%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP152^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:08:34 AM UTC 2026
% Result : Theorem 0.53s 0.41s
% Output : Refutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP152^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n014.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 20:02:01 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.41 % (3141825)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.53/0.41 % (3141831)lrs+10_16_si=on:nwc=1.5:random_seed=3168355905:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.53/0.41 % (3141836)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.53/0.41 % (3141836)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
% 0.53/0.41 % (3141831)Instruction limit reached!
% 0.53/0.41 % (3141831)------------------------------
% 0.53/0.41 % (3141831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141831)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141831)Termination reason: Instruction limit
% 0.53/0.41 % (3141831)Termination phase: shuffling
% 0.53/0.41 % (3141831)Time elapsed: 0.005 s
% 0.53/0.41 % (3141831)Peak memory usage: 10 MB
% 0.53/0.41 % (3141831)Instructions burned: 19 (million)
% 0.53/0.41 % (3141830)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1626134661:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.53/0.41 % (3141832)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3512498761:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.53/0.41 % (3141833)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=1588737674: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)
% 0.53/0.41 % (3141834)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2711796464:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.53/0.41 % (3141835)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2874403450:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.53/0.41 % (3141836)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=2154680012:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.53/0.41 % (3141832)Instruction limit reached!
% 0.53/0.41 % (3141832)------------------------------
% 0.53/0.41 % (3141832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141832)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141832)Termination reason: Instruction limit
% 0.53/0.41 % (3141832)Termination phase: shuffling
% 0.53/0.41 % (3141832)Time elapsed: 0.005 s
% 0.53/0.41 % (3141832)Peak memory usage: 10 MB
% 0.53/0.41 % (3141832)Instructions burned: 7 (million)
% 0.53/0.41 % (3141838)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3083770441:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.41 % (3141838)Instruction limit reached!
% 0.53/0.41 % (3141838)------------------------------
% 0.53/0.41 % (3141838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141838)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141838)Termination reason: Instruction limit
% 0.53/0.41 % (3141838)Termination phase: shuffling
% 0.53/0.41 % (3141838)Time elapsed: 0.002 s
% 0.53/0.41 % (3141838)Peak memory usage: 10 MB
% 0.53/0.41 % (3141838)Instructions burned: 8 (million)
% 0.53/0.41 % (3141834)Instruction limit reached!
% 0.53/0.41 % (3141834)------------------------------
% 0.53/0.41 % (3141834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141834)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141834)Termination reason: Instruction limit
% 0.53/0.41 % (3141834)Termination phase: Property scanning
% 0.53/0.41 % (3141834)Time elapsed: 0.012 s
% 0.53/0.41 % (3141834)Peak memory usage: 10 MB
% 0.53/0.41 % (3141834)Instructions burned: 25 (million)
% 0.53/0.41 % (3141847)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.41 % (3141847)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2958187934:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.53/0.41 % (3141845)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2334012637:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.53/0.41 % (3141847)Instruction limit reached!
% 0.53/0.41 % (3141847)------------------------------
% 0.53/0.41 % (3141847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141847)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141847)Termination reason: Instruction limit
% 0.53/0.41 % (3141847)Termination phase: shuffling
% 0.53/0.41 % (3141847)Time elapsed: 0.003 s
% 0.53/0.41 % (3141847)Peak memory usage: 10 MB
% 0.53/0.41 % (3141847)Instructions burned: 12 (million)
% 0.53/0.41 % (3141845)Instruction limit reached!
% 0.53/0.41 % (3141845)------------------------------
% 0.53/0.41 % (3141845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141845)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141845)Termination reason: Instruction limit
% 0.53/0.41 % (3141845)Termination phase: shuffling
% 0.53/0.41 % (3141845)Time elapsed: 0.004 s
% 0.53/0.41 % (3141845)Peak memory usage: 10 MB
% 0.53/0.41 % (3141845)Instructions burned: 6 (million)
% 0.53/0.41 % (3141848)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=634482706:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.53/0.41 % (3141851)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
% 0.53/0.41 % (3141851)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.41 % (3141851)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=564817372:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.53/0.41 % (3141835)Instruction limit reached!
% 0.53/0.41 % (3141835)------------------------------
% 0.53/0.41 % (3141835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141835)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141835)Termination reason: Instruction limit
% 0.53/0.41 % (3141835)Termination phase: Property scanning
% 0.53/0.41 % (3141835)Time elapsed: 0.038 s
% 0.53/0.41 % (3141835)Peak memory usage: 12 MB
% 0.53/0.41 % (3141835)Instructions burned: 77 (million)
% 0.53/0.41 % (3141848)Instruction limit reached!
