%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP110-1 : 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 : n013.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 6.08s 1.81s
% Output : Refutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 7
% Syntax : Number of formulae : 112 ( 75 unt; 4 def)
% Number of atoms : 159 ( 105 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 44 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 9 ( 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 : 204 ( 0 sgn 204 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
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(X0,double_divide(inverse(double_divide(X1,X0)),double_divide(X1,X2)))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X1,X2),double_divide(X0,double_divide(inverse(double_divide(inverse(double_divide(X1,X0)),X2)),X3)))) = X3,
inference(superposition,[],[f24,f1]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X2,X1)),double_divide(X2,X0)) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(X1,X3))),
inference(superposition,[],[f1,f24]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4] : inverse(double_divide(double_divide(X1,X2),double_divide(double_divide(inverse(double_divide(X3,X1)),double_divide(X3,X0)),double_divide(inverse(double_divide(X0,X2)),X4)))) = X4,
inference(superposition,[],[f25,f24]) ).
fof(f61,plain,
! [X2,X0,X1] : inverse(double_divide(X2,inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1))))) = X0,
inference(superposition,[],[f24,f27]) ).
fof(f75,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(X0,X1)),double_divide(X0,inverse(double_divide(X1,X2)))) = X2,
inference(superposition,[],[f1,f27]) ).
fof(f102,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(X0),double_divide(X1,double_divide(X1,inverse(double_divide(X2,X0)))))) = X2,
inference(superposition,[],[f1,f75]) ).
fof(f103,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X1,X3)),inverse(double_divide(X2,X0))) = inverse(double_divide(double_divide(X1,X2),double_divide(X3,X0))),
inference(superposition,[],[f25,f75]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4] : double_divide(inverse(double_divide(X1,double_divide(inverse(double_divide(X3,X1)),double_divide(X3,X0)))),inverse(double_divide(X2,double_divide(inverse(double_divide(X0,X2)),X4)))) = X4,
inference(backward_demodulation,[],[f35,f103]) ).
fof(f146,plain,
! [X2,X0,X4] : double_divide(X0,inverse(double_divide(X2,double_divide(inverse(double_divide(X0,X2)),X4)))) = X4,
inference(forward_demodulation,[],[f136,f24]) ).
fof(f211,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X0))))),X0)) = X2,
inference(superposition,[],[f61,f24]) ).
fof(f231,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X0)),X2)) = inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X3,double_divide(X3,X0)))),
inference(superposition,[],[f102,f1]) ).
fof(f238,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(inverse(double_divide(X1,inverse(X2))),inverse(double_divide(X0,X2))),
inference(superposition,[],[f146,f102]) ).
fof(f239,plain,
! [X2,X3,X0,X1] : double_divide(X2,double_divide(X2,inverse(double_divide(X0,X1)))) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(inverse(X1),X3))),
inference(superposition,[],[f1,f102]) ).
fof(f292,plain,
! [X2,X0,X1] : inverse(double_divide(X1,X2)) = double_divide(X0,inverse(double_divide(inverse(X2),double_divide(X0,X1)))),
inference(superposition,[],[f146,f238]) ).
fof(f341,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = inverse(double_divide(X1,double_divide(X2,inverse(double_divide(X0,double_divide(X2,double_divide(X3,X1))))))),
inference(superposition,[],[f292,f211]) ).
fof(f361,plain,
! [X0,X1] : inverse(inverse(double_divide(X0,double_divide(X1,X0)))) = X1,
inference(superposition,[],[f61,f292]) ).
fof(f369,plain,
! [X2,X3,X0,X1] : inverse(double_divide(inverse(X1),double_divide(X3,X0))) = inverse(double_divide(X2,double_divide(inverse(double_divide(X3,X2)),inverse(double_divide(X0,X1))))),
inference(superposition,[],[f24,f292]) ).
fof(f379,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(inverse(double_divide(X2,inverse(inverse(double_divide(inverse(X1),double_divide(X3,X0)))))),inverse(inverse(double_divide(X0,X1)))),
inference(superposition,[],[f238,f292]) ).
fof(f398,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f361,f75]) ).
fof(f399,plain,
! [X0,X1] : inverse(X0) = inverse(double_divide(X1,double_divide(X1,X0))),
inference(superposition,[],[f361,f24]) ).
fof(f424,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(inverse(double_divide(X2,double_divide(inverse(X1),double_divide(X3,X0)))),inverse(inverse(double_divide(X0,X1)))),
inference(backward_demodulation,[],[f379,f398]) ).
fof(f427,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[],[f361,f398]) ).
