))))) | (((sP0 @ X0)) = $true) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true) | (((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true)) )),
% 37.84/5.80 inference(beta-eta_normalization,[],[f1012])).
% 37.84/5.80 thf(f1087,plain,(
% 37.84/5.80 ( ! [X18 : term] : ((((sK399 @ id @ X18 @ id)) = $false) | (sP12 != $true) | (((sK398 @ X18)) = $true)) )),
% 37.84/5.80 inference(iff_proxy_clausification,[],[f692])).
% 37.84/5.80 thf(f1090,plain,(
% 37.84/5.80 ( ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((X110 @ id @ X112 @ id)) = $true) | (hoasinduction_lem0_lthm != $true) | ($false = ((sK529 @ X110 @ X112)))) )),
% 37.84/5.80 inference(iff_proxy_clausification,[],[f921])).
% 37.84/5.80 thf(f1091,plain,(
% 37.84/5.80 ( ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((sK529 @ X110 @ X112)) = $true) | ($false = ((X110 @ id @ X112 @ id))) | (hoasinduction_lem0_lthm != $true)) )),
% 37.84/5.80 inference(iff_proxy_clausification,[],[f921])).
% 37.84/5.80 thf(f1149,plain,(
% 37.84/5.80 ( ! [X108 : (term > $o)] : ((hoasinduction_lem0_lthm = $true) | (((X108 @ (sK528 @ X108))) = $true) | (((sK527 @ id @ (sK528 @ X108) @ id)) = $true)) )),
% 37.84/5.80 inference(xor_proxy_clausification,[],[f922])).
% 37.84/5.80 thf(f1150,plain,(
% 37.84/5.80 ( ! [X108 : (term > $o)] : ((hoasinduction_lem0_lthm = $true) | ($false = ((X108 @ (sK528 @ X108)))) | ($false = ((sK527 @ id @ (sK528 @ X108) @ id)))) )),
% 37.84/5.80 inference(xor_proxy_clausification,[],[f922])).
% 37.84/5.80 thf(f1285,definition,(
% 37.84/5.80 spl609_35 <=> (sP1 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_35])],[avatar_definition])).
% 37.84/5.80 thf(f1288,definition,(
% 37.84/5.80 spl609_36 <=> (hoasinduction_lem3 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_36])],[avatar_definition])).
% 37.84/5.80 thf(f1326,definition,(
% 37.84/5.80 spl609_46 <=> (sP12 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_46])],[avatar_definition])).
% 37.84/5.80 thf(f1329,definition,(
% 37.84/5.80 spl609_47 <=> (((sK398 @ (lam @ sK400))) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_47])],[avatar_definition])).
% 37.84/5.80 thf(f1330,plain,(
% 37.84/5.80 (((sK398 @ (lam @ sK400))) != $true) | spl609_47),
% 37.84/5.80 inference(avatar_component_clause,[],[f1329])).
% 37.84/5.80 thf(f1331,plain,(
% 37.84/5.80 ~spl609_46 | ~spl609_47),
% 37.84/5.80 inference(avatar_split_clause,[],[f691,f1329,f1326])).
% 37.84/5.80 thf(f1403,definition,(
% 37.84/5.80 spl609_67 <=> ! [X19 : (term > $o)] : (($false = ((X19 @ (sK388 @ X19)))) | ($false = ((sK387 @ id @ (sK388 @ X19) @ id))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_67])],[avatar_definition])).
% 37.84/5.80 thf(f1404,plain,(
% 37.84/5.80 ( ! [X19 : (term > $o)] : (($false = ((sK387 @ id @ (sK388 @ X19) @ id))) | ($false = ((X19 @ (sK388 @ X19))))) ) | ~spl609_67),
% 37.84/5.80 inference(avatar_component_clause,[],[f1403])).
% 37.84/5.80 thf(f1406,definition,(
% 37.84/5.80 spl609_68 <=> (sP14 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_68])],[avatar_definition])).
% 37.84/5.80 thf(f1410,definition,(
% 37.84/5.80 spl609_69 <=> (sK389 = ((sub @ sK389 @ id)))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_69])],[avatar_definition])).
% 37.84/5.80 thf(f1411,plain,(
% 37.84/5.80 (sK389 != ((sub @ sK389 @ id))) | spl609_69),
% 37.84/5.80 inference(avatar_component_clause,[],[f1410])).
% 37.84/5.80 thf(f1416,definition,(
% 37.84/5.80 spl609_71 <=> (sP13 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_71])],[avatar_definition])).
% 37.84/5.80 thf(f1420,definition,(
% 37.84/5.80 spl609_72 <=> ! [X19 : (term > $o)] : ((((sK387 @ id @ (sK388 @ X19) @ id)) = $true) | (((X19 @ (sK388 @ X19))) = $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_72])],[avatar_definition])).
% 37.84/5.80 thf(f1421,plain,(
% 37.84/5.80 ( ! [X19 : (term > $o)] : ((((sK387 @ id @ (sK388 @ X19) @ id)) = $true) | (((X19 @ (sK388 @ X19))) = $true)) ) | ~spl609_72),
% 37.84/5.80 inference(avatar_component_clause,[],[f1420])).
% 37.84/5.80 thf(f1451,definition,(
% 37.84/5.80 spl609_79 <=> (sP20 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_79])],[avatar_definition])).
% 37.84/5.80 thf(f1479,definition,(
% 37.84/5.80 spl609_87 <=> (((sK341 @ sK340)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_87])],[avatar_definition])).
% 37.84/5.80 thf(f1480,plain,(
% 37.84/5.80 (((sK341 @ sK340)) != $true) | spl609_87),
% 37.84/5.80 inference(avatar_component_clause,[],[f1479])).
% 37.84/5.80 thf(f1481,plain,(
% 37.84/5.80 ~spl609_87 | spl609_79),
% 37.84/5.80 inference(avatar_split_clause,[],[f626,f1451,f1479])).
% 37.84/5.80 thf(f1572,definition,(
% 37.84/5.80 spl609_111 <=> ! [X2 : (subst > term > term)] : (($true = ((sK380 @ id @ (sK384 @ X2) @ id))) | (((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (((X2 @ (comp @ (sK383 @ X2) @ (sK381 @ X2)) @ (sub @ (sK382 @ X2) @ (sK381 @ X2)))) != ((sub @ (X2 @ (sK383 @ X2) @ (sK382 @ X2)) @ (sK381 @ X2)))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_111])],[avatar_definition])).
% 37.84/5.80 thf(f1573,plain,(
% 37.84/5.80 ( ! [X2 : (subst > term > term)] : (($true = ((sK380 @ id @ (sK384 @ X2) @ id))) | (((X2 @ (comp @ (sK383 @ X2) @ (sK381 @ X2)) @ (sub @ (sK382 @ X2) @ (sK381 @ X2)))) != ((sub @ (X2 @ (sK383 @ X2) @ (sK382 @ X2)) @ (sK381 @ X2)))) | (((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) ) | ~spl609_111),
% 37.84/5.80 inference(avatar_component_clause,[],[f1572])).
% 37.84/5.80 thf(f1574,plain,(
% 37.84/5.80 spl609_68 | spl609_111),
% 37.84/5.80 inference(avatar_split_clause,[],[f678,f1572,f1406])).
