%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP107-1 : 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 : 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 10:12:36 AM UTC 2026
% Result : Unsatisfiable 10.84s 2.23s
% Output : Refutation 11.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 7
% Syntax : Number of formulae : 119 ( 73 unt; 4 def)
% Number of atoms : 175 ( 112 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 53 ~; 52 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 178 ( 0 sgn 178 !; 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(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
fof(f7,definition,
( spl0_1
<=> inverse(double_divide(b4,a4)) = inverse(double_divide(a4,b4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,definition,
( spl0_2
<=> inverse(double_divide(c3,inverse(double_divide(b3,a3)))) = inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> a2 = inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f19,definition,
( spl0_4
<=> inverse(double_divide(a1,inverse(a1))) = inverse(double_divide(b1,inverse(b1))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f21,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| spl0_4 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f5,f19,f15,f11,f7]) ).
fof(f23,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(f24,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(f25,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,f24]) ).
fof(f37,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,[],[f23,f23]) ).
fof(f45,plain,
! [X3,X0] : double_divide(X0,inverse(double_divide(inverse(X3),inverse(X0)))) = X3,
inference(forward_demodulation,[],[f37,f1]) ).
fof(f47,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),inverse(inverse(X1))),inverse(X0)) = X1,
inference(superposition,[],[f45,f45]) ).
fof(f49,plain,
! [X0,X1] : double_divide(double_divide(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[],[f1,f45]) ).
fof(f57,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,f45]) ).
fof(f66,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(double_divide(inverse(X0),X1)),inverse(inverse(X2))),X1),inverse(X2)) = X0,
inference(superposition,[],[f25,f49]) ).
fof(f68,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X2,inverse(X2)),X1),inverse(double_divide(inverse(X3),inverse(double_divide(inverse(X0),X1))))))) = X3,
inference(superposition,[],[f23,f49]) ).
fof(f70,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f45,f49]) ).
fof(f87,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,inverse(double_divide(inverse(X2),inverse(double_divide(X1,inverse(X1)))))),inverse(X2)) = X0,
inference(superposition,[],[f24,f70]) ).
fof(f90,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(X0),inverse(double_divide(inverse(X2),inverse(double_divide(X1,inverse(X1)))))))) = X2,
inference(superposition,[],[f1,f70]) ).
fof(f93,plain,
! [X2,X0] : double_divide(X0,inverse(double_divide(inverse(X0),inverse(X2)))) = X2,
inference(forward_demodulation,[],[f90,f70]) ).
fof(f95,plain,
! [X2,X0] : double_divide(double_divide(X0,inverse(X2)),inverse(X2)) = X0,
inference(forward_demodulation,[],[f87,f70]) ).
fof(f98,plain,
! [X2,X0,X1] : double_divide(X1,X2) = double_divide(X0,inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))),
inference(superposition,[],[f95,f1]) ).
fof(f99,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(X0,inverse(X0)),
inference(superposition,[],[f95,f49]) ).
fof(f166,plain,
! [X0,X1] : double_divide(X1,inverse(X0)) = double_divide(inverse(X0),inverse(inverse(X1))),
inference(superposition,[],[f93,f45]) ).
fof(f175,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(inverse(inverse(X2)),X1),inverse(double_divide(inverse(X0),X1))))) = X2,
inference(superposition,[],[f23,f93]) ).
fof(f176,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f70,f93]) ).
fof(f195,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),X1),inverse(X0)) = X1,
inference(backward_demodulation,[],[f47,f176]) ).
fof(f198,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,[],[f57,f176]) ).
fof(f199,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(double_divide(inverse(X0),X1)),X2),X1),inverse(X2)) = X0,
inference(backward_demodulation,[],[f66,f176]) ).
fof(f207,plain,
! [X2,X1] : double_divide(double_divide(inverse(inverse(X2)),X1),X1) = X2,
inference(forward_demodulation,[],[f175,f98]) ).
fof(f208,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = double_divide(X1,inverse(X0)),
inference(forward_demodulation,[],[f166,f176]) ).
