%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 07:58:58 AM UTC 2026
% Result : Theorem 0.17s 5.63s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 8 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('theBenchmark.p',implies_3) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('theBenchmark.p',cn1) ).
fof(luka_cn1,conjecture,
cn1,
file('theBenchmark.p',luka_cn1) ).
fof(luka_cn1_neg,negated_conjecture,
~ cn1,
inference(assume_negation,[status(cth)],[luka_cn1]) ).
cnf(c_46,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))
| ~ implies_3 ),
inference(clausify,[status(thm)],[implies_3]) ).
fof(nnf_19,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ) ),
inference(fof_nnf,[status(thm)],[cn1]) ).
fof(sk_cn1_sk,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| cn1 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(P,sK0),skolemize(Q,sK1),skolemize(R,sK2)],[nnf_19]) ).
fof(sk_cn1,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| cn1 )
& ! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))))
| ~ cn1 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn1_sk]) ).
cnf(c_73,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| cn1 ),
inference(split_conjunct,[status(thm)],[sk_cn1]) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('theBenchmark.p',hilbert_implies_3) ).
cnf(c_103,plain,
implies_3,
inference(clausify,[status(thm)],[hilbert_implies_3]) ).
cnf(c_115,negated_conjecture,
~ cn1,
inference(clausify,[status(thm)],[luka_cn1_neg]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_103,c_46]) ).
cnf(c_132,negated_conjecture,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(resolve,[status(thm)],[c_115,c_73]) ).
cnf(c_131,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_123,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.60 % Computer : n008.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Fri Sep 25 22:36:17 UTC 2026
% 0.17/5.60 % CPUTime :
% 0.17/5.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.60 % Process 2110008 was started by sandbox2 on n008,
% 0.17/5.60 % Fri Sep 25 22:36:17 2026
% 0.17/5.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.61
% 0.17/5.61 % From the command line: assign(max_seconds, 300).
% 0.17/5.63
% 0.17/5.63 % SZS status Theorem for theBenchmark
% 0.17/5.63
% 0.17/5.63 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/5.63 % Length of proof is 9.
% 0.17/5.63 % Level of proof is 3.
% 0.17/5.63 % Maximum clause weight is 53.000.
% 0.17/5.63 % Given clauses 0.
% 0.17/5.63
% 0.17/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------