%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 14.68s 3.18s
% Output : Refutation 14.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 53 unt; 2 def)
% Number of atoms : 53 ( 52 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 : 4 ( 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 : 68 ( 68 !; 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,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f6,plain,
b != multiply(a,inverse(a),b),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF0 = inverse(a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f8,plain,
inverse(a) = sF0,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF1 = multiply(a,sF0,b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f10,plain,
multiply(a,sF0,b) = sF1,
inference(reorient_equations,[],[f9]) ).
fof(f11,plain,
b != sF1,
inference(definition_folding,[],[f6,f10,f8]) ).
fof(f12,plain,
! [X0] : multiply(sF0,a,X0) = X0,
inference(superposition,[],[f4,f8]) ).
fof(f15,plain,
! [X0,X1] : multiply(a,sF0,multiply(b,X0,X1)) = multiply(sF1,X0,multiply(a,sF0,X1)),
inference(superposition,[],[f1,f10]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : multiply(X1,X0,multiply(X2,X3,X0)) = multiply(multiply(X1,X0,X2),X3,X0),
inference(superposition,[],[f1,f2]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : multiply(X1,X0,multiply(X0,X2,X3)) = multiply(X0,X2,multiply(X1,X0,X3)),
inference(superposition,[],[f1,f2]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : multiply(X0,X0,multiply(X1,X2,X3)) = multiply(X0,X2,multiply(X0,X0,X3)),
inference(superposition,[],[f1,f3]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,X2) = multiply(X0,X1,multiply(X2,multiply(X0,X1,X2),X3)),
inference(superposition,[],[f1,f3]) ).
fof(f33,plain,
! [X2,X3,X0,X1] : multiply(X0,X0,multiply(X1,X2,X3)) = multiply(X0,X2,X0),
inference(forward_demodulation,[],[f31,f3]) ).
fof(f35,plain,
! [X2,X0] : multiply(X0,X2,X0) = X0,
inference(forward_demodulation,[],[f33,f3]) ).
fof(f42,plain,
! [X0] : multiply(a,sF0,multiply(b,X0,sF0)) = multiply(sF1,X0,sF0),
inference(superposition,[],[f26,f10]) ).
fof(f63,plain,
! [X0] : multiply(a,sF0,multiply(X0,a,b)) = multiply(X0,a,sF1),
inference(superposition,[],[f27,f10]) ).
fof(f106,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,X1,X2),X3,X0) = multiply(X0,X1,multiply(X2,X3,X0)),
inference(superposition,[],[f1,f35]) ).
fof(f125,plain,
! [X0] : sF1 = multiply(a,sF0,multiply(b,sF1,X0)),
inference(superposition,[],[f32,f10]) ).
fof(f264,plain,
multiply(a,sF0,b) = multiply(sF1,b,sF0),
inference(superposition,[],[f42,f3]) ).
fof(f282,plain,
sF1 = multiply(sF1,b,sF0),
inference(forward_demodulation,[],[f264,f10]) ).
fof(f285,plain,
! [X0,X1] : multiply(sF1,b,multiply(sF0,X0,X1)) = multiply(sF1,X0,multiply(sF1,b,X1)),
inference(superposition,[],[f1,f282]) ).
fof(f286,plain,
! [X0,X1] : multiply(sF1,b,multiply(X0,X1,sF0)) = multiply(multiply(sF1,b,X0),X1,sF1),
inference(superposition,[],[f1,f282]) ).
fof(f287,plain,
! [X0] : multiply(sF1,b,multiply(sF0,X0,b)) = multiply(sF1,X0,b),
inference(superposition,[],[f26,f282]) ).
fof(f293,plain,
! [X0,X1] : multiply(sF1,b,multiply(X0,X1,sF0)) = multiply(sF1,b,multiply(X0,X1,sF1)),
inference(forward_demodulation,[],[f286,f106]) ).
fof(f294,plain,
sF1 = multiply(a,sF0,sF1),
inference(superposition,[],[f125,f2]) ).
fof(f325,plain,
! [X0,X1] : multiply(sF1,X0,multiply(a,sF0,X1)) = multiply(a,sF0,multiply(sF1,X0,X1)),
inference(superposition,[],[f1,f294]) ).
fof(f334,plain,
! [X0,X1] : multiply(a,sF0,multiply(b,X0,X1)) = multiply(a,sF0,multiply(sF1,X0,X1)),
inference(forward_demodulation,[],[f325,f15]) ).
fof(f343,plain,
multiply(sF1,a,b) = multiply(sF1,b,b),
inference(superposition,[],[f287,f12]) ).
fof(f364,plain,
b = multiply(sF1,a,b),
inference(forward_demodulation,[],[f343,f2]) ).
fof(f597,plain,
! [X0] : multiply(sF1,b,X0) = multiply(sF1,a,multiply(sF1,b,X0)),
inference(superposition,[],[f285,f12]) ).
