%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP435-1 : 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 11.15s 1.90s
% Output : CNFRefutation 11.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 50 unt; 4 def)
% Number of atoms : 50 ( 49 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 : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 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(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
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(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(a3,sF3_fnc),
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(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(sF3_fnc,X0)),b3),c3),multiply(X1,inverse(X1)))) = X0,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f14,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(sF1_fnc,X0)),a3),b3),multiply(X1,inverse(X1)))) = X0,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f34,plain,
! [X0] : inverse(multiply(multiply(multiply(inverse(sF0_fnc),a3),b3),multiply(X0,inverse(X0)))) = c3,
inference(paramodulation,[status(thm)],[f6,f14]) ).
fof(f51,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(c3,multiply(inverse(sF0_fnc),a3)),b3),multiply(X0,inverse(X0)))) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f34,f3]) ).
fof(f57,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f51,f51]) ).
fof(f112,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),X2),multiply(X3,inverse(X3)))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f57,f3]) ).
fof(f122,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2),inverse(X2)),multiply(X3,inverse(X3)))) = X1,
inference(paramodulation,[status(thm)],[f57,f3]) ).
fof(f478,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X0))) = inverse(multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f112,f122]) ).
fof(f568,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))) = inverse(multiply(X2,inverse(X2))),
inference(paramodulation,[status(thm)],[f478,f478]) ).
fof(f609,plain,
! [X0,X1,X2] : multiply(X0,inverse(X0)) = multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),
inference(paramodulation,[status(thm)],[f478,f57]) ).
fof(f685,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(X0)) = multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),inverse(multiply(X3,inverse(X3)))),
inference(paramodulation,[status(thm)],[f609,f609]) ).
fof(f941,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(inverse(multiply(X1,inverse(X1))),X2)),inverse(X2)),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(paramodulation,[status(thm)],[f568,f10]) ).
fof(f1077,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),X1),inverse(X1))) = multiply(X2,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f112,f941]) ).
fof(f1441,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f1077,f3]) ).
fof(f7604,plain,
! [X0,X1,X2] : inverse(multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f685,f1441]) ).
fof(f7938,plain,
! [X0,X1] : X0 = inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X0))))),
inference(paramodulation,[status(thm)],[f122,f7604]) ).
fof(f8211,plain,
! [X0,X1,X2] : multiply(X0,inverse(X0)) = inverse(inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2))))))))),
inference(paramodulation,[status(thm)],[f1441,f7938]) ).
fof(f8407,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = inverse(inverse(multiply(X1,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f7938,f8211]) ).
fof(f8691,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(X1,inverse(X1))),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f8407,f7604]) ).
fof(f8790,plain,
! [X0,X1] : inverse(multiply(multiply(X0,inverse(X0)),X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f112,f8691]) ).
fof(f8794,plain,
! [X0] : X0 = inverse(inverse(inverse(inverse(X0)))),
inference(backward_demodulation,[status(thm)],[f8790,f7938]) ).
fof(f9049,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = inverse(inverse(inverse(inverse(X1)))),
inference(paramodulation,[status(thm)],[f8790,f8794]) ).
fof(f9139,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f8794,f9049]) ).
fof(f9148,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,inverse(X1)))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f9139,f7604]) ).
fof(f10686,plain,
! [X0] : inverse(multiply(multiply(inverse(multiply(sF3_fnc,X0)),b3),c3)) = X0,
inference(backward_demodulation,[status(thm)],[f9148,f11]) ).
fof(f10687,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f9148,f3]) ).
fof(f10779,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = inverse(inverse(inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f9148,f8794]) ).
fof(f10833,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f8794,f10779]) ).
fof(f10937,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(multiply(X0,multiply(X1,inverse(X1))),X2)),X0)) = X2,
inference(paramodulation,[status(thm)],[f10833,f10687]) ).
fof(f10978,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f10833,f10937]) ).
fof(f10990,plain,
! [X0,X1] : inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))) = X1,
inference(paramodulation,[status(thm)],[f10833,f10978]) ).
fof(f10992,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f10978,f10978]) ).
fof(f11022,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f9139,f10990]) ).
fof(f11192,plain,
inverse(multiply(sF3_fnc,inverse(sF2_fnc))) = a3,
inference(paramodulation,[status(thm)],[f8,f10992]) ).
fof(f12406,plain,
inverse(multiply(multiply(a3,b3),c3)) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f11192,f10686]) ).
fof(f12428,plain,
inverse(multiply(sF1_fnc,c3)) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f5,f12406]) ).
fof(f12429,plain,
inverse(sF0_fnc) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f6,f12428]) ).
fof(f12440,plain,
inverse(inverse(sF0_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f12429,f11022]) ).
fof(f12450,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f11022,f12440]) ).
fof(f12451,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12450,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP435-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:13:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 11.15/1.90 % Refutation found
% 11.15/1.90 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 11.15/1.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.83/5.11 % Elapsed time: 4.743051 seconds
% 17.83/5.11 % CPU time: 30.263614 seconds
% 17.83/5.11 % Total memory used: 13.113 GB
% 17.83/5.11 % Net memory used: 13.111 GB
%------------------------------------------------------------------------------