% 0.53/0.41 % (3141848)------------------------------
% 0.53/0.41 % (3141848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141848)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141848)Termination reason: Instruction limit
% 0.53/0.41 % (3141848)Termination phase: shuffling
% 0.53/0.41 % (3141848)Time elapsed: 0.006 s
% 0.53/0.41 % (3141848)Peak memory usage: 10 MB
% 0.53/0.41 % (3141848)Instructions burned: 13 (million)
% 0.53/0.41 % (3141830)Instruction limit reached!
% 0.53/0.41 % (3141830)------------------------------
% 0.53/0.41 % (3141830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141830)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141830)Termination reason: Instruction limit
% 0.53/0.41 % (3141830)Termination phase: Property scanning
% 0.53/0.41 % (3141830)Time elapsed: 0.042 s
% 0.53/0.41 % (3141830)Peak memory usage: 12 MB
% 0.53/0.41 % (3141830)Instructions burned: 88 (million)
% 0.53/0.41 % (3141851)Instruction limit reached!
% 0.53/0.41 % (3141851)------------------------------
% 0.53/0.41 % (3141851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141851)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141851)Termination reason: Instruction limit
% 0.53/0.41 % (3141851)Termination phase: shuffling
% 0.53/0.41 % (3141851)Time elapsed: 0.007 s
% 0.53/0.41 % (3141851)Peak memory usage: 11 MB
% 0.53/0.41 % (3141851)Instructions burned: 29 (million)
% 0.53/0.41 % (3141852)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=604868166:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.53/0.41 % (3141856)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.53/0.41 % (3141858)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4108868281:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.53/0.41 % (3141855)lrs+10_1_si=on:cs=on:random_seed=1976066518:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.53/0.41 % (3141856)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=4073284141:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.41 % (3141857)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1759346673:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.53/0.41 % (3141856)Instruction limit reached!
% 0.53/0.41 % (3141856)------------------------------
% 0.53/0.41 % (3141856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141856)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141856)Termination reason: Instruction limit
% 0.53/0.41 % (3141856)Termination phase: shuffling
% 0.53/0.41 % (3141856)Time elapsed: 0.002 s
% 0.53/0.41 % (3141856)Peak memory usage: 10 MB
% 0.53/0.41 % (3141856)Instructions burned: 3 (million)
% 0.53/0.41 % (3141855)Instruction limit reached!
% 0.53/0.41 % (3141855)------------------------------
% 0.53/0.41 % (3141855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141855)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141855)Termination reason: Instruction limit
% 0.53/0.41 % (3141855)Termination phase: shuffling
% 0.53/0.41 % (3141855)Time elapsed: 0.005 s
% 0.53/0.41 % (3141855)Peak memory usage: 10 MB
% 0.53/0.41 % (3141855)Instructions burned: 10 (million)
% 0.53/0.41 % (3141836)Instruction limit reached!
% 0.53/0.41 % (3141836)------------------------------
% 0.53/0.41 % (3141836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141836)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141836)Termination reason: Instruction limit
% 0.53/0.41 % (3141836)Termination phase: Saturation
% 0.53/0.41 % (3141836)Time elapsed: 0.073 s
% 0.53/0.41 % (3141836)Peak memory usage: 14 MB
% 0.53/0.41 % (3141836)Instructions burned: 158 (million)
% 0.53/0.41 % (3141858) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3141825-3141858"...
% 0.53/0.41 % (3141858)...printing done.
% 0.53/0.41 % (3141858)Refutation found. Thanks to Tanya!
% 0.53/0.41 % SZS status Theorem for theBenchmark
% 0.53/0.41 % SZS output start Proof for theBenchmark
% 0.53/0.41 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.53/0.41 thf(type_def_6, type, multiset: $tType > $tType).
% 0.53/0.41 thf(type_def_7, type, set: $tType > $tType).
% 0.53/0.41 thf(type_def_8, type, a: $tType).
% 0.53/0.41 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.53/0.41 thf(func_def_0, type, preorder: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_2, type, plus: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_4, type, minus: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_6, type, top: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_8, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_9, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_10, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 0.53/0.41 thf(func_def_11, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.53/0.41 thf(func_def_12, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.53/0.41 thf(func_def_13, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.53/0.41 thf(func_def_14, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_15, type, add_mset: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0))).
