%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:34:12 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 54 unt; 3 def)
% Number of atoms : 54 ( 53 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 : 9 ( 2 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 : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C,
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,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(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(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(sF1_fnc,X0)),sF2_fnc),b2),multiply(X1,inverse(X1)))) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f13,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(b2,sF2_fnc))) = X2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f19,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(sF0_fnc),sF2_fnc),b2),multiply(X0,inverse(X0)))) = a2,
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f32,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(a2,multiply(inverse(sF0_fnc),sF2_fnc)),b2),multiply(X0,inverse(X0)))) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f19,f3]) ).
fof(f67,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f32,f32]) ).
fof(f115,plain,
! [X0] : multiply(b2,sF2_fnc) = multiply(X0,inverse(X0)),
inference(paramodulation,[status(thm)],[f5,f67]) ).
fof(f131,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(b2,sF2_fnc))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f67,f13]) ).
fof(f141,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(b2,sF2_fnc))) = X1,
inference(paramodulation,[status(thm)],[f67,f13]) ).
fof(f176,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b2,sF2_fnc))) = multiply(X3,inverse(X3)),
inference(forward_demodulation,[status(thm)],[f115,f9]) ).
fof(f177,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(b2,sF2_fnc))) = multiply(b2,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f115,f176]) ).
fof(f234,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),X1),multiply(b2,sF2_fnc))) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f115,f131]) ).
fof(f235,plain,
! [X0,X1] : multiply(b2,sF2_fnc) = inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(b2,sF2_fnc)))),X0),X1)),
inference(paramodulation,[status(thm)],[f177,f234]) ).
fof(f251,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(b2,sF2_fnc),X0)),X1),inverse(X1)),multiply(b2,sF2_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f115,f141]) ).
fof(f367,plain,
! [X0] : multiply(b2,sF2_fnc) = inverse(multiply(multiply(inverse(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc)))),X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f115,f235]) ).
fof(f377,plain,
! [X0] : multiply(b2,sF2_fnc) = inverse(multiply(multiply(inverse(multiply(b2,sF2_fnc)),X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f115,f367]) ).
fof(f418,plain,
multiply(b2,sF2_fnc) = inverse(multiply(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc))),multiply(b2,sF2_fnc))),
inference(paramodulation,[status(thm)],[f377,f235]) ).
fof(f424,plain,
! [X0] : inverse(multiply(multiply(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc))),X0),multiply(b2,sF2_fnc))) = inverse(X0),
inference(paramodulation,[status(thm)],[f377,f13]) ).
fof(f427,plain,
multiply(b2,sF2_fnc) = inverse(multiply(multiply(b2,sF2_fnc),multiply(b2,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f115,f418]) ).
fof(f433,plain,
! [X0] : inverse(multiply(multiply(multiply(b2,sF2_fnc),X0),multiply(b2,sF2_fnc))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f115,f424]) ).
fof(f445,plain,
inverse(multiply(multiply(b2,sF2_fnc),multiply(b2,sF2_fnc))) = inverse(inverse(multiply(b2,sF2_fnc))),
inference(paramodulation,[status(thm)],[f115,f433]) ).
fof(f455,plain,
multiply(b2,sF2_fnc) = inverse(inverse(multiply(b2,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f427,f445]) ).
fof(f458,plain,
multiply(b2,sF2_fnc) = multiply(inverse(multiply(b2,sF2_fnc)),multiply(b2,sF2_fnc)),
inference(paramodulation,[status(thm)],[f455,f115]) ).
fof(f459,plain,
multiply(b2,sF2_fnc) = inverse(multiply(multiply(b2,sF2_fnc),inverse(multiply(b2,sF2_fnc)))),
inference(paramodulation,[status(thm)],[f458,f377]) ).
fof(f460,plain,
! [X0] : inverse(multiply(multiply(multiply(b2,sF2_fnc),X0),multiply(b2,sF2_fnc))) = inverse(multiply(multiply(b2,sF2_fnc),X0)),
inference(paramodulation,[status(thm)],[f458,f234]) ).
fof(f468,plain,
multiply(b2,sF2_fnc) = inverse(multiply(b2,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f115,f459]) ).
fof(f469,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(b2,sF2_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f433,f460]) ).
fof(f480,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(X0),X1),inverse(X1)),multiply(b2,sF2_fnc))) = X0,
inference(backward_demodulation,[status(thm)],[f469,f251]) ).
fof(f626,plain,
! [X0,X1] : X0 = multiply(multiply(X1,inverse(X1)),X0),
inference(paramodulation,[status(thm)],[f13,f480]) ).
fof(f627,plain,
! [X0] : inverse(multiply(multiply(multiply(b2,sF2_fnc),inverse(inverse(inverse(X0)))),multiply(b2,sF2_fnc))) = X0,
inference(paramodulation,[status(thm)],[f115,f480]) ).
fof(f671,plain,
! [X0] : X0 = multiply(multiply(b2,sF2_fnc),X0),
inference(forward_demodulation,[status(thm)],[f115,f626]) ).
fof(f672,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f433,f627]) ).
fof(f688,plain,
! [X0] : inverse(multiply(X0,multiply(b2,sF2_fnc))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f671,f433]) ).
fof(f722,plain,
inverse(inverse(inverse(sF2_fnc))) = b2,
inference(paramodulation,[status(thm)],[f5,f672]) ).
fof(f744,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(backward_demodulation,[status(thm)],[f688,f480]) ).
fof(f760,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = multiply(X0,multiply(b2,sF2_fnc)),
inference(paramodulation,[status(thm)],[f688,f672]) ).
fof(f762,plain,
! [X0] : X0 = multiply(X0,multiply(b2,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f672,f760]) ).
fof(f773,plain,
! [X0] : inverse(multiply(inverse(X0),inverse(multiply(b2,sF2_fnc)))) = X0,
inference(paramodulation,[status(thm)],[f762,f744]) ).
fof(f787,plain,
! [X0] : inverse(multiply(inverse(X0),multiply(b2,sF2_fnc))) = X0,
inference(forward_demodulation,[status(thm)],[f468,f773]) ).
fof(f788,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f762,f787]) ).
fof(f794,plain,
inverse(sF2_fnc) = b2,
inference(backward_demodulation,[status(thm)],[f788,f722]) ).
fof(f806,plain,
multiply(b2,sF2_fnc) = multiply(sF2_fnc,b2),
inference(paramodulation,[status(thm)],[f794,f115]) ).
fof(f807,plain,
multiply(b2,sF2_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6,f806]) ).
fof(f809,plain,
! [X0] : X0 = multiply(sF1_fnc,X0),
inference(backward_demodulation,[status(thm)],[f807,f671]) ).
fof(f882,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f809,f7]) ).
fof(f890,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f882,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:12:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.48 % Elapsed time: 0.082313 seconds
% 0.12/0.48 % CPU time: 0.068516 seconds
% 0.12/0.48 % Total memory used: 2.472 MB
% 0.12/0.48 % Net memory used: 2.412 MB
%------------------------------------------------------------------------------