%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP710-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 07:31:17 AM UTC 2026
% Result : Unsatisfiable 0.05s 15.37s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))) = mult(mult(mult(VAR_0,VAR_1),VAR_1),VAR_2),
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_4,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(copy,[status(thm)],[c_3]) ).
fof(f04,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',f04) ).
cnf(c_5,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',f05) ).
cnf(c_6,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[f05]) ).
fof(goal,axiom,
! [VAR_0] : mult(x0,VAR_0) != x1,
file('theBenchmark.p',goal) ).
cnf(c_7,plain,
mult(x0,A) != x1,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_103,plain,
mult(A,mult(B,mult(B,unit))) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_104,plain,
mult(A,mult(B,B)) = mult(mult(A,B),B),
inference(paramod,[status(thm)],[c_1,c_103]) ).
cnf(c_8,plain,
mult(mult(A,B),B) = mult(A,mult(B,B)),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_105,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_9,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_2,c_105]) ).
cnf(c_15,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_106,plain,
mult(unit,i(A)) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_107,plain,
i(A) = mult(A,mult(i(A),i(A))),
inference(paramod,[status(thm)],[c_2,c_106]) ).
cnf(c_22,plain,
mult(A,mult(i(A),i(A))) = i(A),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_108,plain,
mult(unit,A) = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_109,plain,
A = mult(i(A),mult(A,A)),
inference(paramod,[status(thm)],[c_2,c_108]) ).
cnf(c_23,plain,
mult(i(A),mult(A,A)) = A,
inference(copy,[status(thm)],[c_109]) ).
cnf(c_110,plain,
mult(unit,A) = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_111,plain,
A = mult(i(mult(B,B)),mult(B,mult(B,A))),
inference(paramod,[status(thm)],[c_2,c_110]) ).
cnf(c_50,plain,
mult(i(mult(A,A)),mult(A,mult(A,B))) = B,
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
mult(A,B) = mult(i(A),mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_23,c_15]) ).
cnf(c_53,plain,
mult(i(A),mult(A,mult(A,B))) = mult(A,B),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
mult(i(mult(A,A)),mult(A,unit)) = i(A),
inference(paramod,[status(thm)],[c_5,c_50]) ).
cnf(c_62,plain,
mult(i(mult(A,A)),A) = i(A),
inference(paramod,[status(thm)],[c_1,c_113]) ).
cnf(c_114,plain,
mult(i(mult(i(A),i(A))),mult(i(A),unit)) = A,
inference(paramod,[status(thm)],[c_6,c_50]) ).
cnf(c_115,plain,
mult(i(mult(i(A),i(A))),i(A)) = A,
inference(paramod,[status(thm)],[c_1,c_114]) ).
cnf(c_63,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_62,c_115]) ).
cnf(c_116,plain,
mult(i(mult(A,A)),mult(A,i(A))) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_22,c_50]) ).
cnf(c_117,plain,
mult(i(mult(A,A)),unit) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_5,c_116]) ).
cnf(c_67,plain,
i(mult(A,A)) = mult(i(A),i(A)),
inference(paramod,[status(thm)],[c_1,c_117]) ).
cnf(c_118,plain,
mult(mult(i(A),i(A)),mult(A,mult(A,B))) = B,
inference(paramod,[status(thm)],[c_67,c_50]) ).
cnf(c_119,plain,
mult(i(A),mult(i(A),mult(A,mult(A,B)))) = B,
inference(paramod,[status(thm)],[c_9,c_118]) ).
cnf(c_76,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_53,c_119]) ).
cnf(c_101,plain,
mult(A,mult(i(A),B)) = B,
inference(paramod,[status(thm)],[c_63,c_76]) ).
cnf(c_102,plain,
$false,
inference(resolve,[status(thm)],[c_101,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP710-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/15.34 % Computer : n012.cluster.edu
% 0.05/15.34 % Model : x86_64 x86_64
% 0.05/15.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/15.34 % Memory : 8046.5625MB
% 0.05/15.34 % OS : Linux 6.8.0-71-generic
% 0.05/15.34 % CPULimit : 300
% 0.05/15.34 % WCLimit : 300
% 0.05/15.34 % DateTime : Fri Sep 25 15:39:30 UTC 2026
% 0.05/15.34 % CPUTime :
% 0.05/15.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/15.34 % Process 2455782 was started by sandbox2 on n012,
% 0.05/15.34 % Fri Sep 25 15:39:30 2026
% 0.05/15.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/15.34
% 0.05/15.34 % From the command line: assign(max_seconds, 300).
% 0.05/15.37
% 0.05/15.37 % SZS status Unsatisfiable for theBenchmark
% 0.05/15.37
% 0.05/15.37 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.05/15.37 % Length of proof is 20.
% 0.05/15.37 % Level of proof is 8.
% 0.05/15.37 % Maximum clause weight is 15.000.
% 0.05/15.37 % Given clauses 21.
% 0.05/15.37
% 0.05/15.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------