% 37.84/5.80 thf(f1651,definition,(
% 37.84/5.80 spl609_130 <=> ! [X13 : (subst > term > term)] : ((((sK399 @ id @ (sK404 @ X13) @ id)) = $true) | (((X13 @ (comp @ (sK403 @ X13) @ (sK401 @ X13)) @ (sub @ (sK402 @ X13) @ (sK401 @ X13)))) != ((sub @ (X13 @ (sK403 @ X13) @ (sK402 @ X13)) @ (sK401 @ X13)))) | (((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_130])],[avatar_definition])).
% 37.84/5.80 thf(f1652,plain,(
% 37.84/5.80 ( ! [X13 : (subst > term > term)] : ((((sK399 @ id @ (sK404 @ X13) @ id)) = $true) | (((X13 @ (comp @ (sK403 @ X13) @ (sK401 @ X13)) @ (sub @ (sK402 @ X13) @ (sK401 @ X13)))) != ((sub @ (X13 @ (sK403 @ X13) @ (sK402 @ X13)) @ (sK401 @ X13)))) | (((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true)) ) | ~spl609_130),
% 37.84/5.80 inference(avatar_component_clause,[],[f1651])).
% 37.84/5.80 thf(f1653,plain,(
% 37.84/5.80 spl609_130 | ~spl609_46),
% 37.84/5.80 inference(avatar_split_clause,[],[f693,f1326,f1651])).
% 37.84/5.80 thf(f1776,definition,(
% 37.84/5.80 spl609_161 <=> (((sK61 @ id @ (lam @ sK62) @ id)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_161])],[avatar_definition])).
% 37.84/5.80 thf(f1777,plain,(
% 37.84/5.80 (((sK61 @ id @ (lam @ sK62) @ id)) != $true) | spl609_161),
% 37.84/5.80 inference(avatar_component_clause,[],[f1776])).
% 37.84/5.80 thf(f1778,plain,(
% 37.84/5.80 ~spl609_161 | spl609_35),
% 37.84/5.80 inference(avatar_split_clause,[],[f286,f1285,f1776])).
% 37.84/5.80 thf(f1788,definition,(
% 37.84/5.80 spl609_164 <=> ! [X12 : (subst > term > subst > $o),X11 : term] : ((((X12 @ id @ X11 @ id)) = $true) | (((sP11 @ X12)) = $true) | (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_164])],[avatar_definition])).
% 37.84/5.80 thf(f1789,plain,(
% 37.84/5.80 ( ! [X11 : term,X12 : (subst > term > subst > $o)] : ((((X12 @ id @ X11 @ id)) = $true) | (((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true) | (((sP11 @ X12)) = $true)) ) | ~spl609_164),
% 37.84/5.80 inference(avatar_component_clause,[],[f1788])).
% 37.84/5.80 thf(f1790,plain,(
% 37.84/5.80 ~spl609_69 | spl609_71 | spl609_164 | spl609_46 | ~spl609_68 | spl609_67),
% 37.84/5.80 inference(avatar_split_clause,[],[f1046,f1403,f1406,f1326,f1788,f1416,f1410])).
% 37.84/5.80 thf(f1791,plain,(
% 37.84/5.80 spl609_72 | spl609_71 | spl609_46 | ~spl609_69 | spl609_164 | ~spl609_68),
% 37.84/5.80 inference(avatar_split_clause,[],[f1045,f1406,f1788,f1410,f1326,f1416,f1420])).
% 37.84/5.80 thf(f1967,definition,(
% 37.84/5.80 spl609_206 <=> (sP34 = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_206])],[avatar_definition])).
% 37.84/5.80 thf(f1970,definition,(
% 37.84/5.80 spl609_207 <=> (((sP33 @ sK254)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_207])],[avatar_definition])).
% 37.84/5.80 thf(f1971,plain,(
% 37.84/5.80 (((sP33 @ sK254)) != $true) | spl609_207),
% 37.84/5.80 inference(avatar_component_clause,[],[f1970])).
% 37.84/5.80 thf(f1972,plain,(
% 37.84/5.80 spl609_206 | ~spl609_207),
% 37.84/5.80 inference(avatar_split_clause,[],[f520,f1970,f1967])).
% 37.84/5.80 thf(f2110,plain,(
% 37.84/5.80 spl609_36 | ~spl609_206),
% 37.84/5.80 inference(avatar_split_clause,[],[f902,f1967,f1288])).
% 37.84/5.80 thf(f2449,definition,(
% 37.84/5.80 spl609_325 <=> ! [X6 : (term > $o),X5 : term] : ((((X6 @ X5)) = $true) | (((sP19 @ X6)) = $true) | (((var @ (sK343 @ X6))) = $true) | (((X6 @ (lam @ (sK344 @ X6)))) != $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_325])],[avatar_definition])).
% 37.84/5.80 thf(f2450,plain,(
% 37.84/5.80 ( ! [X6 : (term > $o),X5 : term] : ((((X6 @ X5)) = $true) | (((X6 @ (lam @ (sK344 @ X6)))) != $true) | (((var @ (sK343 @ X6))) = $true) | (((sP19 @ X6)) = $true)) ) | ~spl609_325),
% 37.84/5.80 inference(avatar_component_clause,[],[f2449])).
% 37.84/5.80 thf(f2451,plain,(
% 37.84/5.80 ~spl609_79 | spl609_325),
% 37.84/5.80 inference(avatar_split_clause,[],[f624,f2449,f1451])).
% 37.84/5.80 thf(f2521,definition,(
% 37.84/5.80 spl609_342 <=> ! [X18 : term] : ((((sK399 @ id @ X18 @ id)) = $false) | (((sK398 @ X18)) = $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_342])],[avatar_definition])).
% 37.84/5.80 thf(f2522,plain,(
% 37.84/5.80 ( ! [X18 : term] : ((((sK399 @ id @ X18 @ id)) = $false) | (((sK398 @ X18)) = $true)) ) | ~spl609_342),
% 37.84/5.80 inference(avatar_component_clause,[],[f2521])).
% 37.84/5.80 thf(f2523,plain,(
% 37.84/5.80 ~spl609_46 | spl609_342),
% 37.84/5.80 inference(avatar_split_clause,[],[f1087,f2521,f1326])).
% 37.84/5.80 thf(f2612,definition,(
% 37.84/5.80 spl609_364 <=> ! [X3 : term] : ((((sK341 @ (sK342 @ X3))) = $true) | (((sK341 @ (lam @ X3))) = $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_364])],[avatar_definition])).
% 37.84/5.80 thf(f2613,plain,(
% 37.84/5.80 ( ! [X3 : term] : ((((sK341 @ (lam @ X3))) = $true) | (((sK341 @ (sK342 @ X3))) = $true)) ) | ~spl609_364),
% 37.84/5.80 inference(avatar_component_clause,[],[f2612])).
% 37.84/5.80 thf(f2614,plain,(
% 37.84/5.80 spl609_79 | spl609_364),
% 37.84/5.80 inference(avatar_split_clause,[],[f629,f2612,f1451])).
% 37.84/5.80 thf(f2632,definition,(
% 37.84/5.80 spl609_369 <=> (hoasinduction_lem0_lthm = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_369])],[avatar_definition])).
% 37.84/5.80 thf(f2635,definition,(
% 37.84/5.80 spl609_370 <=> ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((sK529 @ X110 @ X112)) = $true) | ($false = ((X110 @ id @ X112 @ id))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_370])],[avatar_definition])).
