%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP157^2 : 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 : n018.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 08:08:36 AM UTC 2026
% Result : Theorem 0.46s 0.44s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP157^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.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 20:06:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.42 % (575495)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.46/0.42 % (575500)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3718817642:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.46/0.42 % (575506)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.46/0.42 % (575506)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
% 0.46/0.42 % (575501)lrs+10_16_si=on:nwc=1.5:random_seed=3833837685:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.46/0.42 % (575505)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=756503693:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.46/0.42 % (575504)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2380869603:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.46/0.42 % (575503)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=2042308449: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)
% 0.46/0.42 % (575506)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=2476596126:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.46/0.42 % (575502)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=820492157:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.46/0.42 % (575502)Instruction limit reached!
% 0.46/0.42 % (575502)------------------------------
% 0.46/0.42 % (575502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.42 % (575502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.42 % (575502)CaDiCaL version: 2.1.3
% 0.46/0.42 % (575502)Termination reason: Instruction limit
% 0.46/0.42 % (575502)Termination phase: shuffling
% 0.46/0.42 % (575502)Time elapsed: 0.003 s
% 0.46/0.42 % (575502)Peak memory usage: 10 MB
% 0.46/0.42 % (575502)Instructions burned: 4 (million)
% 0.46/0.42 % (575501)Instruction limit reached!
% 0.46/0.42 % (575501)------------------------------
% 0.46/0.42 % (575501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.42 % (575501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.42 % (575501)CaDiCaL version: 2.1.3
% 0.46/0.42 % (575501)Termination reason: Instruction limit
% 0.46/0.42 % (575501)Termination phase: shuffling
% 0.46/0.42 % (575501)Time elapsed: 0.010 s
% 0.46/0.42 % (575501)Peak memory usage: 10 MB
% 0.46/0.42 % (575501)Instructions burned: 19 (million)
% 0.46/0.42 % (575504)Instruction limit reached!
% 0.46/0.42 % (575504)------------------------------
% 0.46/0.42 % (575504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.42 % (575504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.42 % (575504)CaDiCaL version: 2.1.3
% 0.46/0.42 % (575504)Termination reason: Instruction limit
% 0.46/0.42 % (575504)Termination phase: Property scanning
% 0.46/0.42 % (575504)Time elapsed: 0.013 s
% 0.46/0.42 % (575504)Peak memory usage: 10 MB
% 0.46/0.42 % (575504)Instructions burned: 25 (million)
% 0.46/0.42 % (575500)Instruction limit reached!
% 0.46/0.42 % (575500)------------------------------
% 0.46/0.42 % (575500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.42 % (575500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.42 % (575500)CaDiCaL version: 2.1.3
% 0.46/0.42 % (575500)Termination reason: Instruction limit
% 0.46/0.42 % (575500)Termination phase: Property scanning
% 0.46/0.42 % (575500)Time elapsed: 0.024 s
% 0.46/0.42 % (575500)Peak memory usage: 12 MB
% 0.46/0.42 % (575500)Instructions burned: 88 (million)
% 0.46/0.42 % (575514)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3795828758:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.46/0.42 % (575517)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=771142599:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.46/0.42 % (575514)Instruction limit reached!
% 0.46/0.44 % (575514)------------------------------
% 0.46/0.44 % (575514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575514)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575514)Termination reason: Instruction limit
% 0.46/0.44 % (575514)Termination phase: shuffling
% 0.46/0.44 % (575514)Time elapsed: 0.002 s
% 0.46/0.44 % (575514)Peak memory usage: 10 MB
% 0.46/0.44 % (575514)Instructions burned: 3 (million)
% 0.46/0.44 % (575516)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.46/0.44 % (575515)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4034988143:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.46/0.44 % (575517)Instruction limit reached!
