%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:33:39 PM UTC 2026
% Result : Unsatisfiable 5.69s 1.22s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 5
% Syntax : Number of formulae : 94 ( 94 unt; 3 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 21 ( 4 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 : 156 ( 156 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(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,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1))) = b2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)),inverse(multiply(X3,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)))))))))),multiply(X0,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4))))) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f13,plain,
! [X0] : inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc)) = X0,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f14,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(multiply(inverse(b2),b2)))))))),sF1_fnc)) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f16,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(multiply(sF2_fnc,b2)))))))),sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f14]) ).
fof(f17,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f6,f16]) ).
fof(f18,plain,
! [X0] : inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)) = multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f20,plain,
inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(sF2_fnc,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)) = b2,
inference(paramodulation,[status(thm)],[f5,f17]) ).
fof(f75,plain,
multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = b2,
inference(backward_demodulation,[status(thm)],[f18,f20]) ).
fof(f76,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = X0,
inference(backward_demodulation,[status(thm)],[f18,f17]) ).
fof(f84,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),b2)) = X0,
inference(paramodulation,[status(thm)],[f75,f3]) ).
fof(f87,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc),
inference(paramodulation,[status(thm)],[f13,f76]) ).
fof(f96,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X1),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),X0)) = X1,
inference(paramodulation,[status(thm)],[f76,f3]) ).
fof(f101,plain,
! [X0,X1] : b2 = multiply(inverse(multiply(X0,inverse(multiply(inverse(sF2_fnc),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f102,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f3,f9]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X3,inverse(multiply(X1,inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(paramodulation,[status(thm)],[f9,f76]) ).
fof(f157,plain,
! [X0,X1,X2] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f3,f143]) ).
fof(f427,plain,
b2 = multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(sF2_fnc),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),b2),
inference(paramodulation,[status(thm)],[f75,f101]) ).
fof(f501,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(multiply(sF2_fnc,b2)))))))),multiply(X1,b2)),
inference(paramodulation,[status(thm)],[f5,f102]) ).
fof(f502,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X1)),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),X1),
inference(paramodulation,[status(thm)],[f76,f102]) ).
fof(f531,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(sF1_fnc))))))),multiply(X1,b2)),
inference(forward_demodulation,[status(thm)],[f6,f501]) ).
fof(f548,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)),inverse(multiply(b2,inverse(sF1_fnc))))))),multiply(X1,b2)),
inference(paramodulation,[status(thm)],[f18,f531]) ).
fof(f568,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),multiply(X1,b2)),
inference(forward_demodulation,[status(thm)],[f18,f548]) ).
fof(f569,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),multiply(X1,b2)),
inference(forward_demodulation,[status(thm)],[f76,f568]) ).
fof(f816,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)),inverse(multiply(X3,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)))))))))),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X3),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)))) = X1,
inference(backward_demodulation,[status(thm)],[f157,f11]) ).
fof(f834,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc),inverse(multiply(X2,multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)))))))))),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f157,f816]) ).
fof(f835,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f157,f834]) ).
fof(f1264,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(inverse(multiply(b2,inverse(sF1_fnc))))),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(X1,X0)),multiply(X1,b2)),
inference(paramodulation,[status(thm)],[f96,f569]) ).
fof(f1302,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,X0)),sF1_fnc) = multiply(inverse(multiply(X1,X0)),multiply(X1,b2)),
inference(forward_demodulation,[status(thm)],[f96,f1264]) ).
fof(f1876,plain,
multiply(inverse(multiply(sF2_fnc,b2)),sF1_fnc) = multiply(inverse(b2),multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(sF2_fnc),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),b2)),
inference(paramodulation,[status(thm)],[f427,f1302]) ).
fof(f1893,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(b2),multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(sF2_fnc),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),b2)),
inference(forward_demodulation,[status(thm)],[f6,f1876]) ).
fof(f1894,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(sF2_fnc,multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(sF2_fnc),inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),b2)),
inference(forward_demodulation,[status(thm)],[f5,f1893]) ).
