%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG236-1 : 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 : 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 06:49:53 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.68s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_1))) = mult(VAR_0,VAR_1),
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,mult(B,mult(A,B))) = mult(A,B),
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_3))) = mult(VAR_2,mult(VAR_1,mult(VAR_0,VAR_3))),
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))),
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : mult(mult(VAR_0,mult(VAR_1,mult(VAR_2,VAR_1))),VAR_3) = mult(VAR_0,mult(VAR_3,mult(mult(VAR_2,VAR_1),VAR_3))),
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(mult(A,mult(B,mult(C,B))),D) = mult(A,mult(D,mult(mult(C,B),D))),
inference(clausify,[status(thm)],[c03]) ).
fof(goals,axiom,
mult(mult(a,b),mult(c,mult(d,e))) != mult(a,mult(c,mult(mult(d,b),e))),
file('theBenchmark.p',goals) ).
cnf(c_4,plain,
mult(mult(a,b),mult(c,mult(d,e))) != mult(a,mult(c,mult(mult(d,b),e))),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_228,plain,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,mult(D,mult(C,D))))),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
mult(A,mult(B,mult(C,mult(D,mult(A,D))))) = mult(C,mult(B,mult(A,D))),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
mult(A,mult(B,C)) = mult(C,mult(B,mult(A,mult(B,C)))),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
mult(A,mult(B,mult(C,mult(B,A)))) = mult(C,mult(B,A)),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_10,plain,
mult(A,mult(B,mult(C,mult(D,mult(E,F))))) = mult(E,mult(B,mult(A,mult(D,mult(C,F))))),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_230,plain,
mult(mult(A,B),C) = mult(A,mult(C,mult(mult(A,B),C))),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_15,plain,
mult(A,mult(B,mult(mult(A,C),B))) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_17,plain,
mult(mult(A,mult(B,mult(C,B))),D) = mult(mult(C,B),mult(D,mult(A,D))),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_231,plain,
mult(mult(a,b),mult(c,mult(d,e))) != mult(mult(d,b),mult(c,mult(a,e))),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_22,plain,
mult(mult(d,b),mult(c,mult(a,e))) != mult(mult(a,b),mult(c,mult(d,e))),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_28,plain,
mult(mult(d,b),mult(c,mult(a,e))) != mult(d,mult(c,mult(mult(a,b),e))),
inference(paramod,[status(thm)],[c_2,c_22]) ).
cnf(c_232,plain,
mult(mult(A,B),mult(B,mult(A,B))) = mult(A,mult(B,mult(A,B))),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_30,plain,
mult(mult(A,B),mult(B,mult(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_1,c_232]) ).
cnf(c_233,plain,
mult(A,B) = mult(A,mult(B,mult(mult(A,B),B))),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_234,plain,
mult(A,B) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_15,c_233]) ).
cnf(c_43,plain,
mult(mult(A,B),B) = mult(A,B),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_55,plain,
mult(mult(A,mult(B,mult(C,B))),B) = mult(A,mult(B,mult(C,B))),
inference(paramod,[status(thm)],[c_43,c_3]) ).
cnf(c_235,plain,
mult(mult(A,B),C) = mult(mult(A,B),mult(C,mult(A,C))),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_58,plain,
mult(mult(A,B),mult(C,mult(A,C))) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_59,plain,
mult(A,mult(B,mult(mult(C,mult(D,mult(A,E))),B))) = mult(mult(A,mult(D,mult(C,E))),B),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_236,plain,
mult(mult(mult(A,B),C),D) = mult(mult(A,B),mult(D,mult(mult(A,C),D))),
inference(paramod,[status(thm)],[c_58,c_3]) ).
cnf(c_71,plain,
mult(mult(A,B),mult(C,mult(mult(A,D),C))) = mult(mult(mult(A,B),D),C),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_138,plain,
mult(A,mult(B,mult(A,mult(C,mult(D,C))))) = mult(D,mult(B,mult(A,C))),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_237,plain,
mult(mult(mult(A,B),C),D) = mult(mult(A,C),mult(D,mult(mult(A,B),D))),
inference(paramod,[status(thm)],[c_58,c_17]) ).
cnf(c_162,plain,
mult(mult(mult(A,B),C),D) = mult(mult(mult(A,C),B),D),
inference(paramod,[status(thm)],[c_71,c_237]) ).
cnf(c_238,plain,
mult(mult(A,mult(B,mult(mult(C,D),E))),F) = mult(mult(mult(C,mult(B,mult(A,E))),D),F),
inference(paramod,[status(thm)],[c_2,c_162]) ).
cnf(c_175,plain,
mult(mult(mult(A,mult(B,mult(C,D))),E),F) = mult(mult(C,mult(B,mult(mult(A,E),D))),F),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_180,plain,
mult(mult(mult(A,B),C),B) = mult(mult(A,C),B),
inference(paramod,[status(thm)],[c_162,c_43]) ).
cnf(c_239,plain,
mult(mult(A,mult(B,mult(mult(C,mult(D,mult(A,D))),B))),D) = mult(mult(C,B),mult(D,mult(A,D))),
inference(paramod,[status(thm)],[c_180,c_17]) ).
cnf(c_240,plain,
mult(mult(mult(A,mult(D,mult(C,D))),B),D) = mult(mult(C,B),mult(D,mult(A,D))),
inference(paramod,[status(thm)],[c_59,c_239]) ).
cnf(c_241,plain,
mult(mult(C,mult(D,mult(mult(A,B),D))),D) = mult(mult(C,B),mult(D,mult(A,D))),
inference(paramod,[status(thm)],[c_175,c_240]) ).
cnf(c_242,plain,
mult(C,mult(D,mult(mult(A,B),D))) = mult(mult(C,B),mult(D,mult(A,D))),
inference(paramod,[status(thm)],[c_55,c_241]) ).
cnf(c_205,plain,
mult(mult(A,B),mult(C,mult(D,C))) = mult(A,mult(C,mult(mult(D,B),C))),
inference(copy,[status(thm)],[c_242]) ).
cnf(c_243,plain,
mult(A,mult(B,mult(mult(A,C),mult(D,mult(E,D))))) = mult(E,mult(B,mult(mult(A,C),D))),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_244,plain,
mult(A,mult(B,mult(A,mult(D,mult(mult(E,C),D))))) = mult(E,mult(B,mult(mult(A,C),D))),
inference(paramod,[status(thm)],[c_205,c_243]) ).
cnf(c_226,plain,
mult(mult(A,B),mult(C,mult(D,E))) = mult(A,mult(C,mult(mult(D,B),E))),
inference(paramod,[status(thm)],[c_138,c_244]) ).
cnf(c_227,plain,
$false,
inference(resolve,[status(thm)],[c_226,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG236-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n008.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 21:43:41 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 401895 was started by sandbox2 on n008,
% 0.20/0.45 % Sat Sep 26 21:43:41 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.68
% 0.22/0.68 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.68
% 0.22/0.68 % Proof 1 at 0.15 (+ 0.06) seconds.
% 0.22/0.68 % Length of proof is 24.
% 0.22/0.68 % Level of proof is 8.
% 0.22/0.68 % Maximum clause weight is 98.000.
% 0.22/0.68 % Given clauses 29.
% 0.22/0.68
% 0.22/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------