fof(f460,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(inverse(double_divide(X2,double_divide(inverse(X1),double_divide(X3,X0)))),double_divide(X0,X1)),
inference(forward_demodulation,[],[f424,f398]) ).
fof(f509,plain,
! [X0,X1] : double_divide(X0,inverse(inverse(double_divide(X0,X1)))) = X1,
inference(superposition,[],[f146,f427]) ).
fof(f511,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(X0,X1),double_divide(inverse(X0),double_divide(X1,X2)))) = X2,
inference(superposition,[],[f24,f427]) ).
fof(f512,plain,
! [X2,X0,X1] : double_divide(X0,X2) = inverse(double_divide(X1,double_divide(inverse(double_divide(X2,X1)),X0))),
inference(superposition,[],[f24,f427]) ).
fof(f522,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,X2))) = double_divide(X1,inverse(double_divide(X2,X0))),
inference(superposition,[],[f146,f427]) ).
fof(f523,plain,
! [X0,X1] : double_divide(X0,inverse(X0)) = inverse(double_divide(inverse(X1),X1)),
inference(superposition,[],[f292,f427]) ).
fof(f546,plain,
! [X3,X0,X1] : double_divide(inverse(double_divide(X0,X1)),X3) = inverse(double_divide(inverse(X1),double_divide(X3,X0))),
inference(backward_demodulation,[],[f369,f512]) ).
fof(f547,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(X0,inverse(X0))),inverse(double_divide(X1,double_divide(X1,X2)))) = X2,
inference(forward_demodulation,[],[f511,f103]) ).
fof(f548,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f509,f398]) ).
fof(f563,plain,
! [X2,X0] : double_divide(inverse(double_divide(X0,inverse(X0))),inverse(X2)) = X2,
inference(forward_demodulation,[],[f547,f399]) ).
fof(f565,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X0)),X2)) = inverse(double_divide(inverse(double_divide(X1,X2)),X0)),
inference(backward_demodulation,[],[f231,f548]) ).
fof(f570,plain,
! [X3,X0,X1] : inverse(double_divide(X0,X1)) = inverse(double_divide(inverse(double_divide(X0,X3)),double_divide(inverse(X1),X3))),
inference(backward_demodulation,[],[f239,f548]) ).
fof(f592,plain,
! [X3,X0,X1] : inverse(double_divide(X0,X1)) = double_divide(inverse(double_divide(X3,double_divide(X0,X3))),inverse(X1)),
inference(forward_demodulation,[],[f570,f546]) ).
fof(f616,plain,
! [X0,X1] : inverse(double_divide(X0,X1)) = double_divide(inverse(X0),inverse(X1)),
inference(forward_demodulation,[],[f592,f427]) ).
fof(f763,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,X2))) = double_divide(X1,double_divide(inverse(X2),inverse(X0))),
inference(backward_demodulation,[],[f522,f616]) ).
fof(f766,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X0)) = inverse(double_divide(double_divide(inverse(X1),inverse(X0)),X2)),
inference(backward_demodulation,[],[f565,f616]) ).
fof(f786,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(double_divide(inverse(X2),inverse(double_divide(inverse(X1),double_divide(X3,X0)))),double_divide(X0,X1)),
inference(backward_demodulation,[],[f460,f616]) ).
fof(f789,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X0),inverse(double_divide(X2,double_divide(X3,X1))))))),
inference(backward_demodulation,[],[f341,f616]) ).
fof(f796,plain,
! [X2,X0] : double_divide(double_divide(inverse(X0),inverse(inverse(X0))),inverse(X2)) = X2,
inference(backward_demodulation,[],[f563,f616]) ).
fof(f805,plain,
! [X0,X1] : double_divide(X0,inverse(X0)) = double_divide(inverse(inverse(X1)),inverse(X1)),
inference(backward_demodulation,[],[f523,f616]) ).
fof(f808,plain,
( inverse(double_divide(b4,a4)) != double_divide(inverse(a4),inverse(b4))
| spl0_1 ),
inference(backward_demodulation,[],[f9,f616]) ).
fof(f834,plain,
( double_divide(inverse(a4),inverse(b4)) != double_divide(inverse(b4),inverse(a4))
| spl0_1 ),
inference(forward_demodulation,[],[f808,f616]) ).
fof(f837,plain,
! [X0,X1] : double_divide(X0,inverse(X0)) = double_divide(X1,inverse(X1)),
inference(forward_demodulation,[],[f805,f398]) ).
fof(f846,plain,
! [X2,X0] : double_divide(double_divide(inverse(X0),X0),inverse(X2)) = X2,
inference(forward_demodulation,[],[f796,f398]) ).
