%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP587-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:14:55 AM UTC 2026
% Result : Unsatisfiable 5.41s 1.97s
% Output : Refutation 7.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 165 ( 117 unt; 17 def)
% Number of atoms : 319 ( 141 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 304 ( 150 ~; 145 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 253 ( 0 sgn 253 !; 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(definition_unfolding,[],[f3,f2,f2,f2,f2]) ).
fof(f5,definition,
sF0 = double_divide(b3,a3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
double_divide(b3,a3) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = inverse(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
inverse(sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF2 = double_divide(c3,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
double_divide(c3,sF1) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = inverse(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
inverse(sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = double_divide(c3,b3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
double_divide(c3,b3) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = inverse(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
inverse(sF4) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = double_divide(sF5,a3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
double_divide(sF5,a3) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF7 = inverse(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
inverse(sF6) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
sF3 != sF7,
inference(definition_folding,[],[f4,f20,f18,f16,f14,f12,f10,f8,f6]) ).
fof(f22,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(f23,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(f25,definition,
( spl8_1
<=> inverse(sF6) = sF7 ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f27,plain,
( inverse(sF6) = sF7
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,plain,
spl8_1,
inference(avatar_split_clause,[],[f20,f25]) ).
fof(f30,definition,
( spl8_2
<=> inverse(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f32,plain,
( inverse(sF2) = sF3
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,plain,
spl8_2,
inference(avatar_split_clause,[],[f12,f30]) ).
fof(f35,definition,
( spl8_3
<=> double_divide(b3,a3) = sF0 ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f37,plain,
( double_divide(b3,a3) = sF0
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,plain,
spl8_3,
inference(avatar_split_clause,[],[f6,f35]) ).
fof(f41,definition,
( spl8_4
<=> inverse(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f43,plain,
( inverse(sF0) = sF1
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
spl8_4,
inference(avatar_split_clause,[],[f8,f41]) ).
fof(f48,definition,
( spl8_5
<=> double_divide(c3,b3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
fof(f50,plain,
( double_divide(c3,b3) = sF4
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
spl8_5,
inference(avatar_split_clause,[],[f14,f48]) ).
fof(f54,definition,
( spl8_6
<=> double_divide(sF5,a3) = sF6 ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
fof(f56,plain,
( double_divide(sF5,a3) = sF6
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
spl8_6,
inference(avatar_split_clause,[],[f18,f54]) ).
fof(f59,definition,
( spl8_7
<=> inverse(sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f61,plain,
( inverse(sF4) = sF5
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
spl8_7,
inference(avatar_split_clause,[],[f16,f59]) ).
fof(f64,definition,
( spl8_8
<=> double_divide(c3,sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f66,plain,
( double_divide(c3,sF1) = sF2
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
spl8_8,
inference(avatar_split_clause,[],[f10,f64]) ).
fof(f70,definition,
( spl8_9
<=> sF3 = sF7 ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f72,plain,
( sF3 != sF7
| spl8_9 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,plain,
~ spl8_9,
inference(avatar_split_clause,[],[f21,f70]) ).
fof(f116,plain,
! [X0,X1] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(X0)) = X1,
inference(superposition,[],[f22,f1]) ).
fof(f135,plain,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X0))),X2) = double_divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f116,f1]) ).
fof(f136,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,[],[f116,f22]) ).
fof(f137,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(inverse(double_divide(X1,inverse(X0))))) = X1,
inference(superposition,[],[f116,f116]) ).
fof(f151,plain,
! [X3,X1] : double_divide(X1,inverse(double_divide(inverse(X3),inverse(X1)))) = X3,
inference(backward_demodulation,[],[f22,f136]) ).
fof(f166,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,[],[f23,f135]) ).
fof(f205,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,[],[f166,f166]) ).
fof(f224,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f151,f166]) ).
fof(f254,plain,
! [X0,X1] : double_divide(double_divide(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[],[f151,f224]) ).
fof(f257,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(inverse(X0),inverse(inverse(X0))),
inference(superposition,[],[f116,f224]) ).
fof(f258,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(X0)) = double_divide(inverse(X0),inverse(double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))))),
inference(superposition,[],[f166,f224]) ).