% 0.46/0.44 % (575517)------------------------------
% 0.46/0.44 % (575517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575517)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575517)Termination reason: Instruction limit
% 0.46/0.44 % (575517)Termination phase: shuffling
% 0.46/0.44 % (575517)Time elapsed: 0.004 s
% 0.46/0.44 % (575517)Peak memory usage: 10 MB
% 0.46/0.44 % (575517)Instructions burned: 15 (million)
% 0.46/0.44 % (575516)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3248715494:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.46/0.44 % (575515)Instruction limit reached!
% 0.46/0.44 % (575515)------------------------------
% 0.46/0.44 % (575515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575515)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575515)Termination reason: Instruction limit
% 0.46/0.44 % (575515)Termination phase: shuffling
% 0.46/0.44 % (575515)Time elapsed: 0.003 s
% 0.46/0.44 % (575515)Peak memory usage: 10 MB
% 0.46/0.44 % (575515)Instructions burned: 5 (million)
% 0.46/0.44 % (575516)Instruction limit reached!
% 0.46/0.44 % (575516)------------------------------
% 0.46/0.44 % (575516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575516)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575516)Termination reason: Instruction limit
% 0.46/0.44 % (575516)Termination phase: shuffling
% 0.46/0.44 % (575516)Time elapsed: 0.004 s
% 0.46/0.44 % (575516)Peak memory usage: 10 MB
% 0.46/0.44 % (575516)Instructions burned: 8 (million)
% 0.46/0.44 % (575505)Instruction limit reached!
% 0.46/0.44 % (575505)------------------------------
% 0.46/0.44 % (575505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575505)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575505)Termination reason: Instruction limit
% 0.46/0.44 % (575505)Termination phase: Property scanning
% 0.46/0.44 % (575505)Time elapsed: 0.039 s
% 0.46/0.44 % (575505)Peak memory usage: 12 MB
% 0.46/0.44 % (575505)Instructions burned: 75 (million)
% 0.46/0.44 % (575522)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=3015211270:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.46/0.44 % (575520)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
% 0.46/0.44 % (575520)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.46/0.44 % (575520)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3294163010:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.46/0.44 % (575524)lrs+10_1_si=on:cs=on:random_seed=416116072:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.46/0.44 % (575525)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.46/0.44 % (575525)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=2880568462:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.46/0.44 % (575524)Instruction limit reached!
% 0.46/0.44 % (575524)------------------------------
% 0.46/0.44 % (575524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575524)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575524)Termination reason: Instruction limit
% 0.46/0.44 % (575524)Termination phase: shuffling
% 0.46/0.44 % (575524)Time elapsed: 0.005 s
% 0.46/0.44 % (575524)Peak memory usage: 10 MB
% 0.46/0.44 % (575524)Instructions burned: 10 (million)
% 0.46/0.44 % (575526)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3589288444:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.46/0.44 % (575525)Instruction limit reached!
% 0.46/0.44 % (575525)------------------------------
% 0.46/0.44 % (575525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575525)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575525)Termination reason: Instruction limit
% 0.46/0.44 % (575525)Termination phase: shuffling
% 0.46/0.44 % (575525)Time elapsed: 0.002 s
% 0.46/0.44 % (575525)Peak memory usage: 10 MB
% 0.46/0.44 % (575525)Instructions burned: 3 (million)
% 0.46/0.44 % (575520)Instruction limit reached!
% 0.46/0.44 % (575520)------------------------------
% 0.46/0.44 % (575520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575520)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575520)Termination reason: Instruction limit
% 0.46/0.44 % (575520)Termination phase: shuffling
% 0.46/0.44 % (575520)Time elapsed: 0.014 s
% 0.46/0.44 % (575520)Peak memory usage: 10 MB
% 0.46/0.44 % (575520)Instructions burned: 28 (million)
% 0.46/0.44 % (575522)Instruction limit reached!
% 0.46/0.44 % (575522)------------------------------
% 0.46/0.44 % (575522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575522)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575522)Termination reason: Instruction limit
% 0.46/0.44 % (575522)Termination phase: Preprocessing 3
% 0.46/0.44 % (575522)Time elapsed: 0.021 s
% 0.46/0.44 % (575522)Peak memory usage: 11 MB
% 0.46/0.44 % (575522)Instructions burned: 88 (million)
% 0.46/0.44 % (575535)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3164069631:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.46/0.44 % (575532)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3955859824:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.46/0.44 % (575526)Instruction limit reached!
