%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP524-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:14:47 AM UTC 2026
% Result : Unsatisfiable 3.44s 1.36s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 42 unt; 1 def)
% Number of atoms : 42 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f5,definition,
~ sP0(multiply(a,b)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f6,plain,
sP0(multiply(b,a)),
inference(inequality_splitting,[],[f4,f5]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f8,plain,
sP0(divide(b,inverse(a))),
inference(backward_demodulation,[],[f6,f7]) ).
fof(f9,plain,
~ sP0(divide(a,inverse(b))),
inference(backward_demodulation,[],[f5,f7]) ).
fof(f10,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f3,f3]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : divide(X1,divide(divide(X2,divide(X0,divide(X1,X2))),divide(X3,X0))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f17,plain,
! [X2,X0,X1] : divide(X1,divide(divide(X0,divide(X2,X1)),X0)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f18,plain,
! [X2,X0,X1] : divide(X2,X2) = divide(X0,divide(X1,inverse(divide(X0,X1)))),
inference(superposition,[],[f1,f3]) ).
fof(f25,plain,
! [X2,X0,X1] : inverse(divide(X1,divide(X0,divide(inverse(divide(X2,X2)),X1)))) = X0,
inference(superposition,[],[f10,f1]) ).
fof(f26,plain,
! [X0,X1] : inverse(divide(X1,divide(X0,inverse(X1)))) = X0,
inference(forward_demodulation,[],[f25,f10]) ).
fof(f35,plain,
! [X0,X1] : inverse(inverse(divide(X0,inverse(divide(X1,X1))))) = X0,
inference(superposition,[],[f26,f3]) ).
fof(f44,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X1))) = X0,
inference(superposition,[],[f17,f3]) ).
fof(f50,plain,
! [X2,X0,X1] : inverse(divide(divide(X1,divide(X0,divide(X2,X2))),X1)) = X0,
inference(superposition,[],[f3,f17]) ).
fof(f51,plain,
! [X2,X0,X1] : inverse(divide(divide(X1,divide(X0,inverse(divide(X2,X2)))),X1)) = X0,
inference(superposition,[],[f10,f17]) ).
fof(f53,plain,
! [X2,X0] : divide(X2,X2) = divide(X0,X0),
inference(backward_demodulation,[],[f18,f44]) ).
fof(f77,plain,
! [X2,X0,X1] : divide(X1,divide(X1,divide(X2,divide(X0,X0)))) = X2,
inference(superposition,[],[f1,f53]) ).
fof(f79,plain,
! [X2,X0,X1] : divide(X1,X2) = divide(X1,divide(X2,divide(X0,X0))),
inference(superposition,[],[f1,f53]) ).
fof(f81,plain,
! [X0,X1] : inverse(divide(divide(X1,X0),X1)) = X0,
inference(backward_demodulation,[],[f50,f79]) ).
fof(f85,plain,
! [X2,X1] : divide(X1,divide(X1,X2)) = X2,
inference(forward_demodulation,[],[f77,f79]) ).
fof(f88,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X2))) = X0,
inference(backward_demodulation,[],[f51,f81]) ).
fof(f89,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[],[f35,f88]) ).
fof(f125,plain,
! [X2,X3,X0,X1] : divide(X1,X0) = divide(X3,divide(X0,divide(X2,divide(X3,divide(X1,X2))))),
inference(superposition,[],[f16,f17]) ).
fof(f130,plain,
! [X2,X3,X0,X1] : divide(X3,divide(X1,divide(X2,X3))) = divide(divide(X0,X1),divide(X0,X2)),
inference(superposition,[],[f17,f16]) ).
fof(f160,plain,
! [X0,X1] : inverse(X0) = divide(X1,divide(X0,inverse(X1))),
inference(superposition,[],[f89,f26]) ).
fof(f242,plain,
! [X0,X1] : divide(divide(X1,X0),inverse(X0)) = X1,
inference(superposition,[],[f44,f85]) ).
fof(f300,plain,
! [X2,X0,X1] : divide(X2,divide(X0,divide(X1,X2))) = inverse(divide(X0,X1)),
inference(superposition,[],[f81,f1]) ).
fof(f316,plain,
! [X3,X0,X1] : divide(X1,X0) = divide(X3,divide(X0,inverse(divide(X3,X1)))),
inference(backward_demodulation,[],[f125,f300]) ).
fof(f317,plain,
! [X2,X0,X1] : divide(divide(X0,X1),divide(X0,X2)) = inverse(divide(X1,X2)),
inference(backward_demodulation,[],[f130,f300]) ).
fof(f461,plain,
! [X2,X0,X1] : divide(inverse(X1),X2) = divide(divide(X0,X1),divide(X2,inverse(X0))),
inference(superposition,[],[f316,f242]) ).
fof(f486,plain,
! [X0] : sP0(divide(X0,divide(inverse(a),inverse(divide(X0,b))))),
inference(superposition,[],[f8,f316]) ).
fof(f540,plain,
sP0(inverse(divide(inverse(a),b))),
inference(superposition,[],[f486,f85]) ).
fof(f578,plain,
! [X2,X0,X1] : divide(divide(X1,X2),X0) = inverse(divide(X2,divide(X1,X0))),
inference(superposition,[],[f317,f85]) ).
fof(f638,plain,
! [X2,X0,X1] : divide(inverse(X1),X2) = inverse(divide(X1,divide(X0,divide(X2,inverse(X0))))),
inference(backward_demodulation,[],[f461,f578]) ).
fof(f683,plain,
! [X2,X1] : divide(inverse(X1),X2) = inverse(divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f638,f160]) ).
fof(f732,plain,
sP0(inverse(inverse(divide(a,inverse(b))))),
inference(backward_demodulation,[],[f540,f683]) ).
fof(f755,plain,
sP0(divide(a,inverse(b))),
inference(forward_demodulation,[],[f732,f89]) ).
fof(f784,plain,
$false,
inference(forward_subsumption_resolution,[],[f755,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP524-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.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 10:06:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 3.44/1.36 % (2755560)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.44/1.36 % (2755565)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=3116487453:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.44/1.36 % (2755567)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2992694669:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.44/1.36 % (2755569)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1556167031:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.44/1.36 % (2755571)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1862471932:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.44/1.36 % (2755566)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=3698967647:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.44/1.36 % (2755568)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1639423449:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.44/1.36 % (2755570)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2467040126:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.44/1.36 % (2755568)First to succeed.
% 3.44/1.36 % (2755568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2755560"
% 3.44/1.36 % (2755571)Also succeeded, but the first one will report.
% 3.44/1.36 % (2755569)Also succeeded, but the first one will report.
% 3.44/1.36 % (2755570)Also succeeded, but the first one will report.
% 3.44/1.36 % (2755568)Refutation found. Thanks to Tanya!
% 3.44/1.36 % SZS status Unsatisfiable for theBenchmark
% 3.44/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.36 % (2755568)------------------------------
% 3.44/1.36 % (2755568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.36 % (2755568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.36 % (2755568)CaDiCaL version: 2.1.3
% 3.44/1.36 % (2755568)Termination reason: Refutation
% 3.44/1.36 % (2755568)Time elapsed: 0.021 s
% 3.44/1.36 % (2755568)Peak memory usage: 88 MB
% 3.44/1.36 % (2755568)Instructions burned: 33 (million)
% 3.44/1.36 % (2755568)------------------------------
% 3.44/1.36 % (2755568)------------------------------
% 3.44/1.36 % (2755560)Success in time 0.42 s
% 3.44/1.36 % Vampire exiting
%------------------------------------------------------------------------------