%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL403+2 : TPTP v9.3.1. Released v9.1.0.
% 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 07:58:49 AM UTC 2026
% Result : Theorem 117.33s 16.23s
% Output : CNFRefutation 117.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of formulae : 108 ( 56 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 108 ( 54 ~; 52 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 398 ( 89 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] : is_a_theorem(implies(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(G,H),implies(implies(H,I),implies(G,I))),implies(implies(implies(n(J),J),J),K)),K),implies(implies(L,implies(n(L),M)),N)),N),O)),O)),
file('theBenchmark.p',f2) ).
fof(f3,conjecture,
is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
file('theBenchmark.p',f3) ).
fof(f3_neg,negated_conjecture,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
inference(assume_negation,[status(cth)],[f3]) ).
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(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(V6,V7),implies(implies(V7,V8),implies(V6,V8))),implies(implies(implies(n(V9),V9),V9),V10)),V10),implies(implies(V11,implies(n(V11),V12)),V13)),V13),V14)),V14)),
inference(clausify,[status(thm)],[f2]) ).
cnf(c_6,negated_conjecture,
~ is_a_theorem(implies(x,implies(n(y),n(implies(x,y))))),
inference(clausify,[status(thm)],[f3_neg]) ).
cnf(c_22167,plain,
( is_a_theorem(V14)
| ~ is_a_theorem(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(V6,V7),implies(implies(V7,V8),implies(V6,V8))),implies(implies(implies(n(V9),V9),V9),V10)),V10),implies(implies(V11,implies(n(V11),V12)),V13)),V13),V14))) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_22167,c_5]) ).
cnf(c_22168,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_22168,c_7]) ).
cnf(c_22169,plain,
( is_a_theorem(V14)
| ~ is_a_theorem(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(V6,V7),implies(implies(V7,V8),implies(V6,V8))),implies(implies(implies(n(V9),V9),V9),V10)),V10),implies(implies(V11,implies(n(V11),V12)),V13)),V13),V14))) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F)),
inference(resolve,[status(thm)],[c_22169,c_7]) ).
cnf(c_22170,plain,
( is_a_theorem(V14)
| ~ is_a_theorem(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(V6,V7),implies(implies(V7,V8),implies(V6,V8))),implies(implies(implies(n(V9),V9),V9),V10)),V10),implies(implies(V11,implies(n(V11),V12)),V13)),V13),V14))) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_11,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(implies(implies(B,C),implies(implies(C,D),implies(B,D))),implies(implies(implies(n(E),E),E),F)),F),implies(implies(V6,implies(n(V6),V7)),V8)),V8))),
inference(resolve,[status(thm)],[c_22170,c_8]) ).
cnf(c_22171,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_15,plain,
is_a_theorem(implies(A,implies(implies(implies(B,implies(C,B)),implies(implies(D,implies(E,implies(F,E))),V6)),V6))),
inference(resolve,[status(thm)],[c_22171,c_9]) ).
cnf(c_22172,plain,
( is_a_theorem(V14)
| ~ is_a_theorem(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(V6,V7),implies(implies(V7,V8),implies(V6,V8))),implies(implies(implies(n(V9),V9),V9),V10)),V10),implies(implies(V11,implies(n(V11),V12)),V13)),V13),V14))) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(implies(n(B),B),B))),
inference(resolve,[status(thm)],[c_22172,c_15]) ).
cnf(c_22173,plain,
( is_a_theorem(implies(implies(n(B),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_19,plain,
is_a_theorem(implies(implies(n(A),A),A)),
inference(resolve,[status(thm)],[c_22173,c_18]) ).
cnf(c_22174,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(n(A),A)) ),
inference(resolve,[status(thm)],[c_4,c_19]) ).
cnf(c_35,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),implies(implies(implies(n(D),D),D),E)),E),implies(implies(F,implies(n(F),V6)),V7)),V7)),
inference(resolve,[status(thm)],[c_22174,c_11]) ).
cnf(c_22175,plain,
( is_a_theorem(F)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F))) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_36,plain,
is_a_theorem(implies(A,implies(B,implies(n(B),C)))),
inference(resolve,[status(thm)],[c_22175,c_11]) ).
cnf(c_22176,plain,
( is_a_theorem(implies(B,implies(n(B),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_36]) ).
cnf(c_38,plain,
is_a_theorem(implies(A,implies(n(A),B))),
inference(resolve,[status(thm)],[c_22176,c_36]) ).
