%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP106-1 : 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 : n020.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 5.18s 1.66s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 123 ( 82 unt; 4 def)
% Number of atoms : 174 ( 116 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 48 ~; 47 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 10 ( 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 : 227 ( 0 sgn 227 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(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(f24,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(double_divide(X1,X2),inverse(double_divide(X0,X2))),X0)) = X1,
inference(superposition,[],[f1,f1]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(double_divide(X0,X3))))),X0),double_divide(X2,X3))) = X1,
inference(superposition,[],[f24,f1]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,X3),inverse(double_divide(X2,X3))) = inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,X0)))),
inference(superposition,[],[f1,f24]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4] : inverse(double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,X0))),double_divide(X3,X4)),double_divide(X2,inverse(double_divide(X3,inverse(double_divide(X0,X4))))))) = X1,
inference(superposition,[],[f25,f1]) ).
fof(f56,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,X3),inverse(double_divide(X2,X3))) = inverse(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X1))))),
inference(superposition,[],[f27,f27]) ).
fof(f61,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X2)))),X1)) = X2,
inference(superposition,[],[f24,f27]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] : double_divide(X2,X4) = inverse(double_divide(double_divide(X3,inverse(double_divide(X1,X4))),inverse(double_divide(X3,inverse(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X2))))))))),
inference(superposition,[],[f1,f27]) ).
fof(f75,plain,
! [X2,X0,X1] : double_divide(double_divide(inverse(double_divide(X0,X1)),X2),inverse(double_divide(X1,X2))) = X0,
inference(superposition,[],[f1,f27]) ).
fof(f103,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(double_divide(inverse(double_divide(X0,X1)),X2),X2),inverse(X0))) = X1,
inference(superposition,[],[f1,f75]) ).
fof(f104,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X0,X1)),inverse(double_divide(X2,X3))) = inverse(double_divide(double_divide(X0,X2),double_divide(X1,X3))),
inference(superposition,[],[f25,f75]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4] : double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X0))),X2)),inverse(double_divide(double_divide(X3,X4),inverse(double_divide(X3,inverse(double_divide(X0,X4))))))) = X1,
inference(backward_demodulation,[],[f34,f104]) ).
fof(f146,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X0))),X2)),X0) = X1,
inference(forward_demodulation,[],[f134,f1]) ).
fof(f184,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X0,inverse(double_divide(X3,X2))),X3)) = inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X0))))),
inference(superposition,[],[f1,f146]) ).
fof(f185,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X0,inverse(double_divide(X1,X2))),X1)) = inverse(double_divide(double_divide(X0,inverse(double_divide(X3,X2))),X3)),
inference(superposition,[],[f24,f146]) ).
fof(f205,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X1,inverse(double_divide(X0,X2)))) = inverse(double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),X0)),X3)),
inference(superposition,[],[f61,f1]) ).
fof(f211,plain,
! [X2,X0,X1] : inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),X2)),X1)))) = X2,
inference(superposition,[],[f61,f24]) ).
fof(f237,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(inverse(double_divide(X1,X0)),inverse(double_divide(inverse(X1),X2))),
inference(superposition,[],[f146,f103]) ).
fof(f239,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(inverse(double_divide(X2,X0)),X3),X3) = inverse(double_divide(double_divide(X1,inverse(X2)),inverse(double_divide(X1,X0)))),
inference(superposition,[],[f1,f103]) ).
fof(f265,plain,
! [X2,X3,X0,X1,X4] : double_divide(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X2,X3),X0)),X3))),X0) = inverse(double_divide(double_divide(X4,X2),inverse(double_divide(X4,X1)))),
inference(superposition,[],[f27,f211]) ).
fof(f269,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(double_divide(double_divide(X1,X2),X0)),X2)) = inverse(double_divide(double_divide(double_divide(X0,X3),X3),inverse(X1))),
inference(superposition,[],[f103,f211]) ).
fof(f281,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(inverse(double_divide(double_divide(X1,X2),X0)),X2)),X3) = double_divide(X0,inverse(double_divide(inverse(X1),X3))),
inference(superposition,[],[f237,f211]) ).