fof(f683,plain,
! [X0] : multiply(a,sF0,multiply(b,b,X0)) = multiply(sF1,a,multiply(a,sF0,multiply(b,b,X0))),
inference(superposition,[],[f597,f15]) ).
fof(f702,plain,
! [X0] : multiply(a,sF0,multiply(b,b,X0)) = multiply(a,sF0,multiply(sF1,a,multiply(b,b,X0))),
inference(forward_demodulation,[],[f683,f27]) ).
fof(f703,plain,
! [X0] : multiply(a,sF0,multiply(b,b,X0)) = multiply(a,sF0,multiply(b,a,multiply(b,b,X0))),
inference(forward_demodulation,[],[f702,f334]) ).
fof(f704,plain,
multiply(a,sF0,b) = multiply(a,sF0,multiply(b,a,b)),
inference(forward_demodulation,[],[f703,f3]) ).
fof(f705,plain,
multiply(a,sF0,b) = multiply(b,a,sF1),
inference(forward_demodulation,[],[f704,f63]) ).
fof(f706,plain,
sF1 = multiply(b,a,sF1),
inference(forward_demodulation,[],[f705,f10]) ).
fof(f1274,plain,
! [X0,X1] : multiply(multiply(b,X0,X1),a,sF1) = multiply(a,sF0,multiply(b,X0,multiply(X1,a,b))),
inference(superposition,[],[f63,f106]) ).
fof(f1281,plain,
! [X0,X1] : multiply(a,sF0,multiply(b,X1,multiply(X0,a,b))) = multiply(sF1,X1,multiply(X0,a,sF1)),
inference(superposition,[],[f15,f63]) ).
fof(f1300,plain,
! [X0,X1] : multiply(multiply(b,X0,X1),a,sF1) = multiply(sF1,X0,multiply(X1,a,sF1)),
inference(forward_demodulation,[],[f1274,f1281]) ).
fof(f1317,plain,
! [X0] : multiply(b,a,sF1) = multiply(sF1,b,multiply(X0,a,sF1)),
inference(superposition,[],[f1300,f3]) ).
fof(f1345,plain,
! [X0] : multiply(b,a,sF1) = multiply(sF1,b,multiply(X0,a,sF0)),
inference(forward_demodulation,[],[f1317,f293]) ).
fof(f1357,plain,
! [X0] : sF1 = multiply(sF1,b,multiply(X0,a,sF0)),
inference(forward_demodulation,[],[f1345,f706]) ).
fof(f1366,plain,
sF1 = multiply(sF1,b,a),
inference(superposition,[],[f1357,f3]) ).
fof(f1415,plain,
! [X0] : multiply(sF1,X0,b) = multiply(sF1,b,multiply(a,X0,b)),
inference(superposition,[],[f26,f1366]) ).
fof(f1433,plain,
multiply(sF1,a,b) = multiply(sF1,b,a),
inference(superposition,[],[f1415,f3]) ).
fof(f1469,plain,
sF1 = multiply(sF1,a,b),
inference(forward_demodulation,[],[f1433,f1366]) ).
fof(f1479,plain,
b = sF1,
inference(forward_demodulation,[],[f1469,f364]) ).
fof(f1481,plain,
$false,
inference(forward_subsumption_resolution,[],[f1479,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 % Computer : n007.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8046.5625MB
% 0.09/0.28 % OS : Linux 6.8.0-71-generic
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Sep 28 21:00:41 UTC 2026
% 0.09/0.28 % CPUTime :
% 0.09/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 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
% 12.63/2.90 % (2818045)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.63/2.90 % (2818056)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1316500143:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 12.63/2.90 % (2818059)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1752068905:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 12.63/2.90 % (2818056)Instruction limit reached!
% 12.63/2.90 % (2818056)------------------------------
% 12.63/2.90 % (2818056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.63/2.90 % (2818056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.63/2.90 % (2818056)CaDiCaL version: 2.1.3
% 12.63/2.90 % (2818056)Termination reason: Instruction limit
% 12.63/2.90 % (2818056)Termination phase: Saturation
% 12.63/2.90 % (2818056)Time elapsed: 0.072 s
% 12.63/2.90 % (2818056)Peak memory usage: 88 MB
% 12.63/2.90 % (2818056)Instructions burned: 137 (million)
% 12.63/2.90 % (2818054)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=1377427277:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 12.63/2.90 % (2818053)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=1763227585:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 12.63/2.90 % (2818055)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4164617477:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 12.63/2.90 % (2818058)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2619701797:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 12.63/2.90 % (2818057)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1840624299:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 12.63/2.90 % (2818057)Instruction limit reached!