% 37.84/5.80 thf(f2636,plain,(
% 37.84/5.80 ( ! [X112 : term,X110 : (subst > term > subst > $o)] : (($false = ((X110 @ id @ X112 @ id))) | (((sK529 @ X110 @ X112)) = $true)) ) | ~spl609_370),
% 37.84/5.80 inference(avatar_component_clause,[],[f2635])).
% 37.84/5.80 thf(f2637,plain,(
% 37.84/5.80 ~spl609_369 | spl609_370),
% 37.84/5.80 inference(avatar_split_clause,[],[f1091,f2635,f2632])).
% 37.84/5.80 thf(f2639,definition,(
% 37.84/5.80 spl609_371 <=> ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((X110 @ id @ X112 @ id)) = $true) | ($false = ((sK529 @ X110 @ X112))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_371])],[avatar_definition])).
% 37.84/5.80 thf(f2640,plain,(
% 37.84/5.80 ( ! [X112 : term,X110 : (subst > term > subst > $o)] : ((((X110 @ id @ X112 @ id)) = $true) | ($false = ((sK529 @ X110 @ X112)))) ) | ~spl609_371),
% 37.84/5.80 inference(avatar_component_clause,[],[f2639])).
% 37.84/5.80 thf(f2641,plain,(
% 37.84/5.80 ~spl609_369 | spl609_371),
% 37.84/5.80 inference(avatar_split_clause,[],[f1090,f2639,f2632])).
% 37.84/5.80 thf(f2650,definition,(
% 37.84/5.80 spl609_374 <=> (((sK392 @ sK393)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_374])],[avatar_definition])).
% 37.84/5.80 thf(f2651,plain,(
% 37.84/5.80 (((sK392 @ sK393)) != $true) | spl609_374),
% 37.84/5.80 inference(avatar_component_clause,[],[f2650])).
% 37.84/5.80 thf(f2652,plain,(
% 37.84/5.80 ~spl609_374 | ~spl609_71),
% 37.84/5.80 inference(avatar_split_clause,[],[f681,f1416,f2650])).
% 37.84/5.80 thf(f2709,definition,(
% 37.84/5.80 spl609_388 <=> ! [X7 : term] : ((((sK392 @ (lam @ X7))) = $true) | ($true = ((sK392 @ (sK394 @ X7)))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_388])],[avatar_definition])).
% 37.84/5.80 thf(f2710,plain,(
% 37.84/5.80 ( ! [X7 : term] : ((((sK392 @ (lam @ X7))) = $true) | ($true = ((sK392 @ (sK394 @ X7))))) ) | ~spl609_388),
% 37.84/5.80 inference(avatar_component_clause,[],[f2709])).
% 37.84/5.80 thf(f2711,plain,(
% 37.84/5.80 ~spl609_71 | spl609_388),
% 37.84/5.80 inference(avatar_split_clause,[],[f685,f2709,f1416])).
% 37.84/5.80 thf(f2727,plain,(
% 37.84/5.80 ~spl609_35 | ~spl609_36),
% 37.84/5.80 inference(avatar_split_clause,[],[f295,f1288,f1285])).
% 37.84/5.80 thf(f3280,definition,(
% 37.84/5.80 spl609_525 <=> (((sK254 @ id @ (lam @ sK253) @ id)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_525])],[avatar_definition])).
% 37.84/5.80 thf(f3281,plain,(
% 37.84/5.80 (((sK254 @ id @ (lam @ sK253) @ id)) != $true) | spl609_525),
% 37.84/5.80 inference(avatar_component_clause,[],[f3280])).
% 37.84/5.80 thf(f3282,plain,(
% 37.84/5.80 spl609_206 | ~spl609_525),
% 37.84/5.80 inference(avatar_split_clause,[],[f517,f3280,f1967])).
% 37.84/5.80 thf(f3538,definition,(
% 37.84/5.80 spl609_584 <=> ! [X108 : (term > $o)] : (($false = ((X108 @ (sK528 @ X108)))) | ($false = ((sK527 @ id @ (sK528 @ X108) @ id))))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_584])],[avatar_definition])).
% 37.84/5.80 thf(f3539,plain,(
% 37.84/5.80 ( ! [X108 : (term > $o)] : (($false = ((sK527 @ id @ (sK528 @ X108) @ id))) | ($false = ((X108 @ (sK528 @ X108))))) ) | ~spl609_584),
% 37.84/5.80 inference(avatar_component_clause,[],[f3538])).
% 37.84/5.80 thf(f3541,plain,(
% 37.84/5.80 spl609_584 | spl609_369),
% 37.84/5.80 inference(avatar_split_clause,[],[f1150,f2632,f3538])).
% 37.84/5.80 thf(f3543,definition,(
% 37.84/5.80 spl609_585 <=> ! [X108 : (term > $o)] : ((((X108 @ (sK528 @ X108))) = $true) | (((sK527 @ id @ (sK528 @ X108) @ id)) = $true))),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_585])],[avatar_definition])).
% 37.84/5.80 thf(f3544,plain,(
% 37.84/5.80 ( ! [X108 : (term > $o)] : ((((sK527 @ id @ (sK528 @ X108) @ id)) = $true) | (((X108 @ (sK528 @ X108))) = $true)) ) | ~spl609_585),
% 37.84/5.80 inference(avatar_component_clause,[],[f3543])).
% 37.84/5.80 thf(f3545,plain,(
% 37.84/5.80 spl609_369 | spl609_585),
% 37.84/5.80 inference(avatar_split_clause,[],[f1149,f3543,f2632])).
% 37.84/5.80 thf(f3688,definition,(
% 37.84/5.80 spl609_617 <=> (((sP0 @ sK61)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_617])],[avatar_definition])).
% 37.84/5.80 thf(f3689,plain,(
% 37.84/5.80 (((sP0 @ sK61)) != $true) | spl609_617),
% 37.84/5.80 inference(avatar_component_clause,[],[f3688])).
% 37.84/5.80 thf(f3690,plain,(
% 37.84/5.80 spl609_35 | ~spl609_617),
% 37.84/5.80 inference(avatar_split_clause,[],[f285,f3688,f1285])).
% 37.84/5.80 thf(f3757,definition,(
% 37.84/5.80 spl609_633 <=> (((sK380 @ id @ sK379 @ id)) = $true)),
% 37.84/5.80 introduced(definition,[new_symbols(definition,[spl609_633])],[avatar_definition])).
% 37.84/5.80 thf(f3758,plain,(
% 37.84/5.80 (((sK380 @ id @ sK379 @ id)) != $true) | spl609_633),
% 37.84/5.80 inference(avatar_component_clause,[],[f3757])).
% 37.84/5.80 thf(f3759,plain,(
% 37.84/5.80 ~spl609_633 | spl609_68),
% 37.84/5.80 inference(avatar_split_clause,[],[f680,f1406,f3757])).
% 37.84/5.80 thf(f3816,plain,(
% 37.84/5.80 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 37.84/5.80 inference(constrained_superposition,[],[f942,f973])).
% 37.84/5.80 thf(f3819,plain,(
% 37.84/5.80 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 37.84/5.80 inference(constrained_superposition,[],[f947,f876])).