fof(f210,plain,
! [X2,X1] : double_divide(double_divide(X2,X1),X1) = X2,
inference(forward_demodulation,[],[f207,f176]) ).
fof(f234,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X0))) = X1,
inference(superposition,[],[f45,f176]) ).
fof(f235,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,inverse(double_divide(X0,inverse(X1)))),
inference(superposition,[],[f45,f176]) ).
fof(f258,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(superposition,[],[f195,f176]) ).
fof(f262,plain,
! [X0,X1] : inverse(X0) = double_divide(X0,double_divide(X1,inverse(X1))),
inference(superposition,[],[f258,f49]) ).
fof(f266,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[],[f258,f210]) ).
fof(f267,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(superposition,[],[f258,f258]) ).
fof(f269,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[],[f210,f258]) ).
fof(f285,plain,
! [X0,X1] : double_divide(inverse(X1),double_divide(X0,inverse(X0))) = X1,
inference(superposition,[],[f267,f99]) ).
fof(f306,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| spl0_1 ),
inference(superposition,[],[f9,f269]) ).
fof(f318,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f306]) ).
fof(f319,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f320,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f269]) ).
fof(f321,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3))))
| spl0_2 ),
inference(forward_demodulation,[],[f320,f269]) ).
fof(f322,plain,
( inverse(double_divide(a3,inverse(double_divide(b3,c3)))) != inverse(double_divide(c3,inverse(double_divide(a3,b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f321,f269]) ).
fof(f456,plain,
( ! [X0] : inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != double_divide(double_divide(a3,inverse(double_divide(b3,c3))),double_divide(X0,inverse(X0)))
| spl0_2 ),
inference(superposition,[],[f322,f262]) ).
fof(f1314,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(X1),inverse(double_divide(X0,X1))),
inference(superposition,[],[f234,f176]) ).
fof(f1350,plain,
! [X0,X1] : inverse(double_divide(inverse(X0),X1)) = double_divide(X0,inverse(X1)),
inference(superposition,[],[f258,f234]) ).
fof(f1352,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X2,inverse(X2)),X1),inverse(double_divide(inverse(X3),double_divide(X0,inverse(X1))))))) = X3,
inference(backward_demodulation,[],[f68,f1350]) ).
fof(f1361,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(X0,inverse(X2))),inverse(double_divide(X1,inverse(X0)))) = X2,
inference(backward_demodulation,[],[f198,f1350]) ).
fof(f1362,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(double_divide(X0,inverse(X1)),X2),X1),inverse(X2)) = X0,
inference(backward_demodulation,[],[f199,f1350]) ).
fof(f1418,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(double_divide(X0,inverse(X1)),X2)),inverse(X2)) = X0,
inference(forward_demodulation,[],[f1362,f269]) ).
fof(f1424,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X2,inverse(X2)),X1),double_divide(X3,inverse(double_divide(X0,inverse(X1))))))) = X3,
inference(forward_demodulation,[],[f1352,f1350]) ).
fof(f1518,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = inverse(double_divide(X0,inverse(X1))),
inference(superposition,[],[f258,f235]) ).
fof(f1531,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(X0,inverse(X2))),double_divide(inverse(X1),X0)) = X2,
inference(backward_demodulation,[],[f1361,f1518]) ).
fof(f1533,plain,
! [X2,X3,X0,X1] : double_divide(X0,inverse(double_divide(double_divide(double_divide(X2,inverse(X2)),X1),double_divide(X3,double_divide(inverse(X0),X1))))) = X3,
inference(backward_demodulation,[],[f1424,f1518]) ).
fof(f1583,plain,
( ! [X0] : double_divide(double_divide(a3,inverse(double_divide(b3,c3))),double_divide(X0,inverse(X0))) != double_divide(inverse(c3),double_divide(a3,b3))
| spl0_2 ),
inference(backward_demodulation,[],[f456,f1518]) ).
fof(f1618,plain,
( ! [X0] : double_divide(double_divide(a3,inverse(double_divide(b3,c3))),double_divide(X0,inverse(X0))) != double_divide(double_divide(a3,b3),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f1583,f269]) ).
