%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:58:50 AM UTC 2026
% Result : Theorem 0.14s 5.81s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 13 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 6 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm147,conjecture,
~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
file('theBenchmark.p',thm147) ).
fof(thm147_neg,negated_conjecture,
~ ~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
inference(assume_negation,[status(cth)],[thm147]) ).
fof(nnf_1,plain,
( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [X4,X5,R] : a_truth(implies(implies(X4,implies(X5,R)),implies(implies(X4,X5),implies(X4,R))))
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(fof_nnf,[status(thm)],[thm147_neg]) ).
fof(sk_thm147_neg,plain,
( ~ a_truth(implies(sK0,sK0))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [X4,X5,R] : a_truth(implies(implies(X4,implies(X5,R)),implies(implies(X4,X5),implies(X4,R))))
& ! [X2,X3] : a_truth(implies(X2,implies(X3,X2)))
& ! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( a_truth(B)
| ~ a_truth(A)
| ~ a_truth(implies(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_thm147_neg]) ).
cnf(c_3,negated_conjecture,
a_truth(implies(A,implies(B,A))),
inference(split_conjunct,[status(thm)],[sk_thm147_neg]) ).
cnf(c_4,negated_conjecture,
a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(split_conjunct,[status(thm)],[sk_thm147_neg]) ).
cnf(c_6,negated_conjecture,
~ a_truth(implies(sK0,sK0)),
inference(split_conjunct,[status(thm)],[sk_thm147_neg]) ).
cnf(c_19,negated_conjecture,
( a_truth(implies(B,A))
| ~ a_truth(A) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
a_truth(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_19,c_3]) ).
cnf(c_20,negated_conjecture,
( a_truth(implies(implies(A,B),implies(A,C)))
| ~ a_truth(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_10,negated_conjecture,
a_truth(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_20,c_3]) ).
cnf(c_21,negated_conjecture,
( a_truth(implies(A,A))
| ~ a_truth(implies(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_10]) ).
cnf(c_17,negated_conjecture,
a_truth(implies(A,A)),
inference(resolve,[status(thm)],[c_21,c_7]) ).
cnf(c_18,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.79 % Computer : n010.cluster.edu
% 0.11/5.79 % Model : x86_64 x86_64
% 0.11/5.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.79 % Memory : 8046.5625MB
% 0.11/5.79 % OS : Linux 6.8.0-71-generic
% 0.11/5.79 % CPULimit : 300
% 0.11/5.79 % WCLimit : 300
% 0.11/5.79 % DateTime : Fri Sep 25 22:28:51 UTC 2026
% 0.11/5.80 % CPUTime :
% 0.14/5.80 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.80 % Process 1845479 was started by sandbox2 on n010,
% 0.14/5.80 % Fri Sep 25 22:28:51 2026
% 0.14/5.80 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.80
% 0.14/5.80 % From the command line: assign(max_seconds, 300).
% 0.14/5.81
% 0.14/5.81 % SZS status Theorem for theBenchmark
% 0.14/5.81
% 0.14/5.81 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.81 % Length of proof is 9.
% 0.14/5.81 % Level of proof is 4.
% 0.14/5.81 % Maximum clause weight is 14.000.
% 0.14/5.81 % Given clauses 7.
% 0.14/5.81
% 0.14/5.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------