%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP422-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:50 PM UTC 2026
% Result : Unsatisfiable 2.07s 0.87s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 5
% Syntax : Number of formulae : 134 ( 134 unt; 3 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 20 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 165 ( 165 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f6,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f7,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f8,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f4,f7,f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1))) = b2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))),multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))))))))),multiply(X0,multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))))) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a2),inverse(multiply(inverse(a2),a2))))))),sF0_fnc)) = X0,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f17,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(inverse(b2),inverse(multiply(inverse(b2),b2))))))),sF1_fnc)) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(X2,inverse(multiply(X2,multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))))))))),multiply(X0,multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))))) = X1,
inference(forward_demodulation,[status(thm)],[f3,f12]) ).
fof(f24,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(multiply(inverse(b2),b2))))))),sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f17]) ).
fof(f25,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(multiply(sF2_fnc,b2))))))),sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f24]) ).
fof(f26,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f6,f25]) ).
fof(f27,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,X0)),sF1_fnc)) = multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(inverse(inverse(sF1_fnc)),inverse(multiply(inverse(inverse(sF1_fnc)),inverse(sF1_fnc))))))),
inference(paramodulation,[status(thm)],[f3,f26]) ).
fof(f28,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),
inference(paramodulation,[status(thm)],[f26,f26]) ).
fof(f29,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f26]) ).
fof(f30,plain,
inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = b2,
inference(paramodulation,[status(thm)],[f5,f26]) ).
fof(f46,plain,
inverse(multiply(inverse(multiply(sF2_fnc,b2)),sF1_fnc)) = multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(multiply(inverse(inverse(sF1_fnc)),inverse(sF1_fnc))))))),
inference(paramodulation,[status(thm)],[f11,f26]) ).
fof(f48,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(b2,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f11,f26]) ).
fof(f65,plain,
inverse(multiply(inverse(sF1_fnc),sF1_fnc)) = multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(inverse(inverse(sF1_fnc)),inverse(multiply(inverse(inverse(sF1_fnc)),inverse(sF1_fnc))))))),
inference(forward_demodulation,[status(thm)],[f6,f46]) ).
fof(f142,plain,
inverse(multiply(inverse(inverse(multiply(inverse(sF1_fnc),sF1_fnc))),multiply(sF2_fnc,inverse(sF1_fnc)))) = b2,
inference(paramodulation,[status(thm)],[f65,f11]) ).
fof(f174,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,X2))),
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f249,plain,
! [X0,X1,X2] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2)))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))) = X1,
inference(paramodulation,[status(thm)],[f9,f3]) ).
fof(f767,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(sF2_fnc,X1),
inference(paramodulation,[status(thm)],[f174,f26]) ).
fof(f791,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),multiply(inverse(a2),inverse(multiply(inverse(a2),a2))))))),sF0_fnc)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f174,f16]) ).
fof(f840,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(forward_demodulation,[status(thm)],[f16,f791]) ).
fof(f855,plain,
! [X0,X1] : multiply(b2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),X0)) = multiply(inverse(multiply(X1,sF1_fnc)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f840]) ).
fof(f870,plain,
! [X0,X1] : multiply(inverse(sF0_fnc),multiply(sF1_fnc,X0)) = multiply(inverse(multiply(X1,a2)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f7,f840]) ).
fof(f872,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,X0)) = multiply(inverse(multiply(X1,b2)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f840]) ).
fof(f880,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,X0)),sF1_fnc) = multiply(inverse(multiply(X1,X0)),multiply(X1,b2)),
inference(paramodulation,[status(thm)],[f6,f840]) ).
fof(f1844,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(sF2_fnc,X0)),sF1_fnc))),multiply(sF2_fnc,inverse(sF1_fnc)))) = X0,
inference(paramodulation,[status(thm)],[f27,f3]) ).
fof(f1914,plain,
multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc) = b2,
inference(backward_demodulation,[status(thm)],[f28,f30]) ).
fof(f1915,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc) = X0,
inference(backward_demodulation,[status(thm)],[f28,f26]) ).
fof(f2041,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(X2,inverse(multiply(X2,multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X4),inverse(multiply(inverse(X4),X4))))))),multiply(X3,X4))))))))),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)))) = X1,
inference(backward_demodulation,[status(thm)],[f2044,f18]) ).
