%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP189^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:44 AM UTC 2026
% Result : Theorem 0.61s 0.44s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP189^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:14:35 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.43 % (849669)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.43 % (849676)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3622388755:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.43 % (849676)Instruction limit reached!
% 0.61/0.43 % (849676)------------------------------
% 0.61/0.43 % (849676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849676)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849676)Termination reason: Instruction limit
% 0.61/0.43 % (849676)Termination phase: shuffling
% 0.61/0.43 % (849676)Time elapsed: 0.001 s
% 0.61/0.43 % (849676)Peak memory usage: 10 MB
% 0.61/0.43 % (849676)Instructions burned: 5 (million)
% 0.61/0.43 % (849680)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.43 % (849680)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
% 0.61/0.43 % (849674)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1622183157:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.43 % (849679)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2764571327:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.43 % (849677)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=2897377916: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)
% 0.61/0.43 % (849678)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1112113298:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.43 % (849680)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=4074006082:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.43 % (849682)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2143324534:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.43 % (849682)Instruction limit reached!
% 0.61/0.43 % (849682)------------------------------
% 0.61/0.43 % (849682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849682)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849682)Termination reason: Instruction limit
% 0.61/0.43 % (849682)Termination phase: shuffling
% 0.61/0.43 % (849682)Time elapsed: 0.002 s
% 0.61/0.43 % (849682)Peak memory usage: 10 MB
% 0.61/0.43 % (849682)Instructions burned: 6 (million)
% 0.61/0.43 % (849675)lrs+10_16_si=on:nwc=1.5:random_seed=1516787886:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.43 % (849678)Instruction limit reached!
% 0.61/0.43 % (849678)------------------------------
% 0.61/0.43 % (849678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849678)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849678)Termination reason: Instruction limit
% 0.61/0.43 % (849678)Termination phase: shuffling
% 0.61/0.43 % (849678)Time elapsed: 0.012 s
% 0.61/0.43 % (849678)Peak memory usage: 10 MB
% 0.61/0.43 % (849678)Instructions burned: 25 (million)
% 0.61/0.43 % (849689)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1674362957:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.43 % (849689)Instruction limit reached!
% 0.61/0.43 % (849689)------------------------------
% 0.61/0.43 % (849689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849689)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849689)Termination reason: Instruction limit
% 0.61/0.43 % (849689)Termination phase: shuffling
% 0.61/0.43 % (849689)Time elapsed: 0.002 s
% 0.61/0.43 % (849689)Peak memory usage: 10 MB
% 0.61/0.43 % (849689)Instructions burned: 8 (million)
% 0.61/0.43 % (849675)Instruction limit reached!
% 0.61/0.43 % (849675)------------------------------
% 0.61/0.43 % (849675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849675)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849675)Termination reason: Instruction limit
% 0.61/0.43 % (849675)Termination phase: shuffling
% 0.61/0.43 % (849675)Time elapsed: 0.015 s
% 0.61/0.43 % (849675)Peak memory usage: 10 MB
% 0.61/0.43 % (849675)Instructions burned: 19 (million)
% 0.61/0.43 % (849691)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.43 % (849691)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=204367059:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.43 % (849693)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2767166229:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.43 % (849679)Instruction limit reached!
% 0.61/0.43 % (849679)------------------------------
% 0.61/0.43 % (849679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849679)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849693)Instruction limit reached!
% 0.61/0.43 % (849693)------------------------------
% 0.61/0.43 % (849693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849679)Termination reason: Instruction limit
% 0.61/0.43 % (849679)Termination phase: Preprocessing 3
% 0.61/0.43 % (849679)Time elapsed: 0.036 s
% 0.61/0.43 % (849693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849679)Peak memory usage: 12 MB
% 0.61/0.43 % (849679)Instructions burned: 76 (million)
% 0.61/0.43 % (849693)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849693)Termination reason: Instruction limit
% 0.61/0.43 % (849693)Termination phase: shuffling
% 0.61/0.43 % (849693)Time elapsed: 0.003 s
% 0.61/0.43 % (849693)Peak memory usage: 10 MB
% 0.61/0.43 % (849693)Instructions burned: 14 (million)
% 0.61/0.43 % (849691)Instruction limit reached!
% 0.61/0.43 % (849691)------------------------------
% 0.61/0.43 % (849691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849691)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849691)Termination reason: Instruction limit
% 0.61/0.43 % (849691)Termination phase: shuffling
% 0.61/0.43 % (849691)Time elapsed: 0.004 s
% 0.61/0.43 % (849691)Peak memory usage: 10 MB
% 0.61/0.43 % (849691)Instructions burned: 8 (million)
% 0.61/0.43 % (849674)Instruction limit reached!
