%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP001-1 : 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 07:26:06 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 25 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
fof(right_identity,axiom,
! [VAR_0] : product(VAR_0,identity,VAR_0),
file('theBenchmark.p',right_identity) ).
cnf(c_2,plain,
product(A,identity,A),
inference(clausify,[status(thm)],[right_identity]) ).
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_7,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
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(square_element,axiom,
! [VAR_0] : product(VAR_0,VAR_0,identity),
file('theBenchmark.p',square_element) ).
cnf(c_9,plain,
product(A,A,identity),
inference(clausify,[status(thm)],[square_element]) ).
fof(a_times_b_is_c,axiom,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_10,plain,
product(a,b,c),
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
fof(prove_b_times_a_is_c,axiom,
~ product(b,a,c),
file('theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_11,plain,
~ product(b,a,c),
inference(clausify,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_166,plain,
( product(c,A,C)
| ~ product(a,B,C)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_167,plain,
( product(c,b,A)
| ~ product(a,identity,A) ),
inference(resolve,[status(thm)],[c_166,c_9]) ).
cnf(c_130,plain,
product(c,b,a),
inference(resolve,[status(thm)],[c_167,c_2]) ).
cnf(c_168,plain,
( product(C,B,D)
| ~ product(A,identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_169,plain,
( product(C,B,A)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_168,c_2]) ).
cnf(c_151,plain,
~ product(c,a,b),
inference(resolve,[status(thm)],[c_169,c_11]) ).
cnf(c_170,plain,
( product(A,C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_171,plain,
( product(A,C,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_170,c_1]) ).
cnf(c_172,plain,
~ product(c,b,a),
inference(resolve,[status(thm)],[c_171,c_151]) ).
cnf(c_165,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 14:12:53 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1171018 was started by sandbox on n007,
% 0.15/0.42 % Fri Sep 25 14:12:53 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.45 % Length of proof is 10.
% 0.15/0.45 % Level of proof is 2.
% 0.15/0.45 % Maximum clause weight is 21.000.
% 0.15/0.45 % Given clauses 21.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------