% 0.53/0.41 thf(func_def_16, type, comm_monoid_sum_mset: !>[X0: $tType]:(((X0 > X0 > X0) > X0 > multiset @ X0 > X0))).
% 0.53/0.41 thf(func_def_17, type, fold_mset: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X1 > multiset @ X0 > X1))).
% 0.53/0.41 thf(func_def_18, type, is_empty: !>[X0: $tType]:((multiset @ X0 > $o))).
% 0.53/0.41 thf(func_def_19, type, mult: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 0.53/0.41 thf(func_def_20, type, mult1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 0.53/0.41 thf(func_def_21, type, multp: !>[X0: $tType]:(((X0 > X0 > $o) > multiset @ X0 > multiset @ X0 > $o))).
% 0.53/0.41 thf(func_def_22, type, set_mset: !>[X0: $tType]:((multiset @ X0 > set @ X0))).
% 0.53/0.41 thf(func_def_23, type, order_preorder_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_24, type, order_215145569der_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.53/0.41 thf(func_def_26, type, top_top: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_27, type, prefer310429814s_good: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.53/0.41 thf(func_def_28, type, prefer199794634erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_29, type, prefer1997167224erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_30, type, prefer1801827867axioms: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_31, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.53/0.41 thf(func_def_32, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.53/0.41 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.53/0.41 thf(func_def_34, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.53/0.41 thf(func_def_35, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 0.53/0.41 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.53/0.41 thf(func_def_37, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.53/0.41 thf(func_def_38, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.53/0.41 thf(func_def_39, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.53/0.41 thf(func_def_40, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.53/0.41 thf(func_def_41, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 0.53/0.41 thf(func_def_42, type, asym: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_43, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 0.53/0.41 thf(func_def_44, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.53/0.41 thf(func_def_45, type, irrefl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_46, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_47, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_48, type, trans: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.53/0.41 thf(func_def_49, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.53/0.41 thf(func_def_50, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.53/0.41 thf(func_def_51, 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))).
% 0.53/0.41 thf(func_def_52, 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))).
% 0.53/0.41 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.53/0.41 thf(func_def_54, type, carrier: set @ a).
% 0.53/0.41 thf(func_def_55, type, relation: set @ product_prod @ a @ a).
% 0.53/0.41 thf(func_def_56, type, x: a).
% 0.53/0.41 thf(func_def_57, type, y: a).
% 0.53/0.41 thf(func_def_61, type, db1: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_63, type, db0: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_64, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.53/0.41 thf(func_def_65, type, vAND: ($o > $o > $o)).
% 0.53/0.41 thf(func_def_66, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.53/0.41 thf(func_def_67, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.53/0.41 thf(func_def_68, type, vIMP: ($o > $o > $o)).
% 0.53/0.41 thf(func_def_69, type, vNOT: ($o > $o)).
% 0.53/0.41 thf(func_def_70, type, db3: !>[X0: $tType]:(X0)).
% 0.53/0.41 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.53/0.41 thf(func_def_72, type, vOR: ($o > $o > $o)).
% 0.53/0.41 thf(func_def_73, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X5))).
% 0.53/0.41 thf(func_def_74, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X3))).
% 0.53/0.41 thf(func_def_75, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X0))).
% 0.53/0.41 thf(func_def_76, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X4))).
% 0.53/0.41 thf(func_def_77, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X2))).
% 0.53/0.41 thf(func_def_78, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ X0 > X1))).
% 0.53/0.41 thf(func_def_79, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X4))).
% 0.53/0.41 thf(func_def_80, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X0))).
% 0.53/0.41 thf(func_def_81, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X5))).
% 0.53/0.41 thf(func_def_82, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X3))).
% 0.53/0.41 thf(func_def_83, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X2))).
% 0.53/0.41 thf(func_def_84, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ X2 > $o) > X1))).
% 0.53/0.41 thf(func_def_85, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.53/0.41 thf(func_def_86, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > $o) > X3))).
% 0.53/0.41 thf(func_def_87, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > $o) > X1))).
% 0.53/0.41 thf(func_def_88, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > $o) > X2))).
% 0.53/0.41 thf(func_def_89, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X1 > $o) > X0))).
% 0.53/0.41 thf(func_def_90, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X1))).
% 0.53/0.41 thf(func_def_91, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X0))).
% 0.53/0.41 thf(func_def_92, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X3))).