fof(f293,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
inference(superposition,[],[f75,f237]) ).
fof(f294,plain,
! [X2,X0,X1] : inverse(double_divide(X2,X0)) = double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1),
inference(superposition,[],[f146,f237]) ).
fof(f335,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(X1),X2),inverse(double_divide(X0,X2))),X0) = X1,
inference(superposition,[],[f293,f1]) ).
fof(f387,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
inference(superposition,[],[f335,f27]) ).
fof(f412,plain,
! [X2,X0] : inverse(double_divide(double_divide(X0,inverse(X2)),X0)) = X2,
inference(forward_demodulation,[],[f387,f294]) ).
fof(f430,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f412,f75]) ).
fof(f434,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(superposition,[],[f24,f412]) ).
fof(f436,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,X0)))) = double_divide(X2,inverse(X0)),
inference(superposition,[],[f1,f412]) ).
fof(f441,plain,
! [X2,X0,X1] : double_divide(X1,inverse(X0)) = double_divide(double_divide(X0,X2),inverse(double_divide(X1,X2))),
inference(superposition,[],[f75,f412]) ).
fof(f456,plain,
! [X2,X3,X1] : double_divide(double_divide(X2,X3),inverse(double_divide(X2,X3))) = inverse(double_divide(X1,inverse(X1))),
inference(backward_demodulation,[],[f56,f436]) ).
fof(f460,plain,
! [X2,X3,X0] : double_divide(double_divide(inverse(double_divide(X2,X0)),X3),X3) = double_divide(inverse(X2),inverse(X0)),
inference(backward_demodulation,[],[f239,f436]) ).
fof(f471,plain,
! [X2,X3,X1,X4] : double_divide(X2,X4) = inverse(double_divide(double_divide(X3,inverse(double_divide(X1,X4))),inverse(double_divide(X3,inverse(double_divide(X1,inverse(X2))))))),
inference(backward_demodulation,[],[f67,f436]) ).
fof(f491,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X2,X3),X0)),X3))),X0) = double_divide(X2,inverse(X1)),
inference(backward_demodulation,[],[f265,f436]) ).
fof(f510,plain,
! [X2,X3,X0] : inverse(double_divide(double_divide(X0,inverse(double_divide(X3,X2))),X3)) = double_divide(X2,inverse(inverse(X0))),
inference(backward_demodulation,[],[f184,f436]) ).
fof(f515,plain,
! [X2,X0,X1] : inverse(double_divide(X0,inverse(X1))) = inverse(double_divide(inverse(double_divide(double_divide(X1,X2),X0)),X2)),
inference(backward_demodulation,[],[f269,f434]) ).
fof(f545,plain,
! [X2,X3,X0] : double_divide(X2,X0) = inverse(double_divide(double_divide(X0,inverse(double_divide(X3,X2))),X3)),
inference(forward_demodulation,[],[f510,f430]) ).
fof(f556,plain,
! [X2,X1,X4] : double_divide(X2,X4) = double_divide(inverse(double_divide(X1,X4)),inverse(inverse(double_divide(X1,inverse(X2))))),
inference(forward_demodulation,[],[f471,f436]) ).
fof(f561,plain,
! [X2,X0] : inverse(double_divide(X2,X0)) = double_divide(inverse(X2),inverse(X0)),
inference(forward_demodulation,[],[f460,f434]) ).
fof(f563,plain,
! [X2,X1] : inverse(double_divide(X1,inverse(X1))) = double_divide(X2,inverse(X2)),
inference(forward_demodulation,[],[f456,f441]) ).
fof(f577,plain,
! [X3,X0,X1] : double_divide(X0,inverse(double_divide(inverse(X1),X3))) = double_divide(inverse(double_divide(X0,inverse(X1))),X3),
inference(backward_demodulation,[],[f281,f515]) ).
fof(f580,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = double_divide(double_divide(X1,inverse(double_divide(X0,inverse(X2)))),X0),
inference(backward_demodulation,[],[f491,f515]) ).
