%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:35:47 AM UTC 2026
% Result : Unsatisfiable 6.93s 1.68s
% Output : Refutation 6.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 29 unt; 2 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
fof(f4,negated_conjecture,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f5,axiom,
! [X0,X1] : multiply(X0,X1,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
fof(f6,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f7,plain,
b != multiply(a,inverse(a),b),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF0 = inverse(a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
inverse(a) = sF0,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF1 = multiply(a,sF0,b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
multiply(a,sF0,b) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
b != sF1,
inference(definition_folding,[],[f7,f11,f9]) ).
fof(f13,plain,
! [X0] : multiply(sF0,a,X0) = X0,
inference(superposition,[],[f4,f9]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : multiply(X1,X0,multiply(X2,X3,X0)) = multiply(multiply(X1,X0,X2),X3,X0),
inference(superposition,[],[f1,f2]) ).
fof(f39,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,multiply(X2,X3,X0)) = multiply(multiply(X0,X1,X2),X3,X0),
inference(superposition,[],[f1,f5]) ).
fof(f48,plain,
! [X0] : multiply(a,sF0,multiply(b,X0,a)) = multiply(sF1,X0,a),
inference(superposition,[],[f39,f11]) ).
fof(f74,plain,
! [X0] : multiply(a,sF0,multiply(b,X0,sF0)) = multiply(sF1,X0,sF0),
inference(superposition,[],[f27,f11]) ).
fof(f443,plain,
multiply(a,sF0,b) = multiply(sF1,b,a),
inference(superposition,[],[f48,f3]) ).
fof(f464,plain,
sF1 = multiply(sF1,b,a),
inference(forward_demodulation,[],[f443,f11]) ).
fof(f469,plain,
! [X0] : multiply(sF1,b,multiply(a,X0,b)) = multiply(sF1,X0,b),
inference(superposition,[],[f27,f464]) ).
fof(f582,plain,
multiply(a,sF0,b) = multiply(sF1,b,sF0),
inference(superposition,[],[f74,f3]) ).
fof(f603,plain,
sF1 = multiply(sF1,b,sF0),
inference(forward_demodulation,[],[f582,f11]) ).
fof(f608,plain,
! [X0] : multiply(sF1,X0,b) = multiply(sF1,b,multiply(sF0,X0,b)),
inference(superposition,[],[f27,f603]) ).
fof(f799,plain,
multiply(sF1,b,b) = multiply(sF1,a,b),
inference(superposition,[],[f608,f13]) ).
fof(f824,plain,
b = multiply(sF1,a,b),
inference(forward_demodulation,[],[f799,f2]) ).
fof(f1170,plain,
multiply(sF1,b,a) = multiply(sF1,a,b),
inference(superposition,[],[f469,f3]) ).
fof(f1199,plain,
b = multiply(sF1,b,a),
inference(forward_demodulation,[],[f1170,f824]) ).
fof(f1212,plain,
b = sF1,
inference(backward_demodulation,[],[f464,f1199]) ).
fof(f1216,plain,
$false,
inference(forward_subsumption_resolution,[],[f1212,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 % Computer : n011.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Mon Sep 28 21:02:46 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running first-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.93/1.68 % (3783236)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.93/1.68 % (3783243)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4255288493:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.93/1.68 % (3783244)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3733907165:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.93/1.68 % (3783246)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=845805239:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.93/1.68 % (3783242)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=388840623:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.93/1.68 % (3783247)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=709493533:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.93/1.68 % (3783241)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=1857306265:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.93/1.68 % (3783245)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=555605943:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.93/1.68 % (3783245)Refutation not found, incomplete strategy
% 6.93/1.68 % (3783245)------------------------------
% 6.93/1.68 % (3783245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783245)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783245)Termination reason: Refutation not found, incomplete strategy
% 6.93/1.68 % (3783245)Time elapsed: 0.001 s
% 6.93/1.68 % (3783245)Peak memory usage: 87 MB
% 6.93/1.68 % (3783245)Instructions burned: 1 (million)
% 6.93/1.68 % (3783244)Instruction limit reached!
