%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL015-1 : 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 : n017.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 12:33:43 PM UTC 2026
% Result : Unsatisfiable 3.06s 1.35s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 66 unt; 9 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 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(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
fof(f8,negated_conjecture,
! [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,negated_conjecture,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f12,negated_conjecture,
! [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(f15,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f17,negated_conjecture,
composition(top,top) != top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
top != composition(top,top),
inference(reorient_equations,[],[f17]) ).
fof(f31,definition,
! [X0] : sF5(X0) = composition(X0,one),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f32,plain,
! [X0] : composition(X0,one) = sF5(X0),
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
! [X0] : sF5(X0) = X0,
inference(definition_folding,[],[f8,f32]) ).
fof(f34,definition,
! [X0] : sF6(X0) = converse(converse(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f35,plain,
! [X0] : converse(converse(X0)) = sF6(X0),
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
! [X0] : sF6(X0) = X0,
inference(definition_folding,[],[f10,f35]) ).
fof(f42,definition,
! [X0,X1] : sF9(X0,X1) = converse(composition(X0,X1)),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f43,plain,
! [X0,X1] : converse(composition(X0,X1)) = sF9(X0,X1),
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
! [X0,X1] : sF10(X1,X0) = composition(converse(X1),converse(X0)),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f45,plain,
! [X0,X1] : composition(converse(X1),converse(X0)) = sF10(X1,X0),
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
! [X0,X1] : sF9(X0,X1) = sF10(X1,X0),
inference(definition_folding,[],[f12,f45,f43]) ).
fof(f47,definition,
! [X0,X1] : sF11(X0,X1) = complement(composition(X0,X1)),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f48,plain,
! [X0,X1] : complement(composition(X0,X1)) = sF11(X0,X1),
inference(reorient_equations,[],[f47]) ).
fof(f49,definition,
! [X0,X1] : sF12(X0,X1) = composition(converse(X0),sF11(X0,X1)),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f50,plain,
! [X0,X1] : composition(converse(X0),sF11(X0,X1)) = sF12(X0,X1),
inference(reorient_equations,[],[f49]) ).
fof(f51,definition,
! [X0,X1] : sF13(X0,X1) = join(sF12(X0,X1),complement(X1)),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f52,plain,
! [X0,X1] : join(sF12(X0,X1),complement(X1)) = sF13(X0,X1),
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
! [X0,X1] : complement(X1) = sF13(X0,X1),
inference(definition_folding,[],[f14,f52,f50,f48]) ).
fof(f54,definition,
! [X0] : sF14(X0) = join(X0,complement(X0)),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f55,plain,
! [X0] : join(X0,complement(X0)) = sF14(X0),
inference(reorient_equations,[],[f54]) ).
fof(f56,plain,
! [X0] : top = sF14(X0),
inference(definition_folding,[],[f15,f55]) ).
fof(f64,definition,
sF18 = composition(top,top),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f65,plain,
composition(top,top) = sF18,
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
top != sF18,
inference(definition_folding,[],[f18,f65]) ).
fof(f68,plain,
! [X0] : top = join(X0,complement(X0)),
inference(forward_demodulation,[],[f56,f55]) ).
fof(f69,plain,
! [X0,X1] : complement(X1) = join(sF12(X0,X1),complement(X1)),
inference(forward_demodulation,[],[f53,f52]) ).
fof(f70,plain,
! [X0,X1] : composition(converse(X1),converse(X0)) = sF9(X0,X1),
inference(forward_demodulation,[],[f46,f45]) ).
fof(f72,plain,
! [X0] : converse(converse(X0)) = X0,
inference(forward_demodulation,[],[f36,f35]) ).
fof(f73,plain,
! [X0] : composition(X0,one) = X0,
inference(forward_demodulation,[],[f33,f32]) ).
fof(f76,plain,
! [X0,X1] : complement(X1) = join(complement(X1),sF12(X0,X1)),
inference(forward_demodulation,[],[f69,f1]) ).
fof(f77,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(forward_demodulation,[],[f70,f43]) ).
fof(f81,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),sF11(X0,X1))),
inference(forward_demodulation,[],[f76,f50]) ).
fof(f83,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f81,f48]) ).
fof(f89,plain,
! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)),
inference(superposition,[],[f7,f73]) ).
fof(f95,plain,
! [X0,X1] : join(composition(X0,X1),composition(complement(X0),X1)) = composition(top,X1),
inference(superposition,[],[f9,f68]) ).
