%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP043-2 : 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 : 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 07:26:22 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.65s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 28 ~; 22 |; 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 : 55 ( 2 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(b_equals_c,axiom,
equalish(b,c),
file('theBenchmark.p',b_equals_c) ).
cnf(c_4,plain,
equalish(b,c),
inference(clausify,[status(thm)],[b_equals_c]) ).
fof(prove_transitivity,axiom,
~ equalish(a,c),
file('theBenchmark.p',prove_transitivity) ).
cnf(c_5,plain,
~ equalish(a,c),
inference(clausify,[status(thm)],[prove_transitivity]) ).
cnf(c_6,plain,
( ~ product(A,B,c)
| ~ product(A,B,a) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_7,plain,
( product(A,B,c)
| ~ product(A,B,b) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_8,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_10,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_12,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_14,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
cnf(c_15,plain,
( ~ product(A,B,a)
| ~ product(A,B,b) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_56,plain,
( product(multiply(D,A),B,E)
| ~ product(D,C,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_10,c_12]) ).
cnf(c_57,plain,
( product(multiply(A,identity),B,C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_56,c_14]) ).
cnf(c_40,plain,
product(multiply(identity,identity),A,A),
inference(resolve,[status(thm)],[c_57,c_14]) ).
cnf(c_58,plain,
( ~ product(A,B,a)
| ~ product(A,B,a) ),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_54,plain,
~ product(A,B,a),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_55,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.62 % Computer : n016.cluster.edu
% 0.16/0.62 % Model : x86_64 x86_64
% 0.16/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.62 % Memory : 8046.5625MB
% 0.16/0.62 % OS : Linux 6.8.0-71-generic
% 0.16/0.62 % CPULimit : 300
% 0.16/0.62 % WCLimit : 300
% 0.16/0.62 % DateTime : Fri Sep 25 14:24:29 UTC 2026
% 0.16/0.63 % CPUTime :
% 0.16/0.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.63 % Process 2579345 was started by sandbox2 on n016,
% 0.16/0.63 % Fri Sep 25 14:24:29 2026
% 0.16/0.63 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.64
% 0.16/0.64 % From the command line: assign(max_seconds, 300).
% 0.16/0.65
% 0.16/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.65
% 0.16/0.65 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.16/0.65 % Length of proof is 15.
% 0.16/0.65 % Level of proof is 4.
% 0.16/0.65 % Maximum clause weight is 16.000.
% 0.16/0.65 % Given clauses 10.
% 0.16/0.65
% 0.16/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------