%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP598-1 : 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 : n003.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 10:14:57 AM UTC 2026
% Result : Unsatisfiable 2.80s 1.45s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 34 unt; 1 def)
% Number of atoms : 34 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 3 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 : 88 ( 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))),
inference(definition_unfolding,[],[f4,f2,f2]) ).
fof(f6,definition,
~ sP0(inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f7,plain,
sP0(a2),
inference(inequality_splitting,[],[f5,f6]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(X1,X2),inverse(double_divide(inverse(X3),inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))))))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(X1),X2),inverse(double_divide(inverse(X0),X2))),inverse(X0)) = X1,
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(double_divide(inverse(X0),X1),inverse(double_divide(inverse(double_divide(inverse(X2),X3)),X1))),X3),inverse(X0)) = X2,
inference(superposition,[],[f1,f9]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(inverse(inverse(X3)),X2))))),inverse(X0)))) = X3,
inference(superposition,[],[f8,f8]) ).
fof(f28,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,X3),inverse(double_divide(inverse(X0),inverse(double_divide(X2,inverse(double_divide(inverse(inverse(X4)),X3))))))))),inverse(double_divide(X1,inverse(X0)))) = X4,
inference(superposition,[],[f1,f8]) ).
fof(f30,plain,
! [X3,X0] : double_divide(X0,inverse(double_divide(inverse(X3),inverse(X0)))) = X3,
inference(forward_demodulation,[],[f22,f1]) ).
fof(f34,plain,
! [X0,X1] : double_divide(double_divide(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[],[f1,f30]) ).
fof(f42,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,inverse(double_divide(inverse(X0),inverse(inverse(X2))))),inverse(double_divide(X1,inverse(X0)))) = X2,
inference(superposition,[],[f1,f30]) ).
fof(f79,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f30,f34]) ).
fof(f149,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))),inverse(X0)),inverse(X0)) = X1,
inference(superposition,[],[f9,f79]) ).
fof(f166,plain,
! [X0,X1] : double_divide(double_divide(X1,inverse(X0)),inverse(X0)) = X1,
inference(forward_demodulation,[],[f149,f79]) ).
fof(f186,plain,
! [X2,X3,X0,X1,X4,X5] : double_divide(double_divide(X1,inverse(double_divide(double_divide(double_divide(double_divide(inverse(X0),X2),inverse(double_divide(inverse(double_divide(inverse(inverse(X3)),X4)),X2))),X4),inverse(double_divide(inverse(X5),inverse(X0)))))),inverse(double_divide(X1,inverse(X5)))) = X3,
inference(superposition,[],[f28,f9]) ).
fof(f191,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X1,inverse(double_divide(double_divide(double_divide(inverse(inverse(X2)),X3),X3),inverse(X0)))),inverse(double_divide(X1,inverse(X0)))) = X2,
inference(superposition,[],[f28,f79]) ).
fof(f230,plain,
! [X2,X0,X1] : double_divide(X1,X2) = double_divide(X0,inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))),
inference(superposition,[],[f166,f1]) ).
fof(f233,plain,
! [X2,X0,X1] : double_divide(double_divide(inverse(X0),X1),inverse(double_divide(inverse(X2),X1))) = double_divide(X0,inverse(X2)),
inference(superposition,[],[f166,f9]) ).
fof(f234,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(inverse(X1),X2),inverse(double_divide(inverse(double_divide(inverse(X0),X3)),X2))),X3) = double_divide(X0,inverse(X1)),
inference(superposition,[],[f166,f10]) ).
fof(f259,plain,
! [X3,X0,X1,X5] : double_divide(double_divide(X1,inverse(double_divide(double_divide(inverse(X3),inverse(X0)),inverse(double_divide(inverse(X5),inverse(X0)))))),inverse(double_divide(X1,inverse(X5)))) = X3,
inference(backward_demodulation,[],[f186,f234]) ).
fof(f306,plain,
! [X3,X1,X5] : double_divide(double_divide(X1,inverse(double_divide(X3,inverse(X5)))),inverse(double_divide(X1,inverse(X5)))) = X3,
inference(forward_demodulation,[],[f259,f233]) ).
fof(f321,plain,
! [X2,X3] : double_divide(double_divide(inverse(inverse(X2)),X3),X3) = X2,
inference(backward_demodulation,[],[f191,f306]) ).
fof(f404,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f166,f321]) ).
fof(f449,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,X3),inverse(double_divide(inverse(X0),inverse(double_divide(X2,inverse(double_divide(X4,X3))))))))),inverse(double_divide(X1,inverse(X0)))) = X4,
inference(backward_demodulation,[],[f28,f404]) ).
fof(f454,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,inverse(double_divide(inverse(X0),X2))),inverse(double_divide(X1,inverse(X0)))) = X2,
inference(backward_demodulation,[],[f42,f404]) ).
fof(f523,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(X1,inverse(double_divide(X0,inverse(double_divide(inverse(X3),inverse(double_divide(inverse(X0),inverse(double_divide(X4,inverse(double_divide(X2,inverse(X2)))))))))))),inverse(double_divide(X1,inverse(X3)))) = X4,
inference(superposition,[],[f449,f79]) ).
fof(f578,plain,
! [X2,X3,X1,X4] : double_divide(double_divide(X1,inverse(double_divide(inverse(X3),inverse(double_divide(X4,inverse(double_divide(X2,inverse(X2)))))))),inverse(double_divide(X1,inverse(X3)))) = X4,
inference(forward_demodulation,[],[f523,f230]) ).
fof(f582,plain,
! [X2,X4] : inverse(double_divide(X4,inverse(double_divide(X2,inverse(X2))))) = X4,
inference(forward_demodulation,[],[f578,f454]) ).
fof(f583,plain,
~ sP0(a2),
inference(backward_demodulation,[],[f6,f582]) ).
fof(f584,plain,
$false,
inference(forward_subsumption_resolution,[],[f583,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP598-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:09:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.80/1.45 % (277528)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.80/1.45 % (277551)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3702464808:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.80/1.45 % (277549)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=2305049922:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.80/1.45 % (277548)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=2148917805:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.80/1.45 % (277552)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=691275214:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.80/1.45 % (277551)First to succeed.
% 2.80/1.45 % (277551)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-277528"
% 2.80/1.45 % (277550)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2152357392:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.80/1.45 % (277554)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2488693135:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.80/1.45 % (277552)Also succeeded, but the first one will report.
% 2.80/1.45 % (277554)Also succeeded, but the first one will report.
% 2.80/1.45 % (277553)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1140341016:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.80/1.45 % (277551)Refutation found. Thanks to Tanya!
% 2.80/1.45 % SZS status Unsatisfiable for theBenchmark
% 2.80/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.45 % (277551)------------------------------
% 2.80/1.45 % (277551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.45 % (277551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.45 % (277551)CaDiCaL version: 2.1.3
% 2.80/1.45 % (277551)Termination reason: Refutation
% 2.80/1.45 % (277551)Time elapsed: 0.043 s
% 2.80/1.45 % (277551)Peak memory usage: 89 MB
% 2.80/1.45 % (277551)Instructions burned: 132 (million)
% 2.80/1.45 % (277551)------------------------------
% 2.80/1.45 % (277551)------------------------------
% 2.80/1.45 % (277528)Success in time 0.295 s
% 2.80/1.45 % Vampire exiting
%------------------------------------------------------------------------------