%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:35:01 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(X2,X0)) = mult(X0,mult(mult(X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] : mult(X0,mult(mult(X1,rd(X2,X0)),X0)) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f32,plain,
! [X0,X1,X2] : mult(X0,X1) = rd(mult(X0,mult(mult(X1,X2),X0)),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f48,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,rd(X2,X0))),X2) = mult(X0,mult(X1,X0)),
inference(paramodulation,[status(thm)],[f9,f30]) ).
fof(f56,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,X2)),X2) = ld(X2,mult(mult(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f30,f8]) ).
fof(f66,plain,
! [X0,X1,X2] : mult(X0,rd(X1,X2)) = rd(mult(X0,mult(X1,X0)),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f9,f32]) ).
fof(f424,plain,
! [X0,X1] : mult(X0,rd(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f10,f66]) ).
fof(f462,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f424]) ).
fof(f634,plain,
! [X0,X1,X2] : mult(rd(X0,X0),mult(X1,rd(X0,X0))) = mult(mult(rd(X0,X0),rd(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f462,f48]) ).
fof(f642,plain,
! [X0,X1,X2] : mult(rd(X0,X0),X1) = mult(mult(rd(X0,X0),rd(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f424,f634]) ).
fof(f643,plain,
! [X0,X1,X2] : mult(rd(X0,X0),X1) = ld(X2,mult(mult(X2,rd(X0,X0)),X1)),
inference(forward_demodulation,[status(thm)],[f56,f642]) ).
fof(f644,plain,
! [X0,X1,X2] : mult(rd(X0,X0),X1) = ld(X2,mult(X2,X1)),
inference(forward_demodulation,[status(thm)],[f424,f643]) ).
fof(f645,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f8,f644]) ).
fof(f755,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(x1(rd(X0,X0)),mult(x1_2(rd(X0,X0)),rd(X0,X0))),
inference(paramodulation,[status(thm)],[f645,f12]) ).
fof(f794,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f424,f755]) ).
fof(f795,plain,
$false,
inference(equality_resolution,[status(thm)],[f794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:31:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.059489 seconds
% 0.09/0.43 % CPU time: 0.334409 seconds
% 0.09/0.43 % Total memory used: 14.787 MB
% 0.09/0.43 % Net memory used: 14.448 MB
%------------------------------------------------------------------------------