% 37.84/5.80 thf(f3833,plain,(
% 37.84/5.80 ( ! [X0 : term] : ((one = X0)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f822,f3816])).
% 37.84/5.80 thf(f3835,plain,(
% 37.84/5.80 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f3833,f3833])).
% 37.84/5.80 thf(f3862,plain,(
% 37.84/5.80 ( ! [X0 : term] : ((((sK341 @ X0)) != $true)) ) | spl609_87),
% 37.84/5.80 inference(constrained_superposition,[],[f1480,f3835])).
% 37.84/5.80 thf(f3863,plain,(
% 37.84/5.80 ( ! [X0 : term] : ((((sK392 @ X0)) != $true)) ) | spl609_374),
% 37.84/5.80 inference(constrained_superposition,[],[f2651,f3835])).
% 37.84/5.80 thf(f3908,plain,(
% 37.84/5.80 ( ! [X0 : subst] : ((id = X0)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f833,f3819])).
% 37.84/5.80 thf(f3942,plain,(
% 37.84/5.80 (((var @ one)) != $true)),
% 37.84/5.80 inference(constrained_superposition,[],[f1005,f942])).
% 37.84/5.80 thf(f3947,plain,(
% 37.84/5.80 ( ! [X0 : term] : ((((var @ X0)) != $true)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f3942,f3833])).
% 37.84/5.80 thf(f4217,plain,(
% 37.84/5.80 (((sK61 @ id @ one @ id)) != $true) | spl609_161),
% 37.84/5.80 inference(constrained_superposition,[],[f1777,f3833])).
% 37.84/5.80 thf(f4224,plain,(
% 37.84/5.80 ( ! [X0 : subst] : ((((sK61 @ X0 @ one @ X0)) != $true)) ) | spl609_161),
% 37.84/5.80 inference(constrained_superposition,[],[f4217,f3908])).
% 37.84/5.80 thf(f5117,plain,(
% 37.84/5.80 ( ! [X0 : term,X1 : (term > $o)] : ((((sP19 @ X1)) != $true) | (((X1 @ X0)) != $true)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f631,f3835])).
% 37.84/5.80 thf(f6285,plain,(
% 37.84/5.80 ( ! [X0 : term,X1 : (subst > term > subst > $o)] : (($true != ((X1 @ id @ X0 @ id))) | (((sP28 @ X1)) = $true)) )),
% 37.84/5.80 inference(constrained_superposition,[],[f579,f3835])).
% 39.01/5.80 thf(f6347,plain,(
% 39.01/5.80 ( ! [X2 : term,X0 : subst,X1 : (subst > term > subst > $o)] : ((((X1 @ X0 @ X2 @ X0)) != $true) | (((sP28 @ X1)) = $true)) )),
% 39.01/5.80 inference(constrained_superposition,[],[f6285,f3908])).
% 39.01/5.80 thf(f9052,plain,(
% 39.01/5.80 ( ! [X0 : term,X1 : (subst > term > subst > $o)] : (($true != ((X1 @ id @ X0 @ id))) | (((sP11 @ X1)) != $true)) )),
% 39.01/5.80 inference(constrained_superposition,[],[f701,f3835])).
% 39.01/5.80 thf(f9118,plain,(
% 39.01/5.80 ( ! [X2 : term,X0 : subst,X1 : (subst > term > subst > $o)] : ((((X1 @ X0 @ X2 @ X0)) != $true) | (((sP11 @ X1)) != $true)) )),
% 39.01/5.80 inference(constrained_superposition,[],[f9052,f3908])).
% 39.01/5.80 thf(f9413,plain,(
% 39.01/5.80 ( ! [X3 : term] : ((((sK341 @ (lam @ X3))) = $true)) ) | (spl609_87 | ~spl609_364)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f2613,f3862])).
% 39.01/5.80 thf(f9414,plain,(
% 39.01/5.80 $false | (spl609_87 | ~spl609_364)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f9413,f3862])).
% 39.01/5.80 thf(f9415,plain,(
% 39.01/5.80 spl609_87 | ~spl609_364),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f9414])).
% 39.01/5.80 thf(f9416,plain,(
% 39.01/5.80 ( ! [X6 : (term > $o),X5 : term] : ((((X6 @ (lam @ (sK344 @ X6)))) != $true) | (((X6 @ X5)) = $true) | (((sP19 @ X6)) = $true)) ) | ~spl609_325),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f2450,f3947])).
% 39.01/5.80 thf(f9418,plain,(
% 39.01/5.80 ( ! [X6 : (term > $o),X5 : term] : ((((X6 @ (lam @ (sK344 @ X6)))) != $true) | (((X6 @ X5)) = $true)) ) | ~spl609_325),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f9416,f5117])).
% 39.01/5.80 thf(f9427,plain,(
% 39.01/5.80 ( ! [X2 : term,X0 : term,X1 : (term > $o)] : ((((X1 @ X0)) != $true) | (((X1 @ X2)) = $true)) ) | ~spl609_325),
% 39.01/5.80 inference(constrained_superposition,[],[f9418,f3835])).
% 39.01/5.80 thf(f10972,plain,(
% 39.01/5.80 ( ! [X7 : term] : ((((sK392 @ (lam @ X7))) = $true)) ) | (~spl609_325 | ~spl609_388)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f2710,f9427])).
% 39.01/5.80 thf(f10973,plain,(
% 39.01/5.80 $false | (~spl609_325 | spl609_374 | ~spl609_388)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f10972,f3863])).
% 39.01/5.80 thf(f10974,plain,(
% 39.01/5.80 ~spl609_325 | spl609_374 | ~spl609_388),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f10973])).
% 39.01/5.80 thf(f10975,plain,(
% 39.01/5.80 $false | spl609_69),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f1411,f3835])).
% 39.01/5.80 thf(f10976,plain,(
% 39.01/5.80 spl609_69),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f10975])).
% 39.01/5.80 thf(f11054,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((X0 @ id @ (X6 @ id @ (sK308 @ X6 @ X0)) @ id)) != $true) | (((sub @ (X6 @ (sK310 @ X6) @ (sK309 @ X6)) @ (sK311 @ X6))) != ((X6 @ (comp @ (sK310 @ X6) @ (sK311 @ X6)) @ (sub @ (sK309 @ X6) @ (sK311 @ X6))))) | ($true = ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)))) )),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f576,f6347])).
% 39.01/5.80 thf(f11055,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((X0 @ id @ (X6 @ id @ (sK308 @ X6 @ X0)) @ id)) != $true) | ($true = ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)))) )),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f11054,f3835])).
% 39.01/5.80 thf(f11065,plain,(
% 39.01/5.80 ( ! [X2 : (subst > term > term),X0 : term,X1 : (subst > term > subst > $o)] : (($true != ((X1 @ id @ X0 @ id))) | (((X1 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) )),
% 39.01/5.80 inference(constrained_superposition,[],[f11055,f3835])).
% 39.01/5.80 thf(f11133,plain,(
% 39.01/5.80 ( ! [X2 : term,X3 : (subst > term > term),X0 : subst,X1 : (subst > term > subst > $o)] : ((((X1 @ X0 @ X2 @ X0)) != $true) | (((X1 @ X0 @ (lam @ (X3 @ sh @ one)) @ X0)) = $true)) )),
% 39.01/5.80 inference(constrained_superposition,[],[f11065,f3908])).
