%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:00:08 AM UTC 2026
% Result : Theorem 0.14s 20.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 28 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('theBenchmark.p',condensed_detachment) ).
fof(a5,axiom,
! [A,B,C,D,E] : is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))),
file('theBenchmark.p',a5) ).
fof(prove_cn_1,conjecture,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
file('theBenchmark.p',prove_cn_1) ).
fof(prove_cn_1_neg,negated_conjecture,
~ ! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(assume_negation,[status(cth)],[prove_cn_1]) ).
cnf(c_4,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))),
inference(clausify,[status(thm)],[a5]) ).
fof(nnf_3,plain,
? [A,B,C] : ~ is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(fof_nnf,[status(thm)],[prove_cn_1_neg]) ).
fof(sk_prove_cn_1_neg,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_3]) ).
cnf(c_6,negated_conjecture,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(split_conjunct,[status(thm)],[sk_prove_cn_1_neg]) ).
cnf(c_14,plain,
( is_a_theorem(implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(implies(implies(D,implies(E,F)),implies(V6,implies(not(E),not(V7)))),implies(V7,E)),implies(not(B),not(implies(V7,V6))))),implies(implies(V7,V6),B))),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_15,plain,
( is_a_theorem(implies(implies(V7,V6),B))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(implies(D,implies(E,F)),implies(V6,implies(not(E),not(V7)))),implies(V7,E)),implies(not(B),not(implies(V7,V6)))))) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(implies(A,F),implies(not(D),not(implies(implies(V6,implies(F,V7)),implies(B,implies(not(F),not(A)))))))),implies(implies(implies(V6,implies(F,V7)),implies(B,implies(not(F),not(A)))),D)))),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_16,plain,
( is_a_theorem(implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(implies(D,E),F),implies(not(B),not(implies(implies(V6,implies(F,V7)),implies(implies(implies(implies(V8,implies(V9,V10)),implies(E,implies(not(V9),not(D)))),implies(D,V9)),implies(not(F),not(implies(D,E))))))))),implies(implies(implies(V6,implies(F,V7)),implies(implies(implies(implies(V8,implies(V9,V10)),implies(E,implies(not(V9),not(D)))),implies(D,V9)),implies(not(F),not(implies(D,E))))),B))),
inference(resolve,[status(thm)],[c_16,c_7]) ).
cnf(c_17,plain,
( is_a_theorem(implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(implies(implies(implies(D,implies(E,F)),implies(implies(V6,V7),implies(not(E),not(implies(implies(V8,implies(V7,V9)),implies(V10,implies(not(V7),not(V6)))))))),implies(implies(implies(V8,implies(V7,V9)),implies(V10,implies(not(V7),not(V6)))),E)),implies(not(B),not(implies(V6,V10))))),implies(implies(V6,V10),B))),
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_18,plain,
( is_a_theorem(implies(implies(V6,V10),B))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(implies(D,implies(E,F)),implies(implies(V6,V7),implies(not(E),not(implies(implies(V8,implies(V7,V9)),implies(V10,implies(not(V7),not(V6)))))))),implies(implies(implies(V8,implies(V7,V9)),implies(V10,implies(not(V7),not(V6)))),E)),implies(not(B),not(implies(V6,V10)))))) ),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/20.39 % Computer : n006.cluster.edu
% 0.09/20.39 % Model : x86_64 x86_64
% 0.09/20.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.39 % Memory : 8046.5625MB
% 0.09/20.39 % OS : Linux 6.8.0-71-generic
% 0.09/20.39 % CPULimit : 300
% 0.09/20.39 % WCLimit : 300
% 0.09/20.39 % DateTime : Fri Sep 25 23:55:20 UTC 2026
% 0.09/20.39 % CPUTime :
% 0.09/20.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/20.40 % Process 4056099 was started by sandbox2 on n006,
% 0.09/20.40 % Fri Sep 25 23:55:20 2026
% 0.09/20.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/20.40
% 0.14/20.40 % From the command line: assign(max_seconds, 300).
% 0.14/20.41
% 0.14/20.41 % SZS status Theorem for theBenchmark
% 0.14/20.41
% 0.14/20.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/20.41 % Length of proof is 12.
% 0.14/20.41 % Level of proof is 6.
% 0.14/20.41 % Maximum clause weight is 82.000.
% 0.14/20.41 % Given clauses 7.
% 0.14/20.41
% 0.14/20.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------