%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:39 PM UTC 2026
% Result : Unsatisfiable 2.05s 0.69s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 46 unt; 4 def)
% Number of atoms : 46 ( 45 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 : 17 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 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(inverse(a1),a1) != multiply(inverse(b1),b1),
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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f9,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f10,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(f12,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(sF1_fnc,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1))) = a1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f16,plain,
! [X0] : inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(multiply(inverse(b1),b1)))))))),sF2_fnc)) = X0,
inference(paramodulation,[status(thm)],[f8,f3]) ).
fof(f20,plain,
! [X0] : inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(multiply(sF3_fnc,b1)))))))),sF2_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f7,f16]) ).
fof(f21,plain,
! [X0] : inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f20]) ).
fof(f24,plain,
! [X0] : inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc)) = multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f100,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,f10]) ).
fof(f299,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(a1,inverse(multiply(sF1_fnc,a1)))))))),multiply(X1,a1)),
inference(paramodulation,[status(thm)],[f5,f100]) ).
fof(f302,plain,
! [X0] : X0 = multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(multiply(inverse(b1),b1)))))))),sF2_fnc),
inference(paramodulation,[status(thm)],[f8,f100]) ).
fof(f303,plain,
! [X0] : X0 = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),sF0_fnc),
inference(paramodulation,[status(thm)],[f6,f100]) ).
fof(f324,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X0)),inverse(multiply(a1,inverse(sF0_fnc))))))),multiply(X1,a1)),
inference(forward_demodulation,[status(thm)],[f6,f299]) ).
fof(f325,plain,
! [X0] : X0 = multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(multiply(sF3_fnc,b1)))))))),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f7,f302]) ).
fof(f326,plain,
! [X0] : X0 = multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f8,f325]) ).
fof(f327,plain,
! [X0] : X0 = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(a1,inverse(multiply(sF1_fnc,a1)))))))),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f5,f303]) ).
fof(f328,plain,
! [X0] : X0 = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f6,f327]) ).
fof(f348,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X1)),inverse(multiply(b1,inverse(sF2_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),sF2_fnc)))))))),X1),
inference(paramodulation,[status(thm)],[f326,f100]) ).
fof(f349,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(sF2_fnc))))))),inverse(multiply(sF1_fnc,inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),sF2_fnc)))))))),X0)) = a1,
inference(paramodulation,[status(thm)],[f326,f12]) ).
fof(f1082,plain,
! [X0,X1] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc)),inverse(multiply(a1,inverse(sF0_fnc))))))),multiply(X1,a1)),
inference(paramodulation,[status(thm)],[f24,f324]) ).
fof(f1084,plain,
! [X0] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(X0),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc)),inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc),
inference(paramodulation,[status(thm)],[f24,f328]) ).
fof(f1112,plain,
! [X0,X1] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc),inverse(multiply(a1,inverse(sF0_fnc))))))),multiply(X1,a1)),
inference(forward_demodulation,[status(thm)],[f24,f1082]) ).
fof(f1113,plain,
! [X0,X1] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(a1,inverse(sF0_fnc))))))),multiply(X1,a1)),
inference(forward_demodulation,[status(thm)],[f326,f1112]) ).
fof(f1116,plain,
! [X0] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc),inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f24,f1084]) ).
fof(f1117,plain,
! [X0] : multiply(inverse(multiply(sF3_fnc,inverse(multiply(X0,inverse(multiply(b1,inverse(sF2_fnc))))))),sF2_fnc) = multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f326,f1116]) ).
fof(f1855,plain,
! [X0,X1] : multiply(inverse(multiply(sF1_fnc,inverse(multiply(X0,inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc) = multiply(inverse(multiply(X1,inverse(multiply(X0,inverse(multiply(a1,inverse(sF0_fnc))))))),multiply(X1,a1)),
inference(forward_demodulation,[status(thm)],[f1117,f1113]) ).
fof(f2577,plain,
! [X0,X1] : multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(inverse(multiply(a1,inverse(sF0_fnc))))),inverse(multiply(b1,inverse(sF2_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),sF2_fnc)))))))),inverse(multiply(a1,inverse(sF0_fnc))))))),sF0_fnc) = multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,a1)),
inference(paramodulation,[status(thm)],[f348,f1855]) ).
fof(f2634,plain,
! [X0,X1] : multiply(inverse(multiply(sF1_fnc,inverse(X0))),sF0_fnc) = multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,a1)),
inference(forward_demodulation,[status(thm)],[f348,f2577]) ).
fof(f2738,plain,
! [X0,X1] : multiply(inverse(multiply(sF1_fnc,inverse(multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b1,inverse(sF2_fnc))))))),inverse(multiply(sF1_fnc,inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),sF2_fnc)))))))),X0)))),sF0_fnc) = multiply(inverse(multiply(X1,a1)),multiply(X1,a1)),
inference(paramodulation,[status(thm)],[f349,f2634]) ).
fof(f2799,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,a1)),sF0_fnc) = multiply(inverse(multiply(X0,a1)),multiply(X0,a1)),
inference(forward_demodulation,[status(thm)],[f349,f2738]) ).
fof(f2800,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(multiply(X0,a1)),multiply(X0,a1)),
inference(forward_demodulation,[status(thm)],[f6,f2799]) ).
fof(f2813,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(sF3_fnc,inverse(multiply(inverse(inverse(a1)),inverse(multiply(b1,inverse(sF2_fnc))))))),inverse(multiply(inverse(inverse(X0)),inverse(multiply(sF2_fnc,inverse(multiply(inverse(sF2_fnc),sF2_fnc)))))))),a1)),
inference(paramodulation,[status(thm)],[f348,f2800]) ).
fof(f2825,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f348,f2813]) ).
fof(f2839,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f2825,f2825]) ).
fof(f2923,plain,
! [X0] : multiply(sF3_fnc,b1) = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f7,f2839]) ).
fof(f3020,plain,
! [X0] : sF2_fnc = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f8,f2923]) ).
fof(f3093,plain,
sF2_fnc = multiply(sF1_fnc,a1),
inference(paramodulation,[status(thm)],[f5,f3020]) ).
fof(f3120,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f6,f3093]) ).
fof(f3121,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3120,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 20:08:26 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 2.05/0.69 % Refutation found
% 2.05/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.05/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.05/0.72 % Elapsed time: 0.357798 seconds
% 2.05/0.72 % CPU time: 2.655988 seconds
% 2.05/0.72 % Total memory used: 143.951 MB
% 2.05/0.72 % Net memory used: 141.543 MB
%------------------------------------------------------------------------------