fof(f259,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(X1)) = double_divide(inverse(X1),inverse(X0)),
inference(forward_demodulation,[],[f258,f224]) ).
fof(f289,plain,
! [X0,X1] : double_divide(X0,inverse(double_divide(inverse(X0),inverse(X1)))) = X1,
inference(superposition,[],[f151,f259]) ).
fof(f292,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(double_divide(X2,inverse(X0)))) = double_divide(X2,inverse(double_divide(inverse(X0),inverse(X1)))),
inference(superposition,[],[f166,f259]) ).
fof(f406,plain,
! [X0,X1] : double_divide(X1,inverse(X0)) = double_divide(inverse(X0),inverse(inverse(X1))),
inference(superposition,[],[f289,f151]) ).
fof(f411,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f224,f289]) ).
fof(f414,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(X1,inverse(X0))) = X1,
inference(backward_demodulation,[],[f137,f411]) ).
fof(f419,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(inverse(X0),X0),
inference(backward_demodulation,[],[f257,f411]) ).
fof(f422,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = double_divide(X1,inverse(X0)),
inference(forward_demodulation,[],[f406,f411]) ).
fof(f430,plain,
( ! [X0] : double_divide(sF1,X0) = double_divide(X0,sF1)
| ~ spl8_4 ),
inference(superposition,[],[f422,f43]) ).
fof(f441,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(double_divide(X2,X0))) = double_divide(X2,inverse(double_divide(X0,inverse(X1)))),
inference(superposition,[],[f166,f422]) ).
fof(f459,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,inverse(double_divide(X0,inverse(X1)))),
inference(superposition,[],[f151,f411]) ).
fof(f461,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,X2))) = double_divide(X1,inverse(double_divide(X0,X2))),
inference(superposition,[],[f166,f411]) ).
fof(f468,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[],[f422,f411]) ).
fof(f509,plain,
! [X2,X0,X1] : double_divide(inverse(X2),inverse(double_divide(X0,X1))) = double_divide(X1,inverse(double_divide(inverse(X2),X0))),
inference(superposition,[],[f166,f468]) ).
fof(f540,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(X2,X0))) = double_divide(X2,inverse(double_divide(X0,X1))),
inference(superposition,[],[f461,f468]) ).
fof(f545,plain,
( ! [X0] : double_divide(X0,inverse(sF0)) = double_divide(b3,inverse(double_divide(X0,a3)))
| ~ spl8_3 ),
inference(superposition,[],[f461,f37]) ).
fof(f546,plain,
( ! [X0] : double_divide(X0,inverse(sF4)) = double_divide(c3,inverse(double_divide(X0,b3)))
| ~ spl8_5 ),
inference(superposition,[],[f461,f50]) ).
fof(f547,plain,
( ! [X0] : double_divide(X0,inverse(sF2)) = double_divide(c3,inverse(double_divide(X0,sF1)))
| ~ spl8_8 ),
inference(superposition,[],[f461,f66]) ).
fof(f565,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(X1,X2))) = double_divide(inverse(double_divide(X0,X2)),X1),
inference(superposition,[],[f468,f461]) ).
fof(f566,plain,
! [X2,X3,X0,X1] : double_divide(X1,inverse(double_divide(inverse(X3),inverse(double_divide(X0,X2))))) = double_divide(inverse(X3),inverse(double_divide(X0,inverse(double_divide(X1,X2))))),
inference(superposition,[],[f166,f461]) ).
fof(f571,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(X1)) = double_divide(double_divide(X1,X2),inverse(double_divide(X2,inverse(X0)))),
inference(backward_demodulation,[],[f135,f565]) ).
fof(f584,plain,
( ! [X0] : double_divide(X0,sF3) = double_divide(c3,inverse(double_divide(X0,sF1)))
| ~ spl8_2
| ~ spl8_8 ),
inference(forward_demodulation,[],[f547,f32]) ).
fof(f585,plain,
( ! [X0] : double_divide(X0,sF5) = double_divide(c3,inverse(double_divide(X0,b3)))
| ~ spl8_5
| ~ spl8_7 ),
inference(forward_demodulation,[],[f546,f61]) ).
fof(f586,plain,
( ! [X0] : double_divide(X0,sF1) = double_divide(b3,inverse(double_divide(X0,a3)))
| ~ spl8_3
| ~ spl8_4 ),
inference(forward_demodulation,[],[f545,f43]) ).