fof(f1895,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(sF2_fnc,b2),
inference(forward_demodulation,[status(thm)],[f427,f1894]) ).
fof(f1896,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6,f1895]) ).
fof(f1909,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),b2)) = X0,
inference(backward_demodulation,[status(thm)],[f1896,f84]) ).
fof(f1914,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(inverse(sF1_fnc),inverse(multiply(X0,inverse(multiply(sF1_fnc,inverse(multiply(inverse(sF1_fnc),sF1_fnc)))))))),sF1_fnc),
inference(paramodulation,[status(thm)],[f1896,f157]) ).
fof(f1915,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(X0,inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(inverse(sF1_fnc),inverse(multiply(X0,inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1896,f1914]) ).
fof(f2331,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,b2)),sF1_fnc) = multiply(X0,multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),b2)),
inference(paramodulation,[status(thm)],[f1909,f1302]) ).
fof(f2350,plain,
! [X0] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(X0,multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),b2)),
inference(forward_demodulation,[status(thm)],[f6,f2331]) ).
fof(f2351,plain,
! [X0] : sF1_fnc = multiply(X0,multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(X0),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),b2)),
inference(forward_demodulation,[status(thm)],[f1896,f2350]) ).
fof(f2669,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(X1)),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),X1),
inference(forward_demodulation,[status(thm)],[f1896,f502]) ).
fof(f2679,plain,
! [X0] : X0 = multiply(inverse(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),inverse(multiply(b2,inverse(sF1_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF1_fnc,inverse(sF1_fnc))))))),b2),
inference(paramodulation,[status(thm)],[f5,f2669]) ).
fof(f3038,plain,
! [X0] : sF1_fnc = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f2679,f2351]) ).
fof(f3105,plain,
multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(inverse(multiply(sF1_fnc,inverse(sF1_fnc)))),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(inverse(sF1_fnc),inverse(sF1_fnc))),sF1_fnc),
inference(paramodulation,[status(thm)],[f3038,f1915]) ).
fof(f3139,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = multiply(inverse(multiply(inverse(sF1_fnc),inverse(sF1_fnc))),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f76,f3105]) ).
fof(f3151,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = X1,
inference(backward_demodulation,[status(thm)],[f3153,f835]) ).
fof(f3153,plain,
! [X0] : multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X0),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f3038,f87]) ).
fof(f3174,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF2_fnc,inverse(multiply(inverse(X2),inverse(multiply(b2,inverse(sF1_fnc))))))),sF1_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f3153,f3151]) ).
fof(f3175,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f3153,f3174]) ).
fof(f3403,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f106]) ).
fof(f3404,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(multiply(inverse(a2),a2)))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f3403]) ).
fof(f3405,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f3404]) ).
fof(f3406,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(sF1_fnc))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f3405]) ).
fof(f3478,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(X1,inverse(sF1_fnc))),inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X2,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X0,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X2),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))) = multiply(inverse(multiply(X3,inverse(sF1_fnc))),multiply(X3,X1)),
inference(paramodulation,[status(thm)],[f3038,f3406]) ).
fof(f3642,plain,
! [X0,X1] : multiply(X0,inverse(sF1_fnc)) = multiply(inverse(multiply(X1,inverse(sF1_fnc))),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f3175,f3478]) ).
fof(f3648,plain,
multiply(inverse(sF1_fnc),inverse(sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3038,f3642]) ).
fof(f3688,plain,
! [X0] : multiply(X0,inverse(sF1_fnc)) = multiply(inverse(multiply(inverse(X0),inverse(sF1_fnc))),sF1_fnc),
inference(paramodulation,[status(thm)],[f3038,f3642]) ).
fof(f3701,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = multiply(inverse(sF1_fnc),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f3648,f3139]) ).
fof(f3707,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f3038,f3701]) ).
fof(f3960,plain,
! [X0,X1,X2,X3,X4] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(sF1_fnc))))))),multiply(X0,X2)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f104]) ).
