%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 3.31s 0.88s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 72 unt; 3 def)
% Number of atoms : 72 ( 71 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 : 18 ( 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 : 131 ( 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C,
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] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
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] : multiply(X0,inverse(multiply(multiply(multiply(sF2_fnc,b2),inverse(multiply(inverse(multiply(X0,inverse(b2))),X1))),b2))) = X1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X3))),X2))),X3)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1)),multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1)),inverse(multiply(inverse(X2),X3))),multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1)))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f13,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,inverse(b2))),X1))),b2))) = X1,
inference(forward_demodulation,[status(thm)],[f6,f9]) ).
fof(f14,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),X1))),b2))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(X1)),b2))) = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,sF2_fnc)),sF2_fnc)),X1))),b2)),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f23,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(X1)),b2)))) = X1,
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f31,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(multiply(X1,b2)))) = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(sF1_fnc,sF2_fnc)),X1))),b2),
inference(paramodulation,[status(thm)],[f14,f23]) ).
fof(f34,plain,
! [X0] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(multiply(multiply(sF1_fnc,sF2_fnc),b2)))) = b2,
inference(paramodulation,[status(thm)],[f5,f23]) ).
fof(f40,plain,
b2 = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(sF1_fnc,sF2_fnc)),multiply(sF1_fnc,sF2_fnc)))),b2),
inference(paramodulation,[status(thm)],[f34,f31]) ).
fof(f41,plain,
! [X0] : X0 = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(sF1_fnc,sF2_fnc)),multiply(sF1_fnc,inverse(X0))))),b2),
inference(paramodulation,[status(thm)],[f23,f31]) ).
fof(f57,plain,
! [X0,X1] : multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(multiply(X1,b2)))))) = X1,
inference(paramodulation,[status(thm)],[f31,f14]) ).
fof(f91,plain,
! [X0] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(b2))) = multiply(inverse(multiply(sF1_fnc,sF2_fnc)),multiply(sF1_fnc,sF2_fnc)),
inference(paramodulation,[status(thm)],[f40,f23]) ).
fof(f94,plain,
! [X0] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)) = multiply(inverse(multiply(sF1_fnc,sF2_fnc)),multiply(sF1_fnc,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f5,f91]) ).
fof(f110,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))) = multiply(inverse(multiply(sF1_fnc,sF2_fnc)),multiply(sF1_fnc,inverse(X1))),
inference(paramodulation,[status(thm)],[f41,f23]) ).
fof(f118,plain,
! [X0] : b2 = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)))),b2),
inference(paramodulation,[status(thm)],[f94,f40]) ).
fof(f191,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1)))) = X2,
inference(paramodulation,[status(thm)],[f10,f3]) ).
fof(f225,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(X1,inverse(X2))),X3))),X2)))),inverse(X0))),multiply(inverse(X3),X4)))),X0)) = X4,
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f315,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(X1),inverse(X0))),multiply(inverse(X1),X2)))),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f3,f225]) ).
fof(f618,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))) = multiply(inverse(multiply(X2,sF2_fnc)),multiply(X2,inverse(X1))),
inference(paramodulation,[status(thm)],[f110,f110]) ).
fof(f642,plain,
! [X0,X1] : X0 = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,inverse(X0))))),b2),
inference(paramodulation,[status(thm)],[f110,f41]) ).
fof(f760,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(multiply(inverse(X3),inverse(X2))),multiply(inverse(X3),X1)))),X2)),X4)))),X0)) = X4,
inference(paramodulation,[status(thm)],[f315,f315]) ).
fof(f811,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(X2),inverse(X1))),multiply(inverse(X2),X3)))),X1)))) = multiply(inverse(multiply(X4,sF2_fnc)),multiply(X4,X3)),
inference(paramodulation,[status(thm)],[f315,f618]) ).
fof(f838,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,X2)))),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f315,f760]) ).
fof(f861,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,X1)) = multiply(inverse(multiply(X2,sF2_fnc)),multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f315,f811]) ).
fof(f955,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),X1))),b2))) = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X2,sF2_fnc)),multiply(X2,X1)))),b2)),
inference(paramodulation,[status(thm)],[f861,f17]) ).
fof(f997,plain,
! [X0,X1] : X0 = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,X0)))),b2)),
inference(forward_demodulation,[status(thm)],[f14,f955]) ).
fof(f1602,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,inverse(multiply(multiply(sF1_fnc,X0),b2))))),
inference(paramodulation,[status(thm)],[f31,f997]) ).
fof(f2910,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f838,f191]) ).
fof(f3101,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(X4,sF2_fnc)),multiply(X4,inverse(multiply(multiply(sF1_fnc,X1),b2))))))),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f1602,f2910]) ).
fof(f3261,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)],[f1602,f3101]) ).
fof(f3332,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,X0)) = multiply(inverse(multiply(X1,b2)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f3261]) ).
fof(f3353,plain,
! [X0,X1] : multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc) = multiply(inverse(multiply(X1,X0)),multiply(X1,a2)),
inference(paramodulation,[status(thm)],[f7,f3261]) ).