% 39.01/5.80 thf(f13100,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : (($false = ((sK387 @ id @ one @ id))) | ($false = ((X0 @ one)))) ) | ~spl609_67),
% 39.01/5.80 inference(constrained_superposition,[],[f1404,f3833])).
% 39.01/5.80 thf(f13161,definition,(
% 39.01/5.80 spl609_703 <=> ($false = ((sK387 @ id @ one @ id)))),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_703])],[avatar_definition])).
% 39.01/5.80 thf(f13162,plain,(
% 39.01/5.80 ($false = ((sK387 @ id @ one @ id))) | ~spl609_703),
% 39.01/5.80 inference(avatar_component_clause,[],[f13161])).
% 39.01/5.80 thf(f13164,definition,(
% 39.01/5.80 spl609_704 <=> ! [X0 : (term > $o)] : ($false = ((X0 @ one)))),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_704])],[avatar_definition])).
% 39.01/5.80 thf(f13165,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : (($false = ((X0 @ one)))) ) | ~spl609_704),
% 39.01/5.80 inference(avatar_component_clause,[],[f13164])).
% 39.01/5.80 thf(f13166,plain,(
% 39.01/5.80 spl609_703 | spl609_704 | ~spl609_67),
% 39.01/5.80 inference(avatar_split_clause,[],[f13100,f1403,f13164,f13161])).
% 39.01/5.80 thf(f13167,plain,(
% 39.01/5.80 ($false = (((^[Y0 : term]: ($true)) @ one))) | ~spl609_704),
% 39.01/5.80 inference(primitive_instantiation,[],[f13165])).
% 39.01/5.80 thf(f13226,plain,(
% 39.01/5.80 ($false = $true) | ~spl609_704),
% 39.01/5.80 inference(beta-eta_normalization,[],[f13167])).
% 39.01/5.80 thf(f13227,plain,(
% 39.01/5.80 $false | ~spl609_704),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f13226])).
% 39.01/5.80 thf(f13228,plain,(
% 39.01/5.80 ~spl609_704),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f13227])).
% 39.01/5.80 thf(f13250,plain,(
% 39.01/5.80 ( ! [X0 : term] : (($false = ((sK387 @ id @ X0 @ id)))) ) | ~spl609_703),
% 39.01/5.80 inference(constrained_superposition,[],[f13162,f3833])).
% 39.01/5.80 thf(f13710,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : (($false = $true) | (((X0 @ (sK388 @ X0))) = $true)) ) | (~spl609_72 | ~spl609_703)),
% 39.01/5.80 inference(constrained_superposition,[],[f1421,f13250])).
% 39.01/5.80 thf(f13779,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (sK388 @ X0))) = $true)) ) | (~spl609_72 | ~spl609_703)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f13710])).
% 39.01/5.80 thf(f13835,definition,(
% 39.01/5.80 spl609_706 <=> ! [X0 : (term > $o)] : (((X0 @ (sK388 @ X0))) = $true)),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_706])],[avatar_definition])).
% 39.01/5.80 thf(f13836,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (sK388 @ X0))) = $true)) ) | ~spl609_706),
% 39.01/5.80 inference(avatar_component_clause,[],[f13835])).
% 39.01/5.80 thf(f13854,plain,(
% 39.01/5.80 spl609_706 | ~spl609_72 | ~spl609_703),
% 39.01/5.80 inference(avatar_split_clause,[],[f13779,f13161,f1420,f13835])).
% 39.01/5.80 thf(f13859,definition,(
% 39.01/5.80 spl609_712 <=> ! [X0 : (term > $o)] : ($true = ((X0 @ one)))),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_712])],[avatar_definition])).
% 39.01/5.80 thf(f13860,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : (($true = ((X0 @ one)))) ) | ~spl609_712),
% 39.01/5.80 inference(avatar_component_clause,[],[f13859])).
% 39.01/5.80 thf(f13974,plain,(
% 39.01/5.80 ( ! [X2 : (subst > term > term)] : ((((X2 @ (comp @ (sK383 @ X2) @ (sK381 @ X2)) @ (sub @ (sK382 @ X2) @ (sK381 @ X2)))) != ((sub @ (X2 @ (sK383 @ X2) @ (sK382 @ X2)) @ (sK381 @ X2)))) | (((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) ) | ~spl609_111),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f1573,f11065])).
% 39.01/5.80 thf(f13975,plain,(
% 39.01/5.80 ( ! [X2 : (subst > term > term)] : ((((sK380 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) ) | ~spl609_111),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f13974,f3835])).
% 39.01/5.80 thf(f13976,plain,(
% 39.01/5.80 ( ! [X0 : term] : ((((sK380 @ id @ X0 @ id)) != $true)) ) | spl609_633),
% 39.01/5.80 inference(constrained_superposition,[],[f3758,f3835])).
% 39.01/5.80 thf(f13997,plain,(
% 39.01/5.80 $false | (~spl609_111 | spl609_633)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f13975,f13976])).
% 39.01/5.80 thf(f13998,plain,(
% 39.01/5.80 ~spl609_111 | spl609_633),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f13997])).
% 39.01/5.80 thf(f15591,plain,(
% 39.01/5.80 ($false = ((sK529 @ sK61 @ one))) | ($true != $true) | (spl609_161 | ~spl609_371)),
% 39.01/5.80 inference(constrained_superposition,[],[f4224,f2640])).
% 39.01/5.80 thf(f15778,plain,(
% 39.01/5.80 ($false = ((sK529 @ sK61 @ one))) | (spl609_161 | ~spl609_371)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f15591])).
% 39.01/5.80 thf(f15984,definition,(
% 39.01/5.80 spl609_761 <=> ($false = ((sK529 @ sK61 @ one)))),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_761])],[avatar_definition])).
% 39.01/5.80 thf(f15985,plain,(
% 39.01/5.80 ($false = ((sK529 @ sK61 @ one))) | ~spl609_761),
% 39.01/5.80 inference(avatar_component_clause,[],[f15984])).
% 39.01/5.80 thf(f15987,plain,(
% 39.01/5.80 spl609_761 | spl609_161 | ~spl609_371),
% 39.01/5.80 inference(avatar_split_clause,[],[f15778,f2639,f1776,f15984])).
% 39.01/5.80 thf(f19864,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((sK527 @ id @ one @ id)) = $false) | ($false = ((X0 @ one)))) ) | ~spl609_584),
% 39.01/5.80 inference(constrained_superposition,[],[f3539,f3833])).
% 39.01/5.80 thf(f19931,definition,(
% 39.01/5.80 spl609_806 <=> (((sK527 @ id @ one @ id)) = $false)),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_806])],[avatar_definition])).
% 39.01/5.80 thf(f19932,plain,(
% 39.01/5.80 (((sK527 @ id @ one @ id)) = $false) | ~spl609_806),
% 39.01/5.80 inference(avatar_component_clause,[],[f19931])).
% 39.01/5.80 thf(f19933,plain,(
% 39.01/5.80 spl609_704 | spl609_806 | ~spl609_584),
% 39.01/5.80 inference(avatar_split_clause,[],[f19864,f3538,f19931,f13164])).
% 39.01/5.80 thf(f19934,plain,(
% 39.01/5.80 ( ! [X0 : term] : (($false = ((sK527 @ id @ X0 @ id)))) ) | ~spl609_806),
% 39.01/5.80 inference(constrained_superposition,[],[f19932,f3833])).
