%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 10:16:40 AM UTC 2026
% Result : Unsatisfiable 1.59s 0.73s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 126 ( 99 unt; 4 def)
% Number of atoms : 163 ( 119 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 34 ~; 33 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 3 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 : 260 ( 0 sgn 260 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/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/sandbox/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(X1,inverse(double_divide(inverse(double_divide(X0,inverse(X3))),inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X0))),X2))))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X0))),X3) = double_divide(X1,inverse(double_divide(inverse(X0),X2))),
inference(superposition,[],[f1,f1]) ).
fof(f29,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X2),inverse(double_divide(X0,inverse(double_divide(inverse(X1),X2))))) = X1,
inference(superposition,[],[f1,f24]) ).
fof(f44,plain,
! [X0,X1] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(X0)) = X1,
inference(superposition,[],[f23,f1]) ).
fof(f45,plain,
! [X2,X3,X0,X1,X4,X5] : double_divide(X1,inverse(double_divide(inverse(X5),inverse(double_divide(inverse(double_divide(X2,inverse(X0))),inverse(double_divide(inverse(double_divide(double_divide(X1,X3),inverse(X2))),X3))))))) = double_divide(inverse(double_divide(double_divide(X0,X4),inverse(X5))),X4),
inference(superposition,[],[f24,f23]) ).
fof(f59,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X0))),X2) = double_divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f44,f1]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : double_divide(inverse(double_divide(X2,inverse(X0))),inverse(double_divide(inverse(double_divide(double_divide(X1,X3),inverse(X2))),X3))) = double_divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f44,f23]) ).
fof(f61,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(inverse(double_divide(X1,inverse(X0))))) = X1,
inference(superposition,[],[f44,f44]) ).
fof(f69,plain,
! [X0,X1,X4,X5] : double_divide(inverse(double_divide(double_divide(X0,X4),inverse(X5))),X4) = double_divide(X1,inverse(double_divide(inverse(X5),inverse(double_divide(inverse(X0),inverse(X1)))))),
inference(backward_demodulation,[],[f45,f60]) ).
fof(f71,plain,
! [X3,X1] : double_divide(X1,inverse(double_divide(inverse(X3),inverse(X1)))) = X3,
inference(backward_demodulation,[],[f23,f60]) ).
fof(f78,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(inverse(X0),X2))) = double_divide(inverse(X0),inverse(double_divide(X1,X2))),
inference(backward_demodulation,[],[f24,f59]) ).
fof(f79,plain,
! [X0,X1,X5] : double_divide(X1,inverse(double_divide(inverse(X5),inverse(double_divide(inverse(X0),inverse(X1)))))) = double_divide(inverse(X5),inverse(X0)),
inference(forward_demodulation,[],[f69,f59]) ).
fof(f91,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X1),inverse(double_divide(X3,inverse(double_divide(X0,X2))))) = double_divide(X3,inverse(double_divide(X0,inverse(double_divide(inverse(X1),X2))))),
inference(superposition,[],[f78,f78]) ).
fof(f104,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f71,f78]) ).
fof(f123,plain,
! [X0,X1] : double_divide(double_divide(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[],[f71,f104]) ).
fof(f126,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(inverse(X0),inverse(inverse(X0))),
inference(superposition,[],[f44,f104]) ).
fof(f151,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X3),inverse(X0)) = double_divide(double_divide(X1,X2),inverse(double_divide(inverse(X3),inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))))),
inference(superposition,[],[f78,f29]) ).
fof(f188,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(X0)) = double_divide(X2,inverse(double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(X2)))))),
inference(superposition,[],[f79,f78]) ).
fof(f194,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(X2)))) = double_divide(inverse(double_divide(inverse(X0),inverse(X1))),inverse(X2)),
inference(superposition,[],[f44,f79]) ).
fof(f201,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(inverse(X0),inverse(X1)))) = double_divide(inverse(X3),inverse(double_divide(X2,inverse(double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(inverse(X3))))))))),
inference(superposition,[],[f78,f79]) ).
fof(f230,plain,
! [X0,X1] : inverse(double_divide(X0,inverse(X1))) = double_divide(inverse(X0),inverse(inverse(X1))),
inference(superposition,[],[f44,f61]) ).