cnf(c_22177,plain,
( is_a_theorem(V7)
| ~ is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),implies(implies(implies(n(D),D),D),E)),E),implies(implies(F,implies(n(F),V6)),V7))) ),
inference(resolve,[status(thm)],[c_4,c_35]) ).
cnf(c_428,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),implies(implies(implies(n(D),D),D),E)),E)),
inference(resolve,[status(thm)],[c_22177,c_7]) ).
cnf(c_22178,plain,
( is_a_theorem(E)
| ~ is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),implies(implies(implies(n(D),D),D),E))) ),
inference(resolve,[status(thm)],[c_4,c_428]) ).
cnf(c_432,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_22178,c_7]) ).
cnf(c_22179,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_433,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_22179,c_432]) ).
cnf(c_22180,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_543,plain,
is_a_theorem(implies(implies(implies(n(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_22180,c_38]) ).
cnf(c_22181,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_569,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_22181,c_7]) ).
cnf(c_22182,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_570,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))),
inference(resolve,[status(thm)],[c_22182,c_569]) ).
cnf(c_22183,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_569]) ).
cnf(c_573,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_22183,c_432]) ).
cnf(c_22184,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_569]) ).
cnf(c_577,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_22184,c_19]) ).
cnf(c_22185,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_582,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_22185,c_577]) ).
cnf(c_22186,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_583,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_22186,c_582]) ).
cnf(c_22187,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_685,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))),
inference(resolve,[status(thm)],[c_22187,c_573]) ).
cnf(c_22188,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_776,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))),
inference(resolve,[status(thm)],[c_22188,c_583]) ).
cnf(c_22189,plain,
( is_a_theorem(implies(implies(implies(D,A),B),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_570]) ).
cnf(c_1506,plain,
is_a_theorem(implies(implies(implies(A,n(B)),B),B)),
inference(resolve,[status(thm)],[c_22189,c_19]) ).
cnf(c_22190,plain,
( is_a_theorem(implies(A,D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_685]) ).
cnf(c_1629,plain,
is_a_theorem(implies(n(A),implies(A,implies(B,C)))),
inference(resolve,[status(thm)],[c_22190,c_543]) ).
cnf(c_22191,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_1640,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(n(A),D))),
inference(resolve,[status(thm)],[c_22191,c_1629]) ).
cnf(c_22192,plain,
( is_a_theorem(implies(implies(implies(D,D),B),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_776]) ).
cnf(c_2148,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_22192,c_1506]) ).
cnf(c_22193,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_2170,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))),
inference(resolve,[status(thm)],[c_22193,c_2148]) ).
cnf(c_22194,plain,
( is_a_theorem(implies(implies(implies(C,C),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_2170]) ).
cnf(c_2301,plain,
is_a_theorem(implies(implies(implies(A,A),implies(B,C)),implies(implies(C,D),implies(B,D)))),
inference(resolve,[status(thm)],[c_22194,c_432]) ).
cnf(c_22195,plain,
( is_a_theorem(implies(A,D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_685]) ).
cnf(c_4558,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(D,implies(C,B))))),
inference(resolve,[status(thm)],[c_22195,c_433]) ).
cnf(c_22196,plain,
( is_a_theorem(implies(implies(C,A),implies(D,implies(C,B))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_4558]) ).
cnf(c_5102,plain,
is_a_theorem(implies(implies(A,implies(n(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_22196,c_19]) ).
cnf(c_22197,plain,
( is_a_theorem(implies(n(A),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_4,c_1640]) ).
cnf(c_5459,plain,
is_a_theorem(implies(n(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_22197,c_5102]) ).
cnf(c_22198,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(n(B),B))) ),
inference(resolve,[status(thm)],[c_4,c_5102]) ).
cnf(c_5512,plain,
is_a_theorem(implies(A,implies(n(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_22198,c_5459]) ).
cnf(c_22199,plain,
( is_a_theorem(implies(implies(C,D),implies(B,D)))
| ~ is_a_theorem(implies(implies(A,A),implies(B,C))) ),
inference(resolve,[status(thm)],[c_4,c_2301]) ).
cnf(c_5541,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(n(A),C))),
inference(resolve,[status(thm)],[c_22199,c_5512]) ).
cnf(c_22200,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(n(B),B))) ),
inference(resolve,[status(thm)],[c_4,c_5102]) ).