% 0.61/0.43 % (849674)------------------------------
% 0.61/0.43 % (849674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (849674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (849674)CaDiCaL version: 2.1.3
% 0.61/0.43 % (849674)Termination reason: Instruction limit
% 0.61/0.43 % (849674)Termination phase: Property scanning
% 0.61/0.43 % (849674)Time elapsed: 0.042 s
% 0.61/0.43 % (849674)Peak memory usage: 12 MB
% 0.61/0.43 % (849674)Instructions burned: 91 (million)
% 0.61/0.43 % (849694)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
% 0.61/0.44 % (849694)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.44 % (849697)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=1498399169:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.44 % (849694)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=390729193:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.44 % (849699)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.44 % (849698)lrs+10_1_si=on:cs=on:random_seed=430807951:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.44 % (849699)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=4096307955:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.44 % (849699)Instruction limit reached!
% 0.61/0.44 % (849699)------------------------------
% 0.61/0.44 % (849699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849699)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849699)Termination reason: Instruction limit
% 0.61/0.44 % (849699)Termination phase: shuffling
% 0.61/0.44 % (849699)Time elapsed: 0.002 s
% 0.61/0.44 % (849699)Peak memory usage: 10 MB
% 0.61/0.44 % (849699)Instructions burned: 3 (million)
% 0.61/0.44 % (849698)Instruction limit reached!
% 0.61/0.44 % (849698)------------------------------
% 0.61/0.44 % (849698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849698)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849698)Termination reason: Instruction limit
% 0.61/0.44 % (849698)Termination phase: shuffling
% 0.61/0.44 % (849698)Time elapsed: 0.004 s
% 0.61/0.44 % (849698)Peak memory usage: 10 MB
% 0.61/0.44 % (849698)Instructions burned: 8 (million)
% 0.61/0.44 % (849700)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1991456379:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.44 % (849694)Instruction limit reached!
% 0.61/0.44 % (849694)------------------------------
% 0.61/0.44 % (849694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849694)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849694)Termination reason: Instruction limit
% 0.61/0.44 % (849694)Termination phase: shuffling
% 0.61/0.44 % (849694)Time elapsed: 0.014 s
% 0.61/0.44 % (849694)Peak memory usage: 10 MB
% 0.61/0.44 % (849694)Instructions burned: 30 (million)
% 0.61/0.44 % (849697)Instruction limit reached!
% 0.61/0.44 % (849697)------------------------------
% 0.61/0.44 % (849697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849697)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849697)Termination reason: Instruction limit
% 0.61/0.44 % (849697)Termination phase: Preprocessing 1
% 0.61/0.44 % (849697)Time elapsed: 0.020 s
% 0.61/0.44 % (849697)Peak memory usage: 11 MB
% 0.61/0.44 % (849697)Instructions burned: 86 (million)
% 0.61/0.44 % (849705)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2219723939:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.44 % (849709)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=545584909:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.44 % (849700)Instruction limit reached!
% 0.61/0.44 % (849700)------------------------------
% 0.61/0.44 % (849700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849700)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849700)Termination reason: Instruction limit
% 0.61/0.44 % (849700)Termination phase: Property scanning
% 0.61/0.44 % (849700)Time elapsed: 0.017 s
% 0.61/0.44 % (849700)Peak memory usage: 10 MB
% 0.61/0.44 % (849700)Instructions burned: 39 (million)
% 0.61/0.44 % (849706)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2313347120:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.44 % (849708)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4085000976:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.44 % (849708)Instruction limit reached!
% 0.61/0.44 % (849708)------------------------------
% 0.61/0.44 % (849708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849708)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849708)Termination reason: Instruction limit
% 0.61/0.44 % (849708)Termination phase: shuffling
% 0.61/0.44 % (849708)Time elapsed: 0.007 s
% 0.61/0.44 % (849708)Peak memory usage: 10 MB
% 0.61/0.44 % (849708)Instructions burned: 15 (million)
% 0.61/0.44 % (849677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-849669-849677"...
% 0.61/0.44 % (849706)Instruction limit reached!
% 0.61/0.44 % (849706)------------------------------
% 0.61/0.44 % (849706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849706)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849706)Termination reason: Instruction limit
% 0.61/0.44 % (849706)Termination phase: shuffling
% 0.61/0.44 % (849706)Time elapsed: 0.012 s
% 0.61/0.44 % (849706)Peak memory usage: 10 MB
% 0.61/0.44 % (849706)Instructions burned: 26 (million)
% 0.61/0.44 % (849677)...printing done.
% 0.61/0.44 % (849677)Refutation found. Thanks to Tanya!
% 0.61/0.44 % SZS status Theorem for theBenchmark
% 0.61/0.44 % SZS output start Proof for theBenchmark
% 0.61/0.44 thf(type_def_5, type, late_residual: $tType).
% 0.61/0.44 thf(type_def_6, type, late_subject: $tType).
% 0.61/0.44 thf(type_def_7, type, late_freeRes: $tType).
% 0.61/0.44 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.61/0.44 thf(type_def_9, type, noption: $tType > $tType).
% 0.61/0.44 thf(type_def_10, type, name: $tType).
% 0.61/0.44 thf(type_def_11, type, pi: $tType).
% 0.61/0.44 thf(type_def_12, type, set: $tType > $tType).
% 0.61/0.44 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.44 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_1, type, fs_name: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.61/0.44 thf(func_def_6, type, input: (name > name > pi > pi)).
