%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP660-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:15:28 AM UTC 2026
% Result : Unsatisfiable 10.03s 2.39s
% Output : Refutation 10.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 52 unt; 2 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,negated_conjecture,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,negated_conjecture,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,negated_conjecture,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f7,plain,
x0 != mult(rd(x1,x1),x0),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF0 = rd(x1,x1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
rd(x1,x1) = sF0,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF1 = mult(sF0,x0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
mult(sF0,x0) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
x0 != sF1,
inference(definition_folding,[],[f7,f11,f9]) ).
fof(f13,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,X0),mult(X2,X1))) = mult(mult(X0,X2),X1),
inference(superposition,[],[f5,f1]) ).
fof(f16,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X1))),
inference(superposition,[],[f5,f1]) ).
fof(f19,plain,
x0 = ld(sF0,sF1),
inference(superposition,[],[f2,f11]) ).
fof(f20,plain,
x1 = mult(sF0,x1),
inference(superposition,[],[f3,f9]) ).
fof(f42,plain,
x1 = ld(sF0,x1),
inference(superposition,[],[f2,f20]) ).
fof(f71,plain,
! [X2,X0,X1] : mult(ld(X2,X0),mult(X1,X2)) = ld(X2,mult(mult(X0,X1),X2)),
inference(superposition,[],[f2,f13]) ).
fof(f76,plain,
! [X2,X0,X1] : mult(ld(X1,X2),mult(ld(X2,X0),X1)) = ld(X1,mult(X0,X1)),
inference(superposition,[],[f71,f1]) ).
fof(f79,plain,
! [X2,X0,X1] : ld(X1,mult(X0,X1)) = mult(ld(X1,rd(X0,X2)),mult(X2,X1)),
inference(superposition,[],[f71,f3]) ).
fof(f87,plain,
! [X0,X1] : mult(X0,X1) = mult(ld(mult(X0,X1),X0),mult(X1,mult(X0,X1))),
inference(superposition,[],[f2,f71]) ).
fof(f111,plain,
! [X2,X0,X1] : mult(X2,mult(ld(mult(X1,X2),X0),X1)) = ld(X1,mult(X0,X1)),
inference(superposition,[],[f2,f16]) ).
fof(f150,plain,
! [X2,X0,X1] : mult(ld(mult(X0,X2),X1),X0) = ld(X2,ld(X0,mult(X1,X0))),
inference(superposition,[],[f2,f111]) ).
fof(f173,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(mult(X0,X1),X0),X0),
inference(superposition,[],[f150,f2]) ).
fof(f196,plain,
! [X0,X1] : ld(mult(X1,X0),X1) = rd(ld(X0,X1),X1),
inference(superposition,[],[f4,f173]) ).
fof(f204,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(ld(X1,X0),X0),mult(X1,mult(X0,X1))),
inference(backward_demodulation,[],[f87,f196]) ).
fof(f227,plain,
! [X0,X1] : mult(mult(X1,X0),rd(ld(X0,X1),X1)) = X1,
inference(superposition,[],[f1,f196]) ).
fof(f251,plain,
x1 = mult(mult(x1,sF0),rd(x1,x1)),
inference(superposition,[],[f227,f42]) ).
fof(f266,plain,
x1 = mult(mult(x1,sF0),sF0),
inference(forward_demodulation,[],[f251,f9]) ).
fof(f910,plain,
! [X2,X0,X1] : ld(X0,rd(X1,X2)) = rd(ld(X0,mult(X1,X0)),mult(X2,X0)),
inference(superposition,[],[f4,f79]) ).
fof(f1457,plain,
x1 = mult(rd(ld(sF0,mult(x1,sF0)),mult(x1,sF0)),mult(sF0,x1)),
inference(superposition,[],[f204,f266]) ).
fof(f1501,plain,
x1 = mult(rd(ld(sF0,mult(x1,sF0)),mult(x1,sF0)),x1),
inference(forward_demodulation,[],[f1457,f20]) ).
fof(f1526,plain,
x1 = mult(ld(sF0,rd(x1,x1)),x1),
inference(forward_demodulation,[],[f1501,f910]) ).
fof(f1536,plain,
x1 = mult(ld(sF0,sF0),x1),
inference(forward_demodulation,[],[f1526,f9]) ).
fof(f1547,plain,
rd(x1,x1) = ld(sF0,sF0),
inference(superposition,[],[f4,f1536]) ).
fof(f1574,plain,
sF0 = ld(sF0,sF0),
inference(forward_demodulation,[],[f1547,f9]) ).