fof(f583,plain,
! [X2,X0,X1] : inverse(double_divide(X0,inverse(double_divide(X1,X2)))) = inverse(double_divide(X1,inverse(double_divide(X0,X2)))),
inference(backward_demodulation,[],[f205,f515]) ).
fof(f594,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[],[f146,f545]) ).
fof(f597,plain,
! [X2,X3,X0] : double_divide(X2,X0) = inverse(double_divide(double_divide(X0,inverse(double_divide(X3,X2))),X3)),
inference(backward_demodulation,[],[f185,f545]) ).
fof(f609,plain,
! [X2,X1,X4] : double_divide(X2,X4) = double_divide(inverse(double_divide(X1,X4)),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f556,f430]) ).
fof(f649,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(double_divide(inverse(X1),inverse(X0)),inverse(double_divide(inverse(X1),X2))),
inference(backward_demodulation,[],[f237,f561]) ).
fof(f768,plain,
( inverse(double_divide(a4,b4)) != double_divide(inverse(b4),inverse(a4))
| spl0_1 ),
inference(backward_demodulation,[],[f9,f561]) ).
fof(f770,plain,
! [X2,X1] : double_divide(X2,inverse(X2)) = double_divide(inverse(X1),inverse(inverse(X1))),
inference(forward_demodulation,[],[f563,f561]) ).
fof(f780,plain,
! [X2,X0,X1] : inverse(double_divide(X0,inverse(double_divide(X1,X2)))) = double_divide(inverse(X1),inverse(inverse(double_divide(X0,X2)))),
inference(forward_demodulation,[],[f583,f561]) ).
fof(f783,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = double_divide(double_divide(X1,double_divide(inverse(X0),inverse(inverse(X2)))),X0),
inference(forward_demodulation,[],[f580,f561]) ).
fof(f786,plain,
! [X3,X0,X1] : double_divide(X0,inverse(double_divide(inverse(X1),X3))) = double_divide(double_divide(inverse(X0),inverse(inverse(X1))),X3),
inference(forward_demodulation,[],[f577,f561]) ).
fof(f805,plain,
! [X2,X3,X0] : double_divide(X2,X0) = double_divide(inverse(double_divide(X0,inverse(double_divide(X3,X2)))),inverse(X3)),
inference(forward_demodulation,[],[f597,f561]) ).
fof(f810,plain,
! [X2,X1,X4] : double_divide(X2,X4) = double_divide(double_divide(inverse(X1),inverse(X4)),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f609,f561]) ).
fof(f811,plain,
( double_divide(inverse(b4),inverse(a4)) != double_divide(inverse(a4),inverse(b4))
| spl0_1 ),
inference(forward_demodulation,[],[f768,f561]) ).
fof(f924,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(double_divide(inverse(X1),inverse(X0)),double_divide(inverse(inverse(X1)),inverse(X2))),
inference(forward_demodulation,[],[f649,f561]) ).
fof(f964,plain,
! [X2,X1] : double_divide(X2,inverse(X2)) = double_divide(inverse(X1),X1),
inference(forward_demodulation,[],[f770,f430]) ).
fof(f974,plain,
! [X2,X0,X1] : inverse(double_divide(X0,inverse(double_divide(X1,X2)))) = double_divide(inverse(X1),double_divide(X0,X2)),
inference(forward_demodulation,[],[f780,f430]) ).
fof(f977,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = double_divide(double_divide(X1,double_divide(inverse(X0),X2)),X0),
inference(forward_demodulation,[],[f783,f430]) ).
fof(f980,plain,
! [X3,X0,X1] : double_divide(X0,inverse(double_divide(inverse(X1),X3))) = double_divide(double_divide(inverse(X0),X1),X3),
inference(forward_demodulation,[],[f786,f430]) ).
fof(f997,plain,
! [X2,X3,X0] : double_divide(X2,X0) = double_divide(double_divide(inverse(X0),inverse(inverse(double_divide(X3,X2)))),inverse(X3)),
inference(forward_demodulation,[],[f805,f561]) ).