% 0.46/0.44 % (575526)------------------------------
% 0.46/0.44 % (575526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575526)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575526)Termination reason: Instruction limit
% 0.46/0.44 % (575526)Termination phase: Preprocessing 3
% 0.46/0.44 % (575526)Time elapsed: 0.019 s
% 0.46/0.44 % (575526)Peak memory usage: 11 MB
% 0.46/0.44 % (575526)Instructions burned: 38 (million)
% 0.46/0.44 % (575533)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3061945801:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.46/0.44 % (575534)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2892805802:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.46/0.44 % (575506)Instruction limit reached!
% 0.46/0.44 % (575506)------------------------------
% 0.46/0.44 % (575506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575506)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575506)Termination reason: Instruction limit
% 0.46/0.44 % (575506)Termination phase: Saturation
% 0.46/0.44 % (575506)Time elapsed: 0.084 s
% 0.46/0.44 % (575506)Peak memory usage: 14 MB
% 0.46/0.44 % (575506)Instructions burned: 157 (million)
% 0.46/0.44 % (575534)Instruction limit reached!
% 0.46/0.44 % (575534)------------------------------
% 0.46/0.44 % (575534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575534)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575534)Termination reason: Instruction limit
% 0.46/0.44 % (575534)Termination phase: shuffling
% 0.46/0.44 % (575534)Time elapsed: 0.007 s
% 0.46/0.44 % (575534)Peak memory usage: 10 MB
% 0.46/0.44 % (575534)Instructions burned: 14 (million)
% 0.46/0.44 % (575533)Instruction limit reached!
% 0.46/0.44 % (575533)------------------------------
% 0.46/0.44 % (575533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575533)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575533)Termination reason: Instruction limit
% 0.46/0.44 % (575533)Termination phase: Property scanning
% 0.46/0.44 % (575533)Time elapsed: 0.013 s
% 0.46/0.44 % (575533)Peak memory usage: 10 MB
% 0.46/0.44 % (575533)Instructions burned: 27 (million)
% 0.46/0.44 % (575503) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-575495-575503"...
% 0.46/0.44 % (575539)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3972077399:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.46/0.44 % (575503)...printing done.
% 0.46/0.44 % (575503)Refutation found. Thanks to Tanya!
% 0.46/0.44 % SZS status Theorem for theBenchmark
% 0.46/0.44 % SZS output start Proof for theBenchmark
% 0.46/0.44 thf(type_def_5, type, product_unit: $tType).
% 0.46/0.44 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.46/0.44 thf(type_def_7, type, set: $tType > $tType).
% 0.46/0.44 thf(type_def_8, type, a: $tType).
% 0.46/0.44 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.46/0.44 thf(func_def_0, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_2, type, minus: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_3, type, bot: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_5, type, top: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_7, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_8, type, order_top: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_9, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_10, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.46/0.44 thf(func_def_11, type, bNF_Gr: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_12, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_13, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 0.46/0.44 thf(func_def_14, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 0.46/0.44 thf(func_def_15, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.46/0.44 thf(func_def_16, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.46/0.44 thf(func_def_17, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_18, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.46/0.44 thf(func_def_19, type, order_preorder_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.46/0.44 thf(func_def_20, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_21, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.46/0.44 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_23, type, prefer951318096ood_as: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.46/0.44 thf(func_def_24, type, prefer310429814s_good: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.46/0.44 thf(func_def_25, type, prefer1532642881r_than: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.46/0.44 thf(func_def_26, type, prefer199794634erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.46/0.44 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_28, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_29, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.46/0.44 thf(func_def_30, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.46/0.44 thf(func_def_31, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.46/0.44 thf(func_def_32, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 0.46/0.44 thf(func_def_33, type, product_rec_set_bool: !>[X0: $tType]:((X0 > X0 > $o > X0 > $o))).
