%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 12:32:25 PM UTC 2026
% Result : Unsatisfiable 38.28s 10.35s
% Output : CNFRefutation 38.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 2
% Syntax : Number of formulae : 94 ( 90 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 341 ( 341 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(U,inverse(U)))) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f6,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,X4),X5)),X3),X4),multiply(X6,inverse(X6))),X5))) = X2,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(X3,inverse(X3)))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f39,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))) = X1,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f52,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),X1)),
inference(paramodulation,[status(thm)],[f7,f34]) ).
fof(f77,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X0))) = inverse(multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f34,f39]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X4)),X5),inverse(X5)),multiply(X6,inverse(X6))),X4))) = X1,
inference(paramodulation,[status(thm)],[f39,f39]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X4)),X5),inverse(X5)),multiply(X6,inverse(X6))),X4))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f39,f34]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(multiply(multiply(multiply(X3,multiply(inverse(multiply(multiply(X4,X5),X3)),X4)),X5),multiply(X6,inverse(X6))),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X7,X8),X9)),X7),X8),multiply(X10,inverse(X10))),X9)))) = X2,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,X4),X5)),X3),X4),inverse(multiply(multiply(multiply(X6,multiply(inverse(multiply(multiply(X7,X8),X6)),X7)),X8),multiply(X9,inverse(X9))))),X5))) = X2,
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f195,plain,
! [X0,X1,X2] : multiply(X0,inverse(X0)) = multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),
inference(paramodulation,[status(thm)],[f77,f7]) ).
fof(f262,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X3))))),multiply(X4,inverse(X4)))) = X3,
inference(paramodulation,[status(thm)],[f195,f39]) ).
fof(f263,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),X2),multiply(X3,inverse(X3)))) = inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),X2)),
inference(paramodulation,[status(thm)],[f195,f34]) ).
fof(f290,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(inverse(multiply(X1,inverse(X1))),X2)),inverse(X2)),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f195,f5]) ).
fof(f311,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),inverse(X1))) = multiply(X2,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f34,f290]) ).
fof(f361,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f311,f3]) ).
fof(f407,plain,
! [X0,X1] : inverse(inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))))) = X1,
inference(backward_demodulation,[status(thm)],[f361,f262]) ).
fof(f408,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(inverse(inverse(multiply(X1,inverse(X1)))),X0)),
inference(backward_demodulation,[status(thm)],[f361,f263]) ).
fof(f417,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2)))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f408,f52]) ).
fof(f456,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X4)))),X4))) = X1,
inference(paramodulation,[status(thm)],[f407,f39]) ).
fof(f458,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1)))),X1),X2)),X3),inverse(X3)),multiply(X4,inverse(X4)))) = X2,
inference(paramodulation,[status(thm)],[f407,f39]) ).
fof(f459,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X4)))),X4))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f407,f34]) ).
fof(f461,plain,
! [X0,X1,X2] : multiply(X0,inverse(X0)) = multiply(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2)))),X2),
inference(paramodulation,[status(thm)],[f407,f7]) ).
fof(f474,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X1,inverse(X1))))))),X0)),
inference(paramodulation,[status(thm)],[f408,f408]) ).
fof(f497,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0)))))),X1),X2),multiply(X3,inverse(X3)))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f408,f34]) ).
fof(f523,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),multiply(X2,inverse(X2)))) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(paramodulation,[status(thm)],[f195,f417]) ).
fof(f563,plain,
! [X0,X1] : inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f417,f407]) ).
fof(f590,plain,
! [X0,X1] : inverse(inverse(multiply(X0,inverse(X0)))) = inverse(inverse(multiply(X1,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f417,f523]) ).
fof(f655,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),inverse(multiply(X2,inverse(X2)))),inverse(inverse(multiply(X3,inverse(X3))))),multiply(X4,inverse(X4)))) = X1,
inference(paramodulation,[status(thm)],[f590,f39]) ).
fof(f657,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(inverse(multiply(X3,inverse(X3))),inverse(inverse(multiply(X4,inverse(X4))))))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f590,f34]) ).