% 39.01/5.80 thf(f20091,plain,(
% 39.01/5.80 ( ! [X0 : subst,X1 : term] : (($false = ((sK527 @ X0 @ X1 @ X0)))) ) | ~spl609_806),
% 39.01/5.80 inference(constrained_superposition,[],[f19934,f3908])).
% 39.01/5.80 thf(f20514,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (sK528 @ X0))) = $true) | ($false = $true)) ) | (~spl609_585 | ~spl609_806)),
% 39.01/5.80 inference(constrained_superposition,[],[f20091,f3544])).
% 39.01/5.80 thf(f20578,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (sK528 @ X0))) = $true)) ) | (~spl609_585 | ~spl609_806)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f20514])).
% 39.01/5.80 thf(f20613,definition,(
% 39.01/5.80 spl609_807 <=> ! [X0 : (term > $o)] : (((X0 @ (sK528 @ X0))) = $true)),
% 39.01/5.80 introduced(definition,[new_symbols(definition,[spl609_807])],[avatar_definition])).
% 39.01/5.80 thf(f20614,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : ((((X0 @ (sK528 @ X0))) = $true)) ) | ~spl609_807),
% 39.01/5.80 inference(avatar_component_clause,[],[f20613])).
% 39.01/5.80 thf(f20679,plain,(
% 39.01/5.80 spl609_807 | ~spl609_585 | ~spl609_806),
% 39.01/5.80 inference(avatar_split_clause,[],[f20578,f19931,f3543,f20613])).
% 39.01/5.80 thf(f31835,plain,(
% 39.01/5.80 ( ! [X0 : (term > $o)] : (($true = ((X0 @ one)))) ) | ~spl609_706),
% 39.01/5.80 inference(constrained_superposition,[],[f13836,f3833])).
% 39.01/5.80 thf(f32181,plain,(
% 39.01/5.80 spl609_712 | ~spl609_706),
% 39.01/5.80 inference(avatar_split_clause,[],[f31835,f13835,f13859])).
% 39.01/5.80 thf(f32183,plain,(
% 39.01/5.80 ( ! [X13 : (subst > term > term)] : ((((X13 @ (comp @ (sK403 @ X13) @ (sK401 @ X13)) @ (sub @ (sK402 @ X13) @ (sK401 @ X13)))) != ((sub @ (X13 @ (sK403 @ X13) @ (sK402 @ X13)) @ (sK401 @ X13)))) | (((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true)) ) | ~spl609_130),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f1652,f11133])).
% 39.01/5.80 thf(f32184,plain,(
% 39.01/5.80 ( ! [X13 : (subst > term > term)] : ((((sK399 @ id @ (lam @ (X13 @ sh @ one)) @ id)) = $true)) ) | ~spl609_130),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f32183,f3835])).
% 39.01/5.80 thf(f32188,plain,(
% 39.01/5.80 ( ! [X0 : term] : ((((sK398 @ X0)) != $true)) ) | spl609_47),
% 39.01/5.80 inference(constrained_superposition,[],[f1330,f3835])).
% 39.01/5.80 thf(f32435,plain,(
% 39.01/5.80 ( ! [X18 : term] : ((((sK399 @ id @ X18 @ id)) = $false)) ) | (spl609_47 | ~spl609_342)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f2522,f32188])).
% 39.01/5.80 thf(f32439,plain,(
% 39.01/5.80 ($false = $true) | (spl609_47 | ~spl609_130 | ~spl609_342)),
% 39.01/5.80 inference(constrained_superposition,[],[f32435,f32184])).
% 39.01/5.80 thf(f32577,plain,(
% 39.01/5.80 $false | (spl609_47 | ~spl609_130 | ~spl609_342)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f32439])).
% 39.01/5.80 thf(f32578,plain,(
% 39.01/5.80 spl609_47 | ~spl609_130 | ~spl609_342),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f32577])).
% 39.01/5.80 thf(f32583,plain,(
% 39.01/5.80 ( ! [X11 : term,X12 : (subst > term > subst > $o)] : ((((X12 @ id @ (lam @ (sK386 @ X12 @ sh @ one)) @ id)) != $true) | (((X12 @ id @ X11 @ id)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f1789,f9118])).
% 39.01/5.80 thf(f34939,plain,(
% 39.01/5.80 ($true != $true) | ~spl609_712),
% 39.01/5.80 inference(constrained_superposition,[],[f3942,f13860])).
% 39.01/5.80 thf(f35376,plain,(
% 39.01/5.80 $false | ~spl609_712),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f34939])).
% 39.01/5.80 thf(f35377,plain,(
% 39.01/5.80 ~spl609_712),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f35376])).
% 39.01/5.80 thf(f36686,plain,(
% 39.01/5.80 ( ! [X0 : term] : ((((sK254 @ id @ X0 @ id)) != $true)) ) | spl609_525),
% 39.01/5.80 inference(constrained_superposition,[],[f3281,f3835])).
% 39.01/5.80 thf(f36836,plain,(
% 39.01/5.80 ( ! [X0 : subst,X1 : term] : ((((sK254 @ X0 @ X1 @ X0)) != $true)) ) | spl609_525),
% 39.01/5.80 inference(constrained_superposition,[],[f36686,f3908])).
% 39.01/5.80 thf(f38862,plain,(
% 39.01/5.80 ( ! [X2 : term,X0 : term,X1 : (subst > term > subst > $o)] : (($true != ((X1 @ id @ X0 @ id))) | (((X1 @ id @ X2 @ id)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(constrained_superposition,[],[f32583,f3835])).
% 39.01/5.80 thf(f38864,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : term] : (($true != ((X0 @ id @ one @ id))) | (((X0 @ id @ X1 @ id)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(constrained_superposition,[],[f32583,f3833])).
% 39.01/5.80 thf(f38927,plain,(
% 39.01/5.80 ( ! [X2 : term,X0 : subst,X1 : (subst > term > subst > $o)] : ((((X1 @ X0 @ one @ X0)) != $true) | (((X1 @ X0 @ X2 @ X0)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(constrained_superposition,[],[f38864,f3908])).
% 39.01/5.80 thf(f39079,plain,(
% 39.01/5.80 ( ! [X2 : term,X3 : (subst > term > subst > $o),X0 : subst] : (((((^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X3 @ Y0 @ Y1 @ Y2))))))) @ X0 @ one @ X0)) != $true) | ((((^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (~ (X3 @ Y0 @ Y1 @ Y2))))))) @ X0 @ X2 @ X0)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(primitive_instantiation,[],[f38927])).
% 39.01/5.80 thf(f39123,plain,(
% 39.01/5.80 ( ! [X2 : term,X3 : (subst > term > subst > $o),X0 : subst] : ((((~ (X3 @ X0 @ X2 @ X0))) = $true) | ($true != ((~ (X3 @ X0 @ one @ X0))))) ) | ~spl609_164),
% 39.01/5.80 inference(beta-eta_normalization,[],[f39079])).
% 39.01/5.80 thf(f39124,plain,(
% 39.01/5.80 ( ! [X2 : term,X3 : (subst > term > subst > $o),X0 : subst] : (($true != ((~ (X3 @ X0 @ one @ X0)))) | ($false = ((X3 @ X0 @ X2 @ X0)))) ) | ~spl609_164),
% 39.01/5.80 inference(not_proxy_clausification,[],[f39123])).