fof(f599,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(X1)) = double_divide(X2,inverse(double_divide(double_divide(X1,X2),inverse(X0)))),
inference(forward_demodulation,[],[f571,f461]) ).
fof(f600,plain,
( ! [X0] : double_divide(X0,sF3) = double_divide(sF1,inverse(double_divide(c3,X0)))
| ~ spl8_2
| ~ spl8_8 ),
inference(forward_demodulation,[],[f584,f540]) ).
fof(f601,plain,
( ! [X0] : double_divide(X0,sF5) = double_divide(b3,inverse(double_divide(c3,X0)))
| ~ spl8_5
| ~ spl8_7 ),
inference(forward_demodulation,[],[f585,f540]) ).
fof(f602,plain,
( ! [X0] : double_divide(X0,sF1) = double_divide(a3,inverse(double_divide(b3,X0)))
| ~ spl8_3
| ~ spl8_4 ),
inference(forward_demodulation,[],[f586,f540]) ).
fof(f679,plain,
( ! [X0] : double_divide(inverse(X0),inverse(sF6)) = double_divide(sF5,inverse(double_divide(a3,inverse(X0))))
| ~ spl8_6 ),
inference(superposition,[],[f441,f56]) ).
fof(f701,plain,
! [X2,X3,X0,X1] : double_divide(X3,inverse(double_divide(inverse(X0),inverse(double_divide(X1,X2))))) = double_divide(inverse(double_divide(X2,inverse(X0))),inverse(double_divide(X3,X1))),
inference(superposition,[],[f441,f441]) ).
fof(f728,plain,
! [X2,X0,X1] : double_divide(X0,inverse(double_divide(inverse(X2),X1))) = double_divide(X0,inverse(double_divide(X1,inverse(X2)))),
inference(superposition,[],[f461,f441]) ).
fof(f739,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,X2))) = double_divide(X2,inverse(double_divide(X1,inverse(X0)))),
inference(superposition,[],[f461,f441]) ).
fof(f747,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X2))) = double_divide(X2,inverse(double_divide(inverse(X1),inverse(X0)))),
inference(superposition,[],[f166,f441]) ).
fof(f775,plain,
! [X2,X3,X0,X1] : double_divide(X3,inverse(double_divide(inverse(X0),inverse(double_divide(X1,X2))))) = double_divide(X2,inverse(double_divide(inverse(double_divide(X3,X1)),inverse(X0)))),
inference(forward_demodulation,[],[f701,f565]) ).
fof(f787,plain,
( ! [X0] : double_divide(inverse(X0),sF7) = double_divide(sF5,inverse(double_divide(a3,inverse(X0))))
| ~ spl8_1
| ~ spl8_6 ),
inference(forward_demodulation,[],[f679,f27]) ).
fof(f802,plain,
! [X2,X3,X0,X1] : double_divide(X3,inverse(double_divide(inverse(X0),inverse(double_divide(X1,X2))))) = double_divide(X2,inverse(double_divide(X3,inverse(double_divide(inverse(X0),X1))))),
inference(forward_demodulation,[],[f775,f565]) ).
fof(f1015,plain,
( ! [X0] : double_divide(inverse(double_divide(c3,X0)),sF1) = double_divide(a3,inverse(double_divide(X0,sF5)))
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_7 ),
inference(superposition,[],[f602,f601]) ).
fof(f1030,plain,
( ! [X0] : double_divide(inverse(double_divide(c3,X0)),sF1) = double_divide(sF5,inverse(double_divide(a3,X0)))
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_7 ),
inference(forward_demodulation,[],[f1015,f540]) ).
fof(f1044,plain,
( ! [X0] : double_divide(sF1,inverse(double_divide(c3,X0))) = double_divide(sF5,inverse(double_divide(a3,X0)))
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_7 ),
inference(forward_demodulation,[],[f1030,f430]) ).
fof(f1053,plain,
( ! [X0] : double_divide(X0,sF3) = double_divide(sF5,inverse(double_divide(a3,X0)))
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f1044,f600]) ).
fof(f1056,plain,
( ! [X0] : double_divide(inverse(X0),sF7) = double_divide(inverse(X0),sF3)
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(backward_demodulation,[],[f787,f1053]) ).