% 0.46/0.44 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.46/0.44 thf(func_def_35, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 0.46/0.44 thf(func_def_36, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 0.46/0.44 thf(func_def_37, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 0.46/0.44 thf(func_def_38, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.46/0.44 thf(func_def_39, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.46/0.44 thf(func_def_40, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.46/0.44 thf(func_def_41, type, product_product: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_42, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 0.46/0.44 thf(func_def_43, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.46/0.44 thf(func_def_44, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.46/0.44 thf(func_def_45, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_46, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 0.46/0.44 thf(func_def_47, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.46/0.44 thf(func_def_48, type, b: set @ a).
% 0.46/0.44 thf(func_def_49, type, pr: set @ product_prod @ a @ a).
% 0.46/0.44 thf(func_def_50, type, y: a).
% 0.46/0.44 thf(func_def_51, type, z: a).
% 0.46/0.44 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.46/0.44 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_58, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.46/0.44 thf(func_def_59, type, db2: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.46/0.44 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 0.46/0.44 thf(func_def_62, type, db3: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_63, type, vNOT: ($o > $o)).
% 0.46/0.44 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.46/0.44 thf(func_def_65, type, vOR: ($o > $o > $o)).
% 0.46/0.44 thf(func_def_66, type, sK0: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.46/0.44 thf(func_def_67, type, sK1: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.46/0.44 thf(func_def_68, type, sK2: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0) > set @ X1 > X1))).
% 0.46/0.44 thf(func_def_69, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.46/0.44 thf(func_def_70, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.46/0.44 thf(func_def_71, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X3))).
% 0.46/0.44 thf(func_def_72, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.46/0.44 thf(func_def_73, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.46/0.44 thf(func_def_74, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X1))).
% 0.46/0.44 thf(func_def_75, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X2))).
% 0.46/0.44 thf(func_def_76, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X3))).
% 0.46/0.44 thf(func_def_77, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X4))).
% 0.46/0.44 thf(func_def_78, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X4 > $o) > X0))).
% 0.46/0.44 thf(func_def_79, type, sK13: !>[X0: $tType]:((set @ X0 > X0))).
% 0.46/0.44 thf(func_def_80, type, sK14: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.46/0.44 thf(func_def_81, type, sK15: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > X0) > X1))).
% 0.46/0.44 thf(func_def_82, type, sK16: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > (X1 > set @ X0) > X1))).
% 0.46/0.44 thf(func_def_83, type, sK17: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.46/0.44 thf(func_def_84, type, sK18: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.46/0.44 thf(func_def_85, type, sK19: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > X0))).
% 0.46/0.44 thf(func_def_86, type, sK20: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 0.46/0.44 thf(func_def_87, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > product_prod @ X0 @ X1 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_88, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > product_prod @ X0 @ X1 > set @ X0 > X1))).
% 0.46/0.44 thf(func_def_89, type, sK23: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_90, type, sK24: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.46/0.44 thf(func_def_91, type, sK25: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.46/0.44 thf(func_def_92, type, sK26: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_93, type, sK27: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_94, type, sK28: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_95, type, sK29: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_96, type, sK30: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.46/0.44 thf(func_def_97, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.46/0.44 thf(func_def_98, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.46/0.44 thf(func_def_99, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.46/0.44 thf(func_def_100, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.46/0.44 thf(func_def_101, type, sK35: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > set @ X1))).
% 0.46/0.44 thf(func_def_102, type, sK36: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > X1))).
% 0.46/0.44 thf(func_def_103, type, sK37: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_104, type, sK38: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_105, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 0.46/0.44 thf(func_def_106, type, sK40: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_107, type, sK41: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_108, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X0))).
% 0.46/0.44 thf(func_def_109, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X6))).
% 0.46/0.44 thf(func_def_110, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X2))).
% 0.46/0.44 thf(func_def_111, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X5))).
% 0.46/0.44 thf(func_def_112, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X1))).
% 0.46/0.44 thf(func_def_113, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X3))).
