%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 06:49:54 AM UTC 2026
% Result : Unsatisfiable 2.42s 0.67s
% Output : CNFRefutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 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 : 207 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,VAR_2)) = mult(mult(VAR_0,VAR_1),mult(VAR_0,VAR_2)),
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)),
inference(clausify,[status(thm)],[c01]) ).
cnf(c_2,plain,
mult(mult(A,B),mult(A,C)) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(c02,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),VAR_2) = mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_2)),
file('theBenchmark.p',c02) ).
cnf(c_3,plain,
mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)),
inference(clausify,[status(thm)],[c02]) ).
cnf(c_4,plain,
mult(mult(A,B),mult(C,B)) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_3]) ).
fof(c03,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : mult(mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_3)),mult(mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_3)),mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_3)))) = mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_3)),
file('theBenchmark.p',c03) ).
cnf(c_5,plain,
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)),
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : mult(mult(mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_3)),mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_3))),mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_3))) = mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_3)),
file('theBenchmark.p',c04) ).
cnf(c_6,plain,
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)),
inference(clausify,[status(thm)],[c04]) ).
fof(goals,axiom,
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('theBenchmark.p',goals) ).
cnf(c_7,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(clausify,[status(thm)],[goals]) ).
cnf(c_8,plain,
mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_9,plain,
mult(mult(A,mult(B,C)),mult(mult(A,B),D)) = mult(mult(A,B),mult(mult(A,C),D)),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_10,plain,
mult(mult(mult(A,B),C),mult(A,mult(B,D))) = mult(mult(A,B),mult(C,mult(A,D))),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_13,plain,
mult(mult(A,A),B) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_15,plain,
mult(mult(A,mult(B,C)),mult(B,mult(D,C))) = mult(mult(A,mult(B,D)),mult(B,C)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_473,plain,
mult(mult(A,mult(B,C)),mult(mult(mult(A,B),mult(A,C)),mult(mult(A,A),mult(B,C)))) = mult(mult(A,A),mult(B,C)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_474,plain,
mult(mult(A,mult(B,C)),mult(mult(A,mult(B,C)),mult(mult(A,A),mult(B,C)))) = mult(mult(A,A),mult(B,C)),
inference(paramod,[status(thm)],[c_2,c_473]) ).
cnf(c_475,plain,
mult(mult(A,mult(B,C)),mult(mult(A,mult(A,A)),mult(B,C))) = mult(mult(A,A),mult(B,C)),
inference(paramod,[status(thm)],[c_4,c_474]) ).
cnf(c_19,plain,
mult(mult(A,mult(A,mult(A,A))),mult(B,C)) = mult(mult(A,A),mult(B,C)),
inference(paramod,[status(thm)],[c_4,c_475]) ).
cnf(c_476,plain,
mult(mult(mult(A,A),mult(B,C)),mult(mult(mult(A,A),mult(B,C)),mult(A,mult(B,C)))) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_477,plain,
mult(mult(mult(A,A),mult(B,C)),mult(mult(mult(A,A),A),mult(B,C))) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_4,c_476]) ).
cnf(c_478,plain,
mult(mult(mult(A,A),mult(B,C)),mult(mult(A,mult(A,A)),mult(B,C))) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_13,c_477]) ).
cnf(c_479,plain,
mult(mult(mult(A,A),mult(A,mult(A,A))),mult(B,C)) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_4,c_478]) ).
cnf(c_480,plain,
mult(mult(A,mult(A,mult(A,A))),mult(B,C)) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_2,c_479]) ).
cnf(c_481,plain,
mult(mult(A,A),mult(B,C)) = mult(mult(A,B),mult(A,C)),
inference(paramod,[status(thm)],[c_19,c_480]) ).
cnf(c_20,plain,
mult(mult(A,A),mult(B,C)) = mult(A,mult(B,C)),
inference(paramod,[status(thm)],[c_2,c_481]) ).
cnf(c_482,plain,
mult(mult(A,B),mult(mult(A,C),mult(B,C))) = mult(mult(A,mult(A,B)),mult(B,C)),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_483,plain,
mult(mult(A,B),mult(mult(A,B),C)) = mult(mult(A,mult(A,B)),mult(B,C)),
inference(paramod,[status(thm)],[c_4,c_482]) ).
cnf(c_31,plain,
mult(mult(A,mult(A,B)),mult(B,C)) = mult(mult(A,B),mult(mult(A,B),C)),
inference(copy,[status(thm)],[c_483]) ).
cnf(c_484,plain,
mult(mult(mult(A,A),B),mult(mult(A,A),C)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_485,plain,
mult(mult(A,A),mult(B,C)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_2,c_484]) ).