fof(f1123,plain,
! [X2,X0,X1] : double_divide(inverse(X1),inverse(inverse(X2))) = double_divide(X2,inverse(double_divide(double_divide(X0,inverse(X0)),inverse(X1)))),
inference(superposition,[],[f599,f419]) ).
fof(f1148,plain,
! [X0,X1] : inverse(double_divide(X1,X0)) = double_divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f459,f599]) ).
fof(f1151,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(double_divide(double_divide(X1,X2),inverse(X0)),inverse(double_divide(inverse(X0),inverse(X1)))),
inference(superposition,[],[f459,f599]) ).
fof(f1164,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(inverse(X1),inverse(double_divide(double_divide(double_divide(X1,X2),inverse(X0)),inverse(X0)))),
inference(forward_demodulation,[],[f1151,f292]) ).
fof(f1166,plain,
! [X0,X1] : inverse(double_divide(X1,X0)) = double_divide(inverse(X1),inverse(X0)),
inference(backward_demodulation,[],[f259,f1148]) ).
fof(f1171,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X2))) = double_divide(X2,inverse(inverse(double_divide(X0,X1)))),
inference(backward_demodulation,[],[f747,f1148]) ).
fof(f1179,plain,
! [X2,X0,X1] : double_divide(X1,inverse(double_divide(inverse(X2),X0))) = inverse(double_divide(double_divide(X0,X1),X2)),
inference(backward_demodulation,[],[f509,f1148]) ).
fof(f1180,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X3),inverse(double_divide(X0,inverse(double_divide(X1,X2))))) = double_divide(X1,inverse(inverse(double_divide(double_divide(X0,X2),X3)))),
inference(backward_demodulation,[],[f566,f1148]) ).
fof(f1182,plain,
! [X2,X0,X1] : double_divide(X2,inverse(double_divide(X1,inverse(X0)))) = inverse(double_divide(double_divide(X1,X2),X0)),
inference(backward_demodulation,[],[f739,f1148]) ).
fof(f1185,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(X3,inverse(double_divide(inverse(X0),X1))))) = double_divide(X3,inverse(inverse(double_divide(double_divide(X1,X2),X0)))),
inference(backward_demodulation,[],[f802,f1148]) ).
fof(f1190,plain,
! [X2,X3,X0,X1] : double_divide(X3,inverse(double_divide(X0,inverse(double_divide(inverse(X1),X2))))) = inverse(double_divide(double_divide(X3,inverse(double_divide(X0,X2))),X1)),
inference(backward_demodulation,[],[f205,f1148]) ).
fof(f1225,plain,
! [X2,X1] : double_divide(X2,inverse(X1)) = double_divide(inverse(X1),inverse(inverse(X2))),
inference(forward_demodulation,[],[f1123,f254]) ).
fof(f1245,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(inverse(X1),inverse(double_divide(inverse(X0),double_divide(double_divide(X1,X2),inverse(X0))))),
inference(forward_demodulation,[],[f1164,f728]) ).
fof(f1271,plain,
! [X2,X3,X0,X1] : double_divide(X2,inverse(double_divide(X3,inverse(double_divide(inverse(X0),X1))))) = double_divide(X3,double_divide(double_divide(X1,X2),X0)),
inference(forward_demodulation,[],[f1185,f411]) ).
fof(f1281,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X3,inverse(double_divide(X0,X2))),X1)) = inverse(double_divide(double_divide(X0,X3),double_divide(inverse(X1),X2))),
inference(backward_demodulation,[],[f1190,f1182]) ).
fof(f1293,plain,
! [X2,X3,X0,X1] : double_divide(inverse(X3),inverse(double_divide(X0,inverse(double_divide(X1,X2))))) = double_divide(X1,double_divide(double_divide(X0,X2),X3)),
inference(forward_demodulation,[],[f1180,f411]) ).
fof(f1304,plain,
! [X2,X0,X1] : double_divide(inverse(X0),inverse(double_divide(inverse(X1),X2))) = double_divide(X2,double_divide(X0,X1)),
inference(forward_demodulation,[],[f1171,f411]) ).
