%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 11:47:43 AM UTC 2026
% Result : Unsatisfiable 4.72s 1.07s
% Output : CNFRefutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 22 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 118 ( 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U] :
( X = U
| multiply(U,Y) != Z
| multiply(X,Y) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z,U] : multiply(multiply(X,Y),multiply(Z,U)) = multiply(multiply(X,Z),multiply(Y,U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
multiply(an_element,an_element) = an_element,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X,U] :
( X = U
| ! [Y,Z] :
( multiply(U,Y) != Z
| multiply(X,Y) != Z ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| multiply(X3,X1) != X2
| multiply(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),multiply(X2,X3)) = multiply(multiply(X0,X2),multiply(X1,X3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
multiply(an_element,an_element) = an_element,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2] :
( X2 = X0
| multiply(X0,X1) != multiply(X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f7]) ).
fof(f15,plain,
multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),f)),
inference(forward_demodulation,[status(thm)],[f10,f12]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(multiply(X0,X1),multiply(X2,X3)),multiply(X4,X5)) = multiply(multiply(multiply(X0,X2),X4),multiply(multiply(X1,X3),X5)),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f20,plain,
! [X0,X1] : multiply(an_element,multiply(X0,X1)) = multiply(multiply(an_element,X0),multiply(an_element,X1)),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(X0,X1),multiply(multiply(X2,X3),multiply(X4,X5))) = multiply(multiply(X0,multiply(X2,X4)),multiply(X1,multiply(X3,X5))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f23,plain,
! [X0,X1] : multiply(multiply(X0,X1),an_element) = multiply(multiply(X0,an_element),multiply(X1,an_element)),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f33,plain,
! [X0] : multiply(multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),f)),X0) != multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)),X0),
inference(resolution,[status(thm)],[f15,f13]) ).
fof(f46,plain,
! [X0,X1] : multiply(multiply(multiply(a,multiply(d,e)),X0),multiply(multiply(multiply(b,c),f),X1)) != multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f33]) ).
fof(f54,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(an_element,X1)),multiply(X2,multiply(an_element,X3))) = multiply(multiply(X0,X2),multiply(an_element,multiply(X1,X3))),
inference(paramodulation,[status(thm)],[f20,f10]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(multiply(X0,X1),multiply(X2,X3)),multiply(multiply(X4,X5),X6)) = multiply(multiply(multiply(X0,X4),multiply(X1,X3)),multiply(multiply(X2,X5),X6)),
inference(paramodulation,[status(thm)],[f18,f18]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(multiply(X0,X1),X2),multiply(multiply(X3,X4),X5)) = multiply(multiply(multiply(X0,X3),X2),multiply(multiply(X1,X4),X5)),
inference(paramodulation,[status(thm)],[f10,f18]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(multiply(X0,X1),multiply(X2,X3)),multiply(X4,X5)) = multiply(multiply(multiply(X0,X2),multiply(X1,X3)),multiply(X4,X5)),
inference(paramodulation,[status(thm)],[f10,f18]) ).
fof(f310,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,an_element)),multiply(X2,multiply(X3,an_element))) = multiply(multiply(X0,X2),multiply(multiply(X1,X3),an_element)),
inference(paramodulation,[status(thm)],[f23,f10]) ).
fof(f373,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,multiply(X1,X2)),multiply(multiply(X3,X4),multiply(X5,X6))) = multiply(multiply(X0,multiply(X1,X4)),multiply(multiply(X3,X5),multiply(X2,X6))),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f458,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,multiply(X1,an_element)),multiply(multiply(X2,X3),multiply(X4,an_element))) = multiply(multiply(X0,multiply(X2,X4)),multiply(multiply(X1,X3),an_element)),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f551,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,multiply(X1,X2)),multiply(multiply(X3,X4),an_element)) = multiply(multiply(X0,multiply(X1,X4)),multiply(multiply(X3,X2),an_element)),
inference(forward_demodulation,[status(thm)],[f310,f458]) ).