fof(f1596,plain,
sF0 = mult(sF0,sF0),
inference(superposition,[],[f1,f1574]) ).
fof(f1600,plain,
! [X0] : ld(sF0,mult(X0,sF0)) = mult(sF0,mult(ld(sF0,X0),sF0)),
inference(superposition,[],[f76,f1574]) ).
fof(f2012,plain,
! [X0] : mult(sF0,mult(ld(sF0,X0),sF0)) = mult(mult(X0,sF0),sF0),
inference(superposition,[],[f13,f1596]) ).
fof(f2024,plain,
! [X0] : ld(sF0,rd(X0,sF0)) = rd(ld(sF0,mult(X0,sF0)),sF0),
inference(superposition,[],[f910,f1596]) ).
fof(f2035,plain,
! [X0] : ld(sF0,mult(X0,sF0)) = mult(mult(X0,sF0),sF0),
inference(backward_demodulation,[],[f1600,f2012]) ).
fof(f2047,plain,
! [X0] : ld(sF0,rd(X0,sF0)) = rd(mult(mult(X0,sF0),sF0),sF0),
inference(backward_demodulation,[],[f2024,f2035]) ).
fof(f2049,plain,
! [X0] : mult(X0,sF0) = ld(sF0,rd(X0,sF0)),
inference(forward_demodulation,[],[f2047,f4]) ).
fof(f2134,plain,
! [X0] : ld(sF0,X0) = mult(mult(X0,sF0),sF0),
inference(superposition,[],[f2049,f4]) ).
fof(f2163,plain,
! [X0] : ld(sF0,mult(X0,sF0)) = ld(sF0,X0),
inference(backward_demodulation,[],[f2035,f2134]) ).
fof(f2182,plain,
! [X0] : ld(sF0,X0) = ld(sF0,rd(X0,sF0)),
inference(superposition,[],[f2163,f3]) ).
fof(f2189,plain,
! [X0] : mult(X0,sF0) = mult(sF0,ld(sF0,X0)),
inference(superposition,[],[f1,f2163]) ).
fof(f2204,plain,
! [X0] : mult(X0,sF0) = X0,
inference(forward_demodulation,[],[f2189,f1]) ).
fof(f2207,plain,
! [X0] : mult(X0,sF0) = ld(sF0,X0),
inference(forward_demodulation,[],[f2182,f2049]) ).
fof(f2282,plain,
! [X0] : ld(sF0,X0) = X0,
inference(forward_demodulation,[],[f2207,f2204]) ).
fof(f2419,plain,
x0 = sF1,
inference(backward_demodulation,[],[f19,f2282]) ).
fof(f2486,plain,
$false,
inference(forward_subsumption_resolution,[],[f2419,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:35:42 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 5.13/2.20 % (2637452)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.13/2.20 % (2637468)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3217176962:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.13/2.20 % (2637464)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=756391630:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.13/2.20 % (2637465)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2695005184:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.13/2.20 % (2637467)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=463227082:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.13/2.20 % (2637463)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=1574066950:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.13/2.20 % (2637466)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1411144189:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.13/2.20 % (2637469)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1187540703:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.13/2.20 % (2637468)Instruction limit reached!
% 5.13/2.20 % (2637468)------------------------------
% 5.13/2.20 % (2637468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/2.20 % (2637468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/2.20 % (2637468)CaDiCaL version: 2.1.3
% 5.13/2.20 % (2637468)Termination reason: Instruction limit
% 5.13/2.20 % (2637468)Termination phase: Saturation
% 5.13/2.20 % (2637468)Time elapsed: 0.079 s
% 5.13/2.20 % (2637468)Peak memory usage: 91 MB
% 5.13/2.20 % (2637468)Instructions burned: 262 (million)
% 5.13/2.20 % (2637466)Instruction limit reached!
% 5.13/2.20 % (2637466)------------------------------
% 5.13/2.20 % (2637466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/2.20 % (2637466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/2.20 % (2637466)CaDiCaL version: 2.1.3
% 5.13/2.20 % (2637466)Termination reason: Instruction limit
% 5.13/2.20 % (2637466)Termination phase: Saturation
% 5.13/2.20 % (2637466)Time elapsed: 0.083 s
% 5.13/2.20 % (2637466)Peak memory usage: 89 MB
% 5.13/2.20 % (2637466)Instructions burned: 136 (million)
% 5.13/2.20 % (2637467)Instruction limit reached!
