%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 2.21s 0.81s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 24 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 22 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 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(f2,axiom,
! [X,Y,Z,U] :
( Y = U
| multiply(X,U) != 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,negated_conjecture,
multiply(b,b0) = multiply(a,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(d,b0) = multiply(c,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
multiply(b,d0) = multiply(a,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X,U] :
( X = U
| ! [Y,Z] :
( multiply(U,Y) != Z
| multiply(X,Y) != Z ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| multiply(X3,X1) != X2
| multiply(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [Y,U] :
( Y = U
| ! [X,Z] :
( multiply(X,U) != Z
| multiply(X,Y) != Z ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| multiply(X0,X3) != X2
| multiply(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,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(f13,plain,
multiply(b,b0) = multiply(a,a0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
multiply(d,b0) = multiply(c,a0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
multiply(b,d0) = multiply(a,c0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
multiply(d,d0) != multiply(c,c0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X2 = X0
| multiply(X0,X1) != multiply(X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f9]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X2 = X1
| multiply(X0,X1) != multiply(X0,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : multiply(X0,multiply(c,c0)) != multiply(X0,multiply(d,d0)),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f32,plain,
! [X0,X1] : multiply(multiply(X0,multiply(d,d0)),X1) != multiply(multiply(X0,multiply(c,c0)),X1),
inference(resolution,[status(thm)],[f27,f17]) ).
fof(f39,plain,
! [X0,X1] : multiply(multiply(d,b0),multiply(X0,X1)) = multiply(multiply(c,X0),multiply(a0,X1)),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f40,plain,
! [X0,X1] : multiply(multiply(b,d0),multiply(X0,X1)) = multiply(multiply(a,X0),multiply(c0,X1)),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f41,plain,
! [X0,X1] : multiply(multiply(b,b0),multiply(X0,X1)) = multiply(multiply(a,X0),multiply(a0,X1)),
inference(paramodulation,[status(thm)],[f13,f12]) ).
fof(f42,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)],[f12,f12]) ).
fof(f87,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(d,d0)),multiply(X1,X2)) != multiply(multiply(X0,X1),multiply(multiply(c,c0),X2)),
inference(paramodulation,[status(thm)],[f12,f32]) ).
fof(f115,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(a,X1)),multiply(X2,multiply(c0,X3))) = multiply(multiply(X0,X2),multiply(multiply(b,d0),multiply(X1,X3))),
inference(paramodulation,[status(thm)],[f40,f12]) ).
fof(f510,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(X3,X5)),multiply(multiply(X1,X4),multiply(X2,X6))),
inference(paramodulation,[status(thm)],[f12,f42]) ).
fof(f1544,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(a,X1)),multiply(X2,multiply(c0,X3))) = multiply(multiply(X0,multiply(b,X1)),multiply(X2,multiply(d0,X3))),
inference(paramodulation,[status(thm)],[f42,f115]) ).
fof(f2602,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(d,d0)),multiply(multiply(b,b0),multiply(X1,X2))) != multiply(multiply(X0,multiply(a,X1)),multiply(multiply(c,c0),multiply(a0,X2))),
inference(paramodulation,[status(thm)],[f41,f87]) ).
fof(f2641,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(d,d0)),multiply(multiply(b,b0),multiply(X1,X2))) != multiply(multiply(X0,multiply(a,X1)),multiply(multiply(d,b0),multiply(c0,X2))),
inference(forward_demodulation,[status(thm)],[f39,f2602]) ).
fof(f2642,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(d,d0)),multiply(multiply(b,b0),multiply(X1,X2))) != multiply(multiply(X0,multiply(b,X1)),multiply(multiply(d,b0),multiply(d0,X2))),
inference(forward_demodulation,[status(thm)],[f1544,f2641]) ).
fof(f2643,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2642,f510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n012.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 12:51:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 2.21/0.81 % Refutation found
% 2.21/0.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.21/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.21/0.83 % Elapsed time: 0.458044 seconds
% 2.21/0.83 % CPU time: 3.453130 seconds
% 2.21/0.83 % Total memory used: 122.624 MB
% 2.21/0.83 % Net memory used: 122.116 MB
%------------------------------------------------------------------------------