% 0.61/0.44 thf(func_def_7, type, output: (name > name > pi > pi)).
% 0.61/0.44 thf(func_def_8, type, par: (pi > pi > pi)).
% 0.61/0.44 thf(func_def_9, type, piNil: pi).
% 0.61/0.44 thf(func_def_10, type, res: (name > pi > pi)).
% 0.61/0.44 thf(func_def_11, type, sum: (pi > pi > pi)).
% 0.61/0.44 thf(func_def_12, type, tau: (pi > pi)).
% 0.61/0.44 thf(func_def_13, type, subs: (pi > name > name > pi)).
% 0.61/0.44 thf(func_def_14, type, subst_name: (name > name > name > name)).
% 0.61/0.44 thf(func_def_15, type, late_OutputR: (name > name > late_freeRes)).
% 0.61/0.44 thf(func_def_16, type, late_TauR: late_freeRes).
% 0.61/0.44 thf(func_def_17, type, late_freeRes_rec: !>[X0: $tType]:(((name > name > X0) > X0 > late_freeRes > X0))).
% 0.61/0.44 thf(func_def_18, type, late_BoundR: (late_subject > name > pi > late_residual)).
% 0.61/0.44 thf(func_def_19, type, late_FreeR: (late_freeRes > pi > late_residual)).
% 0.61/0.44 thf(func_def_20, type, late_BoundOutputS: (name > late_subject)).
% 0.61/0.44 thf(func_def_21, type, late_InputS: (name > late_subject)).
% 0.61/0.44 thf(func_def_22, type, late_subject_rec: !>[X0: $tType]:(((name > X0) > (name > X0) > late_subject > X0))).
% 0.61/0.44 thf(func_def_23, type, late_transitions: (pi > late_residual > $o)).
% 0.61/0.44 thf(func_def_24, type, abs_fun: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > noption @ X1))).
% 0.61/0.44 thf(func_def_25, type, fresh: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o))).
% 0.61/0.44 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.61/0.44 thf(func_def_28, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.61/0.44 thf(func_def_29, type, eqvt: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.61/0.44 thf(func_def_30, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 0.61/0.44 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.61/0.44 thf(func_def_32, type, strong2129052853vative: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o)).
% 0.61/0.44 thf(func_def_33, type, strong743114133lation: (pi > set @ product_prod @ pi @ pi > pi > $o)).
% 0.61/0.44 thf(func_def_34, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.61/0.44 thf(func_def_35, type, p: pi).
% 0.61/0.44 thf(func_def_36, type, p2: pi).
% 0.61/0.44 thf(func_def_37, type, pxQ: pi).
% 0.61/0.44 thf(func_def_38, type, q: pi).
% 0.61/0.44 thf(func_def_39, type, rel: set @ product_prod @ pi @ pi).
% 0.61/0.44 thf(func_def_40, type, alpha: late_freeRes).
% 0.61/0.44 thf(func_def_41, type, x: name).
% 0.61/0.44 thf(func_def_45, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.44 thf(func_def_46, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.44 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 0.61/0.44 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_52, type, vNOT: ($o > $o)).
% 0.61/0.44 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.61/0.44 thf(func_def_54, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.44 thf(func_def_55, type, db5: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_56, type, db4: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_57, type, db3: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_58, type, db6: !>[X0: $tType]:(X0)).
% 0.61/0.44 thf(func_def_59, type, sP0: (late_subject > name > pi > name > pi > $o)).
% 0.61/0.44 thf(func_def_60, type, sP1: (late_subject > name > pi > pi > pi > $o)).
% 0.61/0.44 thf(func_def_61, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_62, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.44 thf(func_def_63, type, sP4: !>[X0: $tType]:((X0 > pi > set @ product_prod @ pi @ pi > name > pi > $o))).
% 0.61/0.44 thf(func_def_64, type, sP5: (late_residual > name > pi > $o)).
% 0.61/0.44 thf(func_def_65, type, sK6: (late_subject > name > pi > name > pi > late_subject)).
% 0.61/0.44 thf(func_def_66, type, sK7: (late_subject > name > pi > name > pi > name)).
% 0.61/0.44 thf(func_def_67, type, sK8: (late_subject > name > pi > name > pi > pi)).
% 0.61/0.44 thf(func_def_68, type, sK9: (late_subject > name > pi > name > pi > pi)).
% 0.61/0.44 thf(func_def_69, type, sK10: (late_subject > name > pi > name > pi > name)).
% 0.61/0.44 thf(func_def_70, type, sK11: (name > late_subject > name > pi > pi > pi)).
% 0.61/0.44 thf(func_def_71, type, sK12: (name > late_subject > name > pi > pi > name)).
% 0.61/0.44 thf(func_def_72, type, sK13: (name > late_subject > name > pi > pi > name)).
% 0.61/0.44 thf(func_def_73, type, sK14: (name > late_subject > name > pi > pi > pi)).
% 0.61/0.44 thf(func_def_74, type, sK15: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_75, type, sK16: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_76, type, sK17: ((late_residual > $o) > late_freeRes)).