% 0.46/0.44 thf(func_def_114, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ X5 > $o) > X4))).
% 0.46/0.44 thf(func_def_115, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_116, type, sK50: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_117, type, sK51: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ X1 > set @ X0))).
% 0.46/0.44 thf(func_def_118, type, sK52: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_119, type, sK53: !>[X0: $tType]:(X0)).
% 0.46/0.44 thf(func_def_120, type, sK54: !>[X0: $tType]:((set @ X0 > X0))).
% 0.46/0.44 thf(func_def_121, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > (X1 > set @ X0) > X1))).
% 0.46/0.44 thf(func_def_122, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.46/0.44 thf(func_def_123, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X3))).
% 0.46/0.44 thf(func_def_124, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X1))).
% 0.46/0.44 thf(func_def_125, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X4))).
% 0.46/0.44 thf(func_def_126, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X2))).
% 0.46/0.44 thf(func_def_127, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X0))).
% 0.46/0.44 thf(func_def_128, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > set @ X0 > X0))).
% 0.46/0.44 thf(func_def_129, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_130, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.46/0.44 thf(func_def_131, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.46/0.44 thf(func_def_132, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.46/0.44 thf(func_def_133, type, sK67: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_134, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_135, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.46/0.44 thf(func_def_136, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X0 > (X1 > $o) > X1))).
% 0.46/0.44 thf(func_def_137, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X3))).
% 0.46/0.44 thf(func_def_138, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X2))).
% 0.46/0.44 thf(func_def_139, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X0))).
% 0.46/0.44 thf(func_def_140, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X1))).
% 0.46/0.44 thf(func_def_141, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X4))).
% 0.46/0.44 thf(func_def_142, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X5))).
% 0.46/0.44 thf(func_def_143, type, sK77: !>[X0: $tType]:((set @ X0 > X0))).
% 0.46/0.44 thf(func_def_144, type, sK78: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_145, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (X0 > X1) > X0))).
% 0.46/0.44 thf(func_def_146, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.46/0.44 thf(func_def_147, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_148, type, sK82: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.46/0.44 thf(func_def_149, type, sK83: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.46/0.44 thf(func_def_150, type, sK84: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.46/0.44 thf(func_def_151, type, sK85: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.46/0.44 thf(func_def_152, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (set @ X1 > $o) > set @ X0))).
% 0.46/0.44 thf(func_def_153, type, sK87: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (set @ X1 > $o) > set @ X1))).
% 0.46/0.44 thf(func_def_154, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > X3) > product_prod @ X0 @ X3 > (X1 > X0) > set @ product_prod @ X1 @ X2 > X1))).
% 0.46/0.44 thf(func_def_155, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > X3) > product_prod @ X0 @ X3 > (X1 > X0) > set @ product_prod @ X1 @ X2 > X2))).
% 0.46/0.44 thf(func_def_156, type, sK90: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_157, type, sK91: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_158, type, sK92: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_159, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X0))).
% 0.46/0.44 thf(func_def_160, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X4))).
% 0.46/0.44 thf(func_def_161, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X2))).
% 0.46/0.44 thf(func_def_162, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X6))).
% 0.46/0.44 thf(func_def_163, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X3))).
% 0.46/0.44 thf(func_def_164, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X5))).
% 0.46/0.44 thf(func_def_165, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X1))).
% 0.46/0.44 thf(func_def_166, type, sK100: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1 > X0))).
% 0.46/0.44 thf(func_def_167, type, sK101: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.46/0.44 thf(func_def_168, type, sK102: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.46/0.44 thf(func_def_169, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_170, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X4))).
% 0.46/0.44 thf(func_def_171, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X1))).
% 0.46/0.44 thf(func_def_172, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X5))).
% 0.46/0.44 thf(func_def_173, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X2))).
% 0.46/0.44 thf(func_def_174, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ X0 > $o) > X3))).
