%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP195-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 45 ( 0 sgn 5 !; 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(condition,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,multiply(VAR_1,VAR_1)) = multiply(VAR_1,multiply(VAR_1,VAR_0)),
file('theBenchmark.p',condition) ).
cnf(c_2,plain,
multiply(A,multiply(B,B)) = multiply(B,multiply(B,A)),
inference(clausify,[status(thm)],[condition]) ).
fof(prove_this,axiom,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
file('theBenchmark.p',prove_this) ).
cnf(c_3,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_29,plain,
multiply(multiply(A,multiply(A,B)),C) = multiply(B,multiply(multiply(A,A),C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_30,plain,
multiply(A,multiply(multiply(A,B),C)) = multiply(B,multiply(multiply(A,A),C)),
inference(paramod,[status(thm)],[c_1,c_29]) ).
cnf(c_31,plain,
multiply(A,multiply(A,multiply(B,C))) = multiply(B,multiply(multiply(A,A),C)),
inference(paramod,[status(thm)],[c_1,c_30]) ).
cnf(c_32,plain,
multiply(A,multiply(A,multiply(B,C))) = multiply(B,multiply(A,multiply(A,C))),
inference(paramod,[status(thm)],[c_1,c_31]) ).
cnf(c_4,plain,
multiply(A,multiply(B,multiply(B,C))) = multiply(B,multiply(B,multiply(A,C))),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,plain,
multiply(A,multiply(multiply(B,C),multiply(multiply(B,C),D))) = multiply(B,multiply(C,multiply(multiply(B,C),multiply(A,D)))),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_34,plain,
multiply(A,multiply(multiply(B,C),multiply(B,multiply(C,D)))) = multiply(B,multiply(C,multiply(multiply(B,C),multiply(A,D)))),
inference(paramod,[status(thm)],[c_1,c_33]) ).
cnf(c_35,plain,
multiply(A,multiply(B,multiply(C,multiply(B,multiply(C,D))))) = multiply(B,multiply(C,multiply(multiply(B,C),multiply(A,D)))),
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_10,plain,
multiply(A,multiply(B,multiply(C,multiply(B,multiply(C,D))))) = multiply(B,multiply(C,multiply(B,multiply(C,multiply(A,D))))),
inference(paramod,[status(thm)],[c_1,c_35]) ).
cnf(c_19,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,b))))))),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_27,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))) != multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,multiply(b,multiply(a,b))))))),
inference(paramod,[status(thm)],[c_4,c_19]) ).
cnf(c_36,plain,
multiply(B,multiply(C,multiply(B,multiply(C,multiply(A,D))))) = multiply(A,multiply(B,multiply(C,multiply(B,multiply(C,D))))),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_28,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP195-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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 14:42:13 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 2628520 was started by sandbox2 on n016,
% 0.08/0.35 % Fri Sep 25 14:42:13 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 8.
% 0.08/0.37 % Level of proof is 4.
% 0.08/0.37 % Maximum clause weight is 31.000.
% 0.08/0.37 % Given clauses 6.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------