fof(f880,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0)))))),multiply(X1,inverse(X1))),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f563,f417]) ).
fof(f905,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),X1)),
inference(paramodulation,[status(thm)],[f563,f34]) ).
fof(f919,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),inverse(inverse(inverse(inverse(inverse(multiply(X2,inverse(X2))))))))) = inverse(X1),
inference(paramodulation,[status(thm)],[f563,f417]) ).
fof(f922,plain,
! [X0,X1] : inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1))))) = X1,
inference(paramodulation,[status(thm)],[f563,f407]) ).
fof(f932,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))) = X1,
inference(paramodulation,[status(thm)],[f563,f39]) ).
fof(f943,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))) = X1,
inference(paramodulation,[status(thm)],[f563,f3]) ).
fof(f983,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))),inverse(inverse(multiply(X2,inverse(X2))))),multiply(X3,inverse(X3)))) = X0,
inference(backward_demodulation,[status(thm)],[f1054,f655]) ).
fof(f1000,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(inverse(inverse(inverse(X1))),X1),
inference(backward_demodulation,[status(thm)],[f1054,f461]) ).
fof(f1002,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(inverse(inverse(inverse(X3))),X3))) = inverse(multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f1054,f459]) ).
fof(f1003,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(inverse(inverse(X0))),X0),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))) = X1,
inference(backward_demodulation,[status(thm)],[f1054,f458]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(inverse(inverse(inverse(X3))),X3))) = X1,
inference(backward_demodulation,[status(thm)],[f1054,f456]) ).
fof(f1041,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(multiply(multiply(multiply(inverse(X3),X4),inverse(X4)),multiply(X5,inverse(X5))),X3))) = inverse(multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f1054,f107]) ).
fof(f1046,plain,
! [X0,X1,X2,X3,X4,X5] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(multiply(multiply(multiply(inverse(X3),X4),inverse(X4)),multiply(X5,inverse(X5))),X3))) = X1,
inference(backward_demodulation,[status(thm)],[f1054,f99]) ).
fof(f1054,plain,
! [X0,X1] : inverse(multiply(multiply(X0,inverse(X0)),X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f497,f880]) ).
fof(f1060,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1),multiply(X2,inverse(X2)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f408,f905]) ).
fof(f1090,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),inverse(multiply(X2,inverse(X2))))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f1184,f919]) ).
fof(f1091,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),multiply(X2,inverse(X2)))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f1184,f1060]) ).
fof(f1184,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f474,f922]) ).
fof(f1209,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(X0),X1),inverse(X1)),multiply(X2,inverse(X2)))) = X0,
inference(forward_demodulation,[status(thm)],[f474,f932]) ).
fof(f1222,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1209,f943]) ).
fof(f1232,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),inverse(inverse(multiply(X3,inverse(X3)))))) = inverse(multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f1328,f657]) ).
fof(f1328,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X0))),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1184,f1222]) ).
fof(f1361,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),multiply(inverse(inverse(inverse(X2))),X2))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1328,f1002]) ).
fof(f1363,plain,
! [X0,X1] : multiply(multiply(inverse(inverse(inverse(X0))),X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1209,f1003]) ).
fof(f1365,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2))) = X1,
inference(forward_demodulation,[status(thm)],[f1361,f1005]) ).
fof(f1378,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f1054,f1365]) ).
fof(f1396,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(X0,X1),multiply(multiply(multiply(multiply(inverse(X2),X3),inverse(X3)),multiply(X4,inverse(X4))),X2))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1328,f1041]) ).
fof(f1398,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2))) = X1,
inference(forward_demodulation,[status(thm)],[f1396,f1046]) ).
fof(f1462,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1378,f1398]) ).
fof(f1483,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,inverse(X1))))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f1462,f1090]) ).
fof(f1507,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))),inverse(inverse(multiply(X2,inverse(X2)))))) = X0,
inference(backward_demodulation,[status(thm)],[f1545,f983]) ).