% 0.61/0.44 thf(func_def_77, type, sK18: ((late_residual > $o) > pi)).
% 0.61/0.44 thf(func_def_78, type, sK19: ((late_residual > $o) > late_subject)).
% 0.61/0.44 thf(func_def_79, type, sK20: ((late_residual > $o) > name)).
% 0.61/0.44 thf(func_def_80, type, sK21: ((late_residual > $o) > pi)).
% 0.61/0.44 thf(func_def_81, type, sK22: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 0.61/0.44 thf(func_def_82, type, sK23: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 0.61/0.44 thf(func_def_83, type, sK24: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 0.61/0.44 thf(func_def_84, type, sK25: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 0.61/0.44 thf(func_def_85, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X4))).
% 0.61/0.44 thf(func_def_86, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X3))).
% 0.61/0.44 thf(func_def_87, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X5))).
% 0.61/0.44 thf(func_def_88, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X1))).
% 0.61/0.44 thf(func_def_89, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X0))).
% 0.61/0.44 thf(func_def_90, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X4 > X2))).
% 0.61/0.44 thf(func_def_91, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_92, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X2))).
% 0.61/0.44 thf(func_def_93, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X0))).
% 0.61/0.44 thf(func_def_94, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X6))).
% 0.61/0.44 thf(func_def_95, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X5))).
% 0.61/0.44 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X3))).
% 0.61/0.44 thf(func_def_97, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X1))).
% 0.61/0.44 thf(func_def_98, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X3 @ X4 > $o) > X4))).
% 0.61/0.44 thf(func_def_99, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_100, type, sK41: ((late_subject > $o) > name)).
% 0.61/0.44 thf(func_def_101, type, sK42: ((late_subject > $o) > name)).
% 0.61/0.44 thf(func_def_102, type, sK43: ((late_freeRes > $o) > name)).
% 0.61/0.44 thf(func_def_103, type, sK44: ((late_freeRes > $o) > name)).
% 0.61/0.44 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.61/0.44 thf(func_def_105, type, sK46: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_106, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X4))).
% 0.61/0.44 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X6))).
% 0.61/0.44 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X1))).
% 0.61/0.44 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X2))).
% 0.61/0.44 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X3))).
% 0.61/0.44 thf(func_def_111, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X0))).
% 0.61/0.44 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X6 @ X2 > X5))).
% 0.61/0.44 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.61/0.44 thf(func_def_114, type, sK55: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.61/0.44 thf(func_def_115, type, sK56: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 0.61/0.44 thf(func_def_116, type, sK57: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 0.61/0.44 thf(func_def_117, type, sK58: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 0.61/0.44 thf(func_def_118, type, sK59: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 0.61/0.44 thf(func_def_119, type, sK60: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 0.61/0.44 thf(func_def_120, type, sK61: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 0.61/0.44 thf(func_def_121, type, sK62: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 0.61/0.44 thf(func_def_122, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_123, type, sK64: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_124, type, sK65: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_125, type, sK66: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_126, type, sK67: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 0.61/0.44 thf(func_def_127, type, sK68: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 0.61/0.44 thf(func_def_128, type, sK69: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 0.61/0.44 thf(func_def_129, type, sK70: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 0.61/0.44 thf(func_def_130, type, sK71: (pi > pi > late_freeRes > name > pi)).
% 0.61/0.44 thf(func_def_131, type, sK72: (pi > pi > late_freeRes > name > pi)).
% 0.61/0.44 thf(func_def_132, type, sK73: (pi > pi > late_freeRes > name > late_freeRes)).
% 0.61/0.44 thf(func_def_133, type, sK74: (pi > pi > late_freeRes > name > name)).
% 0.61/0.44 thf(func_def_134, type, sK75: (pi > name > late_residual > name > name)).
% 0.61/0.44 thf(func_def_135, type, sK76: (pi > name > late_residual > name > name)).
% 0.61/0.44 thf(func_def_136, type, sK77: (pi > name > late_residual > name > pi)).
% 0.61/0.44 thf(func_def_137, type, sK78: (late_subject > name > pi > pi > pi > pi)).
% 0.61/0.44 thf(func_def_138, type, sK79: (late_subject > name > pi > pi > pi > pi)).
% 0.61/0.44 thf(func_def_139, type, sK80: (late_subject > name > pi > pi > pi > late_subject)).
% 0.61/0.44 thf(func_def_140, type, sK81: (late_subject > name > pi > pi > pi > name)).
% 0.61/0.44 thf(func_def_141, type, sK82: (late_subject > name > pi > pi > pi > pi)).
% 0.61/0.44 thf(func_def_142, type, sK83: (pi > name > late_subject > pi > pi > name)).
% 0.61/0.44 thf(func_def_143, type, sK84: (pi > name > late_subject > pi > pi > pi)).
% 0.61/0.44 thf(func_def_144, type, sK85: (pi > name > late_subject > pi > pi > pi)).
% 0.61/0.44 thf(func_def_145, type, sK86: (pi > name > late_subject > pi > pi > pi)).