fof(f1099,plain,
! [X2,X0,X1] : double_divide(X0,X2) = double_divide(double_divide(inverse(X1),inverse(X0)),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f924,f430]) ).
fof(f1146,plain,
! [X2,X0,X1] : double_divide(inverse(X1),double_divide(X0,X2)) = double_divide(inverse(X0),inverse(inverse(double_divide(X1,X2)))),
inference(forward_demodulation,[],[f974,f561]) ).
fof(f1150,plain,
! [X3,X0,X1] : double_divide(double_divide(inverse(X0),X1),X3) = double_divide(X0,double_divide(inverse(inverse(X1)),inverse(X3))),
inference(forward_demodulation,[],[f980,f561]) ).
fof(f1165,plain,
! [X2,X3,X0] : double_divide(X2,X0) = double_divide(double_divide(inverse(X0),double_divide(X3,X2)),inverse(X3)),
inference(forward_demodulation,[],[f997,f430]) ).
fof(f1254,plain,
! [X2,X4] : double_divide(X4,X2) = double_divide(X2,X4),
inference(backward_demodulation,[],[f810,f1099]) ).
fof(f1294,plain,
! [X2,X0,X1] : double_divide(inverse(X1),double_divide(X0,X2)) = double_divide(inverse(X0),double_divide(X1,X2)),
inference(forward_demodulation,[],[f1146,f430]) ).
fof(f1296,plain,
! [X3,X0,X1] : double_divide(double_divide(inverse(X0),X1),X3) = double_divide(X0,double_divide(X1,inverse(X3))),
inference(forward_demodulation,[],[f1150,f430]) ).
fof(f1668,plain,
( double_divide(inverse(a4),inverse(b4)) != double_divide(inverse(a4),inverse(b4))
| spl0_1 ),
inference(superposition,[],[f811,f1254]) ).
fof(f1675,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[],[f594,f1254]) ).
fof(f1678,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1668]) ).
fof(f1679,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1678]) ).
fof(f1681,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(inverse(double_divide(c3,b3))),inverse(a3))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f561]) ).
fof(f1683,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),inverse(inverse(double_divide(c3,b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f1681,f1254]) ).
fof(f1684,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3))
| spl0_2 ),
inference(forward_demodulation,[],[f1683,f430]) ).
fof(f1685,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(double_divide(c3,b3),inverse(a3))
| spl0_2 ),
inference(forward_demodulation,[],[f1684,f1254]) ).
fof(f1686,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(double_divide(b3,c3),inverse(a3))
| spl0_2 ),
inference(forward_demodulation,[],[f1685,f1254]) ).
fof(f1687,plain,
( double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3))))
| spl0_2 ),
inference(forward_demodulation,[],[f1686,f561]) ).
fof(f1688,plain,
( double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(inverse(c3),double_divide(b3,a3))
| spl0_2 ),
inference(forward_demodulation,[],[f1687,f430]) ).
fof(f1689,plain,
( double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(double_divide(b3,a3),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f1688,f1254]) ).
fof(f1690,plain,
( double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(double_divide(a3,b3),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f1689,f1254]) ).
fof(f1769,plain,
! [X0,X1] : double_divide(inverse(X1),double_divide(X0,inverse(X0))) = X1,
inference(superposition,[],[f1675,f964]) ).
fof(f1771,plain,
! [X0,X1] : double_divide(X0,inverse(X0)) = double_divide(X1,inverse(X1)),
inference(superposition,[],[f1254,f964]) ).
fof(f2205,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),inverse(X2)) = double_divide(inverse(X1),double_divide(X2,X0)),
inference(superposition,[],[f434,f1165]) ).
fof(f2617,plain,
( ! [X0] : double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(double_divide(c3,double_divide(inverse(X0),double_divide(a3,b3))),X0)
| spl0_2 ),
inference(superposition,[],[f1690,f977]) ).
fof(f2653,plain,
( ! [X0] : double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(X0,double_divide(c3,double_divide(inverse(X0),double_divide(a3,b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f2617,f1254]) ).
