%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP492-1 : 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 : n008.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 10:14:08 AM UTC 2026
% Result : Unsatisfiable 2.36s 1.40s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 107 ( 107 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f7,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f6,f3]) ).
fof(f8,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f6,f4]) ).
fof(f9,plain,
! [X0,X1] : identity = double_divide(double_divide(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f4,f6]) ).
fof(f10,plain,
! [X0,X1] : multiply(identity,double_divide(X1,X0)) = inverse(multiply(X0,X1)),
inference(superposition,[],[f7,f6]) ).
fof(f26,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[],[f1,f3]) ).
fof(f27,plain,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(X1,X0),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[],[f26,f6]) ).
fof(f81,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0)))) = X1,
inference(superposition,[],[f27,f3]) ).
fof(f87,plain,
! [X0,X1] : double_divide(double_divide(identity,X1),double_divide(identity,double_divide(multiply(identity,X1),inverse(X0)))) = X0,
inference(superposition,[],[f27,f3]) ).
fof(f88,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(inverse(X1),X0),identity))) = X1,
inference(superposition,[],[f27,f4]) ).
fof(f100,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(inverse(X1),X0)))) = X1,
inference(forward_demodulation,[],[f88,f3]) ).
fof(f121,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(inverse(identity)))) = X0,
inference(superposition,[],[f100,f8]) ).
fof(f127,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,multiply(identity,identity))) = X0,
inference(forward_demodulation,[],[f121,f7]) ).
fof(f128,plain,
identity = double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))),
inference(superposition,[],[f127,f3]) ).
fof(f129,plain,
inverse(identity) = double_divide(identity,double_divide(identity,multiply(identity,identity))),
inference(superposition,[],[f127,f4]) ).
fof(f141,plain,
double_divide(identity,multiply(identity,identity)) = double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))),
inference(superposition,[],[f127,f129]) ).
fof(f150,plain,
identity = double_divide(identity,multiply(identity,identity)),
inference(forward_demodulation,[],[f141,f128]) ).
fof(f153,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(superposition,[],[f127,f150]) ).
fof(f164,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[],[f153,f3]) ).
fof(f166,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f164,f6]) ).
fof(f170,plain,
! [X0] : identity = double_divide(double_divide(identity,X0),X0),
inference(superposition,[],[f9,f166]) ).
fof(f171,plain,
identity = double_divide(identity,identity),
inference(superposition,[],[f150,f166]) ).
fof(f187,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f171,f3]) ).
fof(f210,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[],[f81,f166]) ).
fof(f211,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[],[f210,f187]) ).
fof(f225,plain,
! [X0] : inverse(identity) = multiply(X0,double_divide(identity,X0)),
inference(superposition,[],[f6,f170]) ).
fof(f226,plain,
! [X0] : identity = multiply(X0,double_divide(identity,X0)),
inference(forward_demodulation,[],[f225,f187]) ).
fof(f259,plain,
! [X0,X1] : multiply(identity,X0) = inverse(multiply(double_divide(identity,double_divide(X1,double_divide(X0,X1))),identity)),
inference(superposition,[],[f10,f211]) ).
fof(f261,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(identity,double_divide(X1,double_divide(X0,X1))),identity),
inference(superposition,[],[f6,f211]) ).
fof(f262,plain,
! [X0,X1] : inverse(X0) = double_divide(identity,double_divide(X1,double_divide(X0,X1))),
inference(forward_demodulation,[],[f261,f166]) ).
fof(f264,plain,
! [X0,X1] : multiply(identity,X0) = inverse(double_divide(identity,double_divide(X1,double_divide(X0,X1)))),
inference(forward_demodulation,[],[f259,f166]) ).
fof(f276,plain,
! [X0,X1] : multiply(identity,X0) = multiply(double_divide(X1,double_divide(X0,X1)),identity),
inference(forward_demodulation,[],[f264,f6]) ).
fof(f285,plain,
! [X0,X1] : multiply(identity,X0) = double_divide(X1,double_divide(X0,X1)),
inference(forward_demodulation,[],[f276,f166]) ).
fof(f310,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),double_divide(identity,inverse(identity))) = X0,
inference(superposition,[],[f100,f226]) ).
fof(f311,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),identity) = X0,
inference(forward_demodulation,[],[f310,f4]) ).
fof(f325,plain,
! [X0] : inverse(double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(forward_demodulation,[],[f311,f3]) ).
fof(f335,plain,
! [X0] : multiply(double_divide(identity,inverse(X0)),identity) = X0,
inference(forward_demodulation,[],[f325,f6]) ).
fof(f339,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[],[f335,f166]) ).
fof(f467,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,identity)),X0) = multiply(identity,double_divide(identity,X0)),
inference(superposition,[],[f285,f127]) ).
fof(f496,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,identity)),X0) = inverse(multiply(X0,identity)),
inference(forward_demodulation,[],[f467,f10]) ).
fof(f512,plain,
! [X0] : inverse(X0) = double_divide(double_divide(identity,multiply(identity,identity)),X0),
inference(forward_demodulation,[],[f496,f166]) ).
fof(f520,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(forward_demodulation,[],[f512,f150]) ).
fof(f539,plain,
! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,X0),double_divide(identity,identity)),
inference(superposition,[],[f87,f4]) ).
fof(f549,plain,
! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,X0),inverse(identity)),
inference(forward_demodulation,[],[f539,f3]) ).
fof(f560,plain,
! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,X0),identity),
inference(forward_demodulation,[],[f549,f187]) ).