fof(f2042,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X0,X2))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X1),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f2044,f10]) ).
fof(f2044,plain,
! [X0,X1,X2] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f28,f29]) ).
fof(f2136,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(X2,inverse(multiply(X2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)))))))),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f2044,f2041]) ).
fof(f2321,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(inverse(sF0_fnc),multiply(sF1_fnc,X0)))),multiply(inverse(X0),inverse(multiply(inverse(X0),X0))))) = a2,
inference(paramodulation,[status(thm)],[f870,f249]) ).
fof(f3482,plain,
inverse(multiply(inverse(inverse(multiply(inverse(sF0_fnc),sF0_fnc))),multiply(inverse(a2),inverse(multiply(inverse(a2),a2))))) = a2,
inference(paramodulation,[status(thm)],[f7,f2321]) ).
fof(f5942,plain,
multiply(b2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)),b2),
inference(paramodulation,[status(thm)],[f1914,f855]) ).
fof(f6048,plain,
multiply(b2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(sF2_fnc)),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),b2),
inference(forward_demodulation,[status(thm)],[f28,f5942]) ).
fof(f6049,plain,
multiply(b2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = multiply(sF2_fnc,b2),
inference(forward_demodulation,[status(thm)],[f1915,f6048]) ).
fof(f6050,plain,
multiply(b2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6,f6049]) ).
fof(f6060,plain,
! [X0] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f855,f6050]) ).
fof(f6137,plain,
! [X0] : multiply(inverse(X0),multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f1915,f6060]) ).
fof(f6196,plain,
! [X0] : multiply(inverse(X0),X0) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f1915,f6137]) ).
fof(f6225,plain,
inverse(multiply(inverse(inverse(sF1_fnc)),multiply(inverse(a2),inverse(multiply(inverse(a2),a2))))) = a2,
inference(backward_demodulation,[status(thm)],[f6196,f3482]) ).
fof(f6226,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X1),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(sF1_fnc))))),
inference(backward_demodulation,[status(thm)],[f6196,f9]) ).
fof(f6238,plain,
inverse(multiply(inverse(inverse(sF1_fnc)),multiply(sF2_fnc,inverse(sF1_fnc)))) = b2,
inference(backward_demodulation,[status(thm)],[f6196,f142]) ).
fof(f6242,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a2),inverse(sF1_fnc)))))),sF0_fnc)) = X0,
inference(backward_demodulation,[status(thm)],[f6196,f16]) ).
fof(f6248,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(X2),inverse(sF1_fnc)))))),multiply(X0,X2))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X1),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f6196,f2042]) ).
fof(f6274,plain,
inverse(multiply(inverse(multiply(sF2_fnc,inverse(sF1_fnc))),sF1_fnc)) = multiply(sF2_fnc,inverse(sF1_fnc)),
inference(paramodulation,[status(thm)],[f6196,f767]) ).
fof(f6316,plain,
inverse(multiply(inverse(inverse(sF1_fnc)),multiply(inverse(a2),inverse(sF1_fnc)))) = a2,
inference(forward_demodulation,[status(thm)],[f6196,f6225]) ).
fof(f6317,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X1),multiply(inverse(inverse(sF1_fnc)),inverse(sF1_fnc))))),
inference(forward_demodulation,[status(thm)],[f6196,f6226]) ).
fof(f6318,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X1),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f6196,f6317]) ).
fof(f6431,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)),inverse(multiply(inverse(inverse(multiply(inverse(X1),multiply(X0,inverse(multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc))))))),sF1_fnc))) = X1,
inference(backward_demodulation,[status(thm)],[f6318,f2136]) ).
fof(f6442,plain,
! [X0] : inverse(sF1_fnc) = multiply(inverse(X0),inverse(multiply(inverse(X0),sF1_fnc))),
inference(paramodulation,[status(thm)],[f6196,f6318]) ).
fof(f6493,plain,
! [X0,X1] : multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),inverse(multiply(inverse(inverse(multiply(inverse(X1),multiply(X0,inverse(multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc))))))),sF1_fnc))) = X1,
inference(forward_demodulation,[status(thm)],[f28,f6431]) ).