% 0.61/0.44 thf(func_def_146, type, sK87: (pi > name > late_subject > pi > pi > late_subject)).
% 0.61/0.44 thf(func_def_147, type, sK88: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_148, type, sK89: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_149, type, sK90: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes > pi)).
% 0.61/0.44 thf(func_def_150, type, sK91: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_151, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_152, type, sK93: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_153, type, sK94: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_154, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_155, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.61/0.44 thf(func_def_156, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.61/0.44 thf(func_def_157, type, sK98: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_158, type, sK99: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_159, type, sK100: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 0.61/0.44 thf(func_def_160, type, sK101: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 0.61/0.44 thf(func_def_161, type, sK102: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 0.61/0.44 thf(func_def_162, type, sK103: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 0.61/0.44 thf(func_def_163, type, sK104: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 0.61/0.44 thf(func_def_164, type, sK105: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.44 thf(func_def_165, type, sK106: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.61/0.44 thf(func_def_166, type, sK107: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.61/0.44 thf(func_def_167, type, sK108: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_168, type, sK109: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_169, type, sK110: !>[X0: $tType]:((X0 > pi > set @ product_prod @ pi @ pi > name > pi > late_subject))).
% 0.61/0.44 thf(func_def_170, type, sK111: !>[X0: $tType]:((X0 > pi > set @ product_prod @ pi @ pi > name > pi > pi))).
% 0.61/0.44 thf(func_def_171, type, sK112: !>[X0: $tType]:((X0 > pi > set @ product_prod @ pi @ pi > name > pi > name))).
% 0.61/0.44 thf(func_def_172, type, sK113: (pi > set @ product_prod @ pi @ pi > name > pi > pi)).
% 0.61/0.44 thf(func_def_173, type, sK114: (pi > set @ product_prod @ pi @ pi > name > pi > late_freeRes)).
% 0.61/0.44 thf(func_def_174, type, sK115: (pi > set @ product_prod @ pi @ pi > name > pi > pi)).
% 0.61/0.44 thf(func_def_175, type, sK116: (pi > set @ product_prod @ pi @ pi > name > pi > name)).
% 0.61/0.44 thf(func_def_176, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X2))).
% 0.61/0.44 thf(func_def_177, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X3))).
% 0.61/0.44 thf(func_def_178, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X4))).
% 0.61/0.44 thf(func_def_179, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X1))).
% 0.61/0.44 thf(func_def_180, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X0))).
% 0.61/0.44 thf(func_def_181, type, sK122: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 0.61/0.44 thf(func_def_182, type, sK123: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 0.61/0.44 thf(func_def_183, type, sK124: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 0.61/0.44 thf(func_def_184, type, sK125: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 0.61/0.44 thf(func_def_185, type, sK126: !>[X0: $tType]:((pi > pi > X0 > set @ product_prod @ pi @ pi > late_subject))).
% 0.61/0.44 thf(func_def_186, type, sK127: !>[X0: $tType]:((pi > pi > X0 > set @ product_prod @ pi @ pi > name))).
% 0.61/0.44 thf(func_def_187, type, sK128: !>[X0: $tType]:((pi > pi > X0 > set @ product_prod @ pi @ pi > pi))).
% 0.61/0.44 thf(func_def_188, type, sK129: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 0.61/0.44 thf(func_def_189, type, sK130: (pi > pi > set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_190, type, sK131: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_191, type, sK132: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.44 thf(func_def_192, type, sK133: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_193, type, sK134: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_194, type, sK135: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_195, type, sK136: (set @ product_prod @ pi @ pi > name)).
% 0.61/0.44 thf(func_def_196, type, sK137: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_197, type, sK138: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_198, type, sK139: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_199, type, sK140: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_200, type, sK141: (set @ product_prod @ pi @ pi > name)).
% 0.61/0.44 thf(func_def_201, type, sK142: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_202, type, sK143: (set @ product_prod @ pi @ pi > name)).
% 0.61/0.44 thf(func_def_203, type, sK144: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_204, type, sK145: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_205, type, sK146: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_206, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.61/0.44 thf(func_def_207, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.61/0.44 thf(func_def_208, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.61/0.44 thf(func_def_209, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.61/0.44 thf(func_def_210, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.61/0.44 thf(func_def_211, type, sK152: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_212, type, sK153: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 0.61/0.44 thf(func_def_213, type, sK154: !>[X0: $tType]:((X0 > name))).
% 0.61/0.44 thf(func_def_214, type, sK155: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.61/0.44 thf(func_def_215, type, sK156: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_216, type, sK157: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_217, type, sK158: (set @ product_prod @ pi @ pi > name)).
% 0.61/0.44 thf(func_def_218, type, sK159: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_219, type, sK160: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_220, type, sK161: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 0.61/0.44 thf(func_def_221, type, sK162: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 0.61/0.44 thf(func_def_222, type, sK163: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 0.61/0.44 thf(func_def_223, type, sK164: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 0.61/0.44 thf(func_def_224, type, sK165: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X3))).
