%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP468-1 : 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 : n026.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 10:14:05 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 30 unt; 1 def)
% Number of atoms : 30 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 10 ( 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 : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : divide(divide(X0,X0),divide(X1,divide(divide(X2,divide(X3,X1)),inverse(X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(definition_unfolding,[],[f3,f2,f2,f2,f2]) ).
fof(f5,definition,
~ sP0(divide(divide(a3,inverse(b3)),inverse(c3))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f6,plain,
sP0(divide(a3,inverse(divide(b3,inverse(c3))))),
inference(inequality_splitting,[],[f4,f5]) ).
fof(f7,plain,
! [X2,X3,X0,X1,X4,X5] : divide(divide(X1,X1),divide(divide(X2,divide(divide(X0,divide(X3,X2)),inverse(X3))),divide(divide(X4,X0),inverse(divide(X5,X5))))) = X4,
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1,X4] : divide(X4,X4) = divide(divide(X1,X1),divide(divide(divide(X0,divide(X2,X3)),inverse(X2)),divide(X0,inverse(X3)))),
inference(superposition,[],[f1,f1]) ).
fof(f18,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(superposition,[],[f8,f8]) ).
fof(f23,plain,
! [X2,X3,X0,X1,X6,X4,X5] : divide(divide(X1,X1),divide(divide(divide(divide(X2,divide(X3,X4)),inverse(X3)),divide(X2,inverse(X4))),divide(divide(X5,divide(X0,X0)),inverse(divide(X6,X6))))) = X5,
inference(superposition,[],[f1,f8]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : divide(divide(X1,X1),divide(X2,divide(divide(X3,divide(X0,X0)),inverse(X2)))) = X3,
inference(superposition,[],[f1,f18]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : divide(X7,X7) = divide(divide(X1,X1),divide(divide(X2,divide(divide(divide(divide(divide(X3,divide(X4,X5)),inverse(X4)),divide(X3,inverse(X5))),divide(X6,X2)),inverse(X6))),divide(divide(X0,X0),inverse(divide(X8,X8))))),
inference(superposition,[],[f7,f8]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4,X5] : divide(divide(X1,X1),divide(divide(X2,divide(divide(X3,divide(X4,X2)),inverse(X4))),divide(divide(X0,X0),inverse(divide(X5,X5))))) = X3,
inference(superposition,[],[f7,f18]) ).
fof(f74,plain,
! [X3,X7,X4,X5] : divide(X7,X7) = divide(divide(divide(X3,divide(X4,X5)),inverse(X4)),divide(X3,inverse(X5))),
inference(forward_demodulation,[],[f62,f65]) ).
fof(f141,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : divide(divide(X3,divide(X6,X4)),inverse(X6)) = divide(divide(X1,X1),divide(divide(X2,divide(divide(divide(X3,inverse(X4)),divide(X5,X2)),inverse(X5))),divide(divide(X0,X0),inverse(divide(X7,X7))))),
inference(superposition,[],[f7,f74]) ).
fof(f145,plain,
! [X3,X6,X4] : divide(X3,inverse(X4)) = divide(divide(X3,divide(X6,X4)),inverse(X6)),
inference(forward_demodulation,[],[f141,f65]) ).
fof(f147,plain,
! [X2,X0,X1] : divide(divide(X0,X0),divide(X1,divide(X2,inverse(X1)))) = X2,
inference(backward_demodulation,[],[f1,f145]) ).
fof(f162,plain,
! [X2,X0,X1,X6,X4,X5] : divide(divide(X1,X1),divide(divide(divide(X2,inverse(X4)),divide(X2,inverse(X4))),divide(divide(X5,divide(X0,X0)),inverse(divide(X6,X6))))) = X5,
inference(backward_demodulation,[],[f23,f145]) ).
fof(f238,plain,
! [X3,X0] : divide(X3,divide(X0,X0)) = X3,
inference(backward_demodulation,[],[f42,f147]) ).
