%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Sun Sep 27 06:49:05 AM UTC 2026
% Result : Unsatisfiable 4.08s 0.98s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| multiply(VAR_0,VAR_3) != VAR_2
| multiply(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',right_cancellation) ).
cnf(c_2,plain,
( B = D
| multiply(A,D) != C
| multiply(A,B) != C ),
inference(clausify,[status(thm)],[right_cancellation]) ).
fof(medial_law,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(multiply(VAR_0,VAR_1),multiply(VAR_2,VAR_3)) = multiply(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_3)),
file('theBenchmark.p',medial_law) ).
cnf(c_3,plain,
multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)),
inference(clausify,[status(thm)],[medial_law]) ).
fof(prove_this,axiom,
multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)),
file('theBenchmark.p',prove_this) ).
cnf(c_5,plain,
multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)) != multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_6,plain,
multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f)) != multiply(multiply(a,multiply(d,c)),multiply(multiply(b,e),f)),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_7,plain,
multiply(multiply(multiply(A,B),multiply(C,D)),multiply(E,F)) = multiply(multiply(multiply(A,C),E),multiply(multiply(B,D),F)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_928,plain,
multiply(multiply(A,B),multiply(multiply(C,D),multiply(E,F))) = multiply(multiply(A,multiply(C,E)),multiply(B,multiply(D,F))),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_8,plain,
multiply(multiply(A,multiply(B,C)),multiply(D,multiply(E,F))) = multiply(multiply(A,D),multiply(multiply(B,E),multiply(C,F))),
inference(copy,[status(thm)],[c_928]) ).
cnf(c_929,plain,
( E = multiply(F,V6)
| multiply(multiply(multiply(A,B),multiply(C,D)),E) != multiply(multiply(multiply(A,C),F),multiply(multiply(B,D),V6)) ),
inference(resolve,[status(thm)],[c_2,c_7]) ).
cnf(c_930,plain,
multiply(multiply(multiply(A,B),multiply(C,D)),multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f))) != multiply(multiply(multiply(A,C),multiply(a,multiply(d,c))),multiply(multiply(B,D),multiply(multiply(b,e),f))),
inference(resolve,[status(thm)],[c_929,c_6]) ).
cnf(c_19,plain,
multiply(multiply(multiply(A,B),multiply(a,multiply(d,c))),multiply(multiply(C,D),multiply(multiply(b,e),f))) != multiply(multiply(multiply(A,C),multiply(B,D)),multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f))),
inference(copy,[status(thm)],[c_930]) ).
cnf(c_90,plain,
multiply(multiply(multiply(A,multiply(B,C)),multiply(D,multiply(E,F))),multiply(V6,V7)) = multiply(multiply(multiply(A,multiply(B,E)),V6),multiply(multiply(D,multiply(C,F)),V7)),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_931,plain,
multiply(multiply(multiply(A,B),multiply(a,multiply(d,c))),multiply(multiply(multiply(C,D),multiply(b,e)),multiply(multiply(E,F),f))) != multiply(multiply(multiply(A,multiply(C,E)),multiply(B,multiply(D,F))),multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f))),
inference(paramod,[status(thm)],[c_7,c_19]) ).
cnf(c_926,plain,
multiply(multiply(multiply(A,multiply(B,C)),multiply(D,multiply(E,F))),multiply(multiply(a,multiply(b,c)),multiply(multiply(d,e),f))) != multiply(multiply(multiply(A,D),multiply(a,multiply(d,c))),multiply(multiply(multiply(B,E),multiply(b,e)),multiply(multiply(C,F),f))),
inference(copy,[status(thm)],[c_931]) ).
cnf(c_932,plain,
multiply(multiply(multiply(A,multiply(B,E)),V6),multiply(multiply(D,multiply(C,F)),V7)) = multiply(multiply(multiply(A,multiply(B,C)),multiply(D,multiply(E,F))),multiply(V6,V7)),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_927,plain,
$false,
inference(resolve,[status(thm)],[c_926,c_932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 20:57:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 348598 was started by sandbox2 on n008,
% 0.10/0.37 % Sat Sep 26 20:57:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 4.08/0.98
% 4.08/0.98 % SZS status Unsatisfiable for theBenchmark
% 4.08/0.98
% 4.08/0.98 % Proof 1 at 0.54 (+ 0.06) seconds.
% 4.08/0.98 % Length of proof is 10.
% 4.08/0.98 % Level of proof is 4.
% 4.08/0.98 % Maximum clause weight is 72.000.
% 4.08/0.98 % Given clauses 34.
% 4.08/0.98
% 4.08/0.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------