%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP007-1 : 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 : n002.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 07:26:09 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( 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_6,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[total_function2]) ).
fof(another_left_identity,axiom,
! [VAR_0] : product(c,VAR_0,VAR_0),
file('theBenchmark.p',another_left_identity) ).
cnf(c_9,plain,
product(c,A,A),
inference(clausify,[status(thm)],[another_left_identity]) ).
fof(prove_identity_equals_c,axiom,
identity != c,
file('theBenchmark.p',prove_identity_equals_c) ).
cnf(c_11,plain,
identity != c,
inference(clausify,[status(thm)],[prove_identity_equals_c]) ).
cnf(c_12,plain,
c != identity,
inference(copy,[status(thm)],[c_11]) ).
cnf(c_191,plain,
( A = B
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_192,plain,
c = identity,
inference(resolve,[status(thm)],[c_191,c_9]) ).
cnf(c_190,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n002.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Fri Sep 25 14:18:47 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.58 % Process 3471235 was started by sandbox2 on n002,
% 0.10/10.58 % Fri Sep 25 14:18:47 2026
% 0.10/10.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.59
% 0.10/10.59 % From the command line: assign(max_seconds, 300).
% 0.14/10.60
% 0.14/10.60 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.60
% 0.14/10.60 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/10.60 % Length of proof is 6.
% 0.14/10.60 % Level of proof is 2.
% 0.14/10.60 % Maximum clause weight is 16.000.
% 0.14/10.60 % Given clauses 9.
% 0.14/10.60
% 0.14/10.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------