fof(f1309,plain,
! [X0,X1] : inverse(double_divide(X1,X0)) = inverse(double_divide(X0,X1)),
inference(forward_demodulation,[],[f1166,f1148]) ).
fof(f1332,plain,
! [X2,X1] : inverse(double_divide(inverse(X2),X1)) = double_divide(X2,inverse(X1)),
inference(forward_demodulation,[],[f1225,f1148]) ).
fof(f1352,plain,
! [X2,X0,X1] : inverse(X2) = inverse(double_divide(double_divide(double_divide(double_divide(X1,X2),inverse(X0)),inverse(X1)),X0)),
inference(forward_demodulation,[],[f1245,f1179]) ).
fof(f1375,plain,
! [X2,X3,X0,X1] : double_divide(X3,double_divide(double_divide(X1,X2),X0)) = inverse(double_divide(double_divide(X3,X2),double_divide(inverse(X0),X1))),
inference(forward_demodulation,[],[f1271,f1182]) ).
fof(f1392,plain,
! [X2,X3,X0,X1] : double_divide(X1,double_divide(double_divide(X0,X2),X3)) = inverse(double_divide(double_divide(X0,inverse(X3)),double_divide(X1,X2))),
inference(forward_demodulation,[],[f1293,f1182]) ).
fof(f1400,plain,
! [X2,X0,X1] : double_divide(X2,double_divide(X0,X1)) = inverse(double_divide(double_divide(X2,inverse(X0)),X1)),
inference(forward_demodulation,[],[f1304,f1179]) ).
fof(f1423,plain,
! [X2,X0,X1] : inverse(double_divide(double_divide(X0,X1),X2)) = double_divide(X1,double_divide(X2,inverse(X0))),
inference(backward_demodulation,[],[f1179,f1332]) ).
fof(f1443,plain,
! [X2,X0,X1] : inverse(X2) = inverse(double_divide(X0,double_divide(double_divide(double_divide(X1,X2),inverse(X0)),inverse(X1)))),
inference(forward_demodulation,[],[f1352,f1309]) ).
fof(f1463,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X3,inverse(double_divide(X0,X2))),X1)) = double_divide(X0,double_divide(double_divide(X2,X3),X1)),
inference(backward_demodulation,[],[f1281,f1375]) ).
fof(f1486,plain,
! [X2,X3,X0,X1] : double_divide(X1,double_divide(double_divide(X0,X2),X3)) = double_divide(X0,double_divide(X3,double_divide(X1,X2))),
inference(backward_demodulation,[],[f1392,f1400]) ).
fof(f1506,plain,
! [X0,X1] : inverse(double_divide(double_divide(X0,inverse(X0)),X1)) = X1,
inference(backward_demodulation,[],[f414,f1423]) ).
fof(f1524,plain,
! [X2,X0,X1] : inverse(X2) = inverse(inverse(double_divide(double_divide(X1,X0),double_divide(double_divide(X1,X2),inverse(X0))))),
inference(forward_demodulation,[],[f1443,f1423]) ).
fof(f1541,plain,
! [X2,X3,X0,X1] : double_divide(X0,double_divide(double_divide(X2,X3),X1)) = double_divide(X3,double_divide(double_divide(X0,X2),X1)),
inference(forward_demodulation,[],[f1463,f1400]) ).
fof(f1562,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f1506,f1400]) ).
fof(f1579,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(double_divide(X1,X0),double_divide(double_divide(X1,X2),inverse(X0))),
inference(forward_demodulation,[],[f1524,f411]) ).
fof(f1625,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(X1,double_divide(inverse(X0),double_divide(double_divide(X1,X0),X2))),
inference(forward_demodulation,[],[f1579,f1486]) ).
fof(f1664,plain,
! [X2,X0,X1] : inverse(X2) = double_divide(X1,double_divide(X0,double_divide(double_divide(inverse(X0),X1),X2))),
inference(forward_demodulation,[],[f1625,f1541]) ).
fof(f1946,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,X1),X3) = double_divide(X2,double_divide(X0,double_divide(double_divide(X1,X2),X3))),
inference(superposition,[],[f1562,f1541]) ).
fof(f1957,plain,
! [X2,X0] : inverse(X2) = double_divide(double_divide(X0,inverse(X0)),X2),
inference(backward_demodulation,[],[f1664,f1946]) ).