fof(f1739,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(X0)) = inverse(double_divide(X0,X1)),
inference(superposition,[],[f266,f1314]) ).
fof(f1761,plain,
! [X2,X3,X0,X1] : double_divide(X0,double_divide(inverse(double_divide(X3,double_divide(inverse(X0),X1))),inverse(double_divide(double_divide(X2,inverse(X2)),X1)))) = X3,
inference(backward_demodulation,[],[f1533,f1739]) ).
fof(f1787,plain,
( ! [X0] : double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(double_divide(a3,double_divide(inverse(c3),inverse(b3))),double_divide(X0,inverse(X0)))
| spl0_2 ),
inference(backward_demodulation,[],[f1618,f1739]) ).
fof(f1820,plain,
( ! [X0] : double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(double_divide(a3,double_divide(inverse(b3),inverse(c3))),double_divide(X0,inverse(X0)))
| spl0_2 ),
inference(forward_demodulation,[],[f1787,f208]) ).
fof(f1846,plain,
! [X2,X3,X0,X1] : double_divide(X0,double_divide(inverse(double_divide(X3,double_divide(inverse(X0),X1))),double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))))) = X3,
inference(forward_demodulation,[],[f1761,f1739]) ).
fof(f1894,plain,
! [X2,X3,X0,X1] : double_divide(X0,double_divide(inverse(double_divide(X3,double_divide(inverse(X0),X1))),double_divide(inverse(X1),double_divide(inverse(inverse(X2)),inverse(X2))))) = X3,
inference(forward_demodulation,[],[f1846,f1739]) ).
fof(f1934,plain,
! [X2,X3,X0,X1] : double_divide(X0,double_divide(inverse(double_divide(X3,double_divide(inverse(X0),X1))),double_divide(inverse(X1),double_divide(inverse(X2),inverse(inverse(X2)))))) = X3,
inference(forward_demodulation,[],[f1894,f208]) ).
fof(f1963,plain,
! [X3,X0,X1] : double_divide(X0,double_divide(inverse(double_divide(X3,double_divide(inverse(X0),X1))),X1)) = X3,
inference(forward_demodulation,[],[f1934,f285]) ).
fof(f1988,plain,
! [X3,X0,X1] : double_divide(X0,double_divide(X1,inverse(double_divide(X3,double_divide(inverse(X0),X1))))) = X3,
inference(forward_demodulation,[],[f1963,f269]) ).
fof(f2006,plain,
! [X3,X0,X1] : double_divide(X0,double_divide(X1,double_divide(inverse(double_divide(inverse(X0),X1)),inverse(X3)))) = X3,
inference(forward_demodulation,[],[f1988,f1739]) ).
fof(f2024,plain,
! [X3,X0,X1] : double_divide(X0,double_divide(X1,double_divide(double_divide(inverse(X1),inverse(inverse(X0))),inverse(X3)))) = X3,
inference(forward_demodulation,[],[f2006,f1739]) ).
fof(f2035,plain,
! [X3,X0,X1] : double_divide(X0,double_divide(X1,double_divide(double_divide(inverse(X1),X0),inverse(X3)))) = X3,
inference(forward_demodulation,[],[f2024,f176]) ).
fof(f2323,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(X2,inverse(X0))) = double_divide(X0,double_divide(inverse(X1),X2)),
inference(superposition,[],[f210,f1531]) ).
fof(f2326,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(X2,inverse(X0))) = double_divide(double_divide(inverse(X1),X2),X0),
inference(superposition,[],[f267,f1531]) ).
fof(f2837,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(X0,inverse(inverse(X1))),X2),double_divide(X1,X0)) = X2,
inference(superposition,[],[f2035,f1418]) ).
fof(f2884,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),double_divide(double_divide(X0,inverse(inverse(X1))),X2)) = X2,
inference(forward_demodulation,[],[f2837,f269]) ).
fof(f2900,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),double_divide(double_divide(X0,X1),X2)) = X2,
inference(forward_demodulation,[],[f2884,f176]) ).