% 39.01/5.80 thf(f39125,plain,(
% 39.01/5.80 ( ! [X2 : term,X3 : (subst > term > subst > $o),X0 : subst] : (($true = ((X3 @ X0 @ one @ X0))) | ($false = ((X3 @ X0 @ X2 @ X0)))) ) | ~spl609_164),
% 39.01/5.80 inference(not_proxy_clausification,[],[f39124])).
% 39.01/5.80 thf(f60319,plain,(
% 39.01/5.80 ($true != $true) | ~spl609_807),
% 39.01/5.80 inference(constrained_superposition,[],[f3947,f20614])).
% 39.01/5.80 thf(f60486,plain,(
% 39.01/5.80 $false | ~spl609_807),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f60319])).
% 39.01/5.80 thf(f60487,plain,(
% 39.01/5.80 ~spl609_807),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f60486])).
% 39.01/5.80 thf(f62867,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : term] : (($false = $true) | (((sK529 @ X0 @ one)) = $true) | ($false = ((X0 @ id @ X1 @ id)))) ) | (~spl609_164 | ~spl609_370)),
% 39.01/5.80 inference(constrained_superposition,[],[f39125,f2636])).
% 39.01/5.80 thf(f62918,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : term] : (($false = ((X0 @ id @ X1 @ id))) | (((sK529 @ X0 @ one)) = $true)) ) | (~spl609_164 | ~spl609_370)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f62867])).
% 39.01/5.80 thf(f76087,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK73 @ X1) @ (sK72 @ X1)) @ (sK74 @ X1))) != ((X1 @ (comp @ (sK73 @ X1) @ (sK74 @ X1)) @ (sub @ (sK72 @ X1) @ (sK74 @ X1))))) | (((sP0 @ X0)) = $true) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f1081,f38862])).
% 39.01/5.80 thf(f76088,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (d2term @ d_one) @ id)) = $true) | (((sP0 @ X0)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f76087,f3835])).
% 39.01/5.80 thf(f76184,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o)] : ((((sP0 @ X0)) = $true) | ($false = $true) | (((sK529 @ X0 @ one)) = $true)) ) | (~spl609_164 | ~spl609_370)),
% 39.01/5.80 inference(constrained_superposition,[],[f62918,f76088])).
% 39.01/5.80 thf(f76297,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o)] : ((((sK529 @ X0 @ one)) = $true) | (((sP0 @ X0)) = $true)) ) | (~spl609_164 | ~spl609_370)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f76184])).
% 39.01/5.80 thf(f76721,plain,(
% 39.01/5.80 ( ! [X0 : term,X1 : (subst > term > subst > $o)] : (($true = ((sK529 @ X1 @ X0))) | (((sP0 @ X1)) = $true)) ) | (~spl609_164 | ~spl609_370)),
% 39.01/5.80 inference(constrained_superposition,[],[f76297,f3833])).
% 39.01/5.80 thf(f89164,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP33 @ X0)) = $true) | (((sub @ (X1 @ (sK264 @ X1) @ (sK266 @ X1)) @ (sK265 @ X1))) != ((X1 @ (comp @ (sK264 @ X1) @ (sK265 @ X1)) @ (sub @ (sK266 @ X1) @ (sK265 @ X1))))) | (((X0 @ id @ (sK267 @ X1 @ X0) @ id)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f524,f38862])).
% 39.01/5.80 thf(f89165,plain,(
% 39.01/5.80 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (sK267 @ X1 @ X0) @ id)) = $true) | (((sP33 @ X0)) = $true)) ) | ~spl609_164),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f89164,f3835])).
% 39.01/5.80 thf(f89293,plain,(
% 39.01/5.80 ($true != $true) | (((sP33 @ sK254)) = $true) | (~spl609_164 | spl609_525)),
% 39.01/5.80 inference(constrained_superposition,[],[f36836,f89165])).
% 39.01/5.80 thf(f89524,plain,(
% 39.01/5.80 (((sP33 @ sK254)) = $true) | (~spl609_164 | spl609_525)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f89293])).
% 39.01/5.80 thf(f89591,plain,(
% 39.01/5.80 $false | (~spl609_164 | spl609_207 | spl609_525)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f89524,f1971])).
% 39.01/5.80 thf(f89592,plain,(
% 39.01/5.80 ~spl609_164 | spl609_207 | spl609_525),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f89591])).
% 39.01/5.80 thf(f90081,plain,(
% 39.01/5.80 ($false = $true) | (((sP0 @ sK61)) = $true) | (~spl609_164 | ~spl609_370 | ~spl609_761)),
% 39.01/5.80 inference(constrained_superposition,[],[f15985,f76721])).
% 39.01/5.80 thf(f90118,plain,(
% 39.01/5.80 (((sP0 @ sK61)) = $true) | (~spl609_164 | ~spl609_370 | ~spl609_761)),
% 39.01/5.80 inference(trivial_inequality_removal,[],[f90081])).
% 39.01/5.80 thf(f90126,plain,(
% 39.01/5.80 $false | (~spl609_164 | ~spl609_370 | spl609_617 | ~spl609_761)),
% 39.01/5.80 inference(forward_subsumption_resolution,[],[f90118,f3689])).
% 39.01/5.80 thf(f90127,plain,(
% 39.01/5.80 ~spl609_164 | ~spl609_370 | spl609_617 | ~spl609_761),
% 39.01/5.80 inference(avatar_contradiction_clause,[],[f90126])).
% 39.01/5.80 cnf(s24, plain, ~spl609_46 | ~spl609_47, inference(sat_conversion,[],[f1331])).
% 39.01/5.80 cnf(s49, plain, spl609_79 | ~spl609_87, inference(sat_conversion,[],[f1481])).
% 39.01/5.80 cnf(s65, plain, spl609_68 | spl609_111, inference(sat_conversion,[],[f1574])).
% 39.01/5.80 cnf(s82, plain, ~spl609_46 | spl609_130, inference(sat_conversion,[],[f1653])).
% 39.01/5.80 cnf(s107, plain, spl609_35 | ~spl609_161, inference(sat_conversion,[],[f1778])).
% 39.01/5.80 cnf(s110, plain, spl609_46 | spl609_67 | ~spl609_68 | ~spl609_69 | spl609_71 | spl609_164, inference(sat_conversion,[],[f1790])).
% 39.01/5.80 cnf(s111, plain, spl609_46 | ~spl609_68 | ~spl609_69 | spl609_71 | spl609_72 | spl609_164, inference(sat_conversion,[],[f1791])).
% 39.01/5.80 cnf(s156, plain, spl609_206 | ~spl609_207, inference(sat_conversion,[],[f1972])).
% 39.01/5.80 cnf(s183, plain, spl609_36 | ~spl609_206, inference(sat_conversion,[],[f2110])).
% 39.01/5.80 cnf(s265, plain, ~spl609_79 | spl609_325, inference(sat_conversion,[],[f2451])).
% 39.01/5.80 cnf(s285, plain, ~spl609_46 | spl609_342, inference(sat_conversion,[],[f2523])).
% 39.01/5.80 cnf(s309, plain, spl609_79 | spl609_364, inference(sat_conversion,[],[f2614])).
% 39.01/5.80 cnf(s314, plain, ~spl609_369 | spl609_370, inference(sat_conversion,[],[f2637])).