fof(f234,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = inverse(double_divide(X0,inverse(X0))),
inference(backward_demodulation,[],[f126,f230]) ).
fof(f236,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(inverse(X0),inverse(X1)))) = double_divide(inverse(X3),inverse(double_divide(X2,inverse(double_divide(inverse(X0),inverse(inverse(double_divide(X1,inverse(X3))))))))),
inference(backward_demodulation,[],[f201,f230]) ).
fof(f244,plain,
! [X0,X1] : inverse(double_divide(X0,inverse(double_divide(X1,inverse(X0))))) = X1,
inference(backward_demodulation,[],[f61,f230]) ).
fof(f257,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(inverse(X0),inverse(X1)))) = double_divide(inverse(X3),inverse(double_divide(X2,inverse(inverse(double_divide(X0,inverse(double_divide(X1,inverse(X3))))))))),
inference(forward_demodulation,[],[f236,f230]) ).
fof(f294,plain,
! [X2,X3,X0,X1] : double_divide(X1,inverse(double_divide(X2,inverse(X0)))) = double_divide(inverse(X0),inverse(double_divide(X1,inverse(double_divide(X2,inverse(double_divide(X3,inverse(X3)))))))),
inference(superposition,[],[f91,f104]) ).
fof(f404,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(X0,inverse(X0)),
inference(superposition,[],[f234,f234]) ).
fof(f407,plain,
! [X2,X0,X1] : double_divide(double_divide(double_divide(inverse(X1),X2),X2),inverse(inverse(double_divide(X0,inverse(X0))))) = X1,
inference(superposition,[],[f29,f234]) ).
fof(f411,plain,
! [X2,X0] : double_divide(inverse(double_divide(X0,inverse(X0))),inverse(X2)) = X2,
inference(superposition,[],[f123,f234]) ).
fof(f413,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(X3,inverse(double_divide(inverse(X1),inverse(X3)))))) = double_divide(inverse(X1),inverse(double_divide(X2,inverse(inverse(double_divide(X0,inverse(X0))))))),
inference(superposition,[],[f91,f234]) ).
fof(f417,plain,
! [X2,X0,X1] : double_divide(inverse(X2),inverse(X1)) = double_divide(inverse(X1),inverse(double_divide(inverse(X2),inverse(inverse(double_divide(X0,inverse(X0))))))),
inference(superposition,[],[f79,f234]) ).
fof(f418,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(inverse(double_divide(X0,inverse(X0))))) = X1,
inference(superposition,[],[f71,f234]) ).
fof(f464,plain,
! [X0,X1] : inverse(double_divide(X1,inverse(double_divide(X0,inverse(X0))))) = X1,
inference(forward_demodulation,[],[f418,f230]) ).
fof(f465,plain,
! [X2,X0,X1] : double_divide(inverse(X2),inverse(X1)) = double_divide(inverse(X1),inverse(inverse(double_divide(X2,inverse(double_divide(X0,inverse(X0))))))),
inference(forward_demodulation,[],[f417,f230]) ).
fof(f468,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = double_divide(inverse(X1),inverse(double_divide(X2,inverse(inverse(double_divide(X0,inverse(X0))))))),
inference(forward_demodulation,[],[f413,f244]) ).
fof(f477,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,X2))) = double_divide(X1,inverse(double_divide(X2,inverse(X0)))),
inference(backward_demodulation,[],[f294,f464]) ).
fof(f479,plain,
! [X2,X0,X1] : double_divide(inverse(X2),inverse(X1)) = inverse(double_divide(X1,inverse(double_divide(X2,inverse(double_divide(X0,inverse(X0))))))),
inference(forward_demodulation,[],[f465,f230]) ).
fof(f483,plain,
! [X2,X1] : double_divide(inverse(X2),inverse(X1)) = inverse(double_divide(X1,X2)),
inference(forward_demodulation,[],[f479,f464]) ).
fof(f486,plain,
! [X3,X1] : double_divide(X1,inverse(inverse(double_divide(X1,X3)))) = X3,
inference(backward_demodulation,[],[f71,f483]) ).
