%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP197-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:28:20 AM UTC 2026
% Result : Unsatisfiable 0.76s 0.56s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 47 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 16 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_multiply) ).
cnf(c_1,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity_of_multiply]) ).
fof(right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_2,VAR_1) ),
file('theBenchmark.p',right_cancellation) ).
cnf(c_2,plain,
( A = C
| multiply(A,B) != multiply(C,B) ),
inference(clausify,[status(thm)],[right_cancellation]) ).
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_0,VAR_2) ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_3,plain,
( B = C
| multiply(A,B) != multiply(A,C) ),
inference(clausify,[status(thm)],[left_cancellation]) ).
fof(condition,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,multiply(VAR_0,multiply(VAR_0,multiply(VAR_1,VAR_1)))) = multiply(VAR_1,multiply(VAR_0,multiply(VAR_0,multiply(VAR_1,VAR_0)))),
file('theBenchmark.p',condition) ).
cnf(c_4,plain,
multiply(A,multiply(A,multiply(A,multiply(B,B)))) = multiply(B,multiply(A,multiply(A,multiply(B,A)))),
inference(clausify,[status(thm)],[condition]) ).
cnf(c_5,plain,
multiply(A,multiply(B,multiply(B,multiply(A,B)))) = multiply(B,multiply(B,multiply(B,multiply(A,A)))),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this,axiom,
multiply(b,multiply(b,multiply(a,multiply(a,a)))) != multiply(a,multiply(b,multiply(a,multiply(a,b)))),
file('theBenchmark.p',prove_this) ).
cnf(c_6,plain,
multiply(b,multiply(b,multiply(a,multiply(a,a)))) != multiply(a,multiply(b,multiply(a,multiply(a,b)))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_83,plain,
multiply(multiply(A,multiply(A,multiply(A,multiply(B,B)))),C) = multiply(B,multiply(multiply(A,multiply(A,multiply(B,A))),C)),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_84,plain,
multiply(A,multiply(multiply(A,multiply(A,multiply(B,B))),C)) = multiply(B,multiply(multiply(A,multiply(A,multiply(B,A))),C)),
inference(paramod,[status(thm)],[c_1,c_83]) ).
cnf(c_85,plain,
multiply(A,multiply(A,multiply(multiply(A,multiply(B,B)),C))) = multiply(B,multiply(multiply(A,multiply(A,multiply(B,A))),C)),
inference(paramod,[status(thm)],[c_1,c_84]) ).
cnf(c_86,plain,
multiply(A,multiply(A,multiply(A,multiply(multiply(B,B),C)))) = multiply(B,multiply(multiply(A,multiply(A,multiply(B,A))),C)),
inference(paramod,[status(thm)],[c_1,c_85]) ).
cnf(c_87,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(B,A))),C)),
inference(paramod,[status(thm)],[c_1,c_86]) ).
cnf(c_88,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C))))) = multiply(B,multiply(A,multiply(multiply(A,multiply(B,A)),C))),
inference(paramod,[status(thm)],[c_1,c_87]) ).
cnf(c_89,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C))))) = multiply(B,multiply(A,multiply(A,multiply(multiply(B,A),C)))),
inference(paramod,[status(thm)],[c_1,c_88]) ).
cnf(c_90,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(B,C))))) = multiply(B,multiply(A,multiply(A,multiply(B,multiply(A,C))))),
inference(paramod,[status(thm)],[c_1,c_89]) ).
cnf(c_7,plain,
multiply(A,multiply(B,multiply(B,multiply(A,multiply(B,C))))) = multiply(B,multiply(B,multiply(B,multiply(A,multiply(A,C))))),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,plain,
multiply(A,multiply(A,multiply(A,multiply(multiply(B,C),multiply(B,C))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(multiply(B,C),A))))),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_92,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(C,multiply(B,C)))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(multiply(B,C),A))))),
inference(paramod,[status(thm)],[c_1,c_91]) ).
cnf(c_93,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(C,multiply(B,C)))))) = multiply(B,multiply(C,multiply(A,multiply(A,multiply(B,multiply(C,A)))))),
inference(paramod,[status(thm)],[c_1,c_92]) ).
cnf(c_8,plain,
multiply(A,multiply(B,multiply(C,multiply(C,multiply(A,multiply(B,C)))))) = multiply(C,multiply(C,multiply(C,multiply(A,multiply(B,multiply(A,B)))))),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
multiply(multiply(b,multiply(b,multiply(a,multiply(a,a)))),A) != multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),A),
inference(resolve,[status(thm)],[c_2,c_6]) ).
cnf(c_95,plain,
multiply(b,multiply(multiply(b,multiply(a,multiply(a,a))),A)) != multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),A),
inference(paramod,[status(thm)],[c_1,c_94]) ).
