%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP698-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:35:09 PM UTC 2026
% Result : Unsatisfiable 2.61s 0.79s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(mult(mult(X1,X0),X0),X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2] : rd(mult(X0,mult(mult(mult(X1,X0),X0),X2)),mult(X0,X2)) = mult(mult(X0,X1),X0),
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f49,plain,
! [X0,X1,X2] : rd(mult(X0,mult(mult(X1,X0),X2)),mult(X0,X2)) = mult(mult(X0,rd(X1,X0)),X0),
inference(paramodulation,[status(thm)],[f12,f33]) ).
fof(f117,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X0,X2)) = mult(mult(X0,rd(rd(X1,X0),X0)),X0),
inference(paramodulation,[status(thm)],[f12,f49]) ).
fof(f262,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,mult(X1,X2)),mult(X0,X2)),mult(X0,X3)) = mult(X0,mult(mult(mult(rd(rd(X1,X0),X0),X0),X0),X3)),
inference(paramodulation,[status(thm)],[f117,f16]) ).
fof(f289,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,mult(X1,X2)),mult(X0,X2)),mult(X0,X3)) = mult(X0,mult(mult(rd(X1,X0),X0),X3)),
inference(forward_demodulation,[status(thm)],[f12,f262]) ).
fof(f290,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,mult(X1,X2)),mult(X0,X2)),mult(X0,X3)) = mult(X0,mult(X1,X3)),
inference(forward_demodulation,[status(thm)],[f12,f289]) ).
fof(f660,plain,
! [X0,X1] : rd(mult(X0,mult(X1,X0)),mult(X0,unit)) = mult(mult(X0,rd(X1,X0)),X0),
inference(paramodulation,[status(thm)],[f14,f49]) ).
fof(f765,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X0,X2)) = rd(mult(X0,mult(rd(X1,X0),X0)),X0),
inference(backward_demodulation,[status(thm)],[f811,f117]) ).
fof(f811,plain,
! [X0,X1] : rd(mult(X0,mult(X1,X0)),X0) = mult(mult(X0,rd(X1,X0)),X0),
inference(forward_demodulation,[status(thm)],[f14,f660]) ).
fof(f907,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(X1,X2)),
inference(backward_demodulation,[status(thm)],[f909,f290]) ).
fof(f909,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X0,X2)) = rd(mult(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f12,f765]) ).
fof(f1005,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(backward_demodulation,[status(thm)],[f907,f18]) ).
fof(f1031,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP698-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:33:34 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 2.61/0.79 % Refutation found
% 2.61/0.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.61/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.61/0.80 % Elapsed time: 0.424435 seconds
% 2.61/0.80 % CPU time: 3.131148 seconds
% 2.61/0.80 % Total memory used: 113.793 MB
% 2.61/0.80 % Net memory used: 113.052 MB
%------------------------------------------------------------------------------