fof(f490,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X0,X3)) = double_divide(double_divide(X1,X2),inverse(double_divide(inverse(X3),inverse(double_divide(X1,inverse(double_divide(inverse(X0),X2))))))),
inference(backward_demodulation,[],[f151,f483]) ).
fof(f491,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(X0)) = double_divide(X2,inverse(double_divide(inverse(X0),inverse(inverse(double_divide(X2,X1)))))),
inference(backward_demodulation,[],[f188,f483]) ).
fof(f492,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(X2)))) = double_divide(inverse(inverse(double_divide(X1,X0))),inverse(X2)),
inference(backward_demodulation,[],[f194,f483]) ).
fof(f496,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X3),inverse(double_divide(X2,inverse(inverse(double_divide(X0,inverse(double_divide(X1,inverse(X3))))))))) = double_divide(X2,inverse(inverse(double_divide(X1,X0)))),
inference(backward_demodulation,[],[f257,f483]) ).
fof(f505,plain,
! [X2,X0] : inverse(double_divide(X2,double_divide(X0,inverse(X0)))) = X2,
inference(backward_demodulation,[],[f411,f483]) ).
fof(f507,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(inverse(X0),X2))) = inverse(double_divide(double_divide(X1,X2),X0)),
inference(backward_demodulation,[],[f78,f483]) ).
fof(f520,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(X2,inverse(X0)))) = inverse(double_divide(double_divide(X1,X2),X0)),
inference(backward_demodulation,[],[f477,f483]) ).
fof(f543,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = inverse(double_divide(double_divide(X2,inverse(inverse(double_divide(X0,inverse(X0))))),X1)),
inference(backward_demodulation,[],[f468,f483]) ).
fof(f565,plain,
! [X0,X1] : inverse(double_divide(X0,inverse(X1))) = inverse(double_divide(inverse(X1),X0)),
inference(backward_demodulation,[],[f230,f483]) ).
fof(f592,plain,
! [X0,X1] : inverse(inverse(double_divide(double_divide(X0,X1),X0))) = X1,
inference(backward_demodulation,[],[f244,f520]) ).
fof(f628,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(inverse(double_divide(X1,X0)))) = inverse(double_divide(double_divide(X2,inverse(inverse(double_divide(X0,inverse(double_divide(X1,inverse(X3))))))),X3)),
inference(forward_demodulation,[],[f496,f483]) ).
fof(f632,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(X2)))) = inverse(double_divide(X2,inverse(double_divide(X1,X0)))),
inference(forward_demodulation,[],[f492,f483]) ).
fof(f633,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(X0)) = inverse(double_divide(double_divide(X2,inverse(X0)),inverse(double_divide(X2,X1)))),
inference(forward_demodulation,[],[f491,f520]) ).
fof(f634,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X0,X3)) = inverse(double_divide(double_divide(double_divide(X1,X2),inverse(X3)),double_divide(X1,inverse(double_divide(inverse(X0),X2))))),
inference(forward_demodulation,[],[f490,f520]) ).
fof(f689,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(inverse(double_divide(X1,X0)))) = inverse(double_divide(double_divide(X2,inverse(inverse(inverse(double_divide(double_divide(X0,X1),X3))))),X3)),
inference(forward_demodulation,[],[f628,f520]) ).
fof(f692,plain,
! [X2,X0,X1] : inverse(double_divide(X2,inverse(double_divide(X1,X0)))) = inverse(double_divide(double_divide(inverse(X1),inverse(X2)),X0)),
inference(forward_demodulation,[],[f632,f483]) ).
fof(f693,plain,
! [X2,X0,X1] : inverse(double_divide(X0,X1)) = inverse(double_divide(double_divide(X2,inverse(X0)),inverse(double_divide(X2,X1)))),
inference(forward_demodulation,[],[f633,f483]) ).
fof(f694,plain,
! [X2,X3,X0,X1] : inverse(double_divide(X0,X3)) = inverse(double_divide(double_divide(double_divide(X1,X2),inverse(X3)),inverse(double_divide(double_divide(X1,X2),X0)))),
inference(forward_demodulation,[],[f634,f507]) ).
