%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO034-1 : 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 : 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 06:55:09 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 78 ( 6 sgn 11 !; 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(ternary_multiply_2,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',ternary_multiply_2) ).
cnf(c_3,plain,
multiply(A,A,B) = A,
inference(clausify,[status(thm)],[ternary_multiply_2]) ).
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_single_axiom,axiom,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
file('theBenchmark.p',prove_single_axiom) ).
cnf(c_6,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(clausify,[status(thm)],[prove_single_axiom]) ).
cnf(c_7,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_10,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_11,plain,
multiply(multiply(A,B,C),D,B) = multiply(A,B,multiply(C,D,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_505,plain,
multiply(A,B,C) = multiply(A,B,multiply(C,multiply(A,B,C),D)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_14,plain,
multiply(A,B,multiply(C,multiply(A,B,C),D)) = multiply(A,B,C),
inference(copy,[status(thm)],[c_505]) ).
cnf(c_47,plain,
multiply(A,B,multiply(C,A,B)) = multiply(C,A,B),
inference(paramod,[status(thm)],[c_2,c_10]) ).
cnf(c_506,plain,
multiply(A,B,C) = multiply(C,A,multiply(A,B,inverse(A))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_48,plain,
multiply(A,B,multiply(B,C,inverse(B))) = multiply(B,C,A),
inference(copy,[status(thm)],[c_506]) ).
cnf(c_507,plain,
multiply(A,inverse(A),B) = multiply(B,A,inverse(A)),
inference(paramod,[status(thm)],[c_5,c_47]) ).
cnf(c_78,plain,
multiply(A,inverse(A),B) = B,
inference(paramod,[status(thm)],[c_5,c_507]) ).
cnf(c_86,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(paramod,[status(thm)],[c_78,c_7]) ).
cnf(c_508,plain,
multiply(A,B,C) = multiply(A,C,multiply(inverse(C),B,C)),
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_166,plain,
multiply(A,B,multiply(inverse(B),C,B)) = multiply(A,C,B),
inference(copy,[status(thm)],[c_508]) ).
cnf(c_509,plain,
multiply(A,B,multiply(inverse(B),A,C)) = multiply(A,B,inverse(B)),
inference(paramod,[status(thm)],[c_5,c_14]) ).
cnf(c_333,plain,
multiply(A,B,multiply(inverse(B),A,C)) = A,
inference(paramod,[status(thm)],[c_5,c_509]) ).
cnf(c_510,plain,
A = multiply(inverse(B),A,B),
inference(paramod,[status(thm)],[c_333,c_47]) ).
cnf(c_358,plain,
multiply(inverse(A),B,A) = B,
inference(copy,[status(thm)],[c_510]) ).
cnf(c_367,plain,
multiply(A,B,C) = multiply(A,C,B),
inference(paramod,[status(thm)],[c_358,c_166]) ).
cnf(c_511,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,e,f),c)) != b,
inference(paramod,[status(thm)],[c_367,c_86]) ).
cnf(c_433,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,c,multiply(g,e,f))) != b,
inference(paramod,[status(thm)],[c_367,c_511]) ).
cnf(c_466,plain,
multiply(A,B,inverse(A)) = B,
inference(paramod,[status(thm)],[c_367,c_78]) ).
cnf(c_512,plain,
multiply(A,B,C) = multiply(B,C,A),
inference(paramod,[status(thm)],[c_466,c_48]) ).
cnf(c_481,plain,
multiply(A,B,C) = multiply(C,A,B),
inference(copy,[status(thm)],[c_512]) ).
cnf(c_513,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,c,multiply(f,g,e))) != b,
inference(paramod,[status(thm)],[c_481,c_433]) ).
cnf(c_514,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,c,multiply(f,e,g))) != b,
inference(paramod,[status(thm)],[c_367,c_513]) ).
cnf(c_515,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,c,multiply(e,g,f))) != b,
inference(paramod,[status(thm)],[c_481,c_514]) ).
cnf(c_516,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,c,multiply(e,f,g))) != b,
inference(paramod,[status(thm)],[c_367,c_515]) ).
cnf(c_517,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,multiply(e,f,g),d)) != b,
inference(paramod,[status(thm)],[c_481,c_516]) ).
cnf(c_518,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(c,d,multiply(e,f,g))) != b,
inference(paramod,[status(thm)],[c_367,c_517]) ).
cnf(c_519,plain,
multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(paramod,[status(thm)],[c_367,c_518]) ).
cnf(c_520,plain,
b != b,
inference(paramod,[status(thm)],[c_5,c_519]) ).
cnf(c_504,plain,
$false,
inference(copy,[status(thm)],[c_520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:38:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 534742 was started by sandbox on n008,
% 0.09/0.36 % Sat Sep 26 22:38:39 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 21.
% 0.09/0.43 % Level of proof is 7.
% 0.09/0.43 % Maximum clause weight is 23.000.
% 0.09/0.43 % Given clauses 30.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------