%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP029-1 : 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 : n026.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 07:26:19 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_3,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_4,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_5,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_6,plain,
product(inverse(A),A,identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(prove_there_is_a_right_identity,axiom,
! [VAR_0] : ~ product(not_right_identity(VAR_0),VAR_0,not_right_identity(VAR_0)),
file('theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(c_7,plain,
~ product(not_right_identity(A),A,not_right_identity(A)),
inference(clausify,[status(thm)],[prove_there_is_a_right_identity]) ).
cnf(c_12,plain,
( product(C,D,C)
| ~ product(B,D,B)
| ~ product(A,B,C) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_52,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_3,c_6]) ).
cnf(c_53,plain,
( product(inverse(inverse(A)),identity,B)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_52,c_6]) ).
cnf(c_33,plain,
product(inverse(inverse(A)),identity,A),
inference(resolve,[status(thm)],[c_53,c_5]) ).
cnf(c_54,plain,
( product(B,identity,B)
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_50,plain,
~ product(A,identity,not_right_identity(identity)),
inference(resolve,[status(thm)],[c_54,c_7]) ).
cnf(c_51,plain,
$false,
inference(resolve,[status(thm)],[c_50,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n026.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 14:21:30 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 2716605 was started by sandbox2 on n026,
% 0.16/5.45 % Fri Sep 25 14:21:30 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.16/5.46
% 0.16/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.46
% 0.16/5.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.46 % Length of proof is 9.
% 0.16/5.46 % Level of proof is 3.
% 0.16/5.46 % Maximum clause weight is 21.000.
% 0.16/5.46 % Given clauses 12.
% 0.16/5.46
% 0.16/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------