% 39.01/5.80 cnf(s315, plain, ~spl609_369 | spl609_371, inference(sat_conversion,[],[f2641])).
% 39.01/5.80 cnf(s317, plain, ~spl609_71 | ~spl609_374, inference(sat_conversion,[],[f2652])).
% 39.01/5.80 cnf(s332, plain, ~spl609_71 | spl609_388, inference(sat_conversion,[],[f2711])).
% 39.01/5.80 cnf(s337, plain, ~spl609_35 | ~spl609_36, inference(sat_conversion,[],[f2727])).
% 39.01/5.80 cnf(s477, plain, spl609_206 | ~spl609_525, inference(sat_conversion,[],[f3282])).
% 39.01/5.80 cnf(s550, plain, spl609_369 | spl609_584, inference(sat_conversion,[],[f3541])).
% 39.01/5.80 cnf(s551, plain, spl609_369 | spl609_585, inference(sat_conversion,[],[f3545])).
% 39.01/5.80 cnf(s590, plain, spl609_35 | ~spl609_617, inference(sat_conversion,[],[f3690])).
% 39.01/5.80 cnf(s609, plain, spl609_68 | ~spl609_633, inference(sat_conversion,[],[f3759])).
% 39.01/5.80 cnf(s687, plain, spl609_87 | ~spl609_364, inference(sat_conversion,[],[f9415])).
% 39.01/5.80 cnf(s701, plain, ~spl609_325 | spl609_374 | ~spl609_388, inference(sat_conversion,[],[f10974])).
% 39.01/5.80 cnf(s702, plain, spl609_69, inference(sat_conversion,[],[f10976])).
% 39.01/5.80 cnf(s825, plain, ~spl609_67 | spl609_703 | spl609_704, inference(sat_conversion,[],[f13166])).
% 39.01/5.80 cnf(s830, plain, ~spl609_704, inference(sat_conversion,[],[f13228])).
% 39.01/5.80 cnf(s846, plain, ~spl609_72 | ~spl609_703 | spl609_706, inference(sat_conversion,[],[f13854])).
% 39.01/5.80 cnf(s895, plain, ~spl609_111 | spl609_633, inference(sat_conversion,[],[f13998])).
% 39.01/5.80 cnf(s942, plain, spl609_161 | ~spl609_371 | spl609_761, inference(sat_conversion,[],[f15987])).
% 39.01/5.80 cnf(s1084, plain, ~spl609_584 | spl609_704 | spl609_806, inference(sat_conversion,[],[f19933])).
% 39.01/5.80 cnf(s1104, plain, ~spl609_585 | ~spl609_806 | spl609_807, inference(sat_conversion,[],[f20679])).
% 39.01/5.80 cnf(s1265, plain, ~spl609_706 | spl609_712, inference(sat_conversion,[],[f32181])).
% 39.01/5.80 cnf(s1286, plain, spl609_47 | ~spl609_130 | ~spl609_342, inference(sat_conversion,[],[f32578])).
% 39.01/5.80 cnf(s1548, plain, ~spl609_712, inference(sat_conversion,[],[f35377])).
% 39.01/5.80 cnf(s2232, plain, ~spl609_807, inference(sat_conversion,[],[f60487])).
% 39.01/5.80 cnf(s2553, plain, ~spl609_164 | spl609_207 | spl609_525, inference(sat_conversion,[],[f89592])).
% 39.01/5.80 cnf(s2693, plain, ~spl609_164 | ~spl609_370 | spl609_617 | ~spl609_761, inference(sat_conversion,[],[f90127])).
% 39.01/5.80 cnf(s2708, plain, ~spl609_706, inference(rat,[],[s1265,s1548])).
% 39.01/5.80 cnf(s2729, plain, ~spl609_585 | ~spl609_806, inference(rat,[],[s1104,s2232])).
% 39.01/5.80 cnf(s2831, plain, ~spl609_72 | ~spl609_703, inference(rat,[],[s846,s2708])).
% 39.01/5.80 cnf(s2837, plain, ~spl609_67 | spl609_703, inference(rat,[],[s825,s830])).
% 39.01/5.80 cnf(s2910, plain, spl609_46 | ~spl609_68 | spl609_71 | spl609_72 | spl609_164, inference(rat,[],[s111,s702])).
% 39.01/5.80 cnf(s2911, plain, spl609_46 | spl609_67 | ~spl609_68 | spl609_71 | spl609_164, inference(rat,[],[s110,s702])).
% 39.01/5.80 cnf(s2954, plain, spl609_68, inference(rat,[],[s895,s65,s609])).
% 39.01/5.80 cnf(s2956, plain, spl609_79, inference(rat,[],[s687,s49,s309])).
% 39.01/5.80 cnf(s2959, plain, spl609_325, inference(rat,[],[s265,s2956])).
% 39.01/5.80 cnf(s2964, plain, ~spl609_71, inference(rat,[],[s701,s317,s332,s2959])).
% 39.01/5.80 cnf(s2969, plain, spl609_46 | spl609_164, inference(rat,[],[s2837,s2831,s2911,s2910,s2964,s2954])).
% 39.01/5.80 cnf(s2970, plain, ~spl609_46, inference(rat,[],[s1286,s24,s82,s285])).
% 39.01/5.80 cnf(s2983, plain, spl609_164, inference(rat,[],[s2969,s2970])).
% 39.01/5.80 cnf(s3022, plain, spl609_369, inference(rat,[],[s1084,s2729,s550,s551,s830])).
% 39.01/5.80 cnf(s3023, plain, spl609_371, inference(rat,[],[s315,s3022])).
% 39.01/5.80 cnf(s3024, plain, spl609_370, inference(rat,[],[s314,s3022])).
% 39.01/5.80 cnf(s3025, plain, spl609_35, inference(rat,[],[s2693,s942,s107,s590,s3024,s2983,s3023])).
% 39.01/5.80 cnf(s3029, plain, ~spl609_36, inference(rat,[],[s337,s3025])).
% 39.01/5.80 cnf(s3035, plain, ~spl609_206, inference(rat,[],[s183,s3029])).
% 39.01/5.80 cnf(s3038, plain, ~spl609_525, inference(rat,[],[s477,s3035])).
% 39.01/5.80 cnf(s3040, plain, ~spl609_207, inference(rat,[],[s156,s3035])).
% 39.01/5.80 cnf(s3042, plain, $false, inference(rat,[],[s2553,s2983,s3038,s3040])).
% 39.01/5.80 thf(f90128,plain,(
% 39.01/5.80 $false),
% 39.01/5.80 inference(avatar_sat_refutation,[],[s3042])).
% 39.01/5.80 % SZS output end Proof for theBenchmark
% 39.01/5.80 % (795174)------------------------------
% 39.01/5.80 % (795174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.01/5.80 % (795174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.01/5.80 % (795174)CaDiCaL version: 2.1.3
% 39.01/5.80 % (795174)Termination reason: Refutation
% 39.01/5.80 % (795174)Time elapsed: 1.065 s
% 39.01/5.80 % (795174)Peak memory usage: 35 MB
% 39.01/5.80 % (795174)Instructions burned: 3983 (million)
% 39.01/5.80 % (794510)Success in time 5.526 s
% 39.01/5.80 % Vampire exiting
%------------------------------------------------------------------------------