% 12.63/2.90 % (2818057)------------------------------
% 12.63/2.90 % (2818057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.63/2.90 % (2818057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.63/2.90 % (2818057)CaDiCaL version: 2.1.3
% 12.63/2.90 % (2818057)Termination reason: Instruction limit
% 12.63/2.90 % (2818057)Termination phase: Saturation
% 12.63/2.90 % (2818057)Time elapsed: 0.170 s
% 12.63/2.90 % (2818057)Peak memory usage: 89 MB
% 12.63/2.90 % (2818057)Instructions burned: 181 (million)
% 12.63/2.90 % (2818062)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1056967932:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 12.63/2.90 % (2818058)Instruction limit reached!
% 12.63/2.90 % (2818058)------------------------------
% 12.63/2.90 % (2818058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.63/2.90 % (2818058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.63/2.90 % (2818058)CaDiCaL version: 2.1.3
% 12.63/2.90 % (2818058)Termination reason: Instruction limit
% 12.63/2.90 % (2818058)Termination phase: Saturation
% 12.63/2.90 % (2818058)Time elapsed: 0.264 s
% 12.63/2.90 % (2818058)Peak memory usage: 90 MB
% 12.63/2.90 % (2818058)Instructions burned: 257 (million)
% 12.63/2.90 % (2818068)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3548553852:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 12.63/2.90 % (2818070)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=226397022:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 12.63/2.90 % (2818070)Instruction limit reached!
% 12.63/2.90 % (2818070)------------------------------
% 12.63/2.90 % (2818070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.63/2.90 % (2818070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.63/2.90 % (2818070)CaDiCaL version: 2.1.3
% 12.63/2.90 % (2818070)Termination reason: Instruction limit
% 12.63/2.90 % (2818070)Termination phase: Saturation
% 12.63/2.90 % (2818070)Time elapsed: 0.199 s
% 14.68/3.18 % (2818070)Peak memory usage: 90 MB
% 14.68/3.18 % (2818070)Instructions burned: 215 (million)
% 14.68/3.18 % (2818059)Instruction limit reached!
% 14.68/3.18 % (2818059)------------------------------
% 14.68/3.18 % (2818059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/3.18 % (2818059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/3.18 % (2818059)CaDiCaL version: 2.1.3
% 14.68/3.18 % (2818059)Termination reason: Instruction limit
% 14.68/3.18 % (2818059)Termination phase: Saturation
% 14.68/3.18 % (2818059)Time elapsed: 1.080 s
% 14.68/3.18 % (2818059)Peak memory usage: 101 MB
% 14.68/3.18 % (2818059)Instructions burned: 1191 (million)
% 14.68/3.18 % (2818073)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=147941380:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 14.68/3.18 % (2818062)Instruction limit reached!
% 14.68/3.18 % (2818062)------------------------------
% 14.68/3.18 % (2818062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/3.18 % (2818062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/3.18 % (2818062)CaDiCaL version: 2.1.3
% 14.68/3.18 % (2818062)Termination reason: Instruction limit
% 14.68/3.18 % (2818062)Termination phase: Saturation
% 14.68/3.18 % (2818062)Time elapsed: 1.009 s
% 14.68/3.18 % (2818062)Peak memory usage: 140 MB
% 14.68/3.18 % (2818062)Instructions burned: 2053 (million)
% 14.68/3.18 % (2818055)First to succeed.
% 14.68/3.18 % (2818055)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2818045"
% 14.68/3.18 % (2818074)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2843673812:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 14.68/3.18 % (2818073)Instruction limit reached!
% 14.68/3.18 % (2818073)------------------------------
% 14.68/3.18 % (2818073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/3.18 % (2818073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/3.18 % (2818073)CaDiCaL version: 2.1.3
% 14.68/3.18 % (2818073)Termination reason: Instruction limit
% 14.68/3.18 % (2818073)Termination phase: Saturation
% 14.68/3.18 % (2818073)Time elapsed: 0.326 s
% 14.68/3.18 % (2818073)Peak memory usage: 92 MB
% 14.68/3.18 % (2818073)Instructions burned: 318 (million)
% 14.68/3.18 % (2818076)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1058232684:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2985 on theBenchmark for (2985ds/2836Mi)
% 14.68/3.18 % (2818055)Refutation found. Thanks to Tanya!
% 14.68/3.18 % SZS status Unsatisfiable for theBenchmark
% 14.68/3.18 % SZS output start Proof for theBenchmark
% See solution above
% 14.68/3.18 % (2818055)------------------------------
% 14.68/3.18 % (2818055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.68/3.18 % (2818055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.68/3.18 % (2818055)CaDiCaL version: 2.1.3
% 14.68/3.18 % (2818055)Termination reason: Refutation
% 14.68/3.18 % (2818055)Time elapsed: 1.268 s
% 14.68/3.18 % (2818055)Peak memory usage: 130 MB
% 14.68/3.18 % (2818055)Instructions burned: 1185 (million)
% 14.68/3.18 % (2818055)------------------------------
% 14.68/3.18 % (2818055)------------------------------
% 14.68/3.18 % (2818045)Success in time 1.937 s
% 14.68/3.18 % Vampire exiting
%------------------------------------------------------------------------------