%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP536-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 10:14:48 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.37s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 30 unt; 1 def)
% Number of atoms : 30 ( 22 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 : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,divide(divide(X0,X1),X2)),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f6,definition,
~ sP0(multiply(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f7,plain,
sP0(multiply(b,a)),
inference(inequality_splitting,[],[f5,f6]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(forward_demodulation,[],[f3,f4]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f9,f8]) ).
fof(f11,plain,
sP0(divide(b,inverse(a))),
inference(backward_demodulation,[],[f7,f10]) ).
fof(f12,plain,
~ sP0(divide(a,inverse(b))),
inference(backward_demodulation,[],[f6,f10]) ).
fof(f15,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f20,plain,
! [X0,X1] : divide(inverse(divide(divide(identity,X0),X1)),X0) = X1,
inference(superposition,[],[f1,f8]) ).
fof(f21,plain,
! [X0,X1] : divide(inverse(divide(inverse(X0),X1)),X0) = X1,
inference(forward_demodulation,[],[f20,f8]) ).
fof(f23,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[],[f15,f8]) ).
fof(f25,plain,
! [X0] : divide(identity,inverse(X0)) = X0,
inference(superposition,[],[f23,f4]) ).
fof(f26,plain,
! [X0] : divide(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f23,f8]) ).
fof(f30,plain,
! [X0,X1] : divide(divide(X1,X0),inverse(X0)) = X1,
inference(superposition,[],[f1,f23]) ).
fof(f31,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f25,f8]) ).
fof(f33,plain,
! [X0] : divide(X0,identity) = X0,
inference(backward_demodulation,[],[f26,f31]) ).
fof(f51,plain,
! [X0,X1] : divide(X0,divide(divide(X0,identity),X1)) = X1,
inference(superposition,[],[f1,f33]) ).
fof(f55,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f51,f33]) ).
fof(f163,plain,
! [X0,X1] : divide(X0,inverse(divide(X1,X0))) = X1,
inference(superposition,[],[f30,f55]) ).
fof(f289,plain,
! [X0,X1] : divide(X1,X0) = inverse(divide(X0,X1)),
inference(superposition,[],[f55,f163]) ).
fof(f290,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(divide(X0,inverse(X1))),
inference(superposition,[],[f21,f163]) ).
fof(f500,plain,
sP0(inverse(divide(inverse(a),b))),
inference(superposition,[],[f11,f289]) ).
fof(f506,plain,
sP0(inverse(inverse(divide(a,inverse(b))))),
inference(forward_demodulation,[],[f500,f290]) ).
fof(f512,plain,
sP0(divide(a,inverse(b))),
inference(forward_demodulation,[],[f506,f31]) ).
fof(f514,plain,
$false,
inference(forward_subsumption_resolution,[],[f512,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP536-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.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 10:06:33 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.62/1.37 % (2859856)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.62/1.37 % (2859918)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2442140997:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.62/1.37 % (2859918)First to succeed.
% 2.62/1.37 % (2859918)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2859856"
% 2.62/1.37 % (2859915)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=2140791932:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.62/1.37 % (2859917)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=486150120:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.62/1.37 % (2859916)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=174446339:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.62/1.37 % (2859919)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1142082053:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.62/1.37 % (2859920)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=501605701:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.62/1.37 % (2859921)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3786727074:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.62/1.37 % (2859921)Also succeeded, but the first one will report.
% 2.62/1.37 % (2859919)Also succeeded, but the first one will report.
% 2.62/1.37 % (2859920)Also succeeded, but the first one will report.
% 2.62/1.37 % (2859918)Refutation found. Thanks to Tanya!
% 2.62/1.37 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.37 % (2859918)------------------------------
% 2.62/1.37 % (2859918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.37 % (2859918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.37 % (2859918)CaDiCaL version: 2.1.3
% 2.62/1.37 % (2859918)Termination reason: Refutation
% 2.62/1.37 % (2859918)Time elapsed: 0.007 s
% 2.62/1.37 % (2859918)Peak memory usage: 88 MB
% 2.62/1.37 % (2859918)Instructions burned: 20 (million)
% 2.62/1.37 % (2859918)------------------------------
% 2.62/1.37 % (2859918)------------------------------
% 2.62/1.37 % (2859856)Success in time 0.281 s
% 2.62/1.37 % Vampire exiting
%------------------------------------------------------------------------------