%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 11:49:05 AM UTC 2026
% Result : Unsatisfiable 7.76s 1.72s
% Output : CNFRefutation 8.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 229 ( 229 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] : mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C,D] : mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : mult(X0,mult(X1,X2)) = mult(mult(X0,X1),mult(X0,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))) = mult(mult(X0,X2),mult(X1,X3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(X0,X1),mult(X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1,X2,X3] : mult(mult(X0,X1),mult(X2,mult(X0,X3))) = mult(mult(mult(X0,X1),X2),mult(X0,mult(X1,X3))),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f24,plain,
! [X0,X1] : mult(mult(X0,X0),X1) = mult(X0,mult(X1,X1)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,X1),X2),mult(X3,X1)) = mult(mult(mult(X0,X3),X1),mult(X2,mult(X3,X1))),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),X4)) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),X4)),
inference(paramodulation,[status(thm)],[f8,f6]) ).
fof(f114,plain,
! [X0,X1] : mult(mult(mult(X0,X0),mult(X0,X0)),X1) = mult(X0,mult(mult(X1,X1),mult(X1,X1))),
inference(paramodulation,[status(thm)],[f24,f24]) ).
fof(f115,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),X1),X2) = mult(mult(X0,X1),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f7,f24]) ).
fof(f149,plain,
! [X0,X1] : mult(mult(mult(X0,X0),X0),X1) = mult(X0,mult(mult(X1,X1),mult(X1,X1))),
inference(forward_demodulation,[status(thm)],[f7,f114]) ).
fof(f150,plain,
! [X0,X1] : mult(mult(mult(X0,X0),X0),X1) = mult(X0,mult(mult(X1,X1),X1)),
inference(forward_demodulation,[status(thm)],[f7,f149]) ).
fof(f193,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X1),mult(X0,X1)),X2),mult(mult(X0,X2),mult(X1,X2))),mult(mult(X0,X2),mult(X1,X2))) = mult(mult(X0,X1),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f24,f9]) ).
fof(f208,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X1),mult(X2,X2)),mult(mult(X0,X1),X2)),mult(mult(X0,X2),mult(X1,X2))) = mult(mult(X0,X1),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f211,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X1),mult(X2,X1)),mult(mult(mult(X0,X2),mult(X0,X2)),X1)),mult(mult(X0,X2),mult(X1,X1))) = mult(mult(X0,X1),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f24,f9]) ).
fof(f253,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),X4),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,mult(mult(X0,X2),mult(X1,X3)))),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f278,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X1),X2),mult(mult(X0,X2),mult(X1,X2))),mult(mult(X0,X2),mult(X1,X2))) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f193]) ).
fof(f279,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X1),mult(X0,X1)),mult(X2,X1)),mult(mult(X0,X1),mult(X2,X1))) = mult(mult(X0,X2),mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f25,f278]) ).
fof(f280,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X1),mult(X0,X1)),mult(X0,X1)),mult(X2,X1)) = mult(mult(X0,X2),mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f7,f279]) ).
fof(f281,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),X1),mult(X0,X1)),mult(X2,X1)) = mult(mult(X0,X2),mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f7,f280]) ).
fof(f282,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),X0),X1),mult(X2,X1)) = mult(mult(X0,X2),mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f7,f281]) ).
fof(f283,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),X0),X1),X2) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f282]) ).
fof(f294,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(X2,X2),X2)),mult(mult(X0,X2),mult(X1,X2))) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f6,f208]) ).
fof(f295,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(X2,X2),X2)),mult(mult(X0,X1),X2)) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f294]) ).
fof(f296,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(mult(mult(X2,X2),X2),X2)) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f6,f295]) ).
fof(f308,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X1),X2),mult(mult(mult(X0,X1),mult(X0,X1)),X2)),mult(mult(X0,X1),mult(X2,X2))) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f211]) ).
fof(f309,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),mult(mult(mult(mult(X0,X1),mult(X0,X1)),X2),mult(mult(X0,X1),X2))) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f23,f308]) ).
fof(f310,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),mult(mult(mult(mult(X0,X1),mult(X0,X1)),mult(X0,X1)),X2)) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f309]) ).
fof(f311,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(mult(X0,X1),mult(X0,X1)),mult(X0,X1))),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f310]) ).
fof(f312,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(mult(X0,X0),X1),mult(X0,X1))),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f311]) ).
fof(f313,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(mult(X0,X0),X0),X1)),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f312]) ).
fof(f314,plain,
! [X0,X1,X2] : mult(mult(mult(X0,mult(mult(X0,X0),X0)),X1),X2) = mult(mult(X0,X2),mult(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f313]) ).
fof(f315,plain,
! [X0,X1,X2] : mult(mult(mult(X0,mult(mult(X0,X0),X0)),X1),X2) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f7,f314]) ).
fof(f750,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),mult(X0,X0)),mult(X0,X0)),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f150,f115]) ).
fof(f760,plain,
! [X0,X1] : mult(mult(mult(X0,X0),X1),X1) = mult(mult(X0,X1),X1),
inference(paramodulation,[status(thm)],[f7,f115]) ).
fof(f761,plain,
! [X0,X1] : mult(mult(mult(X0,X0),X1),X0) = mult(X0,mult(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f115]) ).
