%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 10:14:53 AM UTC 2026
% Result : Unsatisfiable 2.61s 1.35s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 70 unt; 9 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f6,plain,
a2 != multiply(identity,a2),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f8,plain,
a2 != double_divide(double_divide(a2,identity),identity),
inference(definition_unfolding,[],[f6,f2]) ).
fof(f9,definition,
! [X2,X0,X1] : sF0(X1,X2,X0) = double_divide(X1,double_divide(X2,X0)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(X2,X0)) = sF0(X1,X2,X0),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2] : sF1(X2) = double_divide(X2,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f12,plain,
! [X2] : double_divide(X2,identity) = sF1(X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF2(X1,X2,X0) = double_divide(sF0(X1,X2,X0),sF1(X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : double_divide(sF0(X1,X2,X0),sF1(X2)) = sF2(X1,X2,X0),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = double_divide(X0,sF2(X1,X2,X0)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : double_divide(X0,sF2(X1,X2,X0)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF4 = double_divide(identity,identity),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
double_divide(identity,identity) = sF4,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X2,X0,X1] : sF5(X0,X1,X2) = double_divide(sF3(X0,X1,X2),sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
! [X2,X0,X1] : double_divide(sF3(X0,X1,X2),sF4) = sF5(X0,X1,X2),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X2,X0,X1] : sF5(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f20,f18,f16,f14,f12,f10]) ).
fof(f22,definition,
! [X0] : sF6(X0) = double_divide(X0,sF1(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
! [X0] : double_divide(X0,sF1(X0)) = sF6(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : identity = sF6(X0),
inference(definition_folding,[],[f7,f23,f12]) ).
fof(f25,definition,
sF7 = double_divide(a2,identity),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f26,plain,
double_divide(a2,identity) = sF7,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF8 = double_divide(sF7,identity),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f28,plain,
double_divide(sF7,identity) = sF8,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
a2 != sF8,
inference(definition_folding,[],[f8,f28,f26]) ).
fof(f30,plain,
! [X0] : identity = double_divide(X0,sF1(X0)),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f31,plain,
! [X2,X0,X1] : double_divide(sF3(X0,X1,X2),sF4) = X1,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f32,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(forward_demodulation,[],[f30,f12]) ).
fof(f33,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,sF2(X1,X2,X0)),sF4) = X1,
inference(forward_demodulation,[],[f31,f16]) ).
fof(f34,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(sF0(X1,X2,X0),sF1(X2))),sF4) = X1,
inference(forward_demodulation,[],[f33,f14]) ).
fof(f35,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(sF0(X1,X2,X0),double_divide(X2,identity))),sF4) = X1,
inference(forward_demodulation,[],[f34,f12]) ).
fof(f36,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),sF4) = X1,
inference(forward_demodulation,[],[f35,f10]) ).
fof(f37,plain,
identity = double_divide(sF7,sF8),
inference(superposition,[],[f32,f28]) ).
fof(f38,plain,
identity = double_divide(a2,sF7),
inference(superposition,[],[f32,f26]) ).
fof(f39,plain,
identity = double_divide(identity,sF4),
inference(superposition,[],[f32,f18]) ).
fof(f41,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,sF8),sF8)),sF4) = X0,
inference(superposition,[],[f36,f28]) ).
fof(f42,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,sF7),sF7)),sF4) = X0,
inference(superposition,[],[f36,f26]) ).
fof(f43,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,sF4),sF4)),sF4) = X0,
inference(superposition,[],[f36,f18]) ).
fof(f48,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),sF4) = X0,
inference(superposition,[],[f36,f32]) ).
fof(f55,plain,
sF7 = double_divide(double_divide(identity,double_divide(identity,sF8)),sF4),
inference(superposition,[],[f41,f37]) ).
fof(f58,plain,
a2 = double_divide(double_divide(identity,double_divide(identity,sF7)),sF4),
inference(superposition,[],[f42,f38]) ).
fof(f61,plain,
identity = double_divide(double_divide(identity,double_divide(identity,sF4)),sF4),
inference(superposition,[],[f43,f39]) ).
fof(f69,plain,
identity = double_divide(double_divide(identity,identity),sF4),
inference(forward_demodulation,[],[f61,f39]) ).
fof(f70,plain,
identity = double_divide(sF4,sF4),
inference(forward_demodulation,[],[f69,f18]) ).
fof(f71,plain,
sF4 = double_divide(double_divide(identity,double_divide(identity,sF4)),sF4),
inference(superposition,[],[f43,f70]) ).