fof(f6494,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(inverse(multiply(inverse(X1),multiply(X0,inverse(multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc))))))),sF1_fnc))) = X1,
inference(forward_demodulation,[status(thm)],[f1915,f6493]) ).
fof(f6545,plain,
! [X0] : inverse(sF1_fnc) = multiply(X0,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(sF2_fnc,X0)),sF1_fnc))),multiply(sF2_fnc,inverse(sF1_fnc)))),sF1_fnc))),
inference(paramodulation,[status(thm)],[f1844,f6442]) ).
fof(f6566,plain,
! [X0] : multiply(b2,inverse(sF1_fnc)) = multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc)))),
inference(paramodulation,[status(thm)],[f6442,f855]) ).
fof(f6581,plain,
! [X0] : inverse(sF1_fnc) = multiply(X0,inverse(multiply(X0,sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f1844,f6545]) ).
fof(f6598,plain,
! [X0] : multiply(b2,inverse(sF1_fnc)) = multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f28,f6566]) ).
fof(f6599,plain,
! [X0] : multiply(b2,inverse(sF1_fnc)) = multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,b2)),
inference(forward_demodulation,[status(thm)],[f1914,f6598]) ).
fof(f6600,plain,
multiply(b2,inverse(sF1_fnc)) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f880,f6599]) ).
fof(f6668,plain,
inverse(sF1_fnc) = multiply(inverse(multiply(sF2_fnc,inverse(sF1_fnc))),multiply(sF2_fnc,inverse(sF1_fnc))),
inference(paramodulation,[status(thm)],[f6274,f6581]) ).
fof(f6679,plain,
inverse(sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6196,f6668]) ).
fof(f6683,plain,
inverse(multiply(inverse(multiply(sF2_fnc,inverse(sF1_fnc))),sF1_fnc)) = multiply(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f6679,f6274]) ).
fof(f6685,plain,
multiply(b2,sF1_fnc) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f6679,f6600]) ).
fof(f6687,plain,
! [X0] : sF1_fnc = multiply(X0,inverse(multiply(X0,sF1_fnc))),
inference(backward_demodulation,[status(thm)],[f6679,f6581]) ).
fof(f6688,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a2),sF1_fnc))))),sF0_fnc)) = X0,
inference(backward_demodulation,[status(thm)],[f6679,f6242]) ).
fof(f6689,plain,
inverse(multiply(inverse(inverse(sF1_fnc)),multiply(inverse(a2),sF1_fnc))) = a2,
inference(backward_demodulation,[status(thm)],[f6679,f6316]) ).
fof(f6690,plain,
inverse(multiply(inverse(inverse(sF1_fnc)),multiply(sF2_fnc,sF1_fnc))) = b2,
inference(backward_demodulation,[status(thm)],[f6679,f6238]) ).
fof(f6697,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc) = X0,
inference(backward_demodulation,[status(thm)],[f6679,f1915]) ).
fof(f6700,plain,
! [X0,X1] : multiply(sF1_fnc,multiply(sF2_fnc,X0)) = multiply(inverse(multiply(X1,b2)),multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f6679,f872]) ).
fof(f6701,plain,
multiply(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f6679,f6196]) ).
fof(f6702,plain,
inverse(multiply(inverse(multiply(sF2_fnc,sF1_fnc)),sF1_fnc)) = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6679,f6683]) ).
fof(f6706,plain,
inverse(multiply(inverse(sF1_fnc),multiply(inverse(a2),sF1_fnc))) = a2,
inference(forward_demodulation,[status(thm)],[f6679,f6689]) ).
fof(f6707,plain,
inverse(multiply(sF1_fnc,multiply(inverse(a2),sF1_fnc))) = a2,
inference(forward_demodulation,[status(thm)],[f6679,f6706]) ).
fof(f6708,plain,
inverse(multiply(inverse(sF1_fnc),multiply(sF2_fnc,sF1_fnc))) = b2,
inference(forward_demodulation,[status(thm)],[f6679,f6690]) ).
fof(f6709,plain,
inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc))) = b2,
inference(forward_demodulation,[status(thm)],[f6679,f6708]) ).
fof(f6711,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(inverse(inverse(multiply(X1,multiply(inverse(X0),inverse(sF1_fnc))))),sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X1),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6318,f6248]) ).