% 0.53/0.41 thf(func_def_93, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X4))).
% 0.53/0.41 thf(func_def_94, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X6))).
% 0.53/0.41 thf(func_def_95, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X5))).
% 0.53/0.41 thf(func_def_96, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X6 @ X1 > $o) > X2))).
% 0.53/0.41 thf(func_def_97, type, sK24: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.53/0.41 thf(func_def_98, type, sK25: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.53/0.41 thf(func_def_99, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X0))).
% 0.53/0.41 thf(func_def_100, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X2))).
% 0.53/0.41 thf(func_def_101, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X1))).
% 0.53/0.41 thf(func_def_102, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X5))).
% 0.53/0.41 thf(func_def_103, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X4))).
% 0.53/0.41 thf(func_def_104, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X6))).
% 0.53/0.41 thf(func_def_105, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X3))).
% 0.53/0.41 thf(func_def_106, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.53/0.41 thf(func_def_107, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.53/0.41 thf(func_def_108, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X3))).
% 0.53/0.41 thf(func_def_109, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X2))).
% 0.53/0.41 thf(func_def_110, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X1))).
% 0.53/0.41 thf(func_def_111, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X0))).
% 0.53/0.41 thf(func_def_112, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ X1 > $o) > X4))).
% 0.53/0.41 thf(func_def_113, type, sK40: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.53/0.41 thf(func_def_114, type, sK41: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.53/0.41 thf(func_def_115, type, sK42: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.53/0.41 thf(func_def_116, type, sK43: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.53/0.41 thf(func_def_117, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.53/0.41 thf(func_def_118, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.53/0.41 thf(func_def_119, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.53/0.41 thf(func_def_120, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X1))).
% 0.53/0.41 thf(func_def_121, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X0))).
% 0.53/0.41 thf(func_def_122, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X3))).
% 0.53/0.41 thf(func_def_123, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X2))).
% 0.53/0.41 thf(func_def_124, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X0 > X0))).
% 0.53/0.41 thf(func_def_125, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X0 > X4))).
% 0.53/0.41 thf(func_def_126, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X0 > X2))).
% 0.53/0.41 thf(func_def_127, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X0 > X1))).
% 0.53/0.41 thf(func_def_128, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X0 > X3))).
% 0.53/0.41 thf(func_def_129, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.53/0.41 thf(func_def_130, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.53/0.41 thf(func_def_131, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.53/0.41 thf(f4,axiom,(
% 0.53/0.41 ! [X0 : a] : ((member @ a @ X0 @ carrier) => ! [X1 : a] : ((member @ a @ X1 @ carrier) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation))))),
% 0.53/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_compl)).
% 0.53/0.41 thf(f288,axiom,(
% 0.53/0.41 (member @ a @ x @ carrier)),
% 0.53/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.53/0.41 thf(f289,axiom,(
% 0.53/0.41 (member @ a @ y @ carrier)),
% 0.53/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.53/0.41 thf(f291,conjecture,(
% 0.53/0.41 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)),
% 0.53/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)).
% 0.53/0.41 thf(f292,negated_conjecture,(
% 0.53/0.41 ~((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation))),
% 0.53/0.41 inference(negated_conjecture,[status(cth)],[f291])).
% 0.53/0.41 thf(f310,plain,(
% 0.53/0.41 (member @ a @ y @ carrier)),
% 0.53/0.41 inference(rectify,[],[f289])).
% 0.53/0.41 thf(f311,plain,(
% 0.53/0.41 (((member @ a @ y @ carrier)) = $true)),
% 0.53/0.41 inference(fool_elimination,[],[f310])).
% 0.53/0.41 thf(f369,plain,(
% 0.53/0.41 ~((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation))),
% 0.53/0.41 inference(rectify,[],[f292])).
% 0.53/0.41 thf(f370,plain,(
% 0.53/0.41 ~((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $true))),
% 0.53/0.41 inference(fool_elimination,[],[f369])).
% 0.53/0.41 thf(f409,plain,(
% 0.53/0.41 (member @ a @ x @ carrier)),
% 0.53/0.41 inference(rectify,[],[f288])).
% 0.53/0.41 thf(f410,plain,(
% 0.53/0.41 (((member @ a @ x @ carrier)) = $true)),
% 0.53/0.41 inference(fool_elimination,[],[f409])).
% 0.53/0.41 thf(f603,plain,(
% 0.53/0.41 ! [X0 : a] : ((member @ a @ X0 @ carrier) => ! [X1 : a] : ((member @ a @ X1 @ carrier) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation))))),
% 0.53/0.41 inference(rectify,[],[f4])).
