%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP028-3 : TPTP v9.3.1. Released v1.1.0.
% 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 07:26:18 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 33 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_3,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(left_soln,axiom,
! [VAR_0,VAR_1] : product(left_solution(VAR_0,VAR_1),VAR_0,VAR_1),
file('theBenchmark.p',left_soln) ).
cnf(c_4,plain,
product(left_solution(A,B),A,B),
inference(clausify,[status(thm)],[left_soln]) ).
fof(right_soln,axiom,
! [VAR_0,VAR_1] : product(VAR_0,right_solution(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',right_soln) ).
cnf(c_5,plain,
product(A,right_solution(A,B),B),
inference(clausify,[status(thm)],[right_soln]) ).
fof(prove_there_is_a_right_identity,axiom,
! [VAR_0] : ~ product(not_identity(VAR_0),VAR_0,not_identity(VAR_0)),
file('theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(c_6,plain,
~ product(not_identity(A),A,not_identity(A)),
inference(clausify,[status(thm)],[prove_there_is_a_right_identity]) ).
cnf(c_27,plain,
( product(D,B,E)
| ~ product(left_solution(A,D),C,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_28,plain,
( product(B,right_solution(A,C),D)
| ~ product(left_solution(A,B),C,D) ),
inference(resolve,[status(thm)],[c_27,c_5]) ).
cnf(c_25,plain,
product(A,right_solution(B,B),A),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP028-3 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 14:18:54 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.34 % Process 1235222 was started by sandbox on n008,
% 0.09/0.34 % Fri Sep 25 14:18:54 2026
% 0.09/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.34
% 0.09/0.34 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.36 % Length of proof is 6.
% 0.09/0.36 % Level of proof is 2.
% 0.09/0.36 % Maximum clause weight is 16.000.
% 0.09/0.36 % Given clauses 5.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------