%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP046-2 : 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 : n009.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 0.18s 5.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 17 !; 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(total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',total_function2) ).
cnf(c_2,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[total_function2]) ).
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]) ).
fof(prove_multiply_substitution1,axiom,
~ equalish(multiply(a,c),multiply(b,c)),
file('theBenchmark.p',prove_multiply_substitution1) ).
cnf(c_4,plain,
~ equalish(multiply(a,c),multiply(b,c)),
inference(clausify,[status(thm)],[prove_multiply_substitution1]) ).
cnf(c_5,plain,
( ~ product(A,B,multiply(b,c))
| ~ product(A,B,multiply(a,c)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_6,plain,
( product(A,B,b)
| ~ product(A,B,a) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
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(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_16,plain,
~ product(b,c,multiply(a,c)),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_47,plain,
product(identity,a,b),
inference(resolve,[status(thm)],[c_6,c_12]) ).
cnf(c_77,plain,
( product(C,D,E)
| ~ product(A,multiply(B,D),E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_78,plain,
( product(B,C,multiply(A,C))
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_77,c_12]) ).
cnf(c_79,plain,
~ product(identity,a,b),
inference(resolve,[status(thm)],[c_78,c_16]) ).
cnf(c_76,plain,
$false,
inference(resolve,[status(thm)],[c_47,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP046-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n009.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Fri Sep 25 14:19:35 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 1782964 was started by sandbox2 on n009,
% 0.18/5.45 % Fri Sep 25 14:19:35 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 0.18/5.47
% 0.18/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/5.47
% 0.18/5.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/5.47 % Length of proof is 12.
% 0.18/5.47 % Level of proof is 3.
% 0.18/5.47 % Maximum clause weight is 16.000.
% 0.18/5.47 % Given clauses 10.
% 0.18/5.47
% 0.18/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------