fof(f739,plain,
! [X2,X0,X1] : inverse(double_divide(X2,inverse(double_divide(X1,X0)))) = inverse(double_divide(inverse(double_divide(X2,X1)),X0)),
inference(forward_demodulation,[],[f692,f483]) ).
fof(f740,plain,
! [X3,X0] : inverse(double_divide(X0,X3)) = inverse(double_divide(X3,X0)),
inference(forward_demodulation,[],[f694,f693]) ).
fof(f853,plain,
! [X0,X1] : double_divide(X1,inverse(inverse(X0))) = inverse(inverse(double_divide(X1,X0))),
inference(superposition,[],[f486,f486]) ).
fof(f854,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,inverse(double_divide(X0,inverse(X0)))),
inference(superposition,[],[f486,f234]) ).
fof(f857,plain,
! [X0,X1] : inverse(X1) = inverse(double_divide(double_divide(X1,X0),X0)),
inference(forward_demodulation,[],[f854,f520]) ).
fof(f861,plain,
! [X3,X1] : inverse(inverse(double_divide(X1,double_divide(X1,X3)))) = X3,
inference(backward_demodulation,[],[f486,f853]) ).
fof(f863,plain,
! [X2,X0,X1] : double_divide(X2,inverse(X1)) = inverse(double_divide(inverse(inverse(double_divide(X2,double_divide(X0,inverse(X0))))),X1)),
inference(backward_demodulation,[],[f543,f853]) ).
fof(f866,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X2,inverse(inverse(inverse(double_divide(double_divide(X0,X1),X3))))),X3)) = inverse(inverse(double_divide(X2,double_divide(X1,X0)))),
inference(backward_demodulation,[],[f689,f853]) ).
fof(f868,plain,
! [X2,X0,X1] : inverse(inverse(double_divide(double_divide(double_divide(inverse(X1),X2),X2),double_divide(X0,inverse(X0))))) = X1,
inference(backward_demodulation,[],[f407,f853]) ).
fof(f870,plain,
! [X0,X1] : inverse(X1) = inverse(double_divide(X0,double_divide(X1,X0))),
inference(forward_demodulation,[],[f857,f740]) ).
fof(f871,plain,
! [X2,X1] : inverse(double_divide(double_divide(inverse(X1),X2),X2)) = X1,
inference(forward_demodulation,[],[f868,f505]) ).
fof(f881,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = inverse(double_divide(X3,double_divide(X2,inverse(inverse(inverse(double_divide(double_divide(X0,X1),X3))))))),
inference(forward_demodulation,[],[f866,f740]) ).
fof(f883,plain,
! [X2,X1] : inverse(double_divide(inverse(X2),X1)) = double_divide(X2,inverse(X1)),
inference(forward_demodulation,[],[f863,f505]) ).
fof(f890,plain,
! [X2,X1] : inverse(double_divide(X2,double_divide(inverse(X1),X2))) = X1,
inference(forward_demodulation,[],[f871,f740]) ).
fof(f902,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = inverse(double_divide(X3,inverse(inverse(double_divide(X2,inverse(double_divide(double_divide(X0,X1),X3))))))),
inference(forward_demodulation,[],[f881,f853]) ).
fof(f904,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(X1,X2),X0)) = double_divide(X1,double_divide(X0,inverse(X2))),
inference(backward_demodulation,[],[f507,f883]) ).
fof(f905,plain,
! [X0,X1] : inverse(double_divide(X0,inverse(X1))) = double_divide(X1,inverse(X0)),
inference(backward_demodulation,[],[f565,f883]) ).
fof(f906,plain,
! [X2,X0,X1] : inverse(double_divide(X2,inverse(double_divide(X1,X0)))) = double_divide(double_divide(X2,X1),inverse(X0)),
inference(backward_demodulation,[],[f739,f883]) ).
fof(f912,plain,
! [X1] : inverse(inverse(X1)) = X1,
inference(forward_demodulation,[],[f890,f870]) ).
fof(f926,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = inverse(inverse(inverse(double_divide(X3,double_divide(X2,inverse(double_divide(double_divide(X0,X1),X3))))))),
inference(forward_demodulation,[],[f902,f853]) ).