% 0.61/0.44 thf(func_def_225, type, sK166: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X2))).
% 0.61/0.44 thf(func_def_226, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X1))).
% 0.61/0.44 thf(func_def_227, type, sK168: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X5))).
% 0.61/0.44 thf(func_def_228, type, sK169: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X0))).
% 0.61/0.44 thf(func_def_229, type, sK170: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ X5 > $o) > X4))).
% 0.61/0.44 thf(func_def_230, type, sK171: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.61/0.44 thf(func_def_231, type, sK172: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.61/0.44 thf(func_def_232, type, sK173: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.61/0.44 thf(func_def_233, type, sK174: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X3))).
% 0.61/0.44 thf(func_def_234, type, sK175: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.61/0.44 thf(func_def_235, type, sK176: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.61/0.44 thf(func_def_236, type, sK177: (set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_237, type, sK178: (late_residual > pi > pi)).
% 0.61/0.44 thf(func_def_238, type, sK179: (late_residual > name > pi > name)).
% 0.61/0.44 thf(func_def_239, type, sK180: (late_residual > name > pi > name)).
% 0.61/0.44 thf(func_def_240, type, sK181: (late_residual > name > pi > late_subject)).
% 0.61/0.44 thf(func_def_241, type, sK182: (late_residual > name > pi > pi)).
% 0.61/0.44 thf(func_def_242, type, sK183: (late_residual > name > pi > pi)).
% 0.61/0.44 thf(func_def_243, type, sK184: (late_residual > pi > name > name)).
% 0.61/0.44 thf(func_def_244, type, sK185: (late_residual > pi > name > late_freeRes)).
% 0.61/0.44 thf(func_def_245, type, sK186: (late_residual > pi > name > pi)).
% 0.61/0.44 thf(func_def_246, type, sK187: (late_residual > pi > name > pi)).
% 0.61/0.44 thf(func_def_247, type, sK188: (late_residual > pi > name > name)).
% 0.61/0.44 thf(func_def_248, type, sK189: (late_residual > pi > name > name)).
% 0.61/0.44 thf(func_def_249, type, sK190: (late_residual > pi > name > pi)).
% 0.61/0.44 thf(func_def_250, type, sK191: (late_residual > pi > name > pi)).
% 0.61/0.44 thf(func_def_251, type, sK192: (pi > name > pi > (pi > $o) > late_subject > pi)).
% 0.61/0.44 thf(func_def_252, type, sK193: (pi > name > pi > (pi > $o) > late_subject > pi)).
% 0.61/0.44 thf(func_def_253, type, sK194: (late_subject > name)).
% 0.61/0.44 thf(func_def_254, type, sK195: (late_subject > name)).
% 0.61/0.44 thf(func_def_255, type, sK196: (late_freeRes > name)).
% 0.61/0.44 thf(func_def_256, type, sK197: (late_freeRes > name)).
% 0.61/0.44 thf(func_def_257, type, sK198: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.61/0.44 thf(func_def_258, type, sK199: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.61/0.44 thf(func_def_259, type, sK200: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X3))).
% 0.61/0.44 thf(func_def_260, type, sK201: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.61/0.44 thf(func_def_261, type, sK202: (name > (pi > $o) > late_freeRes > pi > pi)).
% 0.61/0.44 thf(func_def_262, type, sK203: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 0.61/0.44 thf(func_def_263, type, sK204: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 0.61/0.44 thf(func_def_264, type, sK205: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 0.61/0.44 thf(func_def_265, type, sK206: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 0.61/0.44 thf(func_def_266, type, sK207: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 0.61/0.44 thf(func_def_267, type, sK208: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 0.61/0.44 thf(func_def_268, type, sK209: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 0.61/0.44 thf(func_def_269, type, sK210: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_270, type, sK211: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.44 thf(func_def_271, type, sK212: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.61/0.44 thf(func_def_272, type, sK213: (name > late_residual > pi > name > name)).
% 0.61/0.44 thf(func_def_273, type, sK214: (name > late_residual > pi > name > pi)).
% 0.61/0.44 thf(func_def_274, type, sK215: (name > late_residual > pi > name > name)).
% 0.61/0.44 thf(func_def_275, type, sK216: (late_subject > pi > name > pi > set @ product_prod @ pi @ pi > pi)).
% 0.61/0.44 thf(func_def_276, type, sK217: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.61/0.44 thf(func_def_277, type, sK218: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.61/0.44 thf(func_def_278, type, sK219: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.61/0.44 thf(func_def_279, type, sK220: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.61/0.44 thf(func_def_280, type, sK221: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.61/0.44 thf(f1,axiom,(
% 0.61/0.44 (fresh @ name @ late_freeRes @ x @ alpha)),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062)).
% 0.61/0.44 thf(f2,axiom,(
% 0.61/0.44 (late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062)).
% 0.61/0.44 thf(f12,axiom,(
% 0.61/0.44 ! [X1 : late_freeRes,X0 : pi,X2 : pi,X3 : name] : ((late_transitions @ X0 @ (late_FreeR @ X1 @ X2)) => ((fresh @ name @ late_freeRes @ X3 @ X1) => (late_transitions @ (res @ X3 @ X0) @ (late_FreeR @ X1 @ (res @ X3 @ X2)))))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ResF)).
