%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP527-1 : 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 : n018.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 6.27s 2.27s
% Output : Refutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 34 unt; 1 def)
% Number of atoms : 34 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(X0,X1),divide(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,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f5,definition,
~ sP0(multiply(multiply(a3,b3),c3)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f6,plain,
sP0(multiply(a3,multiply(b3,c3))),
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(a3,inverse(multiply(b3,c3)))),
inference(backward_demodulation,[],[f6,f7]) ).
fof(f9,plain,
~ sP0(multiply(divide(a3,inverse(b3)),c3)),
inference(backward_demodulation,[],[f5,f7]) ).
fof(f10,plain,
~ sP0(divide(divide(a3,inverse(b3)),inverse(c3))),
inference(forward_demodulation,[],[f9,f7]) ).
fof(f11,plain,
sP0(divide(a3,inverse(divide(b3,inverse(c3))))),
inference(forward_demodulation,[],[f8,f7]) ).
fof(f12,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f3,f3]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : divide(X1,divide(divide(X1,divide(divide(X2,X3),divide(X0,X3))),X0)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : divide(X1,X0) = divide(divide(X1,divide(X0,X2)),X2),
inference(superposition,[],[f1,f1]) ).
fof(f23,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X1))) = X0,
inference(superposition,[],[f1,f3]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : divide(X2,divide(X0,divide(X1,X3))) = divide(divide(X2,divide(X0,X1)),X3),
inference(superposition,[],[f22,f22]) ).
fof(f52,plain,
! [X2,X3,X0,X1] : divide(divide(X0,divide(X1,divide(X2,X3))),X2) = divide(divide(X0,X1),X3),
inference(superposition,[],[f22,f22]) ).
fof(f54,plain,
! [X0,X1] : inverse(X1) = divide(divide(X0,X1),X0),
inference(superposition,[],[f3,f22]) ).
fof(f58,plain,
! [X2,X3,X1] : divide(X1,divide(divide(X1,divide(X2,X3)),X3)) = X2,
inference(backward_demodulation,[],[f21,f52]) ).
fof(f61,plain,
! [X2,X0,X1] : divide(X1,X0) = divide(X1,divide(X0,divide(X2,X2))),
inference(backward_demodulation,[],[f22,f46]) ).
fof(f62,plain,
! [X2,X3,X0,X1] : divide(divide(X0,X1),X3) = divide(X0,divide(X1,divide(divide(X2,X3),X2))),
inference(backward_demodulation,[],[f52,f46]) ).
fof(f65,plain,
! [X2,X3,X1] : divide(X1,divide(X1,divide(X2,divide(X3,X3)))) = X2,
inference(forward_demodulation,[],[f58,f46]) ).
fof(f66,plain,
! [X3,X0,X1] : divide(divide(X0,X1),X3) = divide(X0,divide(X1,inverse(X3))),
inference(forward_demodulation,[],[f62,f54]) ).
fof(f67,plain,
! [X2,X1] : divide(X1,divide(X1,X2)) = X2,
inference(forward_demodulation,[],[f65,f61]) ).
fof(f68,plain,
! [X0,X1] : inverse(X1) = divide(X0,divide(X1,inverse(X0))),
inference(backward_demodulation,[],[f54,f66]) ).
fof(f83,plain,
~ sP0(divide(a3,divide(inverse(b3),inverse(inverse(c3))))),
inference(backward_demodulation,[],[f10,f66]) ).
fof(f96,plain,
! [X0,X1] : divide(X1,X0) = inverse(divide(X0,X1)),
inference(superposition,[],[f67,f23]) ).
fof(f99,plain,
! [X0,X1] : inverse(divide(inverse(divide(X1,X1)),X0)) = X0,
inference(superposition,[],[f12,f67]) ).
fof(f100,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f99,f12]) ).
fof(f112,plain,
~ sP0(divide(a3,divide(inverse(b3),c3))),
inference(backward_demodulation,[],[f83,f100]) ).
fof(f453,plain,
! [X0,X1] : divide(X0,inverse(X1)) = divide(X1,inverse(X0)),
inference(superposition,[],[f67,f68]) ).
fof(f1313,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(divide(X0,inverse(X1))),
inference(superposition,[],[f96,f453]) ).
fof(f1336,plain,
~ sP0(divide(a3,inverse(divide(b3,inverse(c3))))),
inference(backward_demodulation,[],[f112,f1313]) ).
fof(f1400,plain,
$false,
inference(forward_subsumption_resolution,[],[f1336,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP527-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n018.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 10:08:53 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.47 Running first-order theorem proving
% 0.13/0.47 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
% 6.27/2.27 % (2101749)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.27/2.27 % (2101754)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=554643991:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.27/2.27 % (2101756)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1828680809:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.27/2.27 % (2101759)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=664225595:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.27/2.27 % (2101755)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=1298164915:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.27/2.27 % (2101758)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3095383999:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.27/2.27 % (2101757)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3133722151:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.27/2.27 % (2101760)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=475444113:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.27/2.27 % (2101757)First to succeed.
% 6.27/2.27 % (2101757)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2101749"
% 6.27/2.27 % (2101759)Also succeeded, but the first one will report.
% 6.27/2.27 % (2101758)Also succeeded, but the first one will report.
% 6.27/2.27 % (2101760)Also succeeded, but the first one will report.
% 6.27/2.27 % (2101757)Refutation found. Thanks to Tanya!
% 6.27/2.27 % SZS status Unsatisfiable for theBenchmark
% 6.27/2.27 % SZS output start Proof for theBenchmark
% See solution above
% 6.27/2.27 % (2101757)------------------------------
% 6.27/2.27 % (2101757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/2.27 % (2101757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/2.27 % (2101757)CaDiCaL version: 2.1.3
% 6.27/2.27 % (2101757)Termination reason: Refutation
% 6.27/2.27 % (2101757)Time elapsed: 0.043 s
% 6.27/2.27 % (2101757)Peak memory usage: 88 MB
% 6.27/2.27 % (2101757)Instructions burned: 42 (million)
% 6.27/2.27 % (2101757)------------------------------
% 6.27/2.27 % (2101757)------------------------------
% 6.27/2.27 % (2101749)Success in time 0.739 s
% 6.27/2.27 % Vampire exiting
%------------------------------------------------------------------------------