fof(f2726,plain,
( ! [X0] : double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(X0,double_divide(c3,double_divide(double_divide(a3,b3),inverse(X0))))
| spl0_2 ),
inference(forward_demodulation,[],[f2653,f1254]) ).
fof(f2796,plain,
( ! [X0] : double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(inverse(c3),double_divide(X0,double_divide(double_divide(a3,b3),inverse(inverse(X0)))))
| spl0_2 ),
inference(superposition,[],[f2726,f1294]) ).
fof(f2799,plain,
( ! [X0] : double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(inverse(c3),double_divide(double_divide(inverse(X0),double_divide(a3,b3)),inverse(X0)))
| spl0_2 ),
inference(forward_demodulation,[],[f2796,f1296]) ).
fof(f2806,plain,
( double_divide(double_divide(b3,c3),inverse(a3)) != double_divide(inverse(c3),double_divide(a3,b3))
| spl0_2 ),
inference(forward_demodulation,[],[f2799,f594]) ).
fof(f2811,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2806,f2205]) ).
fof(f2812,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2811]) ).
fof(f2814,plain,
( a2 != double_divide(inverse(a2),inverse(inverse(double_divide(b2,inverse(b2)))))
| spl0_3 ),
inference(forward_demodulation,[],[f17,f561]) ).
fof(f2816,plain,
( a2 != double_divide(inverse(a2),double_divide(b2,inverse(b2)))
| spl0_3 ),
inference(forward_demodulation,[],[f2814,f430]) ).
fof(f2818,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f2816,f1769]) ).
fof(f2819,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f2818]) ).
fof(f2828,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),inverse(inverse(b1)))
| spl0_4 ),
inference(forward_demodulation,[],[f21,f561]) ).
fof(f2830,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),b1)
| spl0_4 ),
inference(forward_demodulation,[],[f2828,f430]) ).
fof(f2831,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f2830,f1254]) ).
fof(f2832,plain,
( double_divide(b1,inverse(b1)) != double_divide(inverse(a1),inverse(inverse(a1)))
| spl0_4 ),
inference(forward_demodulation,[],[f2831,f561]) ).
fof(f2833,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f2832,f1771]) ).
fof(f2834,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2833]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f1679]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f2812]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f2819]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f2834]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6,s5,s3]) ).
fof(f2835,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n020.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 09:20:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 5.18/1.66 % (3125135)Input is clausal, will run a generic CNF schedule.
% 5.18/1.66 % (3125144)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2793219125:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.18/1.66 % (3125144)Instruction limit reached!
% 5.18/1.66 % (3125144)------------------------------
% 5.18/1.66 % (3125144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125144)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125144)Termination reason: Instruction limit
% 5.18/1.66 % (3125144)Termination phase: Saturation
% 5.18/1.66 % (3125144)Time elapsed: 0.041 s
% 5.18/1.66 % (3125144)Peak memory usage: 90 MB
% 5.18/1.66 % (3125144)Instructions burned: 114 (million)
% 5.18/1.66 % (3125140)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=3542675886:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.18/1.66 % (3125146)dis-21_1_sil=8000:lcm=predicate:random_seed=3198722389: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)
% 5.18/1.66 % (3125142)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3552721307:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.18/1.66 % (3125143)lrs+10_1_sil=8000:sp=occurrence:random_seed=849162907:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.18/1.66 % (3125141)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=391295818:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.18/1.66 % (3125145)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3874621454:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.18/1.66 % (3125146)Refutation not found, incomplete strategy
% 5.18/1.66 % (3125146)------------------------------
% 5.18/1.66 % (3125146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125146)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125146)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.66 % (3125146)Time elapsed: 0.001 s
% 5.18/1.66 % (3125146)Peak memory usage: 88 MB
% 5.18/1.66 % (3125143)Instruction limit reached!
% 5.18/1.66 % (3125143)------------------------------
% 5.18/1.66 % (3125143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125143)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125143)Termination reason: Instruction limit
% 5.18/1.66 % (3125143)Termination phase: Saturation
% 5.18/1.66 % (3125143)Time elapsed: 0.069 s
% 5.18/1.66 % (3125143)Peak memory usage: 89 MB
% 5.18/1.66 % (3125143)Instructions burned: 108 (million)
% 5.18/1.66 % (3125145)Instruction limit reached!