fof(f2122,plain,
( ! [X0] : double_divide(inverse(X0),sF3) = inverse(double_divide(sF2,X0))
| ~ spl8_2 ),
inference(superposition,[],[f1148,f32]) ).
fof(f2170,plain,
( ! [X0] : double_divide(inverse(X0),sF7) = inverse(double_divide(sF2,X0))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(backward_demodulation,[],[f1056,f2122]) ).
fof(f2553,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X1,inverse(X1)),double_divide(double_divide(X0,X2),X3)) = double_divide(X2,double_divide(inverse(X0),X3)),
inference(superposition,[],[f1541,f1957]) ).
fof(f2571,plain,
! [X2,X3,X0] : inverse(double_divide(double_divide(X0,X2),X3)) = double_divide(X2,double_divide(inverse(X0),X3)),
inference(forward_demodulation,[],[f2553,f1957]) ).
fof(f2764,plain,
( ! [X0] : double_divide(sF2,inverse(X0)) = inverse(double_divide(sF3,X0))
| ~ spl8_2 ),
inference(superposition,[],[f1332,f32]) ).
fof(f3081,plain,
( ! [X0] : sF7 = double_divide(inverse(X0),inverse(double_divide(sF2,X0)))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(superposition,[],[f1562,f2170]) ).
fof(f3088,plain,
( ! [X0] : sF7 = double_divide(sF2,inverse(double_divide(inverse(X0),X0)))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3081,f461]) ).
fof(f3107,plain,
( ! [X0] : sF7 = inverse(double_divide(sF3,double_divide(inverse(X0),X0)))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3088,f2764]) ).
fof(f3118,plain,
( ! [X0] : sF7 = inverse(inverse(double_divide(double_divide(X0,sF3),X0)))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3107,f2571]) ).
fof(f3132,plain,
( ! [X0] : sF7 = double_divide(double_divide(X0,sF3),X0)
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3118,f411]) ).
fof(f3135,plain,
( ! [X0] : sF7 = double_divide(X0,double_divide(X0,sF3))
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3132,f468]) ).
fof(f3137,plain,
( sF3 = sF7
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8 ),
inference(forward_demodulation,[],[f3135,f1562]) ).
fof(f3139,plain,
( $false
| ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| spl8_9 ),
inference(forward_subsumption_resolution,[],[f3137,f72]) ).
fof(f3140,plain,
( ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| spl8_9 ),
inference(avatar_contradiction_clause,[],[f3139]) ).
cnf(s1,plain,
spl8_1,
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
spl8_2,
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
spl8_3,
inference(sat_conversion,[],[f38]) ).
cnf(s4,plain,
spl8_4,
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
spl8_5,
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
spl8_6,
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
spl8_7,
inference(sat_conversion,[],[f62]) ).
cnf(s8,plain,
spl8_8,
inference(sat_conversion,[],[f67]) ).
cnf(s9,plain,
~ spl8_9,
inference(sat_conversion,[],[f73]) ).
cnf(s16,plain,
( ~ spl8_1
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| ~ spl8_7
| ~ spl8_8
| spl8_9 ),
inference(sat_conversion,[],[f3140]) ).
cnf(s23,plain,
~ spl8_1,
inference(rat,[],[s16,s9,s8,s7,s6,s5,s4,s3,s2]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s23]) ).
fof(f3141,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP587-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n017.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 10:03:05 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 5.41/1.97 % (2312211)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.41/1.97 % (2312220)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3000063924:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.41/1.97 % (2312216)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1024838583:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.41/1.97 % (2312217)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4069126409:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.41/1.97 % (2312218)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=706730928:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.41/1.97 % (2312221)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1135268499:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.41/1.97 % (2312220)Instruction limit reached!
% 5.41/1.97 % (2312220)------------------------------
% 5.41/1.97 % (2312220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.41/1.97 % (2312220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.41/1.97 % (2312220)CaDiCaL version: 2.1.3
% 5.41/1.97 % (2312220)Termination reason: Instruction limit
% 5.41/1.97 % (2312220)Termination phase: Saturation
% 5.41/1.97 % (2312220)Time elapsed: 0.054 s
% 5.41/1.97 % (2312220)Peak memory usage: 90 MB
% 5.41/1.97 % (2312220)Instructions burned: 182 (million)
% 5.41/1.97 % (2312222)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=909931091:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.41/1.97 % (2312219)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2408156814:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.41/1.97 % (2312228)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1262207489:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 5.41/1.97 % (2312221)Instruction limit reached!
