%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP555-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 10:14:51 AM UTC 2026
% Result : Unsatisfiable 4.11s 1.48s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 63 unt; 11 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(definition_unfolding,[],[f3,f2,f2,f2,f2]) ).
fof(f5,definition,
! [X2,X0,X1] : sF0(X1,X0,X2) = divide(X1,divide(X0,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : divide(X1,divide(X0,X2)) = sF0(X1,X0,X2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF1(X1,X0,X2) = inverse(sF0(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(sF0(X1,X0,X2)) = sF1(X1,X0,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = divide(X0,sF1(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : divide(X0,sF1(X1,X0,X2)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = divide(sF2(X0,X1,X2),X2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X2,X0,X1] : sF3(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f12,f10,f8,f6]) ).
fof(f14,definition,
sF4 = inverse(b3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f15,plain,
inverse(b3) = sF4,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF5 = divide(a3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f17,plain,
divide(a3,sF4) = sF5,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF6 = inverse(c3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f19,plain,
inverse(c3) = sF6,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF7 = divide(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f21,plain,
divide(sF5,sF6) = sF7,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF8 = divide(b3,sF6),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f23,plain,
divide(b3,sF6) = sF8,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF9 = inverse(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f25,plain,
inverse(sF8) = sF9,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF10 = divide(a3,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f27,plain,
divide(a3,sF9) = sF10,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF7 != sF10,
inference(definition_folding,[],[f4,f27,f25,f23,f19,f21,f19,f17,f15]) ).
fof(f29,plain,
! [X2,X0,X1] : divide(sF2(X0,X1,X2),X2) = X1,
inference(forward_demodulation,[],[f13,f12]) ).
fof(f30,plain,
! [X2,X0,X1] : divide(divide(X0,sF1(X1,X0,X2)),X2) = X1,
inference(forward_demodulation,[],[f29,f10]) ).
fof(f31,plain,
! [X2,X0,X1] : divide(divide(X0,inverse(sF0(X1,X0,X2))),X2) = X1,
inference(forward_demodulation,[],[f30,f8]) ).
fof(f32,plain,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
inference(forward_demodulation,[],[f31,f6]) ).
fof(f33,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f32,f32]) ).
fof(f34,plain,
! [X0] : divide(divide(a3,inverse(divide(X0,sF10))),sF9) = X0,
inference(superposition,[],[f32,f27]) ).
fof(f39,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,divide(X1,sF10)))) = divide(divide(a3,inverse(X0)),sF9),
inference(superposition,[],[f34,f32]) ).
fof(f49,plain,
! [X0] : divide(divide(divide(a3,inverse(X0)),sF9),sF10) = X0,
inference(superposition,[],[f32,f39]) ).
fof(f165,plain,
! [X0,X1] : b3 = divide(divide(divide(X0,inverse(divide(sF6,divide(X0,X1)))),inverse(sF8)),X1),
inference(superposition,[],[f33,f23]) ).
fof(f168,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f33,f32]) ).
fof(f186,plain,
! [X0,X1] : b3 = divide(divide(divide(X0,inverse(divide(sF6,divide(X0,X1)))),sF9),X1),
inference(forward_demodulation,[],[f165,f25]) ).
fof(f191,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(superposition,[],[f168,f168]) ).
fof(f215,plain,
! [X0] : divide(X0,a3) = divide(divide(X0,sF9),sF10),
inference(superposition,[],[f49,f168]) ).
fof(f386,plain,
! [X0] : divide(inverse(divide(c3,X0)),sF6) = X0,
inference(superposition,[],[f191,f19]) ).
fof(f445,plain,
divide(sF10,sF10) = divide(a3,a3),
inference(superposition,[],[f215,f27]) ).
fof(f447,plain,
! [X0] : divide(divide(a3,inverse(X0)),a3) = X0,
inference(superposition,[],[f215,f49]) ).
fof(f500,plain,
sF10 = divide(sF10,inverse(divide(a3,a3))),
inference(superposition,[],[f168,f445]) ).
fof(f645,plain,
! [X0] : divide(X0,divide(a3,a3)) = X0,
inference(superposition,[],[f447,f32]) ).
fof(f676,plain,
divide(a3,a3) = divide(inverse(c3),sF6),
inference(superposition,[],[f386,f645]) ).
fof(f679,plain,
divide(a3,a3) = divide(sF6,sF6),
inference(forward_demodulation,[],[f676,f19]) ).