fof(f6712,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(inverse(inverse(multiply(X1,multiply(inverse(X0),sF1_fnc)))),sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X1),multiply(sF2_fnc,inverse(sF1_fnc)))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6679,f6711]) ).
fof(f6713,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(inverse(inverse(multiply(X1,multiply(inverse(X0),sF1_fnc)))),sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X1),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6679,f6712]) ).
fof(f6751,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(inverse(multiply(inverse(X1),multiply(X0,inverse(multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc))))))),sF1_fnc))) = X1,
inference(forward_demodulation,[status(thm)],[f6679,f6494]) ).
fof(f6822,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,X1)) = multiply(inverse(sF1_fnc),multiply(sF1_fnc,X1)),
inference(paramodulation,[status(thm)],[f6701,f840]) ).
fof(f6834,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,X1)) = multiply(sF1_fnc,multiply(sF1_fnc,X1)),
inference(forward_demodulation,[status(thm)],[f6679,f6822]) ).
fof(f7033,plain,
inverse(multiply(b2,sF1_fnc)) = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6685,f6702]) ).
fof(f7034,plain,
sF1_fnc = multiply(b2,multiply(sF2_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f7033,f6687]) ).
fof(f7370,plain,
! [X0] : multiply(multiply(sF2_fnc,b2),inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(multiply(sF2_fnc,b2),inverse(multiply(multiply(sF2_fnc,b2),multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc))))),sF1_fnc))))))),sF1_fnc))) = X0,
inference(paramodulation,[status(thm)],[f6700,f6751]) ).
fof(f7373,plain,
! [X0] : multiply(inverse(X0),inverse(multiply(inverse(inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc)))),sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),b2))),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc),
inference(paramodulation,[status(thm)],[f6700,f6713]) ).
fof(f7400,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(multiply(sF2_fnc,b2),inverse(multiply(multiply(sF2_fnc,b2),multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc))))),sF1_fnc))))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6,f7370]) ).
fof(f7401,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(multiply(sF2_fnc,b2),multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc))))),sF1_fnc))))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6,f7400]) ).
fof(f7402,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc))))),sF1_fnc))))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6,f7401]) ).
fof(f7403,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(inverse(multiply(sF2_fnc,b2)),sF1_fnc))))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6709,f7402]) ).
fof(f7404,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(inverse(sF1_fnc),sF1_fnc))))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6,f7403]) ).
fof(f7405,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(sF1_fnc,inverse(multiply(sF1_fnc,sF1_fnc)))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6196,f7404]) ).
fof(f7406,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),sF1_fnc))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f6687,f7405]) ).
fof(f7408,plain,
! [X0] : multiply(inverse(X0),inverse(multiply(inverse(b2),sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),b2))),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6709,f7373]) ).
fof(f7409,plain,
! [X0] : multiply(inverse(X0),inverse(multiply(sF2_fnc,sF1_fnc))) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(multiply(inverse(X0),b2))),multiply(sF2_fnc,sF1_fnc))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f5,f7408]) ).
fof(f7410,plain,
! [X0] : multiply(inverse(X0),inverse(multiply(sF2_fnc,sF1_fnc))) = multiply(inverse(X0),b2),
inference(forward_demodulation,[status(thm)],[f6697,f7409]) ).
fof(f7438,plain,
! [X0] : multiply(X0,inverse(multiply(sF2_fnc,sF1_fnc))) = multiply(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),multiply(inverse(a2),sF1_fnc))))),sF0_fnc)),b2),
inference(paramodulation,[status(thm)],[f6688,f7410]) ).
fof(f7460,plain,
! [X0] : multiply(X0,inverse(multiply(sF2_fnc,sF1_fnc))) = multiply(X0,b2),
inference(forward_demodulation,[status(thm)],[f6688,f7438]) ).
fof(f7655,plain,
! [X0] : multiply(inverse(multiply(inverse(X0),sF1_fnc)),sF1_fnc) = multiply(sF1_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f6196,f6834]) ).
fof(f7785,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(b2,multiply(sF2_fnc,sF1_fnc))))),sF1_fnc)) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6679,f48]) ).
fof(f7786,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(sF1_fnc))),sF1_fnc)) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f7034,f7785]) ).