% 5.41/1.97 % (2312221)------------------------------
% 5.41/1.97 % (2312221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.41/1.97 % (2312221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.41/1.97 % (2312221)CaDiCaL version: 2.1.3
% 5.41/1.97 % (2312221)Termination reason: Instruction limit
% 5.41/1.97 % (2312221)Termination phase: Saturation
% 5.41/1.97 % (2312221)Time elapsed: 0.155 s
% 5.41/1.97 % (2312221)Peak memory usage: 89 MB
% 5.41/1.97 % (2312221)Instructions burned: 257 (million)
% 5.41/1.97 % (2312219)Instruction limit reached!
% 5.41/1.97 % (2312219)------------------------------
% 5.41/1.97 % (2312219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.41/1.97 % (2312219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.41/1.97 % (2312219)CaDiCaL version: 2.1.3
% 5.41/1.97 % (2312219)Termination reason: Instruction limit
% 5.41/1.97 % (2312219)Termination phase: Saturation
% 5.41/1.97 % (2312219)Time elapsed: 0.134 s
% 5.41/1.97 % (2312219)Peak memory usage: 88 MB
% 5.41/1.97 % (2312219)Instructions burned: 138 (million)
% 5.41/1.97 % (2312232)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1214180671:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 5.41/1.97 % (2312233)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2121590586:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.41/1.97 % (2312233)Instruction limit reached!
% 5.41/1.97 % (2312233)------------------------------
% 5.41/1.97 % (2312233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.41/1.97 % (2312233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.41/1.97 % (2312233)CaDiCaL version: 2.1.3
% 5.41/1.97 % (2312233)Termination reason: Instruction limit
% 5.41/1.97 % (2312233)Termination phase: Saturation
% 5.41/1.97 % (2312233)Time elapsed: 0.171 s
% 5.41/1.97 % (2312233)Peak memory usage: 89 MB
% 5.41/1.97 % (2312233)Instructions burned: 215 (million)
% 5.41/1.97 % (2312238)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3199712016:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 5.41/1.97 % (2312222)Instruction limit reached!
% 5.41/1.97 % (2312222)------------------------------
% 5.41/1.97 % (2312222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.41/1.97 % (2312222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.41/1.97 % (2312222)CaDiCaL version: 2.1.3
% 5.41/1.97 % (2312222)Termination reason: Instruction limit
% 5.41/1.97 % (2312222)Termination phase: Saturation
% 5.41/1.97 % (2312222)Time elapsed: 0.649 s
% 5.41/1.97 % (2312222)Peak memory usage: 102 MB
% 5.41/1.97 % (2312222)Instructions burned: 1187 (million)
% 5.41/1.97 % (2312216)First to succeed.
% 5.41/1.97 % (2312216)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2312211"
% 5.41/1.97 % (2312217)Also succeeded, but the first one will report.
% 5.41/1.97 % (2312228)Also succeeded, but the first one will report.
% 5.41/1.97 % (2312254)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2865545742:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 5.41/1.97 % (2312216)Refutation found. Thanks to Tanya!
% 5.41/1.97 % SZS status Unsatisfiable for theBenchmark
% 5.41/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 7.81/2.17 % (2312216)------------------------------
% 7.81/2.17 % (2312216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.81/2.17 % (2312216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.81/2.17 % (2312216)CaDiCaL version: 2.1.3
% 7.81/2.17 % (2312216)Termination reason: Refutation
% 7.81/2.17 % (2312216)Time elapsed: 0.689 s
% 7.81/2.17 % (2312216)Peak memory usage: 132 MB
% 7.81/2.17 % (2312216)Instructions burned: 1312 (million)
% 7.81/2.17 % (2312216)------------------------------
% 7.81/2.17 % (2312216)------------------------------
% 7.81/2.17 % (2312211)Success in time 1.011 s
% 7.81/2.17 % Vampire exiting
%------------------------------------------------------------------------------