%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL371+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 : n002.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 40.95s 6.33s
% Output : CNFRefutation 40.95s
% 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 362 ( 86 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),y),implies(implies(y,x),x))),
file('theBenchmark.p',f3) ).
fof(f3_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,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),y),implies(implies(y,x),x))),
inference(clausify,[status(thm)],[f3_neg]) ).
cnf(c_21795,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_21795,c_5]) ).
cnf(c_21796,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_21796,c_7]) ).
cnf(c_21797,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_21797,c_7]) ).
cnf(c_21798,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_21798,c_8]) ).
cnf(c_21799,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_21799,c_9]) ).
cnf(c_21800,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_21800,c_15]) ).
cnf(c_21801,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_19,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_21801,c_11]) ).
cnf(c_21802,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_20,plain,
is_a_theorem(implies(A,implies(B,implies(n(B),C)))),
inference(resolve,[status(thm)],[c_21802,c_11]) ).
cnf(c_21803,plain,
( is_a_theorem(implies(implies(n(B),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_18]) ).
cnf(c_23,plain,
is_a_theorem(implies(implies(n(A),A),A)),
inference(resolve,[status(thm)],[c_21803,c_18]) ).
cnf(c_21804,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(n(A),A)) ),
inference(resolve,[status(thm)],[c_4,c_23]) ).
cnf(c_25,plain,
is_a_theorem(implies(A,implies(n(A),B))),
inference(resolve,[status(thm)],[c_21804,c_20]) ).
cnf(c_21805,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_19]) ).
cnf(c_48,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_21805,c_7]) ).
cnf(c_21806,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_48]) ).
cnf(c_130,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_21806,c_7]) ).
cnf(c_21807,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_131,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_21807,c_130]) ).
cnf(c_21808,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_154,plain,
is_a_theorem(implies(implies(implies(n(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_21808,c_25]) ).
cnf(c_21809,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_170,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_21809,c_7]) ).
cnf(c_21810,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_171,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,A),B),C))),
inference(resolve,[status(thm)],[c_21810,c_170]) ).
cnf(c_21811,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_170]) ).
cnf(c_174,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_21811,c_130]) ).
cnf(c_21812,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_4,c_170]) ).
cnf(c_177,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_21812,c_23]) ).
cnf(c_21813,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_183,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_21813,c_177]) ).
cnf(c_21814,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_184,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_21814,c_183]) ).
cnf(c_21815,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_237,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))),
inference(resolve,[status(thm)],[c_21815,c_174]) ).
cnf(c_21816,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_274,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(D,D),B),C))),
inference(resolve,[status(thm)],[c_21816,c_184]) ).
cnf(c_21817,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_171]) ).
cnf(c_785,plain,
is_a_theorem(implies(implies(implies(A,n(B)),B),B)),
inference(resolve,[status(thm)],[c_21817,c_23]) ).
cnf(c_21818,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_237]) ).
cnf(c_909,plain,
is_a_theorem(implies(n(A),implies(A,implies(B,C)))),
inference(resolve,[status(thm)],[c_21818,c_154]) ).
cnf(c_21819,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_928,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(n(A),D))),
inference(resolve,[status(thm)],[c_21819,c_909]) ).
cnf(c_21820,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_274]) ).
cnf(c_1329,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_21820,c_785]) ).
cnf(c_21821,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_1365,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(C,C),A),B))),
inference(resolve,[status(thm)],[c_21821,c_1329]) ).
cnf(c_21822,plain,
( is_a_theorem(implies(implies(implies(C,C),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_1365]) ).
cnf(c_1510,plain,
is_a_theorem(implies(implies(implies(A,A),implies(B,C)),implies(implies(C,D),implies(B,D)))),
inference(resolve,[status(thm)],[c_21822,c_130]) ).
cnf(c_21823,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_237]) ).
cnf(c_3511,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(D,implies(C,B))))),
inference(resolve,[status(thm)],[c_21823,c_131]) ).
cnf(c_21824,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_3511]) ).
cnf(c_4047,plain,
is_a_theorem(implies(implies(A,implies(n(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_21824,c_23]) ).
cnf(c_21825,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_928]) ).
cnf(c_4344,plain,
is_a_theorem(implies(n(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_21825,c_4047]) ).
cnf(c_21826,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_4047]) ).
cnf(c_4397,plain,
is_a_theorem(implies(A,implies(n(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_21826,c_4344]) ).
cnf(c_21827,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_1510]) ).
cnf(c_4426,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(n(A),C))),
inference(resolve,[status(thm)],[c_21827,c_4397]) ).
cnf(c_21828,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_4047]) ).
cnf(c_4497,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_21828,c_4426]) ).
cnf(c_21829,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_4497]) ).
cnf(c_5323,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_21829,c_4497]) ).
cnf(c_21830,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_131]) ).
cnf(c_5360,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21830,c_5323]) ).
cnf(c_21831,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_237]) ).
cnf(c_5417,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_21831,c_5360]) ).
cnf(c_21832,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_130]) ).
cnf(c_5490,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_21832,c_5417]) ).
cnf(c_21833,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_4,c_5490]) ).
cnf(c_14112,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_21833,c_131]) ).
cnf(c_21834,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_4,c_14112]) ).
cnf(c_14389,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_21834,c_5323]) ).
cnf(c_21835,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_131]) ).
cnf(c_21793,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_21835,c_14389]) ).
cnf(c_21794,plain,
$false,
inference(resolve,[status(thm)],[c_21793,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL371+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:23:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 148419 was started by sandbox2 on n002,
% 0.09/0.36 % Fri Sep 25 22:23:20 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 40.95/6.33
% 40.95/6.33 % given #500 (A,wt=41): 199 is_a_theorem(implies(n(implies(A,implies(B,implies(C,A)))),D)). [hyper(4,a,25,a,b,180,a)].
% 40.95/6.33
% 40.95/6.33 % SZS status Theorem for theBenchmark
% 40.95/6.33
% 40.95/6.33 % Proof 1 at 4.00 (+ 1.91) seconds.
% 40.95/6.33 % Length of proof is 48.
% 40.95/6.33 % Level of proof is 25.
% 40.95/6.33 % Maximum clause weight is 116.000.
% 40.95/6.33 % Given clauses 625.
% 40.95/6.33
% 40.95/6.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
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