%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:26:22 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product_substitution3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_1)
| ~ product(VAR_2,VAR_3,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',product_substitution3) ).
cnf(c_1,plain,
( product(C,D,B)
| ~ product(C,D,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[product_substitution3]) ).
fof(a_equals_b,axiom,
equalish(a,b),
file('theBenchmark.p',a_equals_b) ).
cnf(c_3,plain,
equalish(a,b),
inference(clausify,[status(thm)],[a_equals_b]) ).
cnf(c_4,plain,
( product(A,B,b)
| ~ product(A,B,a) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
fof(prove_product_with_b,axiom,
~ product(c,b,result),
file('theBenchmark.p',prove_product_with_b) ).
cnf(c_6,plain,
~ product(c,b,result),
inference(clausify,[status(thm)],[prove_product_with_b]) ).
fof(product_with_a,axiom,
product(c,a,result),
file('theBenchmark.p',product_with_a) ).
cnf(c_7,plain,
product(c,a,result),
inference(clausify,[status(thm)],[product_with_a]) ).
fof(associativity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity2) ).
cnf(c_8,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(associativity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_0,VAR_4,VAR_5)
| ~ product(VAR_2,VAR_3,VAR_5)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity1) ).
cnf(c_9,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
fof(total_function1,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',total_function1) ).
cnf(c_10,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[total_function1]) ).
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_12,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
cnf(c_70,plain,
product(identity,a,b),
inference(resolve,[status(thm)],[c_12,c_4]) ).
cnf(c_167,plain,
( product(multiply(D,A),B,E)
| ~ product(D,C,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_168,plain,
( product(multiply(A,identity),B,C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_167,c_12]) ).
cnf(c_89,plain,
product(multiply(c,identity),a,result),
inference(resolve,[status(thm)],[c_168,c_7]) ).
cnf(c_169,plain,
( product(D,C,E)
| ~ product(multiply(D,A),B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_170,plain,
( product(A,b,B)
| ~ product(multiply(A,identity),a,B) ),
inference(resolve,[status(thm)],[c_169,c_70]) ).
cnf(c_171,plain,
~ product(multiply(c,identity),a,result),
inference(resolve,[status(thm)],[c_170,c_6]) ).
cnf(c_166,plain,
$false,
inference(resolve,[status(thm)],[c_89,c_171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:19:36 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 3349637 was started by sandbox2 on n004,
% 0.09/0.36 % Fri Sep 25 14:19:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.09/0.37
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 12.
% 0.09/0.37 % Level of proof is 3.
% 0.09/0.37 % Maximum clause weight is 21.000.
% 0.09/0.37 % Given clauses 15.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------