fof(f678,plain,
! [X0,X1] : multiply(multiply(multiply(a,multiply(d,e)),X0),multiply(multiply(multiply(b,c),f),X1)) != multiply(multiply(multiply(a,multiply(b,e)),X0),multiply(multiply(multiply(d,c),f),X1)),
inference(paramodulation,[status(thm)],[f18,f46]) ).
fof(f697,plain,
! [X0,X1] : multiply(multiply(multiply(a,multiply(d,e)),X0),multiply(multiply(multiply(b,c),f),X1)) != multiply(multiply(multiply(a,multiply(d,c)),X0),multiply(multiply(multiply(b,e),f),X1)),
inference(forward_demodulation,[status(thm)],[f65,f678]) ).
fof(f873,plain,
! [X0,X1] : multiply(multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)),multiply(X0,X1)) != multiply(multiply(multiply(a,multiply(d,c)),X0),multiply(multiply(multiply(b,e),f),X1)),
inference(paramodulation,[status(thm)],[f18,f697]) ).
fof(f888,plain,
! [X0,X1] : multiply(multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),f)),multiply(X0,X1)) != multiply(multiply(multiply(a,multiply(d,c)),X0),multiply(multiply(multiply(b,e),f),X1)),
inference(forward_demodulation,[status(thm)],[f95,f873]) ).
fof(f974,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),f)),multiply(multiply(X0,X1),multiply(an_element,multiply(X2,X3)))) != multiply(multiply(multiply(a,multiply(d,c)),multiply(X0,multiply(an_element,X2))),multiply(multiply(multiply(b,e),f),multiply(X1,multiply(an_element,X3)))),
inference(paramodulation,[status(thm)],[f54,f888]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,e)),multiply(multiply(b,c),an_element)),multiply(multiply(X0,f),multiply(X1,multiply(X2,X3)))) != multiply(multiply(multiply(a,multiply(d,c)),multiply(X0,multiply(an_element,X2))),multiply(multiply(multiply(b,e),f),multiply(X1,multiply(an_element,X3)))),
inference(forward_demodulation,[status(thm)],[f373,f974]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),an_element)),multiply(multiply(X0,f),multiply(X1,multiply(X2,X3)))) != multiply(multiply(multiply(a,multiply(d,c)),multiply(X0,multiply(an_element,X2))),multiply(multiply(multiply(b,e),f),multiply(X1,multiply(an_element,X3)))),
inference(forward_demodulation,[status(thm)],[f551,f1005]) ).
fof(f1007,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),an_element)),multiply(multiply(X0,f),multiply(X1,multiply(X2,X3)))) != multiply(multiply(multiply(a,X0),multiply(multiply(b,e),f)),multiply(multiply(multiply(d,c),multiply(an_element,X2)),multiply(X1,multiply(an_element,X3)))),
inference(forward_demodulation,[status(thm)],[f18,f1006]) ).
fof(f1008,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),an_element)),multiply(multiply(X0,f),multiply(X1,multiply(X2,X3)))) != multiply(multiply(multiply(a,X0),multiply(multiply(b,e),f)),multiply(multiply(multiply(d,c),X1),multiply(an_element,multiply(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f54,f1007]) ).
fof(f1009,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),an_element)),multiply(multiply(X0,f),multiply(X1,multiply(X2,X3)))) != multiply(multiply(multiply(a,X0),multiply(multiply(d,c),an_element)),multiply(multiply(multiply(b,e),f),multiply(X1,multiply(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f21,f1008]) ).
fof(f1010,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1009,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 12:52:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.72/1.07 % Refutation found
% 4.72/1.07 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.72/1.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.72/1.09 % Elapsed time: 0.722503 seconds
% 4.72/1.09 % CPU time: 5.428125 seconds
% 4.72/1.09 % Total memory used: 130.474 MB
% 4.72/1.09 % Net memory used: 129.604 MB
%------------------------------------------------------------------------------