fof(f853,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(inverse(X1),inverse(double_divide(X2,double_divide(inverse(X0),inverse(double_divide(X2,double_divide(X3,X1))))))),
inference(forward_demodulation,[],[f789,f616]) ).
fof(f856,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(double_divide(inverse(X2),double_divide(inverse(inverse(X1)),inverse(double_divide(X3,X0)))),double_divide(X0,X1)),
inference(forward_demodulation,[],[f786,f616]) ).
fof(f874,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X0)) = double_divide(inverse(double_divide(inverse(X1),inverse(X0))),inverse(X2)),
inference(forward_demodulation,[],[f766,f616]) ).
fof(f877,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(inverse(X2),inverse(X0))) = double_divide(X0,double_divide(inverse(X1),inverse(X2))),
inference(forward_demodulation,[],[f763,f616]) ).
fof(f1033,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(inverse(X1),double_divide(inverse(X2),inverse(double_divide(inverse(X0),inverse(double_divide(X2,double_divide(X3,X1))))))),
inference(forward_demodulation,[],[f853,f616]) ).
fof(f1036,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(double_divide(inverse(X2),double_divide(inverse(inverse(X1)),double_divide(inverse(X3),inverse(X0)))),double_divide(X0,X1)),
inference(forward_demodulation,[],[f856,f616]) ).
fof(f1052,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X0)) = double_divide(double_divide(inverse(inverse(X1)),inverse(inverse(X0))),inverse(X2)),
inference(forward_demodulation,[],[f874,f616]) ).
fof(f1198,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(double_divide(inverse(X0),inverse(double_divide(X2,double_divide(X3,X1)))),double_divide(inverse(inverse(X1)),inverse(X2))),
inference(forward_demodulation,[],[f1033,f877]) ).
fof(f1201,plain,
! [X2,X3,X0,X1] : double_divide(X2,X3) = double_divide(double_divide(inverse(X2),double_divide(X1,double_divide(inverse(X3),inverse(X0)))),double_divide(X0,X1)),
inference(forward_demodulation,[],[f1036,f398]) ).
fof(f1212,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X0)) = double_divide(double_divide(inverse(inverse(X1)),X0),inverse(X2)),
inference(forward_demodulation,[],[f1052,f398]) ).
fof(f1334,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(double_divide(inverse(X0),inverse(double_divide(X2,double_divide(X3,X1)))),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f1198,f398]) ).
fof(f1342,plain,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(X1,X2)),X0)) = double_divide(double_divide(X1,X0),inverse(X2)),
inference(forward_demodulation,[],[f1212,f398]) ).
fof(f1441,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(double_divide(inverse(X0),double_divide(inverse(X2),inverse(double_divide(X3,X1)))),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f1334,f616]) ).
fof(f1447,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),inverse(X2)) = double_divide(inverse(inverse(double_divide(X1,X2))),inverse(X0)),
inference(forward_demodulation,[],[f1342,f616]) ).
fof(f1523,plain,
! [X2,X3,X0,X1] : double_divide(X3,X0) = double_divide(double_divide(inverse(X0),double_divide(inverse(X2),double_divide(inverse(X3),inverse(X1)))),double_divide(X1,inverse(X2))),
inference(forward_demodulation,[],[f1441,f616]) ).
fof(f1528,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,X0),inverse(X2)) = double_divide(double_divide(X1,X2),inverse(X0)),
inference(forward_demodulation,[],[f1447,f398]) ).
fof(f1581,plain,
! [X3,X0] : double_divide(X0,X3) = double_divide(X3,X0),
inference(forward_demodulation,[],[f1523,f1201]) ).
fof(f1674,plain,
( double_divide(inverse(a4),inverse(b4)) != double_divide(inverse(a4),inverse(b4))
| spl0_1 ),
inference(superposition,[],[f834,f1581]) ).
fof(f1678,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1674]) ).
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,f616]) ).
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,f1581]) ).
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,f398]) ).
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,f1581]) ).
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,f1581]) ).
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,f616]) ).
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,f398]) ).