fof(f950,plain,
! [X2,X0,X1] : double_divide(double_divide(X2,X1),inverse(X0)) = double_divide(double_divide(X1,X0),inverse(X2)),
inference(backward_demodulation,[],[f906,f905]) ).
fof(f961,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[],[f592,f912]) ).
fof(f969,plain,
! [X3,X1] : double_divide(X1,double_divide(X1,X3)) = X3,
inference(backward_demodulation,[],[f861,f912]) ).
fof(f978,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = inverse(double_divide(X3,double_divide(X2,inverse(double_divide(double_divide(X0,X1),X3))))),
inference(forward_demodulation,[],[f926,f912]) ).
fof(f1021,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = inverse(inverse(double_divide(double_divide(X3,double_divide(double_divide(X0,X1),X3)),X2))),
inference(forward_demodulation,[],[f978,f904]) ).
fof(f1048,plain,
! [X2,X3,X0,X1] : inverse(inverse(double_divide(X2,double_divide(X1,X0)))) = double_divide(double_divide(X3,double_divide(double_divide(X0,X1),X3)),X2),
inference(forward_demodulation,[],[f1021,f912]) ).
fof(f1066,plain,
! [X2,X3,X0,X1] : double_divide(X2,double_divide(X1,X0)) = double_divide(double_divide(X3,double_divide(double_divide(X0,X1),X3)),X2),
inference(forward_demodulation,[],[f1048,f912]) ).
fof(f1095,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[],[f961,f969]) ).
fof(f1096,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(superposition,[],[f961,f961]) ).
fof(f1100,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,X1),X2) = double_divide(X2,double_divide(X1,X0)),
inference(backward_demodulation,[],[f1066,f1096]) ).
fof(f1236,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| spl0_1 ),
inference(superposition,[],[f9,f1095]) ).
fof(f1249,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1236]) ).
fof(f1250,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1249]) ).
fof(f1275,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,f740]) ).
fof(f1276,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(double_divide(c3,b3),inverse(a3))
| spl0_2 ),
inference(forward_demodulation,[],[f1275,f905]) ).
fof(f1277,plain,
( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(double_divide(b3,a3),inverse(c3))
| spl0_2 ),
inference(forward_demodulation,[],[f1276,f950]) ).
fof(f1278,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1277,f905]) ).
fof(f1279,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1278]) ).
fof(f1281,plain,
( a2 != double_divide(double_divide(b2,inverse(b2)),inverse(a2))
| spl0_3 ),
inference(forward_demodulation,[],[f17,f905]) ).
fof(f1283,plain,
( a2 != double_divide(double_divide(a2,b2),inverse(inverse(b2)))
| spl0_3 ),
inference(forward_demodulation,[],[f1281,f950]) ).
fof(f1285,plain,
( a2 != double_divide(inverse(inverse(b2)),double_divide(b2,a2))
| spl0_3 ),
inference(forward_demodulation,[],[f1283,f1100]) ).
fof(f1286,plain,
( a2 != double_divide(b2,double_divide(b2,a2))
| spl0_3 ),
inference(forward_demodulation,[],[f1285,f912]) ).
fof(f1287,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f1286,f969]) ).
fof(f1288,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f1287]) ).
fof(f1290,plain,
( inverse(double_divide(a1,inverse(a1))) != double_divide(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f21,f905]) ).
fof(f1292,plain,
( double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f1290,f905]) ).
fof(f1294,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f1292,f404]) ).
fof(f1295,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f1294]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f1250]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f1279]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f1288]) ).
cnf(s6,plain,
spl0_4,
inference(sat_conversion,[],[f1295]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5,s4,s3]) ).
fof(f1297,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:19:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/0.73 % (3727926)Will run a generic schedule for satisfiability detection.
% 1.59/0.73 % (3727942)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1294635926:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.59/0.73 % (3727937)% WARNING: option uhcvi not known.