% 0.61/0.44 thf(f274,conjecture,(
% 0.61/0.44 (late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.44 thf(f275,negated_conjecture,(
% 0.61/0.44 ~(late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 0.61/0.44 inference(negated_conjecture,[status(cth)],[f274])).
% 0.61/0.44 thf(f288,plain,(
% 0.61/0.44 (fresh @ name @ late_freeRes @ x @ alpha)),
% 0.61/0.44 inference(rectify,[],[f1])).
% 0.61/0.44 thf(f289,plain,(
% 0.61/0.44 (((fresh @ name @ late_freeRes @ x @ alpha)) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f288])).
% 0.61/0.44 thf(f408,plain,(
% 0.61/0.44 (late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))),
% 0.61/0.44 inference(rectify,[],[f2])).
% 0.61/0.44 thf(f409,plain,(
% 0.61/0.44 (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f408])).
% 0.61/0.44 thf(f668,plain,(
% 0.61/0.44 ! [X0 : late_freeRes,X1 : pi,X2 : pi,X3 : name] : ((late_transitions @ X1 @ (late_FreeR @ X0 @ X2)) => ((fresh @ name @ late_freeRes @ X3 @ X0) => (late_transitions @ (res @ X3 @ X1) @ (late_FreeR @ X0 @ (res @ X3 @ X2)))))),
% 0.61/0.44 inference(rectify,[],[f12])).
% 0.61/0.44 thf(f669,plain,(
% 0.61/0.44 ! [X1 : pi,X0 : late_freeRes,X2 : pi,X3 : name] : (($true = ((late_transitions @ X1 @ (late_FreeR @ X0 @ X2)))) => ((((fresh @ name @ late_freeRes @ X3 @ X0)) = $true) => (((late_transitions @ (res @ X3 @ X1) @ (late_FreeR @ X0 @ (res @ X3 @ X2)))) = $true)))),
% 0.61/0.44 inference(fool_elimination,[],[f668])).
% 0.61/0.44 thf(f680,plain,(
% 0.61/0.44 ~(late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))),
% 0.61/0.44 inference(rectify,[],[f275])).
% 0.61/0.44 thf(f681,plain,(
% 0.61/0.44 ~ (((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))) = $true)),
% 0.61/0.44 inference(fool_elimination,[],[f680])).
% 0.61/0.44 thf(f786,plain,(
% 0.61/0.44 (((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))) != $true)),
% 0.61/0.44 inference(flattening,[],[f681])).
% 0.61/0.44 thf(f902,plain,(
% 0.61/0.44 ! [X1 : pi,X0 : late_freeRes,X2 : pi,X3 : name] : (((((late_transitions @ (res @ X3 @ X1) @ (late_FreeR @ X0 @ (res @ X3 @ X2)))) = $true) | (((fresh @ name @ late_freeRes @ X3 @ X0)) != $true)) | ($true != ((late_transitions @ X1 @ (late_FreeR @ X0 @ X2)))))),
% 0.61/0.44 inference(ennf_transformation,[],[f669])).
% 0.61/0.44 thf(f903,plain,(
% 0.61/0.44 ! [X0 : late_freeRes,X3 : name,X1 : pi,X2 : pi] : (($true != ((late_transitions @ X1 @ (late_FreeR @ X0 @ X2)))) | (((late_transitions @ (res @ X3 @ X1) @ (late_FreeR @ X0 @ (res @ X3 @ X2)))) = $true) | (((fresh @ name @ late_freeRes @ X3 @ X0)) != $true))),
% 0.61/0.44 inference(flattening,[],[f902])).
% 0.61/0.44 thf(f1079,plain,(
% 0.61/0.44 ! [X0 : late_freeRes,X1 : name,X2 : pi,X3 : pi] : ((((late_transitions @ X2 @ (late_FreeR @ X0 @ X3))) != $true) | ($true = ((late_transitions @ (res @ X1 @ X2) @ (late_FreeR @ X0 @ (res @ X1 @ X3))))) | (((fresh @ name @ late_freeRes @ X1 @ X0)) != $true))),
% 0.61/0.44 inference(rectify,[],[f903])).
% 0.61/0.44 thf(f1412,plain,(
% 0.61/0.44 ( ! [X2 : pi,X3 : pi,X0 : late_freeRes,X1 : name] : (($true = ((late_transitions @ (res @ X1 @ X2) @ (late_FreeR @ X0 @ (res @ X1 @ X3))))) | (((fresh @ name @ late_freeRes @ X1 @ X0)) != $true) | (((late_transitions @ X2 @ (late_FreeR @ X0 @ X3))) != $true)) )),
% 0.61/0.44 inference(cnf_transformation,[],[f1079])).
% 0.61/0.44 thf(f1635,plain,(
% 0.61/0.44 (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) = $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f409])).