fof(f2996,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != inverse(double_divide(double_divide(inverse(b3),inverse(c3)),a3))
| spl0_2 ),
inference(superposition,[],[f1820,f2900]) ).
fof(f3008,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(X1,X2)) = double_divide(double_divide(X2,X1),X0),
inference(superposition,[],[f258,f2900]) ).
fof(f3009,plain,
! [X2,X0,X1] : double_divide(double_divide(X2,X1),X0) = double_divide(double_divide(X1,X2),X0),
inference(superposition,[],[f266,f2900]) ).
fof(f3025,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(a3),inverse(double_divide(inverse(b3),inverse(c3))))
| spl0_2 ),
inference(forward_demodulation,[],[f2996,f1739]) ).
fof(f3068,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(a3),double_divide(inverse(inverse(c3)),inverse(inverse(b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f3025,f1739]) ).
fof(f3082,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(b3),double_divide(inverse(inverse(a3)),inverse(inverse(c3))))
| spl0_2 ),
inference(forward_demodulation,[],[f3068,f2323]) ).
fof(f3087,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(double_divide(inverse(inverse(b3)),inverse(inverse(a3))),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f3082,f2326]) ).
fof(f3090,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(double_divide(inverse(inverse(a3)),inverse(inverse(b3))),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f3087,f3009]) ).
fof(f3093,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(c3),double_divide(inverse(inverse(b3)),inverse(inverse(a3))))
| spl0_2 ),
inference(forward_demodulation,[],[f3090,f3008]) ).
fof(f3096,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(c3),double_divide(inverse(inverse(a3)),inverse(inverse(b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f3093,f208]) ).
fof(f3098,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(c3),double_divide(inverse(inverse(a3)),b3))
| spl0_2 ),
inference(forward_demodulation,[],[f3096,f176]) ).
fof(f3099,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(c3),double_divide(b3,inverse(inverse(a3))))
| spl0_2 ),
inference(forward_demodulation,[],[f3098,f269]) ).
fof(f3100,plain,
( double_divide(double_divide(a3,b3),inverse(c3)) != double_divide(inverse(c3),double_divide(b3,a3))
| spl0_2 ),
inference(forward_demodulation,[],[f3099,f176]) ).
fof(f3101,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f3100,f3008]) ).
fof(f3102,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f3101]) ).
fof(f3104,plain,
( a2 != double_divide(inverse(inverse(double_divide(b2,inverse(b2)))),inverse(a2))
| spl0_3 ),
inference(forward_demodulation,[],[f17,f1739]) ).
fof(f3106,plain,
( a2 != double_divide(inverse(a2),inverse(inverse(double_divide(b2,inverse(b2)))))
| spl0_3 ),
inference(forward_demodulation,[],[f3104,f208]) ).
fof(f3108,plain,
( a2 != double_divide(inverse(a2),double_divide(b2,inverse(b2)))
| spl0_3 ),
inference(forward_demodulation,[],[f3106,f176]) ).
fof(f3110,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f3108,f285]) ).
fof(f3111,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f3110]) ).
fof(f3118,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(inverse(b1)),inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f21,f1739]) ).
fof(f3120,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),inverse(inverse(b1)))
| spl0_4 ),
inference(forward_demodulation,[],[f3118,f208]) ).
fof(f3122,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),b1)
| spl0_4 ),
inference(forward_demodulation,[],[f3120,f176]) ).
fof(f3123,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f3122,f269]) ).
fof(f3124,plain,
( double_divide(b1,inverse(b1)) != double_divide(inverse(inverse(a1)),inverse(a1))
| spl0_4 ),
inference(forward_demodulation,[],[f3123,f1739]) ).
fof(f3125,plain,
( double_divide(b1,inverse(b1)) != double_divide(inverse(a1),inverse(inverse(a1)))
| spl0_4 ),
inference(forward_demodulation,[],[f3124,f208]) ).
fof(f3126,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3125,f99]) ).
fof(f3127,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f3126]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f319]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f3102]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f3111]) ).
cnf(s6,plain,
spl0_4,
inference(sat_conversion,[],[f3127]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5,s4,s3]) ).
fof(f3128,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:21:10 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 10.84/2.23 % (240627)Input is clausal, will run a generic CNF schedule.