fof(f96,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f68]) ).
fof(f137,plain,
! [X0] : converse(X0) = composition(converse(one),converse(X0)),
inference(superposition,[],[f77,f73]) ).
fof(f151,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(superposition,[],[f137,f72]) ).
fof(f156,plain,
one = converse(one),
inference(superposition,[],[f151,f73]) ).
fof(f161,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(superposition,[],[f89,f151]) ).
fof(f162,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[],[f161,f151]) ).
fof(f309,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(superposition,[],[f96,f68]) ).
fof(f357,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(superposition,[],[f83,f151]) ).
fof(f367,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f357,f162]) ).
fof(f387,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f96,f367]) ).
fof(f393,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f387,f68]) ).
fof(f401,plain,
! [X0] : top = join(X0,top),
inference(superposition,[],[f393,f309]) ).
fof(f416,plain,
! [X0] : top = join(top,X0),
inference(superposition,[],[f401,f1]) ).
fof(f1389,plain,
! [X0] : composition(top,X0) = join(X0,composition(complement(converse(one)),X0)),
inference(superposition,[],[f95,f151]) ).
fof(f1434,plain,
! [X0] : composition(top,X0) = join(X0,composition(complement(one),X0)),
inference(forward_demodulation,[],[f1389,f156]) ).
fof(f2776,plain,
top = composition(top,top),
inference(superposition,[],[f416,f1434]) ).
fof(f2781,plain,
top = sF18,
inference(forward_demodulation,[],[f2776,f65]) ).
fof(f2799,plain,
top != top,
inference(superposition,[],[f66,f2781]) ).
fof(f2834,plain,
$false,
inference(trivial_inequality_removal,[],[f2799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL015-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 22:46:06 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 3.06/1.35 % (3035139)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.06/1.35 % (3035253)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=768981919:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.06/1.35 % (3035254)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=551022618:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.06/1.35 % (3035251)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=1297631417:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.06/1.35 % (3035258)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2145305482:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.06/1.35 % (3035249)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=829503609:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.06/1.35 % (3035256)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3122535947:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.06/1.35 % (3035257)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3421660880:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.06/1.35 % (3035256)First to succeed.
% 3.06/1.35 % (3035256)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3035139"
% 3.06/1.35 % (3035258)Also succeeded, but the first one will report.
% 3.06/1.35 % (3035254)Instruction limit reached!
% 3.06/1.35 % (3035254)------------------------------
% 3.06/1.35 % (3035254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (3035254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (3035254)CaDiCaL version: 2.1.3
% 3.06/1.35 % (3035254)Termination reason: Instruction limit
% 3.06/1.35 % (3035254)Termination phase: Saturation
% 3.06/1.35 % (3035254)Time elapsed: 0.085 s
% 3.06/1.35 % (3035254)Peak memory usage: 89 MB
% 3.06/1.35 % (3035254)Instructions burned: 137 (million)
% 3.06/1.35 % (3035257)Instruction limit reached!
% 3.06/1.35 % (3035257)------------------------------
% 3.06/1.35 % (3035257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (3035257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (3035257)CaDiCaL version: 2.1.3
% 3.06/1.35 % (3035257)Termination reason: Instruction limit
% 3.06/1.35 % (3035257)Termination phase: Saturation
% 3.06/1.35 % (3035257)Time elapsed: 0.169 s
% 3.06/1.35 % (3035257)Peak memory usage: 90 MB
% 3.06/1.35 % (3035257)Instructions burned: 258 (million)
% 3.06/1.35 % (3035295)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=701155082:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.06/1.35 % (3035333)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=902555231:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 3.06/1.35 % (3035256)Refutation found. Thanks to Tanya!
% 3.06/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.06/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.55 % (3035256)------------------------------
% 3.88/1.55 % (3035256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.55 % (3035256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.55 % (3035256)CaDiCaL version: 2.1.3
% 3.88/1.55 % (3035256)Termination reason: Refutation
% 3.88/1.55 % (3035256)Time elapsed: 0.046 s
% 3.88/1.55 % (3035256)Peak memory usage: 89 MB
% 3.88/1.55 % (3035256)Instructions burned: 76 (million)
% 3.88/1.55 % (3035256)------------------------------
% 3.88/1.55 % (3035256)------------------------------
% 3.88/1.55 % (3035139)Success in time 0.445 s
% 3.88/1.55 % Vampire exiting
%------------------------------------------------------------------------------