% 0.53/0.41 thf(f604,plain,(
% 0.53/0.41 ! [X0 : a] : ((((member @ a @ X0 @ carrier)) = $true) => ! [X1 : a] : ((((member @ a @ X1 @ carrier)) = $true) => ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) = $true))))),
% 0.53/0.41 inference(fool_elimination,[],[f603])).
% 0.53/0.41 thf(f739,plain,(
% 0.53/0.41 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) != $true) & (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) != $true)),
% 0.53/0.41 inference(ennf_transformation,[],[f370])).
% 0.53/0.41 thf(f744,plain,(
% 0.53/0.41 ! [X0 : a] : (! [X1 : a] : (((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) = $true)) | (((member @ a @ X1 @ carrier)) != $true)) | (((member @ a @ X0 @ carrier)) != $true))),
% 0.53/0.41 inference(ennf_transformation,[],[f604])).
% 0.53/0.41 thf(f745,plain,(
% 0.53/0.41 ! [X0 : a] : (! [X1 : a] : ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) = $true) | (((member @ a @ X1 @ carrier)) != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) = $true)) | (((member @ a @ X0 @ carrier)) != $true))),
% 0.53/0.41 inference(flattening,[],[f744])).
% 0.53/0.41 thf(f795,plain,(
% 0.53/0.41 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) != $true)),
% 0.53/0.41 inference(cnf_transformation,[],[f739])).
% 0.53/0.41 thf(f796,plain,(
% 0.53/0.41 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) != $true)),
% 0.53/0.41 inference(cnf_transformation,[],[f739])).
% 0.53/0.41 thf(f797,plain,(
% 0.53/0.41 ( ! [X0 : a,X1 : a] : ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X0) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X0 @ X1) @ relation)) = $true) | (((member @ a @ X0 @ carrier)) != $true) | (((member @ a @ X1 @ carrier)) != $true)) )),
% 0.53/0.41 inference(cnf_transformation,[],[f745])).
% 0.53/0.41 thf(f806,plain,(
% 0.53/0.41 (((member @ a @ x @ carrier)) = $true)),
% 0.53/0.41 inference(cnf_transformation,[],[f410])).
% 0.53/0.41 thf(f808,plain,(
% 0.53/0.41 (((member @ a @ y @ carrier)) = $true)),
% 0.53/0.41 inference(cnf_transformation,[],[f311])).
% 0.53/0.41 thf(f821,plain,(
% 0.53/0.41 ($true != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $true) | (((member @ a @ x @ carrier)) != $true) | (((member @ a @ y @ carrier)) != $true)),
% 0.53/0.41 inference(superposition,[],[f795,f797])).
% 0.53/0.41 thf(f826,plain,(
% 0.53/0.41 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $true) | (((member @ a @ y @ carrier)) != $true) | (((member @ a @ x @ carrier)) != $true)),
% 0.53/0.41 inference(trivial_inequality_removal,[],[f821])).
% 0.53/0.41 thf(f832,plain,(
% 0.53/0.41 (((member @ a @ y @ carrier)) != $true) | (((member @ a @ x @ carrier)) != $true)),
% 0.53/0.41 inference(forward_subsumption_resolution,[],[f826,f796])).
% 0.53/0.41 thf(f833,plain,(
% 0.53/0.41 (((member @ a @ x @ carrier)) != $true)),
% 0.53/0.41 inference(forward_subsumption_resolution,[],[f832,f808])).
% 0.53/0.41 thf(f834,plain,(
% 0.53/0.41 $false),
% 0.53/0.41 inference(forward_subsumption_resolution,[],[f833,f806])).
% 0.53/0.41 % SZS output end Proof for theBenchmark
% 0.53/0.41 % (3141858)------------------------------
% 0.53/0.41 % (3141858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.41 % (3141858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.41 % (3141858)CaDiCaL version: 2.1.3
% 0.53/0.41 % (3141858)Termination reason: Refutation
% 0.53/0.41 % (3141858)Time elapsed: 0.018 s
% 0.53/0.41 % (3141858)Peak memory usage: 13 MB
% 0.53/0.41 % (3141858)Instructions burned: 68 (million)
% 0.53/0.41 % (3141825)Success in time 0.136 s
% 0.53/0.41 % Vampire exiting
%------------------------------------------------------------------------------