% 0.46/0.44 thf(func_def_175, type, sK109: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_176, type, sK110: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 0.46/0.44 thf(func_def_177, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.46/0.44 thf(func_def_178, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.46/0.44 thf(func_def_179, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.46/0.44 thf(func_def_180, type, sK114: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.46/0.44 thf(func_def_181, type, sK115: !>[X0: $tType]:((set @ X0 > X0))).
% 0.46/0.44 thf(f1,axiom,(
% 0.46/0.44 (member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))),
% 0.46/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms)).
% 0.46/0.44 thf(f2,axiom,(
% 0.46/0.44 ! [X0 : $tType,X2 : X0,X4 : set @ product_prod @ X0 @ X0,X1 : X0,X3 : set @ X0] : ((member @ X0 @ X1 @ (prefer310429814s_good @ X0 @ X2 @ X3 @ X4)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X1 @ X2) @ X4))),
% 0.46/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_at__lst__asgd__ge)).
% 0.46/0.44 thf(f290,conjecture,(
% 0.46/0.44 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)),
% 0.46/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.46/0.44 thf(f291,negated_conjecture,(
% 0.46/0.44 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)),
% 0.46/0.44 inference(negated_conjecture,[status(cth)],[f290])).
% 0.46/0.44 thf(f360,plain,(
% 0.46/0.44 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)),
% 0.46/0.44 inference(rectify,[],[f291])).
% 0.46/0.44 thf(f361,plain,(
% 0.46/0.44 ~ (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) = $true)),
% 0.46/0.44 inference(fool_elimination,[],[f360])).
% 0.46/0.44 thf(f563,plain,(
% 0.46/0.44 ! [X0 : $tType,X1 : X0,X2 : set @ product_prod @ X0 @ X0,X3 : X0,X4 : set @ X0] : ((member @ X0 @ X3 @ (prefer310429814s_good @ X0 @ X1 @ X4 @ X2)) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X1) @ X2))),
% 0.46/0.44 inference(rectify,[],[f2])).
% 0.46/0.44 thf(f564,plain,(
% 0.46/0.44 ! [X0 : $tType,X1 : X0,X4 : set @ X0,X2 : set @ product_prod @ X0 @ X0,X3 : X0] : ((((member @ X0 @ X3 @ (prefer310429814s_good @ X0 @ X1 @ X4 @ X2))) = $true) => ($true = ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X1) @ X2))))),
% 0.46/0.44 inference(fool_elimination,[],[f563])).
% 0.46/0.44 thf(f615,plain,(
% 0.46/0.44 (member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))),
% 0.46/0.44 inference(rectify,[],[f1])).
% 0.46/0.44 thf(f616,plain,(
% 0.46/0.44 (((member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))) = $true)),
% 0.46/0.44 inference(fool_elimination,[],[f615])).
% 0.46/0.44 thf(f771,plain,(
% 0.46/0.44 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) != $true)),
% 0.46/0.44 inference(flattening,[],[f361])).
% 0.46/0.44 thf(f905,plain,(
% 0.46/0.44 ! [X0 : $tType,X1 : X0,X4 : set @ X0,X2 : set @ product_prod @ X0 @ X0,X3 : X0] : ((((member @ X0 @ X3 @ (prefer310429814s_good @ X0 @ X1 @ X4 @ X2))) != $true) | ($true = ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X1) @ X2))))),
% 0.46/0.44 inference(ennf_transformation,[],[f564])).
% 0.46/0.44 thf(f1144,plain,(
% 0.46/0.44 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ product_prod @ X0 @ X0,X4 : X0] : (($true != ((member @ X0 @ X4 @ (prefer310429814s_good @ X0 @ X1 @ X2 @ X3)))) | (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X4 @ X1) @ X3)) = $true))),
% 0.46/0.44 inference(rectify,[],[f905])).
% 0.46/0.44 thf(f1385,plain,(
% 0.46/0.44 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) != $true)),
% 0.46/0.44 inference(cnf_transformation,[],[f771])).