fof(f3669,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,b2)) = multiply(inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))))),b2)),X1),
inference(paramodulation,[status(thm)],[f642,f3332]) ).
fof(f3670,plain,
! [X0] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,b2)) = multiply(inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)))),b2)),b2),
inference(paramodulation,[status(thm)],[f118,f3332]) ).
fof(f3738,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(X1))))),b2)),X1),
inference(forward_demodulation,[status(thm)],[f6,f3669]) ).
fof(f3739,plain,
! [X0] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f997,f3738]) ).
fof(f3740,plain,
! [X0] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)))),b2)),b2),
inference(forward_demodulation,[status(thm)],[f6,f3670]) ).
fof(f3741,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = multiply(sF2_fnc,b2),
inference(forward_demodulation,[status(thm)],[f997,f3740]) ).
fof(f3742,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6,f3741]) ).
fof(f3813,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X3))),X2))),X3)),
inference(backward_demodulation,[status(thm)],[f3815,f10]) ).
fof(f3814,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
inference(backward_demodulation,[status(thm)],[f3815,f3]) ).
fof(f3815,plain,
! [X0] : sF1_fnc = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f3742,f3739]) ).
fof(f3872,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(X1)),X2))) = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X2))),inverse(X3))),X1))),X3)),
inference(forward_demodulation,[status(thm)],[f3815,f3813]) ).
fof(f4078,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X2)))),X1))) = inverse(multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X2)),
inference(paramodulation,[status(thm)],[f3815,f3872]) ).
fof(f4141,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0)),
inference(forward_demodulation,[status(thm)],[f3814,f4078]) ).
fof(f4183,plain,
! [X0,X1] : multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0) = multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(X1,sF2_fnc)),multiply(X1,inverse(X0))))),b2),
inference(paramodulation,[status(thm)],[f4141,f642]) ).
fof(f4197,plain,
! [X0] : multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0) = X0,
inference(forward_demodulation,[status(thm)],[f642,f4183]) ).
fof(f4201,plain,
! [X0,X1] : X0 = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(multiply(sF1_fnc,inverse(sF1_fnc)),inverse(X1))),X0))),X1)),
inference(paramodulation,[status(thm)],[f3814,f4197]) ).
fof(f4206,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc) = multiply(inverse(multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0)),a2),
inference(paramodulation,[status(thm)],[f4197,f3353]) ).
fof(f4208,plain,
! [X0] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,X0)) = multiply(inverse(b2),multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0)),
inference(paramodulation,[status(thm)],[f4197,f3332]) ).
fof(f4246,plain,
! [X0,X1] : X0 = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X1)),X0))),X1)),
inference(forward_demodulation,[status(thm)],[f4197,f4201]) ).
fof(f4251,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,X0)),sF0_fnc) = multiply(inverse(X0),a2),
inference(forward_demodulation,[status(thm)],[f4197,f4206]) ).
fof(f4253,plain,
! [X0] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,X0)) = multiply(sF2_fnc,multiply(multiply(sF1_fnc,inverse(sF1_fnc)),X0)),
inference(forward_demodulation,[status(thm)],[f5,f4208]) ).
fof(f4254,plain,
! [X0] : multiply(inverse(sF1_fnc),multiply(sF2_fnc,X0)) = multiply(sF2_fnc,X0),
inference(forward_demodulation,[status(thm)],[f4197,f4253]) ).
fof(f4297,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),X0) = multiply(sF2_fnc,inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(multiply(sF2_fnc,inverse(X1))),X0))),X1))),
inference(paramodulation,[status(thm)],[f3814,f4254]) ).
fof(f4309,plain,
! [X0] : multiply(inverse(sF1_fnc),X0) = X0,
inference(forward_demodulation,[status(thm)],[f3814,f4297]) ).
fof(f4322,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,inverse(b2))))) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f4309,f57]) ).
fof(f4363,plain,
! [X0] : multiply(sF1_fnc,inverse(multiply(inverse(multiply(X0,sF2_fnc)),multiply(X0,sF2_fnc)))) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f5,f4322]) ).
fof(f4364,plain,
multiply(sF1_fnc,inverse(sF1_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3815,f4363]) ).
fof(f4426,plain,
multiply(inverse(inverse(sF1_fnc)),sF0_fnc) = multiply(inverse(inverse(sF1_fnc)),a2),
inference(paramodulation,[status(thm)],[f4364,f4251]) ).
fof(f5325,plain,
sF0_fnc = inverse(multiply(multiply(sF1_fnc,inverse(multiply(inverse(inverse(sF1_fnc)),a2))),sF1_fnc)),
inference(paramodulation,[status(thm)],[f4426,f4246]) ).
fof(f5330,plain,
sF0_fnc = a2,
inference(forward_demodulation,[status(thm)],[f4246,f5325]) ).
fof(f5331,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5330,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:15:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 3.31/0.88 % Refutation found
% 3.31/0.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.31/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.33/0.92 % Elapsed time: 0.544590 seconds
% 0.33/0.92 % CPU time: 4.089887 seconds
% 0.33/0.92 % Total memory used: 163.852 MB
% 0.33/0.92 % Net memory used: 158.231 MB
%------------------------------------------------------------------------------