% 5.18/1.66 % (3125145)------------------------------
% 5.18/1.66 % (3125145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125145)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125145)Termination reason: Instruction limit
% 5.18/1.66 % (3125145)Termination phase: Saturation
% 5.18/1.66 % (3125145)Time elapsed: 0.105 s
% 5.18/1.66 % (3125145)Peak memory usage: 90 MB
% 5.18/1.66 % (3125145)Instructions burned: 181 (million)
% 5.18/1.66 % (3125148)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=809977677:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.18/1.66 % (3125148)Refutation not found, incomplete strategy
% 5.18/1.66 % (3125148)------------------------------
% 5.18/1.66 % (3125148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125148)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125148)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.66 % (3125148)Time elapsed: 0.001 s
% 5.18/1.66 % (3125148)Peak memory usage: 88 MB
% 5.18/1.66 % (3125155)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1601312189: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)
% 5.18/1.66 % (3125155)Refutation not found, incomplete strategy
% 5.18/1.66 % (3125155)------------------------------
% 5.18/1.66 % (3125155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125155)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125155)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.66 % (3125155)Time elapsed: 0.002 s
% 5.18/1.66 % (3125155)Peak memory usage: 88 MB
% 5.18/1.66 % (3125146)------------------------------
% 5.18/1.66 % (3125146)------------------------------
% 5.18/1.66 % (3125156)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1248575623:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.18/1.66 % (3125148)------------------------------
% 5.18/1.66 % (3125148)------------------------------
% 5.18/1.66 % (3125156)Refutation not found, incomplete strategy
% 5.18/1.66 % (3125156)------------------------------
% 5.18/1.66 % (3125156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125156)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125156)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.66 % (3125156)Time elapsed: 0.001 s
% 5.18/1.66 % (3125156)Peak memory usage: 88 MB
% 5.18/1.66 % (3125161)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=67446894:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.18/1.66 % (3125159)lrs+10_64_to=lpo:sil=8000:random_seed=3883394717:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.18/1.66 % (3125161)First to succeed.
% 5.18/1.66 % (3125161)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3125135"
% 5.18/1.66 % (3125155)------------------------------
% 5.18/1.66 % (3125155)------------------------------
% 5.18/1.66 % (3125159)Instruction limit reached!
% 5.18/1.66 % (3125159)------------------------------
% 5.18/1.66 % (3125159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.66 % (3125159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.66 % (3125159)CaDiCaL version: 2.1.3
% 5.18/1.66 % (3125159)Termination reason: Instruction limit
% 5.18/1.66 % (3125159)Termination phase: Saturation
% 5.18/1.66 % (3125159)Time elapsed: 0.075 s
% 5.18/1.66 % (3125159)Peak memory usage: 89 MB
% 5.18/1.66 % (3125159)Instructions burned: 126 (million)
% 5.18/1.66 % (3125156)------------------------------
% 5.18/1.66 % (3125156)------------------------------
% 5.18/1.66 % (3125161)Refutation found. Thanks to Tanya!
% 5.18/1.66 % SZS status Unsatisfiable for theBenchmark
% 5.18/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 6.21/1.86 % (3125161)------------------------------
% 6.21/1.86 % (3125161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.86 % (3125161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.86 % (3125161)CaDiCaL version: 2.1.3
% 6.21/1.86 % (3125161)Termination reason: Refutation
% 6.21/1.86 % (3125161)Time elapsed: 0.062 s
% 6.21/1.86 % (3125161)Peak memory usage: 91 MB
% 6.21/1.86 % (3125161)Instructions burned: 189 (million)
% 6.21/1.86 % (3125161)------------------------------
% 6.21/1.86 % (3125161)------------------------------
% 6.21/1.86 % (3125135)Success in time 0.793 s
% 6.21/1.86 % Vampire exiting
%------------------------------------------------------------------------------