fof(f3961,plain,
! [X0,X1,X2,X3,X4] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(sF1_fnc))))))),multiply(X0,X2)))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X4,inverse(sF1_fnc))))))),multiply(X3,X4)),
inference(forward_demodulation,[status(thm)],[f3038,f3960]) ).
fof(f4014,plain,
! [X0,X1,X2,X3,X4] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(sF1_fnc))))))),multiply(X0,X2)))) = inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X4),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc),inverse(multiply(X4,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X4),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc))))))))),multiply(X3,multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(X4),inverse(multiply(a2,inverse(sF1_fnc))))))),sF0_fnc)))),
inference(paramodulation,[status(thm)],[f3406,f3961]) ).
fof(f4109,plain,
! [X0,X1,X2] : inverse(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(sF1_fnc))))))),multiply(X0,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f3175,f4014]) ).
fof(f8011,plain,
! [X0] : inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,inverse(multiply(inverse(sF1_fnc),inverse(sF1_fnc))))))),sF1_fnc))) = X0,
inference(paramodulation,[status(thm)],[f3707,f4109]) ).
fof(f8058,plain,
! [X0] : inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,inverse(sF1_fnc))))),sF1_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f3648,f8011]) ).
fof(f8079,plain,
inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(sF1_fnc))),sF1_fnc))) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f3648,f8058]) ).
fof(f8081,plain,
inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(sF1_fnc))),sF1_fnc))) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3707,f8058]) ).
fof(f8109,plain,
inverse(inverse(multiply(inverse(sF1_fnc),sF1_fnc))) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3707,f8079]) ).
fof(f8110,plain,
inverse(inverse(sF1_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3038,f8109]) ).
fof(f8112,plain,
inverse(inverse(multiply(inverse(sF1_fnc),sF1_fnc))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f3707,f8081]) ).
fof(f8113,plain,
inverse(inverse(sF1_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f3038,f8112]) ).
fof(f8173,plain,
! [X0] : inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,sF1_fnc)))),sF1_fnc))) = X0,
inference(backward_demodulation,[status(thm)],[f8210,f8058]) ).
fof(f8191,plain,
! [X0] : multiply(X0,inverse(sF1_fnc)) = multiply(inverse(multiply(inverse(X0),sF1_fnc)),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f8210,f3688]) ).
fof(f8210,plain,
sF1_fnc = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8113,f8110]) ).
fof(f8231,plain,
! [X0] : multiply(X0,sF1_fnc) = multiply(inverse(multiply(inverse(X0),sF1_fnc)),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8210,f8191]) ).
fof(f8956,plain,
! [X0] : inverse(inverse(multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,sF1_fnc)))),sF1_fnc))) = inverse(multiply(inverse(X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f8231,f8173]) ).
fof(f8971,plain,
! [X0] : X0 = inverse(multiply(inverse(X0),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f8173,f8956]) ).
fof(f8995,plain,
! [X0] : inverse(multiply(sF1_fnc,inverse(multiply(X0,sF1_fnc)))) = X0,
inference(backward_demodulation,[status(thm)],[f8971,f8173]) ).
fof(f9574,plain,
! [X0] : inverse(multiply(sF1_fnc,X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f8971,f8995]) ).
fof(f10000,plain,
! [X0] : multiply(sF1_fnc,X0) = inverse(multiply(inverse(X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f9574,f8971]) ).
fof(f10024,plain,
! [X0] : multiply(sF1_fnc,X0) = X0,
inference(forward_demodulation,[status(thm)],[f8971,f10000]) ).
fof(f10032,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f10024,f7]) ).
fof(f10064,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10032,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n015.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:16:20 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 5.69/1.22 % Refutation found
% 5.69/1.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.69/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.02/1.27 % Elapsed time: 0.909646 seconds
% 5.02/1.27 % CPU time: 6.954080 seconds
% 5.02/1.27 % Total memory used: 273.406 MB
% 5.02/1.27 % Net memory used: 252.723 MB
%------------------------------------------------------------------------------