fof(f569,plain,
! [X0] : multiply(identity,X0) = inverse(double_divide(identity,X0)),
inference(forward_demodulation,[],[f560,f3]) ).
fof(f577,plain,
! [X0] : multiply(identity,X0) = multiply(X0,identity),
inference(forward_demodulation,[],[f569,f6]) ).
fof(f579,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f577,f166]) ).
fof(f1410,plain,
! [X0,X1] : inverse(X0) = inverse(double_divide(X1,double_divide(X0,X1))),
inference(forward_demodulation,[],[f262,f520]) ).
fof(f1411,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
inference(forward_demodulation,[],[f1410,f6]) ).
fof(f1423,plain,
! [X2,X0,X1] : inverse(double_divide(identity,X1)) = multiply(X0,double_divide(identity,double_divide(multiply(X2,X1),double_divide(X0,X2)))),
inference(superposition,[],[f1411,f27]) ).
fof(f1425,plain,
! [X0,X1] : inverse(double_divide(identity,X1)) = multiply(X0,double_divide(identity,inverse(multiply(inverse(X0),X1)))),
inference(superposition,[],[f1411,f100]) ).
fof(f1453,plain,
! [X0,X1] : inverse(double_divide(identity,X1)) = multiply(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f1425,f339]) ).
fof(f1455,plain,
! [X2,X0,X1] : inverse(double_divide(identity,X1)) = multiply(X0,inverse(double_divide(multiply(X2,X1),double_divide(X0,X2)))),
inference(forward_demodulation,[],[f1423,f520]) ).
fof(f1470,plain,
! [X0,X1] : multiply(X1,identity) = multiply(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f1453,f6]) ).
fof(f1472,plain,
! [X2,X0,X1] : inverse(double_divide(identity,X1)) = multiply(X0,multiply(double_divide(X0,X2),multiply(X2,X1))),
inference(forward_demodulation,[],[f1455,f6]) ).
fof(f1478,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f1470,f166]) ).
fof(f1480,plain,
! [X2,X0,X1] : multiply(X1,identity) = multiply(X0,multiply(double_divide(X0,X2),multiply(X2,X1))),
inference(forward_demodulation,[],[f1472,f6]) ).
fof(f1483,plain,
! [X2,X0,X1] : multiply(X0,multiply(double_divide(X0,X2),multiply(X2,X1))) = X1,
inference(forward_demodulation,[],[f1480,f166]) ).
fof(f1487,plain,
! [X2,X0,X1] : multiply(double_divide(X1,X0),multiply(multiply(X0,X1),X2)) = X2,
inference(superposition,[],[f1478,f6]) ).
fof(f3265,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(identity,X0),multiply(double_divide(X0,X1),X2))) = X2,
inference(superposition,[],[f1483,f285]) ).
fof(f3411,plain,
! [X2,X0,X1] : multiply(X1,multiply(X0,multiply(double_divide(X0,X1),X2))) = X2,
inference(forward_demodulation,[],[f3265,f579]) ).
fof(f4100,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X2,X0)),
inference(superposition,[],[f3411,f1487]) ).
fof(f4808,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(superposition,[],[f5,f4100]) ).
fof(f4840,plain,
$false,
inference(trivial_inequality_removal,[],[f4808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP492-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n008.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 10:06:40 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 2.36/1.40 % (998330)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.36/1.40 % (998375)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3999799427:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.36/1.40 % (998379)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1681568190:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.36/1.40 % (998373)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=2929342109:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.36/1.40 % (998374)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=297667223:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.36/1.40 % (998377)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2198773345:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.36/1.40 % (998376)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3721040926:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.36/1.40 % (998378)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3940256537:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.36/1.40 % (998379)First to succeed.
% 2.36/1.40 % (998379)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-998330"
% 2.36/1.40 % (998376)Instruction limit reached!
% 2.36/1.40 % (998376)------------------------------
% 2.36/1.40 % (998376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.36/1.40 % (998376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.40 % (998376)CaDiCaL version: 2.1.3
% 2.36/1.40 % (998376)Termination reason: Instruction limit
% 2.36/1.40 % (998376)Termination phase: Saturation
% 2.36/1.40 % (998376)Time elapsed: 0.081 s
% 2.36/1.40 % (998376)Peak memory usage: 88 MB
% 2.36/1.40 % (998376)Instructions burned: 137 (million)
% 2.36/1.40 % (998377)Also succeeded, but the first one will report.
% 2.36/1.40 % (998378)Also succeeded, but the first one will report.
% 2.36/1.40 % (998390)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4112224131:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 2.36/1.40 % (998379)Refutation found. Thanks to Tanya!
% 2.36/1.40 % SZS status Unsatisfiable for theBenchmark
% 2.36/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/1.50 % (998379)------------------------------
% 0.25/1.50 % (998379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/1.50 % (998379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/1.50 % (998379)CaDiCaL version: 2.1.3
% 0.25/1.50 % (998379)Termination reason: Refutation
% 0.25/1.50 % (998379)Time elapsed: 0.068 s
% 0.25/1.50 % (998379)Peak memory usage: 89 MB
% 0.25/1.50 % (998379)Instructions burned: 120 (million)
% 0.25/1.50 % (998379)------------------------------
% 0.25/1.50 % (998379)------------------------------
% 0.25/1.50 % (998330)Success in time 0.493 s
% 0.25/1.50 % Vampire exiting
%------------------------------------------------------------------------------