% 10.84/2.23 % (240648)dis-21_1_sil=8000:lcm=predicate:random_seed=437553602:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 10.84/2.23 % (240646)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2119899482:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.84/2.23 % (240645)lrs+10_1_sil=8000:sp=occurrence:random_seed=2879460606:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.84/2.23 % (240642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3399047671:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.84/2.23 % (240644)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4016675464:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.84/2.23 % (240643)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=471357916:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.84/2.23 % (240648)Refutation not found, incomplete strategy
% 10.84/2.23 % (240648)------------------------------
% 10.84/2.23 % (240648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240648)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240648)Termination reason: Refutation not found, incomplete strategy
% 10.84/2.23 % (240648)Time elapsed: 0.001 s
% 10.84/2.23 % (240648)Peak memory usage: 88 MB
% 10.84/2.23 % (240647)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3599593276:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.84/2.23 % (240645)Instruction limit reached!
% 10.84/2.23 % (240645)------------------------------
% 10.84/2.23 % (240645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240645)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240645)Termination reason: Instruction limit
% 10.84/2.23 % (240645)Termination phase: Saturation
% 10.84/2.23 % (240645)Time elapsed: 0.065 s
% 10.84/2.23 % (240645)Peak memory usage: 90 MB
% 10.84/2.23 % (240645)Instructions burned: 107 (million)
% 10.84/2.23 % (240646)Instruction limit reached!
% 10.84/2.23 % (240646)------------------------------
% 10.84/2.23 % (240646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240646)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240646)Termination reason: Instruction limit
% 10.84/2.23 % (240646)Termination phase: Saturation
% 10.84/2.23 % (240646)Time elapsed: 0.074 s
% 10.84/2.23 % (240646)Peak memory usage: 89 MB
% 10.84/2.23 % (240646)Instructions burned: 115 (million)
% 10.84/2.23 % (240647)Instruction limit reached!
% 10.84/2.23 % (240647)------------------------------
% 10.84/2.23 % (240647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240647)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240647)Termination reason: Instruction limit
% 10.84/2.23 % (240647)Termination phase: Saturation
% 10.84/2.23 % (240647)Time elapsed: 0.128 s
% 10.84/2.23 % (240647)Peak memory usage: 90 MB
% 10.84/2.23 % (240647)Instructions burned: 180 (million)
% 10.84/2.23 % (240669)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2275519421:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 10.84/2.23 % (240669)Refutation not found, incomplete strategy
% 10.84/2.23 % (240669)------------------------------
% 10.84/2.23 % (240669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240669)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240669)Termination reason: Refutation not found, incomplete strategy
% 10.84/2.23 % (240669)Time elapsed: 0.002 s
% 10.84/2.23 % (240669)Peak memory usage: 88 MB
% 10.84/2.23 % (240670)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1685811902:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 10.84/2.23 % (240648)------------------------------
% 10.84/2.23 % (240648)------------------------------
% 10.84/2.23 % (240670)Refutation not found, incomplete strategy
% 10.84/2.23 % (240670)------------------------------
% 10.84/2.23 % (240670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240670)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240670)Termination reason: Refutation not found, incomplete strategy
% 10.84/2.23 % (240670)Time elapsed: 0.002 s
% 10.84/2.23 % (240670)Peak memory usage: 88 MB
% 10.84/2.23 % (240671)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=577065543:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 10.84/2.23 % (240671)Refutation not found, incomplete strategy
% 10.84/2.23 % (240671)------------------------------
% 10.84/2.23 % (240671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240671)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240671)Termination reason: Refutation not found, incomplete strategy
% 10.84/2.23 % (240671)Time elapsed: 0.001 s
% 10.84/2.23 % (240671)Peak memory usage: 88 MB
% 10.84/2.23 % (240682)lrs+10_64_to=lpo:sil=8000:random_seed=2585728046:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 10.84/2.23 % (240669)------------------------------
% 10.84/2.23 % (240669)------------------------------
% 10.84/2.23 % (240670)------------------------------
% 10.84/2.23 % (240670)------------------------------
% 10.84/2.23 % (240682)Instruction limit reached!