fof(f73,plain,
sF4 = double_divide(double_divide(identity,identity),sF4),
inference(forward_demodulation,[],[f71,f39]) ).
fof(f74,plain,
sF4 = double_divide(sF4,sF4),
inference(forward_demodulation,[],[f73,f18]) ).
fof(f75,plain,
identity = sF4,
inference(forward_demodulation,[],[f74,f70]) ).
fof(f81,plain,
sF7 = double_divide(double_divide(identity,double_divide(identity,sF8)),identity),
inference(superposition,[],[f55,f75]) ).
fof(f87,plain,
identity = double_divide(double_divide(identity,double_divide(identity,sF8)),sF7),
inference(superposition,[],[f32,f81]) ).
fof(f95,plain,
double_divide(identity,double_divide(identity,sF8)) = double_divide(double_divide(identity,double_divide(identity,sF7)),sF4),
inference(superposition,[],[f42,f87]) ).
fof(f98,plain,
a2 = double_divide(identity,double_divide(identity,sF8)),
inference(forward_demodulation,[],[f95,f58]) ).
fof(f100,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity) = X0,
inference(forward_demodulation,[],[f48,f75]) ).
fof(f104,plain,
identity = double_divide(double_divide(sF8,double_divide(a2,double_divide(identity,identity))),sF4),
inference(superposition,[],[f36,f98]) ).
fof(f107,plain,
identity = double_divide(double_divide(sF8,double_divide(a2,double_divide(identity,identity))),identity),
inference(forward_demodulation,[],[f104,f75]) ).
fof(f110,plain,
identity = double_divide(double_divide(sF8,double_divide(a2,sF4)),identity),
inference(forward_demodulation,[],[f107,f18]) ).
fof(f112,plain,
identity = double_divide(double_divide(sF8,double_divide(a2,identity)),identity),
inference(forward_demodulation,[],[f110,f75]) ).
fof(f113,plain,
identity = double_divide(double_divide(sF8,sF7),identity),
inference(forward_demodulation,[],[f112,f26]) ).
fof(f125,plain,
double_divide(sF8,sF7) = double_divide(double_divide(identity,double_divide(identity,identity)),identity),
inference(superposition,[],[f100,f113]) ).
fof(f137,plain,
double_divide(identity,identity) = double_divide(sF8,sF7),
inference(forward_demodulation,[],[f125,f32]) ).
fof(f141,plain,
sF4 = double_divide(sF8,sF7),
inference(forward_demodulation,[],[f137,f18]) ).
fof(f144,plain,
identity = double_divide(sF8,sF7),
inference(forward_demodulation,[],[f141,f75]) ).
fof(f147,plain,
sF8 = double_divide(double_divide(identity,double_divide(identity,sF7)),sF4),
inference(superposition,[],[f42,f144]) ).
fof(f150,plain,
a2 = sF8,
inference(forward_demodulation,[],[f147,f58]) ).
fof(f152,plain,
a2 != a2,
inference(superposition,[],[f29,f150]) ).
fof(f161,plain,
$false,
inference(trivial_inequality_removal,[],[f152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n019.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 27 10:07:18 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 2.61/1.35 % (2862400)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.61/1.35 % (2862496)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3143451439:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.61/1.35 % (2862496)First to succeed.
% 2.61/1.35 % (2862496)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2862400"
% 2.61/1.35 % (2862494)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3426097054:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.61/1.35 % (2862491)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=1021928277:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.61/1.35 % (2862489)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=1687664946:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.61/1.35 % (2862493)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3323367568:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.61/1.35 % (2862499)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3762532683:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.61/1.35 % (2862498)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4171565857:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.61/1.35 % (2862494)Also succeeded, but the first one will report.
% 2.61/1.35 % (2862499)Also succeeded, but the first one will report.
% 2.61/1.35 % (2862496)Refutation found. Thanks to Tanya!
% 2.61/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.61/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.35 % (2862496)------------------------------
% 2.61/1.35 % (2862496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.35 % (2862496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.35 % (2862496)CaDiCaL version: 2.1.3
% 2.61/1.35 % (2862496)Termination reason: Refutation
% 2.61/1.35 % (2862496)Time elapsed: 0.003 s
% 2.61/1.35 % (2862496)Peak memory usage: 88 MB
% 2.61/1.35 % (2862496)Instructions burned: 8 (million)
% 2.61/1.35 % (2862496)------------------------------
% 2.61/1.35 % (2862496)------------------------------
% 2.61/1.35 % (2862400)Success in time 0.289 s
% 2.61/1.35 % Vampire exiting
%------------------------------------------------------------------------------