% 1.59/0.73 % (3727936)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1328332089_3000 on theBenchmark for (3000ds/0Mi)
% 1.59/0.73 % (3727943)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2510006219:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.59/0.73 % TRYING [1]
% 1.59/0.73 % (3727937)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4088311064:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.59/0.73 % TRYING [2]
% 1.59/0.73 % (3727941)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3347439907:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.59/0.73 % TRYING [3]
% 1.59/0.73 % (3727938)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4113216604:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.59/0.73 % (3727940)dis+10_1_sil=32000:sp=arity:random_seed=3673571546:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.59/0.73 % TRYING [4]
% 1.59/0.73 % (3727942)Instruction limit reached!
% 1.59/0.73 % (3727942)------------------------------
% 1.59/0.73 % (3727942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.73 % (3727942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.73 % (3727942)CaDiCaL version: 2.1.3
% 1.59/0.73 % (3727942)Termination reason: Instruction limit
% 1.59/0.73 % (3727942)Termination phase: Saturation
% 1.59/0.73 % (3727942)Time elapsed: 0.060 s
% 1.59/0.73 % (3727942)Peak memory usage: 13 MB
% 1.59/0.73 % (3727942)Instructions burned: 133 (million)
% 1.59/0.73 % (3727952)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=568711569:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.59/0.73 % TRYING [1]
% 1.59/0.73 % TRYING [2]
% 1.59/0.73 % TRYING [3]
% 1.59/0.73 % TRYING [4]
% 1.59/0.73 % (3727940)Instruction limit reached!
% 1.59/0.73 % (3727940)------------------------------
% 1.59/0.73 % (3727940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.73 % (3727940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.73 % (3727940)CaDiCaL version: 2.1.3
% 1.59/0.73 % (3727940)Termination reason: Instruction limit
% 1.59/0.73 % (3727940)Termination phase: Saturation
% 1.59/0.73 % (3727940)Time elapsed: 0.088 s
% 1.59/0.73 % (3727940)Peak memory usage: 12 MB
% 1.59/0.73 % (3727940)Instructions burned: 104 (million)
% 1.59/0.73 % (3727941)Instruction limit reached!
% 1.59/0.73 % (3727941)------------------------------
% 1.59/0.73 % (3727941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.73 % (3727941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.73 % (3727941)CaDiCaL version: 2.1.3
% 1.59/0.73 % (3727941)Termination reason: Instruction limit
% 1.59/0.73 % (3727941)Termination phase: Saturation
% 1.59/0.73 % (3727941)Time elapsed: 0.104 s
% 1.59/0.73 % (3727941)Peak memory usage: 13 MB
% 1.59/0.73 % (3727941)Instructions burned: 117 (million)
% 1.59/0.73 % (3727943)Instruction limit reached!
% 1.59/0.73 % (3727943)------------------------------
% 1.59/0.73 % (3727943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.73 % (3727943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.73 % (3727943)CaDiCaL version: 2.1.3
% 1.59/0.73 % (3727943)Termination reason: Instruction limit
% 1.59/0.73 % (3727943)Termination phase: Saturation
% 1.59/0.73 % (3727943)Time elapsed: 0.121 s
% 1.59/0.73 % (3727943)Peak memory usage: 12 MB
% 1.59/0.73 % (3727943)Instructions burned: 159 (million)
% 1.59/0.73 % (3727955)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=14924573:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.59/0.73 % (3727954)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=714862284:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.59/0.73 % (3727956)ott-21_1_sil=16000:fs=off:random_seed=254177617:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.59/0.73 % (3727954) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3727926-3727954"...
% 1.59/0.73 % (3727954)...printing done.
% 1.59/0.73 % (3727954)Refutation found. Thanks to Tanya!
% 1.59/0.73 % SZS status Unsatisfiable for theBenchmark
% 1.59/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 1.59/0.74 % (3727954)------------------------------
% 1.59/0.74 % (3727954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.59/0.74 % (3727954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/0.74 % (3727954)CaDiCaL version: 2.1.3
% 1.59/0.74 % (3727954)Termination reason: Refutation
% 1.59/0.74 % (3727954)Time elapsed: 0.119 s
% 1.59/0.74 % (3727954)Peak memory usage: 13 MB
% 1.59/0.74 % (3727954)Instructions burned: 118 (million)
% 1.59/0.74 % (3727926)Success in time 0.306 s
% 1.59/0.74 % Vampire exiting
%------------------------------------------------------------------------------