% 0.46/0.44 thf(f1468,plain,(
% 0.46/0.44 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ product_prod @ X0 @ X0,X1 : X0,X4 : X0] : (($true != ((member @ X0 @ X4 @ (prefer310429814s_good @ X0 @ X1 @ X2 @ X3)))) | (((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X4 @ X1) @ X3)) = $true)) )),
% 0.46/0.44 inference(cnf_transformation,[],[f1144])).
% 0.46/0.44 thf(f1635,plain,(
% 0.46/0.44 (((member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))) = $true)),
% 0.46/0.44 inference(cnf_transformation,[],[f616])).
% 0.46/0.44 thf(f1793,definition,(
% 0.46/0.44 spl116_1 <=> (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) = $true)),
% 0.46/0.44 introduced(definition,[new_symbols(definition,[spl116_1])],[avatar_definition])).
% 0.46/0.44 thf(f1795,plain,(
% 0.46/0.44 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) != $true) | spl116_1),
% 0.46/0.44 inference(avatar_component_clause,[],[f1793])).
% 0.46/0.44 thf(f1796,plain,(
% 0.46/0.44 ~spl116_1),
% 0.46/0.44 inference(avatar_split_clause,[],[f1385,f1793])).
% 0.46/0.44 thf(f1848,definition,(
% 0.46/0.44 spl116_12 <=> (((member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))) = $true)),
% 0.46/0.44 introduced(definition,[new_symbols(definition,[spl116_12])],[avatar_definition])).
% 0.46/0.44 thf(f1850,plain,(
% 0.46/0.44 (((member @ a @ z @ (prefer310429814s_good @ a @ y @ b @ pr))) = $true) | ~spl116_12),
% 0.46/0.44 inference(avatar_component_clause,[],[f1848])).
% 0.46/0.44 thf(f1851,plain,(
% 0.46/0.44 spl116_12),
% 0.46/0.44 inference(avatar_split_clause,[],[f1635,f1848])).
% 0.46/0.44 thf(f1990,plain,(
% 0.46/0.44 ($true != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) = $true) | ~spl116_12),
% 0.46/0.44 inference(superposition,[],[f1468,f1850])).
% 0.46/0.44 thf(f1991,plain,(
% 0.46/0.44 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ z @ y) @ pr)) = $true) | ~spl116_12),
% 0.46/0.44 inference(trivial_inequality_removal,[],[f1990])).
% 0.46/0.44 thf(f1992,plain,(
% 0.46/0.44 $false | (spl116_1 | ~spl116_12)),
% 0.46/0.44 inference(forward_subsumption_resolution,[],[f1991,f1795])).
% 0.46/0.44 thf(f1993,plain,(
% 0.46/0.44 spl116_1 | ~spl116_12),
% 0.46/0.44 inference(avatar_contradiction_clause,[],[f1992])).
% 0.46/0.44 cnf(s1, plain, ~spl116_1, inference(sat_conversion,[],[f1796])).
% 0.46/0.44 cnf(s12, plain, spl116_12, inference(sat_conversion,[],[f1851])).
% 0.46/0.44 cnf(s13, plain, spl116_1 | ~spl116_12, inference(sat_conversion,[],[f1993])).
% 0.46/0.44 cnf(s14, plain, spl116_1, inference(rat,[],[s13,s12])).
% 0.46/0.44 cnf(s15, plain, $false, inference(rat,[],[s1,s14])).
% 0.46/0.44 thf(f1994,plain,(
% 0.46/0.44 $false),
% 0.46/0.44 inference(avatar_sat_refutation,[],[s15])).
% 0.46/0.44 % SZS output end Proof for theBenchmark
% 0.46/0.44 % (575503)------------------------------
% 0.46/0.44 % (575503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.44 % (575503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.44 % (575503)CaDiCaL version: 2.1.3
% 0.46/0.44 % (575503)Termination reason: Refutation
% 0.46/0.44 % (575503)Time elapsed: 0.095 s
% 0.46/0.44 % (575503)Peak memory usage: 15 MB
% 0.46/0.44 % (575503)Instructions burned: 174 (million)
% 0.46/0.44 % (575495)Success in time 0.154 s
% 0.46/0.44 % Vampire exiting
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