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,f1581]) ).
fof(f1690,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1689,f1528]) ).
fof(f1691,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1690]) ).
fof(f1693,plain,
( a2 != double_divide(inverse(a2),inverse(inverse(double_divide(b2,inverse(b2)))))
| spl0_3 ),
inference(forward_demodulation,[],[f17,f616]) ).
fof(f1695,plain,
( a2 != double_divide(inverse(a2),double_divide(b2,inverse(b2)))
| spl0_3 ),
inference(forward_demodulation,[],[f1693,f398]) ).
fof(f1697,plain,
( a2 != double_divide(double_divide(b2,inverse(b2)),inverse(a2))
| spl0_3 ),
inference(forward_demodulation,[],[f1695,f1581]) ).
fof(f1795,plain,
( ! [X0] : a2 != double_divide(double_divide(X0,inverse(X0)),inverse(a2))
| spl0_3 ),
inference(superposition,[],[f1697,f837]) ).
fof(f1801,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(X0)),inverse(X1)) = X1,
inference(superposition,[],[f846,f1581]) ).
fof(f1822,plain,
( a2 != a2
| spl0_3 ),
inference(backward_demodulation,[],[f1795,f1801]) ).
fof(f1826,plain,
( $false
| spl0_3 ),
inference(trivial_inequality_removal,[],[f1822]) ).
fof(f1827,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f1826]) ).
fof(f1830,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),inverse(inverse(b1)))
| spl0_4 ),
inference(forward_demodulation,[],[f21,f616]) ).
fof(f1832,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(inverse(b1),b1)
| spl0_4 ),
inference(forward_demodulation,[],[f1830,f398]) ).
fof(f1833,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f1832,f1581]) ).
fof(f1834,plain,
( double_divide(b1,inverse(b1)) != double_divide(inverse(a1),inverse(inverse(a1)))
| spl0_4 ),
inference(forward_demodulation,[],[f1833,f616]) ).
fof(f1835,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f1834,f837]) ).
fof(f1836,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f1835]) ).
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(s4,plain,
spl0_2,
inference(sat_conversion,[],[f1691]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f1827]) ).
cnf(s7,plain,
spl0_4,
inference(sat_conversion,[],[f1836]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6,s4,s3]) ).
fof(f1837,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:19:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 6.08/1.81 % (4151432)Input is clausal, will run a generic CNF schedule.
% 6.08/1.81 % (4151452)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1951365318:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.08/1.81 % (4151449)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1959448602:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.08/1.81 % (4151451)lrs+10_1_sil=8000:sp=occurrence:random_seed=526350530:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.08/1.81 % (4151446)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=2486176728:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.08/1.81 % (4151447)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2916196370:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.08/1.81 % (4151452)Instruction limit reached!
% 6.08/1.81 % (4151452)------------------------------
% 6.08/1.81 % (4151452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151452)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151452)Termination reason: Instruction limit
% 6.08/1.81 % (4151452)Termination phase: Saturation
% 6.08/1.81 % (4151452)Time elapsed: 0.043 s
% 6.08/1.81 % (4151452)Peak memory usage: 90 MB
% 6.08/1.81 % (4151452)Instructions burned: 115 (million)
% 6.08/1.81 % (4151454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2120262934:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.08/1.81 % (4151455)dis-21_1_sil=8000:lcm=predicate:random_seed=3569271311: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)
% 6.08/1.81 % (4151455)Refutation not found, incomplete strategy
% 6.08/1.81 % (4151455)------------------------------
% 6.08/1.81 % (4151455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151455)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151455)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.81 % (4151455)Time elapsed: 0.001 s
% 6.08/1.81 % (4151455)Peak memory usage: 88 MB
% 6.08/1.81 % (4151451)Instruction limit reached!
% 6.08/1.81 % (4151451)------------------------------
% 6.08/1.81 % (4151451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151451)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151451)Termination reason: Instruction limit
% 6.08/1.81 % (4151451)Termination phase: Saturation
% 6.08/1.81 % (4151451)Time elapsed: 0.070 s
% 6.08/1.81 % (4151451)Peak memory usage: 89 MB
% 6.08/1.81 % (4151451)Instructions burned: 108 (million)
% 6.08/1.81 % (4151454)Instruction limit reached!