fof(f1534,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,X4),X5)),X3),X4),inverse(multiply(multiply(X6,multiply(inverse(multiply(multiply(X7,X8),X6)),X7)),X8))),X5))) = X2,
inference(backward_demodulation,[status(thm)],[f1545,f141]) ).
fof(f1545,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f1328,f1091]) ).
fof(f1689,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),inverse(inverse(multiply(X2,inverse(X2)))))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1328,f1232]) ).
fof(f1845,plain,
! [X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(X1,inverse(X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f1689,f1507]) ).
fof(f1862,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(backward_demodulation,[status(thm)],[f1889,f1363]) ).
fof(f1864,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f1889,f1000]) ).
fof(f1889,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1483,f1845]) ).
fof(f1933,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f1862,f4]) ).
fof(f1942,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f1933]) ).
fof(f1984,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(multiply(multiply(multiply(X3,multiply(inverse(multiply(multiply(X4,X5),X3)),X4)),X5),multiply(X6,inverse(X6))),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X7,X8),X9)),X7),X8),multiply(X10,inverse(X10))),X9)))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f77,f129]) ).
fof(f1991,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : inverse(multiply(multiply(multiply(inverse(multiply(X0,X1)),multiply(X2,inverse(X2))),X0),multiply(multiply(multiply(multiply(X3,multiply(inverse(multiply(multiply(X4,X5),X3)),X4)),X5),multiply(X6,inverse(X6))),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X7,X8),X9)),X7),X8),multiply(X10,inverse(X10))),X9)))) = X1,
inference(paramodulation,[status(thm)],[f1462,f129]) ).
fof(f2045,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] : inverse(multiply(multiply(X0,X1),multiply(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X3,X4),X2)),X3)),X4),multiply(X5,inverse(X5))),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X6,X7),X8)),X6),X7),multiply(X9,inverse(X9))),X8)))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1328,f1984]) ).
fof(f2052,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(X0,X1)),multiply(X2,inverse(X2))),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f2045,f1991]) ).
fof(f2116,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f1864,f1864]) ).
fof(f2139,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f1942,f2116]) ).
fof(f2411,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(X0,multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f1545,f1889]) ).
fof(f2433,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f2509,f2052]) ).
fof(f2509,plain,
! [X0,X1] : X0 = multiply(X0,multiply(X1,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f1889,f2411]) ).
fof(f2677,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f2433,f2433]) ).
fof(f2906,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f2677,f1889]) ).
fof(f3350,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : inverse(multiply(multiply(X0,X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X2,X3),X4)),X2),X3),inverse(multiply(multiply(X5,multiply(inverse(multiply(multiply(X6,X7),X5)),X6)),X7))),X4))) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f1328,f1534]) ).
fof(f3364,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : inverse(multiply(multiply(multiply(inverse(inverse(X0)),X1),X2),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,X4),X5)),X3),X4),inverse(multiply(multiply(X6,multiply(inverse(multiply(multiply(X7,X8),X6)),X7)),X8))),X5))) = inverse(multiply(X0,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f2906,f1534]) ).
fof(f3526,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(inverse(X0)),X1),X2)) = inverse(multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[status(thm)],[f3350,f3364]) ).
fof(f3556,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),X2)) = inverse(multiply(X0,multiply(X1,X2))),
inference(forward_demodulation,[status(thm)],[f1889,f3526]) ).
fof(f6466,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,multiply(X1,X2)))) = multiply(multiply(X0,X1),X2),
inference(paramodulation,[status(thm)],[f3556,f1889]) ).
fof(f6600,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f6620,f2139]) ).
fof(f6620,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f1889,f6466]) ).
fof(f7114,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n015.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sun Sep 20 19:59:25 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.46 % Drodi V4.1.1
% 38.28/10.35 % Refutation found
% 38.28/10.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 38.28/10.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.30/10.42 % Elapsed time: 4.952774 seconds
% 1.30/10.42 % CPU time: 38.949297 seconds
% 1.30/10.42 % Total memory used: 222.605 MB
% 1.30/10.42 % Net memory used: 216.447 MB
%------------------------------------------------------------------------------