%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP008-1 : 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 : n001.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 55 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 52 ( 23 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : product(identity,VAR_0,VAR_0),
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
product(identity,A,A),
inference(clausify,[status(thm)],[left_identity]) ).
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(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_7,plain,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associativity1]) ).
fof(unknown_meaning3,axiom,
! [VAR_0] :
( q(VAR_0)
| product(VAR_0,j(VAR_0),h(VAR_0))
| product(j(VAR_0),VAR_0,h(VAR_0)) ),
file('theBenchmark.p',unknown_meaning3) ).
cnf(c_10,plain,
( q(A)
| product(A,j(A),h(A))
| product(j(A),A,h(A)) ),
inference(clausify,[status(thm)],[unknown_meaning3]) ).
fof(unknown_meaning4,axiom,
! [VAR_0] :
( q(VAR_0)
| ~ product(VAR_0,j(VAR_0),h(VAR_0))
| ~ product(j(VAR_0),VAR_0,h(VAR_0)) ),
file('theBenchmark.p',unknown_meaning4) ).
cnf(c_11,plain,
( q(A)
| ~ product(A,j(A),h(A))
| ~ product(j(A),A,h(A)) ),
inference(clausify,[status(thm)],[unknown_meaning4]) ).
fof(prove_identity_is_q,axiom,
~ q(identity),
file('theBenchmark.p',prove_identity_is_q) ).
cnf(c_12,plain,
~ q(identity),
inference(clausify,[status(thm)],[prove_identity_is_q]) ).
cnf(c_25,plain,
( B = A
| ~ product(identity,A,B) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_30,plain,
( product(identity,C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_1]) ).
cnf(c_126,plain,
( q(A)
| product(A,j(A),h(A))
| product(identity,B,h(A))
| ~ product(j(A),A,B) ),
inference(resolve,[status(thm)],[c_30,c_10]) ).
cnf(c_149,plain,
( q(identity)
| product(identity,j(identity),h(identity))
| ~ product(j(identity),identity,j(identity)) ),
inference(factor,[status(thm)],[c_126]) ).
cnf(c_150,plain,
( q(identity)
| product(identity,j(identity),h(identity)) ),
inference(resolve,[status(thm)],[c_2,c_149]) ).
cnf(c_131,plain,
product(identity,j(identity),h(identity)),
inference(resolve,[status(thm)],[c_12,c_150]) ).
cnf(c_151,plain,
h(identity) = j(identity),
inference(resolve,[status(thm)],[c_131,c_25]) ).
cnf(c_147,plain,
j(identity) = h(identity),
inference(copy,[status(thm)],[c_151]) ).
cnf(c_152,plain,
( q(identity)
| ~ product(j(identity),identity,h(identity)) ),
inference(resolve,[status(thm)],[c_131,c_11]) ).
cnf(c_153,plain,
( q(identity)
| ~ product(h(identity),identity,h(identity)) ),
inference(paramod,[status(thm)],[c_147,c_152]) ).
cnf(c_154,plain,
q(identity),
inference(resolve,[status(thm)],[c_2,c_153]) ).
cnf(c_148,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:21:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3487568 was started by sandbox2 on n001,
% 0.08/0.35 % Fri Sep 25 14:21:56 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 13.
% 0.12/0.38 % Level of proof is 5.
% 0.12/0.38 % Maximum clause weight is 28.000.
% 0.12/0.38 % Given clauses 45.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------