%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL024-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Tue Sep 29 12:33:50 PM UTC 2026
% Result : Unsatisfiable 8.28s 2.08s
% Output : Refutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
composition(meet(sk1,converse(sk2)),sk3) != join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) != join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3)),
inference(definition_unfolding,[],[f18,f6,f6,f6,f6]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f4,f1]) ).
fof(f22,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f14,f1]) ).
fof(f23,plain,
composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) != join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))),
inference(forward_demodulation,[],[f19,f1]) ).
fof(f51,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f92,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f98,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f22,f10]) ).
fof(f139,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f51,f8]) ).
fof(f140,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f139,f10]) ).
fof(f152,plain,
one = converse(one),
inference(superposition,[],[f8,f140]) ).
fof(f158,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f140,f152]) ).
fof(f174,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f2,f21]) ).
fof(f231,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f98,f158]) ).
fof(f232,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f231,f140]) ).
fof(f278,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(complement(join(complement(X0),X1)),X0),
inference(superposition,[],[f174,f21]) ).
fof(f281,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f174,f232]) ).
fof(f297,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f281,f21]) ).
fof(f300,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f278,f1]) ).
fof(f312,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f300,f297]) ).
fof(f335,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f312,f1]) ).
fof(f2978,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f92,f12]) ).
fof(f2997,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f2978,f11]) ).
fof(f3010,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f2997,f11]) ).
fof(f3019,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f3010,f12]) ).
fof(f3039,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f3019]) ).
fof(f3055,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f3039,f10]) ).
fof(f3100,plain,
composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) != composition(complement(join(complement(sk1),complement(converse(sk2)))),join(sk3,complement(join(complement(sk2),complement(sk3))))),
inference(superposition,[],[f23,f3055]) ).
fof(f3115,plain,
composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3) != composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),
inference(forward_demodulation,[],[f3100,f335]) ).
fof(f3116,plain,
$false,
inference(trivial_inequality_removal,[],[f3115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL024-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:53:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.96 % (3858096)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.17/1.96 % (3858207)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4147571932:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.17/1.96 % (3858204)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4050099016:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.17/1.96 % (3858202)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3121586602:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.17/1.96 % (3858203)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=114688664:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.17/1.96 % (3858206)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1415703403:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.17/1.96 % (3858208)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1273940514:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.17/1.96 % (3858205)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3188489108:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.17/1.96 % (3858207)Instruction limit reached!
% 6.17/1.96 % (3858207)------------------------------
% 6.17/1.96 % (3858207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.96 % (3858207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.96 % (3858207)CaDiCaL version: 2.1.3
% 6.17/1.96 % (3858207)Termination reason: Instruction limit
% 6.17/1.96 % (3858207)Termination phase: Saturation
% 6.17/1.96 % (3858207)Time elapsed: 0.092 s
% 6.17/1.96 % (3858207)Peak memory usage: 90 MB
% 6.17/1.96 % (3858207)Instructions burned: 259 (million)
% 6.17/1.96 % (3858205)Instruction limit reached!
% 6.17/1.96 % (3858205)------------------------------
% 6.17/1.96 % (3858205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.96 % (3858205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.96 % (3858205)CaDiCaL version: 2.1.3
% 6.17/1.96 % (3858205)Termination reason: Instruction limit
% 6.17/1.96 % (3858205)Termination phase: Saturation
% 6.17/1.96 % (3858205)Time elapsed: 0.100 s
% 6.17/1.96 % (3858205)Peak memory usage: 88 MB
% 6.17/1.96 % (3858205)Instructions burned: 136 (million)
% 6.17/1.96 % (3858206)Instruction limit reached!
% 6.17/1.96 % (3858206)------------------------------
% 6.17/1.96 % (3858206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.96 % (3858206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.96 % (3858206)CaDiCaL version: 2.1.3
% 6.17/1.96 % (3858206)Termination reason: Instruction limit
% 6.17/1.96 % (3858206)Termination phase: Saturation
% 6.17/1.96 % (3858206)Time elapsed: 0.129 s
% 6.17/1.96 % (3858206)Peak memory usage: 89 MB
% 6.17/1.96 % (3858206)Instructions burned: 181 (million)
% 6.17/1.96 % (3858223)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3974240092:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.17/1.96 % (3858244)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3493403535:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.17/1.96 % (3858246)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=451702821:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 6.17/1.96 % (3858246)Instruction limit reached!
% 6.17/1.96 % (3858246)------------------------------
% 6.17/1.96 % (3858246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.96 % (3858246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.96 % (3858246)CaDiCaL version: 2.1.3
% 6.17/1.96 % (3858246)Termination reason: Instruction limit
% 6.17/1.96 % (3858246)Termination phase: Saturation
% 6.17/1.96 % (3858246)Time elapsed: 0.106 s
% 8.28/2.08 % (3858246)Peak memory usage: 90 MB
% 8.28/2.08 % (3858246)Instructions burned: 215 (million)
% 8.28/2.08 % (3858259)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=2841164453:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 8.28/2.08 % (3858203)First to succeed.
% 8.28/2.08 % (3858203)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3858096"
% 8.28/2.08 % (3858208)Instruction limit reached!
% 8.28/2.08 % (3858208)------------------------------
% 8.28/2.08 % (3858208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.28/2.08 % (3858208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.28/2.08 % (3858208)CaDiCaL version: 2.1.3
% 8.28/2.08 % (3858208)Termination reason: Instruction limit
% 8.28/2.08 % (3858208)Termination phase: Saturation
% 8.28/2.08 % (3858208)Time elapsed: 0.776 s
% 8.28/2.08 % (3858208)Peak memory usage: 98 MB
% 8.28/2.08 % (3858208)Instructions burned: 1188 (million)
% 8.28/2.08 % (3858223)Also succeeded, but the first one will report.
% 8.28/2.08 % (3858259)Instruction limit reached!
% 8.28/2.08 % (3858259)------------------------------
% 8.28/2.08 % (3858259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.28/2.08 % (3858259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.28/2.08 % (3858259)CaDiCaL version: 2.1.3
% 8.28/2.08 % (3858259)Termination reason: Instruction limit
% 8.28/2.08 % (3858259)Termination phase: Saturation
% 8.28/2.08 % (3858259)Time elapsed: 0.201 s
% 8.28/2.08 % (3858259)Peak memory usage: 93 MB
% 8.28/2.08 % (3858259)Instructions burned: 317 (million)
% 8.28/2.08 % (3858202)Also succeeded, but the first one will report.
% 8.28/2.08 % (3858203)Refutation found. Thanks to Tanya!
% 8.28/2.08 % SZS status Unsatisfiable for theBenchmark
% 8.28/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 8.28/2.08 % (3858203)------------------------------
% 8.28/2.08 % (3858203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.28/2.08 % (3858203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.28/2.08 % (3858203)CaDiCaL version: 2.1.3
% 8.28/2.08 % (3858203)Termination reason: Refutation
% 8.28/2.08 % (3858203)Time elapsed: 0.770 s
% 8.28/2.08 % (3858203)Peak memory usage: 130 MB
% 8.28/2.08 % (3858203)Instructions burned: 1181 (million)
% 8.28/2.08 % (3858203)------------------------------
% 8.28/2.08 % (3858203)------------------------------
% 8.28/2.08 % (3858096)Success in time 1.103 s
% 8.28/2.08 % Vampire exiting
%------------------------------------------------------------------------------