% 0.61/0.44 thf(f1674,plain,(
% 0.61/0.44 (((fresh @ name @ late_freeRes @ x @ alpha)) = $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f289])).
% 0.61/0.44 thf(f1757,plain,(
% 0.61/0.44 (((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))) != $true)),
% 0.61/0.44 inference(cnf_transformation,[],[f786])).
% 0.61/0.44 thf(f1888,definition,(
% 0.61/0.44 spl222_2 <=> (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl222_2])],[avatar_definition])).
% 0.61/0.44 thf(f1890,plain,(
% 0.61/0.44 (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) = $true) | ~spl222_2),
% 0.61/0.44 inference(avatar_component_clause,[],[f1888])).
% 0.61/0.44 thf(f1891,plain,(
% 0.61/0.44 spl222_2),
% 0.61/0.44 inference(avatar_split_clause,[],[f1635,f1888])).
% 0.61/0.44 thf(f1903,definition,(
% 0.61/0.44 spl222_5 <=> (((fresh @ name @ late_freeRes @ x @ alpha)) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl222_5])],[avatar_definition])).
% 0.61/0.44 thf(f1905,plain,(
% 0.61/0.44 (((fresh @ name @ late_freeRes @ x @ alpha)) = $true) | ~spl222_5),
% 0.61/0.44 inference(avatar_component_clause,[],[f1903])).
% 0.61/0.44 thf(f1906,plain,(
% 0.61/0.44 spl222_5),
% 0.61/0.44 inference(avatar_split_clause,[],[f1674,f1903])).
% 0.61/0.44 thf(f1943,definition,(
% 0.61/0.44 spl222_13 <=> (((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))) = $true)),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl222_13])],[avatar_definition])).
% 0.61/0.44 thf(f1945,plain,(
% 0.61/0.44 (((late_transitions @ (res @ x @ (par @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ (par @ p2 @ q))))) != $true) | spl222_13),
% 0.61/0.44 inference(avatar_component_clause,[],[f1943])).
% 0.61/0.44 thf(f1946,plain,(
% 0.61/0.44 ~spl222_13),
% 0.61/0.44 inference(avatar_split_clause,[],[f1757,f1943])).
% 0.61/0.44 thf(f2024,plain,(
% 0.61/0.44 ($true != $true) | (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) != $true) | (((fresh @ name @ late_freeRes @ x @ alpha)) != $true) | spl222_13),
% 0.61/0.44 inference(superposition,[],[f1945,f1412])).
% 0.61/0.44 thf(f2028,plain,(
% 0.61/0.44 (((late_transitions @ (par @ p @ q) @ (late_FreeR @ alpha @ (par @ p2 @ q)))) != $true) | (((fresh @ name @ late_freeRes @ x @ alpha)) != $true) | spl222_13),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f2024])).
% 0.61/0.44 thf(f2031,plain,(
% 0.61/0.44 (((fresh @ name @ late_freeRes @ x @ alpha)) != $true) | (~spl222_2 | spl222_13)),
% 0.61/0.44 inference(forward_subsumption_resolution,[],[f2028,f1890])).
% 0.61/0.44 thf(f2032,plain,(
% 0.61/0.44 $false | (~spl222_2 | ~spl222_5 | spl222_13)),
% 0.61/0.44 inference(forward_subsumption_resolution,[],[f2031,f1905])).
% 0.61/0.44 thf(f2033,plain,(
% 0.61/0.44 ~spl222_2 | ~spl222_5 | spl222_13),
% 0.61/0.44 inference(avatar_contradiction_clause,[],[f2032])).
% 0.61/0.44 cnf(s2, plain, spl222_2, inference(sat_conversion,[],[f1891])).
% 0.61/0.44 cnf(s5, plain, spl222_5, inference(sat_conversion,[],[f1906])).
% 0.61/0.44 cnf(s13, plain, ~spl222_13, inference(sat_conversion,[],[f1946])).
% 0.61/0.44 cnf(s22, plain, ~spl222_2 | ~spl222_5 | spl222_13, inference(sat_conversion,[],[f2033])).
% 0.61/0.44 cnf(s23, plain, ~spl222_2, inference(rat,[],[s22,s13,s5])).
% 0.61/0.44 cnf(s24, plain, $false, inference(rat,[],[s2,s23])).
% 0.61/0.44 thf(f2034,plain,(
% 0.61/0.44 $false),
% 0.61/0.44 inference(avatar_sat_refutation,[],[s24])).
% 0.61/0.44 % SZS output end Proof for theBenchmark
% 0.61/0.44 % (849677)------------------------------
% 0.61/0.44 % (849677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (849677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (849677)CaDiCaL version: 2.1.3
% 0.61/0.44 % (849677)Termination reason: Refutation
% 0.61/0.44 % (849677)Time elapsed: 0.093 s
% 0.61/0.44 % (849677)Peak memory usage: 15 MB
% 0.61/0.44 % (849677)Instructions burned: 196 (million)
% 0.61/0.44 % (849669)Success in time 0.152 s
% 0.61/0.44 % Vampire exiting
%------------------------------------------------------------------------------