%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP029-2 : 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 : n004.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 25 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 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 : 49 ( 0 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_12,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_13,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_14,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_15,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_16,plain,
~ product(not_right_identity(A),A,not_right_identity(A)),
inference(clausify,[status(thm)],[prove_there_is_a_right_identity]) ).
cnf(c_117,plain,
( product(inverse(A),C,D)
| ~ product(identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_118,plain,
( product(inverse(inverse(A)),identity,B)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_117,c_15]) ).
cnf(c_37,plain,
product(inverse(inverse(A)),identity,A),
inference(resolve,[status(thm)],[c_118,c_14]) ).
cnf(c_119,plain,
( product(A,identity,D)
| ~ product(C,B,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_120,plain,
( product(A,identity,B)
| ~ product(A,inverse(B),identity) ),
inference(resolve,[status(thm)],[c_119,c_14]) ).
cnf(c_53,plain,
~ product(not_right_identity(identity),inverse(not_right_identity(identity)),identity),
inference(resolve,[status(thm)],[c_120,c_16]) ).
cnf(c_121,plain,
( product(B,C,D)
| ~ product(A,C,D)
| ~ product(A,identity,B) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_122,plain,
( product(B,A,identity)
| ~ product(inverse(A),identity,B) ),
inference(resolve,[status(thm)],[c_121,c_15]) ).
cnf(c_115,plain,
~ product(inverse(inverse(not_right_identity(identity))),identity,not_right_identity(identity)),
inference(resolve,[status(thm)],[c_122,c_53]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:18:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3346936 was started by sandbox2 on n004,
% 0.14/0.36 % Fri Sep 25 14:18:36 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.39 % Length of proof is 9.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 16.000.
% 0.14/0.39 % Given clauses 18.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------