% 6.93/1.68 % (3783244)------------------------------
% 6.93/1.68 % (3783244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783244)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783244)Termination reason: Instruction limit
% 6.93/1.68 % (3783244)Termination phase: Saturation
% 6.93/1.68 % (3783244)Time elapsed: 0.082 s
% 6.93/1.68 % (3783244)Peak memory usage: 88 MB
% 6.93/1.68 % (3783244)Instructions burned: 137 (million)
% 6.93/1.68 % (3783246)Instruction limit reached!
% 6.93/1.68 % (3783246)------------------------------
% 6.93/1.68 % (3783246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783246)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783246)Termination reason: Instruction limit
% 6.93/1.68 % (3783246)Termination phase: Saturation
% 6.93/1.68 % (3783246)Time elapsed: 0.163 s
% 6.93/1.68 % (3783246)Peak memory usage: 90 MB
% 6.93/1.68 % (3783246)Instructions burned: 257 (million)
% 6.93/1.68 % (3783245)------------------------------
% 6.93/1.68 % (3783245)------------------------------
% 6.93/1.68 % (3783255)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1392160331:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.93/1.68 % (3783256)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1298684622:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 6.93/1.68 % (3783258)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1543790523:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 6.93/1.68 % (3783258)Instruction limit reached!
% 6.93/1.68 % (3783258)------------------------------
% 6.93/1.68 % (3783258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783258)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783258)Termination reason: Instruction limit
% 6.93/1.68 % (3783258)Termination phase: Saturation
% 6.93/1.68 % (3783258)Time elapsed: 0.062 s
% 6.93/1.68 % (3783258)Peak memory usage: 91 MB
% 6.93/1.68 % (3783258)Instructions burned: 215 (million)
% 6.93/1.68 % (3783243)First to succeed.
% 6.93/1.68 % (3783243)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3783236"
% 6.93/1.68 % (3783261)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=506787221: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)
% 6.93/1.68 % (3783247)Instruction limit reached!
% 6.93/1.68 % (3783247)------------------------------
% 6.93/1.68 % (3783247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783247)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783247)Termination reason: Instruction limit
% 6.93/1.68 % (3783247)Termination phase: Saturation
% 6.93/1.68 % (3783247)Time elapsed: 0.651 s
% 6.93/1.68 % (3783247)Peak memory usage: 99 MB
% 6.93/1.68 % (3783247)Instructions burned: 1189 (million)
% 6.93/1.68 % (3783261)Instruction limit reached!
% 6.93/1.68 % (3783261)------------------------------
% 6.93/1.68 % (3783261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783261)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783261)Termination reason: Instruction limit
% 6.93/1.68 % (3783261)Termination phase: Saturation
% 6.93/1.68 % (3783261)Time elapsed: 0.107 s
% 6.93/1.68 % (3783261)Peak memory usage: 92 MB
% 6.93/1.68 % (3783261)Instructions burned: 321 (million)
% 6.93/1.68 % (3783241)Also succeeded, but the first one will report.
% 6.93/1.68 % (3783243)Refutation found. Thanks to Tanya!
% 6.93/1.68 % SZS status Unsatisfiable for theBenchmark
% 6.93/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.93/1.68 % (3783243)------------------------------
% 6.93/1.68 % (3783243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.68 % (3783243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.68 % (3783243)CaDiCaL version: 2.1.3
% 6.93/1.68 % (3783243)Termination reason: Refutation
% 6.93/1.68 % (3783243)Time elapsed: 0.522 s
% 6.93/1.68 % (3783243)Peak memory usage: 130 MB
% 6.93/1.68 % (3783243)Instructions burned: 1128 (million)
% 6.93/1.68 % (3783243)------------------------------
% 6.93/1.68 % (3783243)------------------------------
% 6.93/1.68 % (3783236)Success in time 0.919 s
% 6.93/1.68 % Vampire exiting
%------------------------------------------------------------------------------