fof(f270,plain,
! [X2,X1,X6,X4,X5] : divide(divide(X1,X1),divide(divide(divide(X2,inverse(X4)),divide(X2,inverse(X4))),divide(X5,inverse(divide(X6,X6))))) = X5,
inference(backward_demodulation,[],[f162,f238]) ).
fof(f296,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(superposition,[],[f147,f238]) ).
fof(f297,plain,
! [X2,X1] : inverse(divide(X1,divide(X2,inverse(X1)))) = X2,
inference(backward_demodulation,[],[f147,f296]) ).
fof(f305,plain,
! [X2,X6,X4,X5] : inverse(divide(divide(divide(X2,inverse(X4)),divide(X2,inverse(X4))),divide(X5,inverse(divide(X6,X6))))) = X5,
inference(backward_demodulation,[],[f270,f296]) ).
fof(f334,plain,
! [X6,X5] : inverse(inverse(divide(X5,inverse(divide(X6,X6))))) = X5,
inference(forward_demodulation,[],[f305,f296]) ).
fof(f356,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X0))) = X1,
inference(superposition,[],[f238,f296]) ).
fof(f364,plain,
! [X5] : inverse(inverse(X5)) = X5,
inference(backward_demodulation,[],[f334,f356]) ).
fof(f399,plain,
! [X0,X1] : inverse(X0) = divide(X1,divide(X0,inverse(X1))),
inference(superposition,[],[f364,f297]) ).
fof(f747,plain,
! [X2,X0,X1] : divide(X1,inverse(divide(X0,inverse(X2)))) = divide(divide(X1,inverse(X0)),inverse(X2)),
inference(superposition,[],[f145,f399]) ).
fof(f793,plain,
~ sP0(divide(a3,inverse(divide(b3,inverse(c3))))),
inference(backward_demodulation,[],[f5,f747]) ).
fof(f806,plain,
$false,
inference(forward_subsumption_resolution,[],[f793,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP468-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:08:12 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.18/1.30 % (2596433)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.18/1.30 % (2596483)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1048184354:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.18/1.30 % (2596484)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1883501325:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.18/1.30 % (2596480)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=566412576:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.18/1.30 % (2596482)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=627073004:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.18/1.30 % (2596481)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=274785212:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.18/1.30 % (2596479)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=499790511:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.18/1.30 % (2596485)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1541205218:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.18/1.30 % (2596482)First to succeed.
% 0.18/1.30 % (2596482)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2596433"
% 0.18/1.30 % (2596483)Instruction limit reached!
% 0.18/1.30 % (2596483)------------------------------
% 0.18/1.30 % (2596483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (2596483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (2596483)CaDiCaL version: 2.1.3
% 0.18/1.30 % (2596483)Termination reason: Instruction limit
% 0.18/1.30 % (2596483)Termination phase: Saturation
% 0.18/1.30 % (2596483)Time elapsed: 0.048 s
% 0.18/1.30 % (2596483)Peak memory usage: 89 MB
% 0.18/1.30 % (2596483)Instructions burned: 182 (million)
% 0.18/1.30 % (2596484)Also succeeded, but the first one will report.
% 0.18/1.30 % (2596493)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3994975270:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 0.18/1.30 % (2596485)Also succeeded, but the first one will report.
% 0.18/1.30 % (2596482)Refutation found. Thanks to Tanya!
% 0.18/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.30 % (2596482)------------------------------
% 0.18/1.30 % (2596482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.30 % (2596482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.30 % (2596482)CaDiCaL version: 2.1.3
% 0.18/1.30 % (2596482)Termination reason: Refutation
% 0.18/1.30 % (2596482)Time elapsed: 0.038 s
% 0.18/1.30 % (2596482)Peak memory usage: 88 MB
% 0.18/1.30 % (2596482)Instructions burned: 66 (million)
% 0.18/1.30 % (2596482)------------------------------
% 0.18/1.30 % (2596482)------------------------------
% 0.18/1.30 % (2596433)Success in time 0.449 s
% 0.18/1.30 % Vampire exiting
%------------------------------------------------------------------------------