%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL370+2 : 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 : n026.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 07:58:42 AM UTC 2026
% Result : Theorem 43.42s 6.83s
% Output : CNFRefutation 43.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of formulae : 90 ( 47 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 45 ~; 43 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 364 ( 88 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(implies(implies(x,y),z),implies(implies(z,x),x))),
file('theBenchmark.p',f3) ).
fof(f3_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(z,x),x))),
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(implies(implies(x,y),z),implies(implies(z,x),x))),
inference(clausify,[status(thm)],[f3_neg]) ).
cnf(c_21057,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_21057,c_5]) ).
cnf(c_21058,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_21058,c_7]) ).
cnf(c_21059,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_21059,c_7]) ).
cnf(c_21060,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_21060,c_8]) ).
cnf(c_21061,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_21061,c_9]) ).
cnf(c_21062,plain,
( is_a_theorem(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))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_11]) ).
cnf(c_17,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_21062,c_11]) ).
cnf(c_21063,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_18,plain,
is_a_theorem(implies(A,implies(B,implies(n(B),C)))),
inference(resolve,[status(thm)],[c_21063,c_11]) ).
cnf(c_21064,plain,
( is_a_theorem(implies(B,implies(n(B),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,implies(n(A),B))),
inference(resolve,[status(thm)],[c_21064,c_18]) ).
cnf(c_21065,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_43,plain,
is_a_theorem(implies(A,implies(implies(n(B),B),B))),
inference(resolve,[status(thm)],[c_21065,c_15]) ).
cnf(c_21066,plain,
( is_a_theorem(implies(implies(n(B),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_43]) ).
cnf(c_44,plain,
is_a_theorem(implies(implies(n(A),A),A)),
inference(resolve,[status(thm)],[c_21066,c_43]) ).
cnf(c_21067,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_17]) ).
cnf(c_70,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_21067,c_7]) ).
cnf(c_21068,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_70]) ).
cnf(c_118,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_21068,c_7]) ).
cnf(c_21069,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_119,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_21069,c_118]) ).
cnf(c_21070,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_145,plain,
is_a_theorem(implies(implies(implies(n(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_21070,c_20]) ).
cnf(c_21071,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_156,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_21071,c_7]) ).
cnf(c_21072,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_157,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))),
inference(resolve,[status(thm)],[c_21072,c_156]) ).
cnf(c_21073,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_156]) ).
cnf(c_160,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_21073,c_118]) ).
cnf(c_21074,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_156]) ).
cnf(c_162,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_21074,c_44]) ).
cnf(c_21075,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_169,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_21075,c_162]) ).
cnf(c_21076,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_173,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_21076,c_169]) ).
cnf(c_21077,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_216,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))),
inference(resolve,[status(thm)],[c_21077,c_160]) ).
cnf(c_21078,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_249,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))),
inference(resolve,[status(thm)],[c_21078,c_173]) ).
cnf(c_21079,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_157]) ).
cnf(c_709,plain,
is_a_theorem(implies(implies(implies(A,n(B)),B),B)),
inference(resolve,[status(thm)],[c_21079,c_44]) ).
cnf(c_21080,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_216]) ).
cnf(c_844,plain,
is_a_theorem(implies(n(A),implies(A,implies(B,C)))),
inference(resolve,[status(thm)],[c_21080,c_145]) ).
cnf(c_21081,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_856,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(n(A),D))),
inference(resolve,[status(thm)],[c_21081,c_844]) ).
cnf(c_21082,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_249]) ).
cnf(c_1244,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_21082,c_709]) ).
cnf(c_21083,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_1265,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))),
inference(resolve,[status(thm)],[c_21083,c_1244]) ).
cnf(c_21084,plain,
( is_a_theorem(implies(implies(implies(C,C),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_1265]) ).
cnf(c_1405,plain,
is_a_theorem(implies(implies(implies(A,A),implies(B,C)),implies(implies(C,D),implies(B,D)))),
inference(resolve,[status(thm)],[c_21084,c_118]) ).
cnf(c_21085,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_216]) ).
cnf(c_3313,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(D,implies(C,B))))),
inference(resolve,[status(thm)],[c_21085,c_119]) ).
cnf(c_21086,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_3313]) ).
cnf(c_3799,plain,
is_a_theorem(implies(implies(A,implies(n(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_21086,c_44]) ).
cnf(c_21087,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_856]) ).
cnf(c_4082,plain,
is_a_theorem(implies(n(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_21087,c_3799]) ).
cnf(c_21088,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_3799]) ).
cnf(c_4135,plain,
is_a_theorem(implies(A,implies(n(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_21088,c_4082]) ).
cnf(c_21089,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_1405]) ).
cnf(c_4164,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(n(A),C))),
inference(resolve,[status(thm)],[c_21089,c_4135]) ).
cnf(c_21090,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_3799]) ).
cnf(c_4225,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_21090,c_4164]) ).
cnf(c_21091,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_4225]) ).
cnf(c_4988,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_21091,c_4225]) ).
cnf(c_21092,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_119]) ).
cnf(c_5025,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21092,c_4988]) ).
cnf(c_21093,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_216]) ).
cnf(c_5096,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_21093,c_5025]) ).
cnf(c_21094,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_118]) ).
cnf(c_5152,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_21094,c_5096]) ).
cnf(c_21095,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_4,c_5152]) ).
cnf(c_11682,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_21095,c_119]) ).
cnf(c_21096,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_11682]) ).
cnf(c_11942,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21096,c_4988]) ).
cnf(c_21097,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_119]) ).
cnf(c_21055,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_21097,c_11942]) ).
cnf(c_21056,plain,
$false,
inference(resolve,[status(thm)],[c_21055,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL370+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n026.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Fri Sep 25 22:23:11 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.57 % Process 3612244 was started by sandbox2 on n026,
% 0.08/0.57 % Fri Sep 25 22:23:11 2026
% 0.08/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.57
% 0.08/0.57 % From the command line: assign(max_seconds, 300).
% 43.42/6.83
% 43.42/6.83 % Assigning unary symbol n kb_weight 0 and highest precedence (6).
% 43.42/6.83
% 43.42/6.83 % given #500 (W,wt=35): 18418 is_a_theorem(implies(A,n(implies(implies(B,B),n(A))))). [hyper(4,a,8791,a,b,4198,a)].
% 43.42/6.83
% 43.42/6.83 % SZS status Theorem for theBenchmark
% 43.42/6.83
% 43.42/6.83 % Proof 1 at 4.37 (+ 1.71) seconds.
% 43.42/6.83 % Length of proof is 48.
% 43.42/6.83 % Level of proof is 25.
% 43.42/6.83 % Maximum clause weight is 116.000.
% 43.42/6.83 % Given clauses 547.
% 43.42/6.83
% 43.42/6.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------