fof(f7787,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(sF2_fnc,sF1_fnc)),sF1_fnc)) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6679,f7786]) ).
fof(f7788,plain,
! [X0,X1] : inverse(multiply(b2,sF1_fnc)) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6685,f7787]) ).
fof(f7789,plain,
! [X0,X1] : multiply(sF2_fnc,sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(multiply(inverse(X1),X1))))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f7033,f7788]) ).
fof(f7790,plain,
! [X0,X1] : multiply(sF2_fnc,sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),inverse(sF1_fnc)))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6196,f7789]) ).
fof(f7791,plain,
! [X0,X1] : multiply(sF2_fnc,sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,multiply(inverse(X1),sF1_fnc))))),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6679,f7790]) ).
fof(f7801,plain,
! [X0] : multiply(sF2_fnc,sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,sF1_fnc)))),multiply(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f6196,f7791]) ).
fof(f7872,plain,
! [X0] : multiply(sF2_fnc,sF1_fnc) = multiply(inverse(multiply(X0,b2)),multiply(X0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f7460,f7801]) ).
fof(f7873,plain,
multiply(sF2_fnc,sF1_fnc) = multiply(sF1_fnc,multiply(sF2_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f6700,f7872]) ).
fof(f8009,plain,
inverse(multiply(sF2_fnc,sF1_fnc)) = b2,
inference(backward_demodulation,[status(thm)],[f7873,f6709]) ).
fof(f8043,plain,
! [X0] : multiply(b2,multiply(sF2_fnc,X0)) = multiply(sF1_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f8009,f6834]) ).
fof(f8045,plain,
! [X0] : inverse(multiply(b2,multiply(sF2_fnc,X0))) = multiply(inverse(X0),inverse(multiply(inverse(sF1_fnc),sF1_fnc))),
inference(paramodulation,[status(thm)],[f8009,f6318]) ).
fof(f8062,plain,
! [X0] : inverse(multiply(b2,multiply(sF2_fnc,X0))) = multiply(inverse(X0),inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f6196,f8045]) ).
fof(f8063,plain,
! [X0] : inverse(multiply(b2,multiply(sF2_fnc,X0))) = multiply(inverse(X0),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f6679,f8062]) ).
fof(f12935,plain,
! [X0] : multiply(inverse(multiply(inverse(X0),sF1_fnc)),sF1_fnc) = multiply(b2,multiply(sF2_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f8043,f7655]) ).
fof(f12962,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(inverse(multiply(b2,multiply(sF2_fnc,X0)))),sF1_fnc))) = multiply(inverse(X0),sF1_fnc),
inference(paramodulation,[status(thm)],[f12935,f7406]) ).
fof(f13014,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(X0),sF1_fnc)),sF1_fnc))) = multiply(inverse(X0),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8063,f12962]) ).
fof(f13015,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(b2,multiply(sF2_fnc,X0)))) = multiply(inverse(X0),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f12935,f13014]) ).
fof(f13016,plain,
! [X0] : multiply(sF1_fnc,multiply(inverse(X0),sF1_fnc)) = multiply(inverse(X0),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8063,f13015]) ).
fof(f13377,plain,
inverse(multiply(inverse(a2),sF1_fnc)) = a2,
inference(backward_demodulation,[status(thm)],[f13016,f6707]) ).
fof(f13469,plain,
multiply(sF1_fnc,inverse(multiply(inverse(a2),sF1_fnc))) = a2,
inference(paramodulation,[status(thm)],[f13377,f7406]) ).
fof(f13501,plain,
multiply(sF1_fnc,a2) = a2,
inference(forward_demodulation,[status(thm)],[f13377,f13469]) ).
fof(f13502,plain,
sF0_fnc = a2,
inference(forward_demodulation,[status(thm)],[f7,f13501]) ).
fof(f13503,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f13502,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP422-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:13:24 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 2.07/0.87 % Refutation found
% 2.07/0.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.07/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.41/0.91 % Elapsed time: 0.544072 seconds
% 3.41/0.91 % CPU time: 4.105986 seconds
% 3.41/0.91 % Total memory used: 144.364 MB
% 3.41/0.91 % Net memory used: 140.078 MB
%------------------------------------------------------------------------------