% 6.08/1.81 % (4151454)------------------------------
% 6.08/1.81 % (4151454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151454)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151454)Termination reason: Instruction limit
% 6.08/1.81 % (4151454)Termination phase: Saturation
% 6.08/1.81 % (4151454)Time elapsed: 0.105 s
% 6.08/1.81 % (4151454)Peak memory usage: 90 MB
% 6.08/1.81 % (4151454)Instructions burned: 180 (million)
% 6.08/1.81 % (4151517)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=2673616262:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.08/1.81 % (4151517)Refutation not found, incomplete strategy
% 6.08/1.81 % (4151517)------------------------------
% 6.08/1.81 % (4151517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151517)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151517)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.81 % (4151517)Time elapsed: 0.001 s
% 6.08/1.81 % (4151517)Peak memory usage: 88 MB
% 6.08/1.81 % (4151533)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1719052799: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)
% 6.08/1.81 % (4151533)Refutation not found, incomplete strategy
% 6.08/1.81 % (4151533)------------------------------
% 6.08/1.81 % (4151533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151533)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151533)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.81 % (4151533)Time elapsed: 0.002 s
% 6.08/1.81 % (4151533)Peak memory usage: 88 MB
% 6.08/1.81 % (4151455)------------------------------
% 6.08/1.81 % (4151455)------------------------------
% 6.08/1.81 % (4151546)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3139279445:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.08/1.81 % (4151517)------------------------------
% 6.08/1.81 % (4151517)------------------------------
% 6.08/1.81 % (4151546)Refutation not found, incomplete strategy
% 6.08/1.81 % (4151546)------------------------------
% 6.08/1.81 % (4151546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151546)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151546)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.81 % (4151546)Time elapsed: 0.001 s
% 6.08/1.81 % (4151546)Peak memory usage: 88 MB
% 6.08/1.81 % (4151552)lrs+10_64_to=lpo:sil=8000:random_seed=952681402:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.08/1.81 % (4151554)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2937672397:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.08/1.81 % (4151552)Instruction limit reached!
% 6.08/1.81 % (4151552)------------------------------
% 6.08/1.81 % (4151552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151552)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151552)Termination reason: Instruction limit
% 6.08/1.81 % (4151552)Termination phase: Saturation
% 6.08/1.81 % (4151552)Time elapsed: 0.042 s
% 6.08/1.81 % (4151552)Peak memory usage: 89 MB
% 6.08/1.81 % (4151552)Instructions burned: 127 (million)
% 6.08/1.81 % (4151533)------------------------------
% 6.08/1.81 % (4151533)------------------------------
% 6.08/1.81 % (4151546)------------------------------
% 6.08/1.81 % (4151546)------------------------------
% 6.08/1.81 % (4151554)First to succeed.
% 6.08/1.81 % (4151554)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4151432"
% 6.08/1.81 % (4151598)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2148371190:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.08/1.81 % (4151598)Instruction limit reached!
% 6.08/1.81 % (4151598)------------------------------
% 6.08/1.81 % (4151598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151598)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151598)Termination reason: Instruction limit
% 6.08/1.81 % (4151598)Termination phase: Saturation
% 6.08/1.81 % (4151598)Time elapsed: 0.055 s
% 6.08/1.81 % (4151598)Peak memory usage: 92 MB
% 6.08/1.81 % (4151598)Instructions burned: 159 (million)
% 6.08/1.81 % (4151612)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1901699841:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.08/1.81 % (4151617)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=810762504:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.08/1.81 % (4151617)Instruction limit reached!
% 6.08/1.81 % (4151617)------------------------------
% 6.08/1.81 % (4151617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151617)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151617)Termination reason: Instruction limit
% 6.08/1.81 % (4151617)Termination phase: Saturation
% 6.08/1.81 % (4151617)Time elapsed: 0.065 s
% 6.08/1.81 % (4151617)Peak memory usage: 89 MB
% 6.08/1.81 % (4151617)Instructions burned: 107 (million)
% 6.08/1.81 % (4151619)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1998002456:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 6.08/1.81 % (4151619)Refutation not found, incomplete strategy
% 6.08/1.81 % (4151619)------------------------------
% 6.08/1.81 % (4151619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.81 % (4151619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.81 % (4151619)CaDiCaL version: 2.1.3
% 6.08/1.81 % (4151619)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.81 % (4151619)Time elapsed: 0.0000 s
% 6.08/1.81 % (4151619)Peak memory usage: 88 MB
% 6.08/1.81 % (4151554)Refutation found. Thanks to Tanya!
% 6.08/1.81 % SZS status Unsatisfiable for theBenchmark
% 6.08/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 7.30/2.01 % (4151554)------------------------------
% 7.30/2.01 % (4151554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/2.01 % (4151554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/2.01 % (4151554)CaDiCaL version: 2.1.3
% 7.30/2.01 % (4151554)Termination reason: Refutation
% 7.30/2.01 % (4151554)Time elapsed: 0.097 s
% 7.30/2.01 % (4151554)Peak memory usage: 91 MB
% 7.30/2.01 % (4151554)Instructions burned: 154 (million)
% 7.30/2.01 % (4151554)------------------------------
% 7.30/2.01 % (4151554)------------------------------
% 7.30/2.01 % (4151432)Success in time 0.969 s
% 7.30/2.01 % Vampire exiting
%------------------------------------------------------------------------------