% 10.84/2.23 % (240682)------------------------------
% 10.84/2.23 % (240682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240682)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240682)Termination reason: Instruction limit
% 10.84/2.23 % (240682)Termination phase: Saturation
% 10.84/2.23 % (240682)Time elapsed: 0.118 s
% 10.84/2.23 % (240682)Peak memory usage: 89 MB
% 10.84/2.23 % (240682)Instructions burned: 126 (million)
% 10.84/2.23 % (240671)------------------------------
% 10.84/2.23 % (240671)------------------------------
% 10.84/2.23 % (240696)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3882402780:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 10.84/2.23 % (240697)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1661436837:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 10.84/2.23 % (240701)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1726700398:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2991 on theBenchmark for (2991ds/106Mi)
% 10.84/2.23 % (240698)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3673675490:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 10.84/2.23 % (240701)Instruction limit reached!
% 10.84/2.23 % (240701)------------------------------
% 10.84/2.23 % (240701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240701)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240701)Termination reason: Instruction limit
% 10.84/2.23 % (240701)Termination phase: Saturation
% 10.84/2.23 % (240701)Time elapsed: 0.048 s
% 10.84/2.23 % (240701)Peak memory usage: 89 MB
% 10.84/2.23 % (240701)Instructions burned: 108 (million)
% 10.84/2.23 % (240696)First to succeed.
% 10.84/2.23 % (240696)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-240627"
% 10.84/2.23 % (240697)Instruction limit reached!
% 10.84/2.23 % (240697)------------------------------
% 10.84/2.23 % (240697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240697)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240697)Termination reason: Instruction limit
% 10.84/2.23 % (240697)Termination phase: Saturation
% 10.84/2.23 % (240697)Time elapsed: 0.147 s
% 10.84/2.23 % (240697)Peak memory usage: 92 MB
% 10.84/2.23 % (240697)Instructions burned: 157 (million)
% 10.84/2.23 % (240644)Also succeeded, but the first one will report.
% 10.84/2.23 % (240643)Also succeeded, but the first one will report.
% 10.84/2.23 % (240710)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3816542761:i=107_2988 on theBenchmark for (2988ds/107Mi)
% 10.84/2.23 % (240710)Refutation not found, incomplete strategy
% 10.84/2.23 % (240710)------------------------------
% 10.84/2.23 % (240710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.84/2.23 % (240710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.84/2.23 % (240710)CaDiCaL version: 2.1.3
% 10.84/2.23 % (240710)Termination reason: Refutation not found, incomplete strategy
% 10.84/2.23 % (240710)Time elapsed: 0.002 s
% 10.84/2.23 % (240710)Peak memory usage: 88 MB
% 10.84/2.23 % (240714)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3452343376:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2987 on theBenchmark for (2987ds/242Mi)
% 10.84/2.23 % (240696)Refutation found. Thanks to Tanya!
% 10.84/2.23 % SZS status Unsatisfiable for theBenchmark
% 10.84/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 11.65/2.48 % (240696)------------------------------
% 11.65/2.48 % (240696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.65/2.48 % (240696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.65/2.48 % (240696)CaDiCaL version: 2.1.3
% 11.65/2.48 % (240696)Termination reason: Refutation
% 11.65/2.48 % (240696)Time elapsed: 0.173 s
% 11.65/2.48 % (240696)Peak memory usage: 90 MB
% 11.65/2.48 % (240696)Instructions burned: 170 (million)
% 11.65/2.48 % (240696)------------------------------
% 11.65/2.48 % (240696)------------------------------
% 11.65/2.48 % (240627)Success in time 1.612 s
% 11.65/2.48 % Vampire exiting
%------------------------------------------------------------------------------