%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG245-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.90s 0.51s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 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 : 121 ( 0 sgn 15 !; 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(c05,axiom,
! [VAR_0] : mult(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',c05) ).
cnf(c_7,plain,
mult(A,A) = A,
inference(clausify,[status(thm)],[c05]) ).
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_8,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_9,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_8]) ).
cnf(c_10,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_11,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_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_18,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_450,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_10,c_4]) ).
cnf(c_451,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_450]) ).
cnf(c_24,plain,
mult(mult(A,mult(A,B)),mult(B,C)) = mult(mult(A,B),mult(mult(A,B),C)),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,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_24]) ).
cnf(c_453,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_452]) ).
cnf(c_454,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_7,c_453]) ).
cnf(c_455,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_7,c_454]) ).
cnf(c_456,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_18,c_455]) ).
cnf(c_73,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_456]) ).
cnf(c_457,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_11,c_4]) ).
cnf(c_458,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_457]) ).
cnf(c_459,plain,
mult(mult(A,B),mult(mult(B,A),C)) = mult(mult(A,mult(B,A)),mult(B,C)),
inference(paramod,[status(thm)],[c_18,c_458]) ).
cnf(c_94,plain,
mult(mult(A,mult(B,A)),mult(B,C)) = mult(mult(A,B),mult(mult(B,A),C)),
inference(copy,[status(thm)],[c_459]) ).
cnf(c_460,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_94]) ).
cnf(c_410,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_460]) ).
cnf(c_461,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_410]) ).
cnf(c_462,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_7,c_461]) ).
cnf(c_463,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_7,c_462]) ).
cnf(c_464,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_18,c_463]) ).
cnf(c_448,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_73,c_464]) ).
cnf(c_449,plain,
$false,
inference(resolve,[status(thm)],[c_448,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG245-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:47:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2744759 was started by sandbox2 on n002,
% 0.10/0.38 % Sat Sep 26 21:47:21 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.90/0.51
% 0.90/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.90/0.51
% 0.90/0.51 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.90/0.51 % Length of proof is 19.
% 0.90/0.51 % Level of proof is 6.
% 0.90/0.51 % Maximum clause weight is 80.000.
% 0.90/0.51 % Given clauses 20.
% 0.90/0.51
% 0.90/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------