fof(f764,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))),mult(mult(X0,X2),mult(X1,X3))),X4) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,X4)),
inference(paramodulation,[status(thm)],[f9,f115]) ).
fof(f765,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X1),mult(X2,X3))),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))),X4) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(X4,X4)),
inference(paramodulation,[status(thm)],[f8,f115]) ).
fof(f768,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),mult(mult(X0,X0),X0)),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f150,f115]) ).
fof(f770,plain,
! [X0,X1,X2,X3] : mult(mult(mult(mult(X0,X1),mult(X0,X1)),mult(X2,X2)),X3) = mult(mult(mult(mult(X0,X0),X1),X2),mult(X3,X3)),
inference(paramodulation,[status(thm)],[f115,f115]) ).
fof(f774,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),mult(mult(X1,X1),X1)),X2) = mult(mult(mult(mult(X0,X0),X0),X1),mult(X2,X2)),
inference(paramodulation,[status(thm)],[f150,f115]) ).
fof(f879,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),mult(X0,X0)),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f750]) ).
fof(f880,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),X0),X0),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f879]) ).
fof(f893,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X0),X0),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(backward_demodulation,[status(thm)],[f760,f880]) ).
fof(f898,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(mult(X2,X2),X2)) = mult(mult(X0,X1),mult(X2,X2)),
inference(backward_demodulation,[status(thm)],[f760,f296]) ).
fof(f899,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X0),X0),X1),X2) = mult(mult(X0,X1),mult(X2,X2)),
inference(backward_demodulation,[status(thm)],[f760,f283]) ).
fof(f902,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),mult(mult(X0,X2),mult(X1,X3)))),X4) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,X4)),
inference(forward_demodulation,[status(thm)],[f253,f764]) ).
fof(f903,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3)))),X4) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(X4,X4)),
inference(forward_demodulation,[status(thm)],[f64,f902]) ).
fof(f904,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3)))),X4) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(X4,X4)),
inference(forward_demodulation,[status(thm)],[f6,f765]) ).
fof(f908,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3)))),X4) = mult(mult(mult(X0,X2),mult(X1,X3)),X4),
inference(backward_demodulation,[status(thm)],[f909,f903]) ).
fof(f909,plain,
! [X0,X1,X2,X3,X4] : mult(mult(mult(X0,X1),mult(X2,X3)),X4) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(X4,X4)),
inference(forward_demodulation,[status(thm)],[f8,f904]) ).
fof(f916,plain,
! [X0,X1,X2] : mult(mult(mult(mult(mult(X0,X0),mult(X0,X0)),X0),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f7,f768]) ).
fof(f917,plain,
! [X0,X1,X2] : mult(mult(mult(X0,mult(mult(X0,X0),X0)),X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f761,f916]) ).
fof(f918,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(mult(X1,X1),X1)),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f315,f917]) ).
fof(f921,plain,
! [X0,X1,X2,X3] : mult(mult(mult(mult(X0,X1),mult(X0,X1)),X2),X3) = mult(mult(mult(mult(X0,X0),X1),X2),mult(X3,X3)),
inference(forward_demodulation,[status(thm)],[f909,f770]) ).
fof(f922,plain,
! [X0,X1,X2,X3] : mult(mult(mult(mult(X0,X0),X1),X2),X3) = mult(mult(mult(mult(X0,X0),X1),X2),mult(X3,X3)),
inference(forward_demodulation,[status(thm)],[f7,f921]) ).
fof(f927,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),mult(mult(X1,X1),X1)),X2) = mult(mult(mult(mult(X0,X0),X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f922,f774]) ).
fof(f1031,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),mult(mult(X1,X1),X1)),X2) = mult(mult(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f1043,f927]) ).
fof(f1043,plain,
! [X0,X1,X2] : mult(mult(mult(mult(X0,X0),X0),X1),X2) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f918,f893]) ).
fof(f1120,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X1),mult(X2,X2)),
inference(forward_demodulation,[status(thm)],[f1043,f899]) ).
fof(f1223,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),mult(X1,X1)),X2) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f898,f1031]) ).
fof(f1272,plain,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
inference(backward_demodulation,[status(thm)],[f1279,f761]) ).
fof(f1279,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X0),X1),X2) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f1120,f1223]) ).
fof(f2118,plain,
! [X0,X1,X2,X3] : mult(mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3)))),mult(mult(X0,X1),mult(X2,X3))) = mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))),
inference(paramodulation,[status(thm)],[f9,f1272]) ).
fof(f2249,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,X1),mult(X2,X3)),mult(mult(X0,X2),mult(X1,X3))) = mult(mult(mult(X0,X2),mult(X1,X3)),mult(mult(X0,X1),mult(X2,X3))),
inference(forward_demodulation,[status(thm)],[f908,f2118]) ).
fof(f2250,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f10,f2249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.60 % Computer : n006.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Mon Sep 21 13:09:42 UTC 2026
% 0.12/0.61 % CPUTime :
% 0.20/0.62 % Drodi V4.1.1
% 7.76/1.72 % Refutation found
% 7.76/1.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.76/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.48/1.78 % Elapsed time: 1.150990 seconds
% 8.48/1.78 % CPU time: 8.758861 seconds
% 8.48/1.78 % Total memory used: 133.149 MB
% 8.48/1.78 % Net memory used: 131.202 MB
%------------------------------------------------------------------------------