%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 06:55:00 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 30 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : multiply(multiply(VAR_0,VAR_1,VAR_2),VAR_3,multiply(VAR_0,VAR_1,VAR_4)) = multiply(VAR_0,VAR_1,multiply(VAR_2,VAR_3,VAR_4)),
file('theBenchmark.p',associativity) ).
cnf(c_1,plain,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)),
inference(clausify,[status(thm)],[associativity]) ).
fof(ternary_multiply_1,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1,VAR_1) = VAR_1,
file('theBenchmark.p',ternary_multiply_1) ).
cnf(c_2,plain,
multiply(A,B,B) = B,
inference(clausify,[status(thm)],[ternary_multiply_1]) ).
fof(right_inverse,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1,inverse(VAR_1)) = VAR_0,
file('theBenchmark.p',right_inverse) ).
cnf(c_5,plain,
multiply(A,B,inverse(B)) = A,
inference(clausify,[status(thm)],[right_inverse]) ).
fof(prove_inverse_is_self_cancelling,axiom,
inverse(inverse(a)) != a,
file('theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(c_6,plain,
inverse(inverse(a)) != a,
inference(clausify,[status(thm)],[prove_inverse_is_self_cancelling]) ).
cnf(c_9,plain,
multiply(A,B,multiply(C,A,D)) = multiply(C,A,multiply(A,B,D)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_51,plain,
multiply(A,B,multiply(C,A,B)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_2,c_9]) ).
cnf(c_89,plain,
multiply(A,inverse(A),B) = multiply(B,A,inverse(A)),
inference(paramod,[status(thm)],[c_5,c_51]) ).
cnf(c_78,plain,
multiply(A,inverse(A),B) = B,
inference(paramod,[status(thm)],[c_5,c_89]) ).
cnf(c_87,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_78,c_5]) ).
cnf(c_88,plain,
$false,
inference(resolve,[status(thm)],[c_87,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:31:09 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 648978 was started by sandbox on n007,
% 0.09/0.38 % Sat Sep 26 22:31:09 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (4).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 9.
% 0.09/0.40 % Level of proof is 5.
% 0.09/0.40 % Maximum clause weight is 33.000.
% 0.09/0.40 % Given clauses 11.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------