cnf(c_96,plain,
multiply(b,multiply(b,multiply(multiply(a,multiply(a,a)),A))) != multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),A),
inference(paramod,[status(thm)],[c_1,c_95]) ).
cnf(c_97,plain,
multiply(b,multiply(b,multiply(a,multiply(multiply(a,a),A)))) != multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),A),
inference(paramod,[status(thm)],[c_1,c_96]) ).
cnf(c_98,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,A))))) != multiply(multiply(a,multiply(b,multiply(a,multiply(a,b)))),A),
inference(paramod,[status(thm)],[c_1,c_97]) ).
cnf(c_99,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,A))))) != multiply(a,multiply(multiply(b,multiply(a,multiply(a,b))),A)),
inference(paramod,[status(thm)],[c_1,c_98]) ).
cnf(c_100,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,A))))) != multiply(a,multiply(b,multiply(multiply(a,multiply(a,b)),A))),
inference(paramod,[status(thm)],[c_1,c_99]) ).
cnf(c_101,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,A))))) != multiply(a,multiply(b,multiply(a,multiply(multiply(a,b),A)))),
inference(paramod,[status(thm)],[c_1,c_100]) ).
cnf(c_12,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,A))))) != multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,A))))),
inference(paramod,[status(thm)],[c_1,c_101]) ).
cnf(c_36,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,B))))) = multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,A))))),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_38,plain,
multiply(A,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,A)))))) = multiply(A,multiply(A,multiply(B,multiply(B,multiply(A,multiply(A,B)))))),
inference(paramod,[status(thm)],[c_8,c_7]) ).
cnf(c_102,plain,
multiply(multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,B))))),C) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_36,c_1]) ).
cnf(c_103,plain,
multiply(A,multiply(multiply(A,multiply(A,multiply(B,multiply(A,B)))),C)) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_102]) ).
cnf(c_104,plain,
multiply(A,multiply(A,multiply(multiply(A,multiply(B,multiply(A,B))),C))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_103]) ).
cnf(c_105,plain,
multiply(A,multiply(A,multiply(A,multiply(multiply(B,multiply(A,B)),C)))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_104]) ).
cnf(c_106,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(multiply(A,B),C))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_105]) ).
cnf(c_107,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(multiply(A,multiply(A,multiply(A,multiply(B,A)))),C)),
inference(paramod,[status(thm)],[c_1,c_106]) ).
cnf(c_108,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(A,multiply(multiply(A,multiply(A,multiply(B,A))),C))),
inference(paramod,[status(thm)],[c_1,c_107]) ).
cnf(c_109,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(multiply(A,multiply(B,A)),C)))),
inference(paramod,[status(thm)],[c_1,c_108]) ).
cnf(c_110,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(multiply(B,A),C))))),
inference(paramod,[status(thm)],[c_1,c_109]) ).
cnf(c_111,plain,
multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(A,multiply(A,multiply(A,multiply(B,multiply(A,C)))))),
inference(paramod,[status(thm)],[c_1,c_110]) ).
cnf(c_40,plain,
multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,C)))))) = multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,C)))))),
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
multiply(A,multiply(A,multiply(B,multiply(A,multiply(B,B))))) = multiply(B,multiply(A,multiply(A,multiply(B,multiply(B,A))))),
inference(resolve,[status(thm)],[c_3,c_38]) ).
cnf(c_71,plain,
multiply(A,multiply(B,multiply(B,multiply(A,multiply(A,B))))) = multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,A))))),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_76,plain,
multiply(b,multiply(b,multiply(a,multiply(a,multiply(a,multiply(b,a)))))) != multiply(a,multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,b)))))),
inference(paramod,[status(thm)],[c_71,c_12]) ).
cnf(c_81,plain,
multiply(A,multiply(A,multiply(B,multiply(B,multiply(B,multiply(A,B)))))) = multiply(B,multiply(B,multiply(B,multiply(A,multiply(B,multiply(A,A)))))),
inference(paramod,[status(thm)],[c_36,c_40]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_81,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP197-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:37:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3126277 was started by sandbox on n006,
% 0.08/0.35 % Fri Sep 25 14:37:10 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.76/0.56
% 0.76/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.76/0.56
% 0.76/0.56 % Proof 1 at 0.11 (+ 0.02) seconds.
% 0.76/0.56 % Length of proof is 16.
% 0.76/0.56 % Level of proof is 6.
% 0.76/0.56 % Maximum clause weight is 82.000.
% 0.76/0.56 % Given clauses 25.
% 0.76/0.56
% 0.76/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------