%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP565-1 : 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 : n012.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 10:14:52 AM UTC 2026
% Result : Unsatisfiable 2.00s 0.88s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 55 unt; 11 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 16 ( 16 usr; 6 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(X0,X2)),double_divide(identity,X2))),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(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f6,plain,
identity != multiply(inverse(a1),a1),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f8,plain,
identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity),
inference(definition_unfolding,[],[f6,f2,f3]) ).
fof(f9,definition,
! [X2,X0,X1] : sF0(X1,X0,X2) = double_divide(X1,double_divide(X0,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(X0,X2)) = sF0(X1,X0,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X2] : sF1(X2) = double_divide(identity,X2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f12,plain,
! [X2] : double_divide(identity,X2) = sF1(X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF2(X1,X0,X2) = double_divide(sF0(X1,X0,X2),sF1(X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : double_divide(sF0(X1,X0,X2),sF1(X2)) = sF2(X1,X0,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = double_divide(X0,sF2(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : double_divide(X0,sF2(X1,X0,X2)) = 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,identity),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f23,plain,
! [X0] : double_divide(X0,identity) = sF6(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
! [X0] : sF7(X0) = double_divide(X0,sF6(X0)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f25,plain,
! [X0] : double_divide(X0,sF6(X0)) = sF7(X0),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
! [X0] : identity = sF7(X0),
inference(definition_folding,[],[f7,f25,f23]) ).
fof(f27,definition,
sF8 = double_divide(a1,identity),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f28,plain,
double_divide(a1,identity) = sF8,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF9 = double_divide(a1,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f30,plain,
double_divide(a1,sF8) = sF9,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF10 = double_divide(sF9,identity),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f32,plain,
double_divide(sF9,identity) = sF10,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
identity != sF10,
inference(definition_folding,[],[f8,f32,f30,f28]) ).
fof(f34,plain,
! [X0] : identity = double_divide(X0,sF6(X0)),
inference(forward_demodulation,[],[f26,f25]) ).
fof(f35,plain,
! [X2,X0,X1] : double_divide(sF3(X0,X1,X2),sF4) = X1,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f36,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(forward_demodulation,[],[f34,f23]) ).
fof(f37,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,sF2(X1,X0,X2)),sF4) = X1,
inference(forward_demodulation,[],[f35,f16]) ).
fof(f38,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(sF0(X1,X0,X2),sF1(X2))),sF4) = X1,
inference(forward_demodulation,[],[f37,f14]) ).
fof(f39,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(sF0(X1,X0,X2),double_divide(identity,X2))),sF4) = X1,
inference(forward_demodulation,[],[f38,f12]) ).
fof(f40,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),sF4) = X1,
inference(forward_demodulation,[],[f39,f10]) ).
fof(f41,plain,
identity = double_divide(identity,sF4),
inference(superposition,[],[f36,f18]) ).
fof(f42,plain,
identity = double_divide(a1,sF8),
inference(superposition,[],[f36,f28]) ).
fof(f44,plain,
identity = sF9,
inference(forward_demodulation,[],[f42,f30]) ).
fof(f45,plain,
double_divide(identity,identity) = sF10,
inference(superposition,[],[f32,f44]) ).
fof(f46,plain,
sF4 = sF10,
inference(forward_demodulation,[],[f45,f18]) ).
fof(f47,plain,
identity != sF4,
inference(superposition,[],[f33,f46]) ).
fof(f52,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,sF4),sF4)),sF4) = X0,
inference(superposition,[],[f40,f18]) ).
fof(f57,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,double_divide(identity,identity))),sF4) = X0,
inference(superposition,[],[f40,f36]) ).
fof(f62,plain,
! [X0] : double_divide(double_divide(X0,identity),sF4) = X0,
inference(forward_demodulation,[],[f57,f36]) ).
fof(f69,plain,
identity = double_divide(sF4,sF4),
inference(superposition,[],[f62,f18]) ).
fof(f84,plain,
sF4 = double_divide(double_divide(identity,double_divide(identity,sF4)),sF4),
inference(superposition,[],[f52,f69]) ).
fof(f88,plain,
sF4 = double_divide(double_divide(identity,identity),sF4),
inference(forward_demodulation,[],[f84,f41]) ).
fof(f90,plain,
identity = sF4,
inference(forward_demodulation,[],[f88,f62]) ).
fof(f93,plain,
identity != identity,
inference(superposition,[],[f47,f90]) ).
fof(f98,plain,
$false,
inference(trivial_inequality_removal,[],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP565-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 10:07:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.00/0.88 % (2145602)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.00/0.88 % (2145666)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2007980385:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.00/0.88 % (2145660)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=2810533321:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.00/0.88 % (2145665)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2178030362:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.00/0.88 % (2145664)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1063646651:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.00/0.88 % (2145662)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1027371397:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.00/0.88 % (2145663)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2548964882:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.00/0.88 % (2145659)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=1475646662:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.00/0.88 % (2145664)First to succeed.
% 2.00/0.88 % (2145663)Also succeeded, but the first one will report.
% 2.00/0.88 % (2145666)Also succeeded, but the first one will report.
% 2.00/0.88 % (2145664)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2145602"
% 2.00/0.88 % (2145665)Also succeeded, but the first one will report.
% 2.00/0.88 % (2145664)Refutation found. Thanks to Tanya!
% 2.00/0.88 % SZS status Unsatisfiable for theBenchmark
% 2.00/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.00/0.88 % (2145664)------------------------------
% 2.00/0.88 % (2145664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.00/0.88 % (2145664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (2145664)CaDiCaL version: 2.1.3
% 2.00/0.88 % (2145664)Termination reason: Refutation
% 2.00/0.88 % (2145664)Time elapsed: 0.002 s
% 2.00/0.88 % (2145664)Peak memory usage: 88 MB
% 2.00/0.88 % (2145664)Instructions burned: 4 (million)
% 2.00/0.88 % (2145664)------------------------------
% 2.00/0.88 % (2145664)------------------------------
% 2.00/0.88 % (2145602)Success in time 0.254 s
% 2.00/0.88 % Vampire exiting
%------------------------------------------------------------------------------