cnf(c_486,plain,
mult(A,mult(B,C)) = mult(A,mult(mult(B,C),mult(B,C))),
inference(paramod,[status(thm)],[c_20,c_485]) ).
cnf(c_487,plain,
mult(A,mult(B,C)) = mult(A,mult(B,mult(C,C))),
inference(paramod,[status(thm)],[c_2,c_486]) ).
cnf(c_42,plain,
mult(A,mult(B,mult(C,C))) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_487]) ).
cnf(c_488,plain,
mult(A,mult(mult(B,A),mult(B,A))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_489,plain,
mult(A,mult(B,mult(A,A))) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_2,c_488]) ).
cnf(c_490,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_42,c_489]) ).
cnf(c_50,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
mult(mult(A,B),mult(mult(B,C),mult(A,C))) = mult(mult(mult(A,B),A),mult(B,C)),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_492,plain,
mult(mult(A,B),mult(mult(B,A),C)) = mult(mult(mult(A,B),A),mult(B,C)),
inference(paramod,[status(thm)],[c_4,c_491]) ).
cnf(c_493,plain,
mult(mult(A,B),mult(mult(B,A),C)) = mult(mult(A,mult(B,A)),mult(B,C)),
inference(paramod,[status(thm)],[c_50,c_492]) ).
cnf(c_63,plain,
mult(mult(A,mult(B,A)),mult(B,C)) = mult(mult(A,B),mult(mult(B,A),C)),
inference(copy,[status(thm)],[c_493]) ).
cnf(c_494,plain,
mult(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(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_6,c_31]) ).
cnf(c_495,plain,
mult(mult(mult(A,C),mult(B,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_5,c_494]) ).
cnf(c_496,plain,
mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(mult(B,D),mult(B,D)))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_495]) ).
cnf(c_497,plain,
mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,mult(D,D)))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_496]) ).
cnf(c_498,plain,
mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_42,c_497]) ).
cnf(c_499,plain,
mult(mult(A,C),mult(mult(B,D),mult(B,D))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_498]) ).
cnf(c_500,plain,
mult(mult(A,C),mult(B,mult(D,D))) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_2,c_499]) ).
cnf(c_501,plain,
mult(mult(A,C),mult(B,D)) = mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D))),
inference(paramod,[status(thm)],[c_42,c_500]) ).
cnf(c_502,plain,
mult(mult(A,C),mult(B,D)) = mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D)))),
inference(paramod,[status(thm)],[c_50,c_501]) ).
cnf(c_113,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D)))) = mult(mult(A,C),mult(B,D)),
inference(copy,[status(thm)],[c_502]) ).
cnf(c_503,plain,
mult(mult(A,mult(B,C)),mult(B,A)) = mult(mult(A,B),mult(mult(B,A),mult(C,A))),
inference(paramod,[status(thm)],[c_15,c_63]) ).
cnf(c_433,plain,
mult(mult(A,mult(B,C)),mult(B,A)) = mult(mult(A,B),mult(mult(B,C),A)),
inference(paramod,[status(thm)],[c_4,c_503]) ).
cnf(c_504,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_5,c_433]) ).
cnf(c_505,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(mult(B,D),mult(B,D)))) = mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_2,c_504]) ).
cnf(c_506,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,mult(D,D)))) = mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_2,c_505]) ).
cnf(c_507,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))) = mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,C),mult(B,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_42,c_506]) ).
cnf(c_508,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))) = mult(mult(mult(A,C),mult(mult(B,D),mult(B,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_2,c_507]) ).
cnf(c_509,plain,
mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))) = mult(mult(mult(A,C),mult(B,mult(D,D))),mult(mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_2,c_508]) ).
cnf(c_510,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(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))),mult(mult(A,C),mult(B,D)))),
inference(paramod,[status(thm)],[c_42,c_509]) ).
cnf(c_511,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(mult(A,C),mult(B,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))))),
inference(paramod,[status(thm)],[c_50,c_510]) ).
cnf(c_471,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(paramod,[status(thm)],[c_113,c_511]) ).
cnf(c_472,plain,
$false,
inference(resolve,[status(thm)],[c_471,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 21:43:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3168553 was started by sandbox on n005,
% 0.07/0.35 % Sat Sep 26 21:43:16 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 2.42/0.67
% 2.42/0.67 % SZS status Unsatisfiable for theBenchmark
% 2.42/0.67
% 2.42/0.67 % Proof 1 at 0.24 (+ 0.08) seconds.
% 2.42/0.67 % Length of proof is 22.
% 2.42/0.67 % Level of proof is 9.
% 2.42/0.67 % Maximum clause weight is 80.000.
% 2.42/0.67 % Given clauses 26.
% 2.42/0.67
% 2.42/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------