cnf(c_5589,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_22200,c_5541]) ).
cnf(c_22201,plain,
( is_a_theorem(implies(n(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_5541]) ).
cnf(c_5658,plain,
is_a_theorem(implies(n(n(A)),A)),
inference(resolve,[status(thm)],[c_22201,c_19]) ).
cnf(c_22202,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_5677,plain,
is_a_theorem(implies(implies(A,B),implies(n(n(A)),B))),
inference(resolve,[status(thm)],[c_22202,c_5658]) ).
cnf(c_22203,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_5589]) ).
cnf(c_6448,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_22203,c_5589]) ).
cnf(c_22204,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_433]) ).
cnf(c_6485,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_22204,c_6448]) ).
cnf(c_22205,plain,
( is_a_theorem(implies(A,D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_685]) ).
cnf(c_6542,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_22205,c_6485]) ).
cnf(c_22206,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_432]) ).
cnf(c_6598,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_22206,c_6542]) ).
cnf(c_22207,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(n(B),B))) ),
inference(resolve,[status(thm)],[c_4,c_5102]) ).
cnf(c_7430,plain,
is_a_theorem(implies(A,implies(implies(B,n(B)),n(B)))),
inference(resolve,[status(thm)],[c_22207,c_5677]) ).
cnf(c_22208,plain,
( is_a_theorem(implies(implies(B,n(B)),n(B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7430]) ).
cnf(c_8065,plain,
is_a_theorem(implies(implies(A,n(A)),n(A))),
inference(resolve,[status(thm)],[c_22208,c_7430]) ).
cnf(c_22209,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_433]) ).
cnf(c_13192,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_22209,c_6598]) ).
cnf(c_22210,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_4,c_6598]) ).
cnf(c_13229,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_22210,c_433]) ).
cnf(c_22211,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_13229]) ).
cnf(c_13451,plain,
is_a_theorem(implies(implies(A,implies(B,n(B))),implies(A,n(B)))),
inference(resolve,[status(thm)],[c_22211,c_8065]) ).
cnf(c_22212,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_4,c_433]) ).
cnf(c_20031,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,n(A)),n(A)))),
inference(resolve,[status(thm)],[c_22212,c_13451]) ).
cnf(c_22213,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_4,c_13192]) ).
cnf(c_21826,plain,
is_a_theorem(implies(implies(A,n(B)),implies(implies(B,A),n(B)))),
inference(resolve,[status(thm)],[c_22213,c_20031]) ).
cnf(c_22214,plain,
( is_a_theorem(implies(n(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_5541]) ).
cnf(c_22003,plain,
is_a_theorem(implies(n(A),implies(implies(B,A),n(B)))),
inference(resolve,[status(thm)],[c_22214,c_21826]) ).
cnf(c_22215,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_4,c_13192]) ).
cnf(c_22124,plain,
is_a_theorem(implies(implies(A,B),implies(n(B),n(A)))),
inference(resolve,[status(thm)],[c_22215,c_22003]) ).
cnf(c_22216,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_4,c_6598]) ).
cnf(c_22165,plain,
is_a_theorem(implies(A,implies(n(B),n(implies(A,B))))),
inference(resolve,[status(thm)],[c_22216,c_22124]) ).
cnf(c_22166,plain,
$false,
inference(resolve,[status(thm)],[c_22165,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL403+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 22:30:57 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2427730 was started by sandbox on n015,
% 0.18/0.45 % Fri Sep 25 22:30:57 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 117.33/16.23
% 117.33/16.23 % Assigning unary symbol n kb_weight 0 and highest precedence (5).
% 117.33/16.23
% 117.33/16.23 % given #500 (W,wt=37): 5802 is_a_theorem(implies(n(implies(A,B)),implies(n(implies(C,A)),D))). [hyper(4,a,5608,a,b,5653,a)].
% 117.33/16.23
% 117.33/16.23 % SZS status Theorem for theBenchmark
% 117.33/16.23
% 117.33/16.23 % Proof 1 at 5.30 (+ 2.30) seconds.
% 117.33/16.23 % Length of proof is 57.
% 117.33/16.23 % Level of proof is 31.
% 117.33/16.23 % Maximum clause weight is 116.000.
% 117.33/16.23 % Given clauses 694.
% 117.33/16.23
% 117.33/16.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------