fof(f766,plain,
sF10 = divide(sF10,inverse(divide(sF6,sF6))),
inference(forward_demodulation,[],[f500,f679]) ).
fof(f824,plain,
b3 = divide(sF6,divide(a3,sF10)),
inference(superposition,[],[f186,f49]) ).
fof(f932,plain,
sF6 = divide(divide(a3,inverse(b3)),sF10),
inference(superposition,[],[f32,f824]) ).
fof(f946,plain,
sF6 = divide(divide(a3,sF4),sF10),
inference(forward_demodulation,[],[f932,f15]) ).
fof(f950,plain,
sF6 = divide(sF5,sF10),
inference(forward_demodulation,[],[f946,f17]) ).
fof(f1124,plain,
! [X0] : divide(divide(sF10,inverse(divide(X0,sF10))),inverse(divide(sF6,sF6))) = X0,
inference(superposition,[],[f32,f766]) ).
fof(f1140,plain,
! [X0] : divide(X0,inverse(divide(sF6,sF6))) = X0,
inference(forward_demodulation,[],[f1124,f168]) ).
fof(f2332,plain,
! [X0] : inverse(divide(divide(sF6,sF6),X0)) = X0,
inference(superposition,[],[f1140,f191]) ).
fof(f2535,plain,
! [X0] : divide(divide(a3,inverse(divide(sF6,sF6))),sF9) = divide(X0,divide(X0,sF10)),
inference(superposition,[],[f39,f2332]) ).
fof(f2555,plain,
! [X0] : divide(a3,sF9) = divide(X0,divide(X0,sF10)),
inference(forward_demodulation,[],[f2535,f1140]) ).
fof(f2562,plain,
! [X0] : sF10 = divide(X0,divide(X0,sF10)),
inference(forward_demodulation,[],[f2555,f27]) ).
fof(f2584,plain,
divide(sF5,sF6) = sF10,
inference(superposition,[],[f2562,f950]) ).
fof(f2621,plain,
sF7 = sF10,
inference(forward_demodulation,[],[f2584,f21]) ).
fof(f2629,plain,
sF7 != sF7,
inference(superposition,[],[f28,f2621]) ).
fof(f2653,plain,
$false,
inference(trivial_inequality_removal,[],[f2629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP555-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.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 10:07:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.11/1.48 % (571417)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.11/1.48 % (571518)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=3846206997:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.11/1.48 % (571519)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2890621167:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.11/1.48 % (571517)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=1392355002:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.11/1.48 % (571520)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1101600122:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.11/1.48 % (571521)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1725440349:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.11/1.48 % (571523)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=534477539:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.11/1.48 % (571522)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1052842901:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.11/1.48 % (571521)First to succeed.
% 4.11/1.48 % (571521)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-571417"
% 4.11/1.48 % (571522)Also succeeded, but the first one will report.
% 4.11/1.48 % (571520)Instruction limit reached!
% 4.11/1.48 % (571520)------------------------------
% 4.11/1.48 % (571520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.48 % (571520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.48 % (571520)CaDiCaL version: 2.1.3
% 4.11/1.48 % (571520)Termination reason: Instruction limit
% 4.11/1.48 % (571520)Termination phase: Saturation
% 4.11/1.48 % (571520)Time elapsed: 0.087 s
% 4.11/1.48 % (571520)Peak memory usage: 89 MB
% 4.11/1.48 % (571520)Instructions burned: 136 (million)
% 4.11/1.48 % (571523)Also succeeded, but the first one will report.
% 4.11/1.48 % (571561)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=994678964:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.11/1.48 % (571521)Refutation found. Thanks to Tanya!
% 4.11/1.48 % SZS status Unsatisfiable for theBenchmark
% 4.11/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.48 % (571521)------------------------------
% 4.11/1.48 % (571521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.48 % (571521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.48 % (571521)CaDiCaL version: 2.1.3
% 4.11/1.48 % (571521)Termination reason: Refutation
% 4.11/1.48 % (571521)Time elapsed: 0.068 s
% 4.11/1.48 % (571521)Peak memory usage: 89 MB
% 4.11/1.48 % (571521)Instructions burned: 117 (million)
% 4.11/1.48 % (571521)------------------------------
% 4.11/1.48 % (571521)------------------------------
% 4.11/1.48 % (571417)Success in time 0.513 s
% 4.11/1.48 % Vampire exiting
%------------------------------------------------------------------------------