% 5.13/2.20 % (2637467)------------------------------
% 5.13/2.20 % (2637467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/2.20 % (2637467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/2.20 % (2637467)CaDiCaL version: 2.1.3
% 5.13/2.20 % (2637467)Termination reason: Instruction limit
% 5.13/2.20 % (2637467)Termination phase: Saturation
% 5.13/2.20 % (2637467)Time elapsed: 0.109 s
% 5.13/2.20 % (2637467)Peak memory usage: 89 MB
% 5.13/2.20 % (2637467)Instructions burned: 181 (million)
% 5.13/2.20 % (2637477)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=653693059:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 5.13/2.20 % (2637478)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3522666848:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.13/2.20 % (2637479)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3867292495:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 5.13/2.20 % (2637479)Instruction limit reached!
% 5.13/2.20 % (2637479)------------------------------
% 5.13/2.20 % (2637479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/2.20 % (2637479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/2.20 % (2637479)CaDiCaL version: 2.1.3
% 5.13/2.20 % (2637479)Termination reason: Instruction limit
% 5.13/2.20 % (2637479)Termination phase: Saturation
% 5.13/2.20 % (2637479)Time elapsed: 0.117 s
% 10.03/2.39 % (2637479)Peak memory usage: 90 MB
% 10.03/2.39 % (2637479)Instructions burned: 216 (million)
% 10.03/2.39 % (2637483)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=3748506859:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 10.03/2.39 % (2637483)Instruction limit reached!
% 10.03/2.39 % (2637483)------------------------------
% 10.03/2.39 % (2637483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.03/2.39 % (2637483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.03/2.39 % (2637483)CaDiCaL version: 2.1.3
% 10.03/2.39 % (2637483)Termination reason: Instruction limit
% 10.03/2.39 % (2637483)Termination phase: Saturation
% 10.03/2.39 % (2637483)Time elapsed: 0.188 s
% 10.03/2.39 % (2637483)Peak memory usage: 93 MB
% 10.03/2.39 % (2637483)Instructions burned: 318 (million)
% 10.03/2.39 % (2637469)Instruction limit reached!
% 10.03/2.39 % (2637469)------------------------------
% 10.03/2.39 % (2637469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.03/2.39 % (2637469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.03/2.39 % (2637469)CaDiCaL version: 2.1.3
% 10.03/2.39 % (2637469)Termination reason: Instruction limit
% 10.03/2.39 % (2637469)Termination phase: Saturation
% 10.03/2.39 % (2637469)Time elapsed: 0.672 s
% 10.03/2.39 % (2637469)Peak memory usage: 102 MB
% 10.03/2.39 % (2637469)Instructions burned: 1187 (million)
% 10.03/2.39 % (2637485)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=4233033995:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.03/2.39 % (2637486)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2670051056:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 10.03/2.39 % (2637477)Instruction limit reached!
% 10.03/2.39 % (2637477)------------------------------
% 10.03/2.39 % (2637477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.03/2.39 % (2637477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.03/2.39 % (2637477)CaDiCaL version: 2.1.3
% 10.03/2.39 % (2637477)Termination reason: Instruction limit
% 10.03/2.39 % (2637477)Termination phase: Saturation
% 10.03/2.39 % (2637477)Time elapsed: 0.750 s
% 10.03/2.39 % (2637477)Peak memory usage: 141 MB
% 10.03/2.39 % (2637477)Instructions burned: 2051 (million)
% 10.03/2.39 % (2637465)First to succeed.
% 10.03/2.39 % (2637465)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2637452"
% 10.03/2.39 % (2637489)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2503411942:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2989 on theBenchmark for (2989ds/14534Mi)
% 10.03/2.39 % (2637463)Also succeeded, but the first one will report.
% 10.03/2.39 % (2637465)Refutation found. Thanks to Tanya!
% 10.03/2.39 % SZS status Unsatisfiable for theBenchmark
% 10.03/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 10.03/2.39 % (2637465)------------------------------
% 10.03/2.39 % (2637465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.03/2.39 % (2637465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.03/2.39 % (2637465)CaDiCaL version: 2.1.3
% 10.03/2.39 % (2637465)Termination reason: Refutation
% 10.03/2.39 % (2637465)Time elapsed: 0.941 s
% 10.03/2.39 % (2637465)Peak memory usage: 134 MB
% 10.03/2.39 % (2637465)Instructions burned: 1463 (million)
% 10.03/2.39 % (2637465)------------------------------
% 10.03/2.39 % (2637465)------------------------------
% 10.03/2.39 % (2637452)Success in time 1.341 s
% 10.03/2.39 % Vampire exiting
%------------------------------------------------------------------------------