%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP013-1 : 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 : n015.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 07:26:10 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 31 ( 0 sgn 10 !; 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_8,plain,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity2]) ).
fof(squareness,axiom,
! [VAR_0] : product(VAR_0,VAR_0,identity),
file('theBenchmark.p',squareness) ).
cnf(c_9,plain,
product(A,A,identity),
inference(clausify,[status(thm)],[squareness]) ).
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(inverse_a_times_inverse_b_is_d,axiom,
product(inverse(a),inverse(b),d),
file('theBenchmark.p',inverse_a_times_inverse_b_is_d) ).
cnf(c_11,plain,
product(inverse(a),inverse(b),d),
inference(clausify,[status(thm)],[inverse_a_times_inverse_b_is_d]) ).
fof(inverses_have_property,axiom,
! [VAR_0,VAR_1,VAR_2] :
( product(VAR_0,VAR_2,VAR_1)
| ~ product(inverse(VAR_0),inverse(VAR_1),VAR_2) ),
file('theBenchmark.p',inverses_have_property) ).
cnf(c_12,plain,
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
inference(clausify,[status(thm)],[inverses_have_property]) ).
fof(prove_c_times_d_is_identity,axiom,
~ product(c,d,identity),
file('theBenchmark.p',prove_c_times_d_is_identity) ).
cnf(c_13,plain,
~ product(c,d,identity),
inference(clausify,[status(thm)],[prove_c_times_d_is_identity]) ).
cnf(c_95,plain,
product(a,d,b),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_123,plain,
( product(C,B,D)
| ~ product(A,identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_124,plain,
( product(B,A,identity)
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_123,c_9]) ).
cnf(c_98,plain,
~ product(identity,d,c),
inference(resolve,[status(thm)],[c_124,c_13]) ).
cnf(c_125,plain,
( product(identity,B,D)
| ~ product(A,C,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_126,plain,
( product(identity,A,c)
| ~ product(a,A,b) ),
inference(resolve,[status(thm)],[c_125,c_10]) ).
cnf(c_121,plain,
~ product(a,d,b),
inference(resolve,[status(thm)],[c_126,c_98]) ).
cnf(c_122,plain,
$false,
inference(resolve,[status(thm)],[c_121,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 14:19:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1550988 was started by sandbox on n015,
% 0.11/0.38 % Fri Sep 25 14:19:42 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 10.
% 0.11/0.41 % Level of proof is 3.
% 0.11/0.41 % Maximum clause weight is 16.000.
% 0.11/0.41 % Given clauses 15.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------