%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL416-1 : 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 : n007.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 07:58:51 AM UTC 2026
% Result : Unsatisfiable 29.62s 4.36s
% Output : CNFRefutation 29.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 29 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(equivalent(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(xcb,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_2,VAR_1)),VAR_2))),
file('theBenchmark.p',xcb) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
inference(clausify,[status(thm)],[xcb]) ).
fof(prove_reflexivity,axiom,
~ is_a_theorem(equivalent(a,a)),
file('theBenchmark.p',prove_reflexivity) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,a)),
inference(clausify,[status(thm)],[prove_reflexivity]) ).
cnf(c_4,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_4051,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D)),E)),
inference(resolve,[status(thm)],[c_4051,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D)),E),F),equivalent(V6,F)),V6)),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D))) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_4052,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E))),
inference(resolve,[status(thm)],[c_4052,c_2]) ).
cnf(c_4053,plain,
( is_a_theorem(V6)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D)),E),F),equivalent(V6,F))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D)),E),F),V6),equivalent(F,V6))),
inference(resolve,[status(thm)],[c_4053,c_2]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E)),F),equivalent(V6,F)),V6)),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_4054,plain,
( is_a_theorem(equivalent(D,E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F),A))),
inference(resolve,[status(thm)],[c_4054,c_8]) ).
cnf(c_4055,plain,
( is_a_theorem(equivalent(D,E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F)),A)),
inference(resolve,[status(thm)],[c_4055,c_5]) ).
cnf(c_4056,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F),A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(E,D)),E),equivalent(equivalent(equivalent(equivalent(F,equivalent(equivalent(equivalent(F,V6),equivalent(V7,V6)),V7)),V8),V9),equivalent(V8,V9)))),
inference(resolve,[status(thm)],[c_4056,c_8]) ).
cnf(c_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F)),A),V6),equivalent(V7,V6)),V7)),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_53,plain,
( is_a_theorem(V6)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E)),F),equivalent(V6,F))) ),
inference(resolve,[status(thm)],[c_12,c_1]) ).
cnf(c_4057,plain,
( is_a_theorem(V6)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E)),F),equivalent(V6,F))) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_55,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E)),F),V6),equivalent(F,V6))),
inference(resolve,[status(thm)],[c_4057,c_2]) ).
cnf(c_4058,plain,
( is_a_theorem(equivalent(F,V6))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),E),equivalent(D,E)),F),V6)) ),
inference(resolve,[status(thm)],[c_1,c_55]) ).
cnf(c_76,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(equivalent(C,equivalent(equivalent(equivalent(C,D),equivalent(E,D)),E)),F),equivalent(V6,F)),V6)),B),A))),
inference(resolve,[status(thm)],[c_4058,c_11]) ).
cnf(c_4059,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(equivalent(C,equivalent(equivalent(equivalent(C,D),equivalent(E,D)),E)),F),equivalent(V6,F)),V6)),B),A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_76]) ).
cnf(c_97,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F)),A),equivalent(V6,equivalent(equivalent(equivalent(V6,V7),equivalent(V8,V7)),V8)))),
inference(resolve,[status(thm)],[c_4059,c_2]) ).
cnf(c_4060,plain,
( is_a_theorem(V7)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),D)),E),equivalent(F,E)),F)),A),V6),equivalent(V7,V6))) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_129,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),equivalent(equivalent(equivalent(D,E),equivalent(F,E)),F))),
inference(resolve,[status(thm)],[c_4060,c_21]) ).
cnf(c_153,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_129,c_7]) ).
cnf(c_165,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),equivalent(D,C)),D)),
inference(resolve,[status(thm)],[c_153,c_4]) ).
cnf(c_4061,plain,
( is_a_theorem(equivalent(equivalent(equivalent(D,E),equivalent(F,E)),F))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_129]) ).
cnf(c_197,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),D),equivalent(C,D)),E),equivalent(F,E)),F)),
inference(resolve,[status(thm)],[c_4061,c_165]) ).
cnf(c_4062,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_165]) ).
cnf(c_204,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),D),equivalent(C,D))),
inference(resolve,[status(thm)],[c_4062,c_2]) ).
cnf(c_4063,plain,
( is_a_theorem(equivalent(C,D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_204]) ).
cnf(c_218,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,C)),A))),
inference(resolve,[status(thm)],[c_4063,c_204]) ).
cnf(c_4064,plain,
( is_a_theorem(equivalent(C,D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_204]) ).
cnf(c_225,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,C))),A)),
inference(resolve,[status(thm)],[c_4064,c_165]) ).
cnf(c_243,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,C)),A)),D),equivalent(E,D)),E)),
inference(resolve,[status(thm)],[c_218,c_4]) ).
cnf(c_295,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),equivalent(D,E)),equivalent(D,E))),
inference(resolve,[status(thm)],[c_225,c_53]) ).
cnf(c_491,plain,
( is_a_theorem(equivalent(D,E))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),equivalent(D,E))) ),
inference(resolve,[status(thm)],[c_295,c_1]) ).
cnf(c_599,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,C)),A)),D),E),equivalent(D,E))),
inference(resolve,[status(thm)],[c_243,c_491]) ).
cnf(c_958,plain,
( is_a_theorem(equivalent(D,E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,C)),A)),D),E)) ),
inference(resolve,[status(thm)],[c_599,c_1]) ).
cnf(c_4065,plain,
( is_a_theorem(F)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C),D),equivalent(C,D)),E),equivalent(F,E))) ),
inference(resolve,[status(thm)],[c_1,c_197]) ).
cnf(c_4030,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C)),D),D)),
inference(resolve,[status(thm)],[c_4065,c_97]) ).
cnf(c_4049,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_4030,c_958]) ).
cnf(c_4050,plain,
$false,
inference(resolve,[status(thm)],[c_4049,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.46 % DateTime : Fri Sep 25 22:26:53 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2075272 was started by sandbox2 on n007,
% 0.19/0.46 % Fri Sep 25 22:26:53 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 29.62/4.36
% 29.62/4.36 % SZS status Unsatisfiable for theBenchmark
% 29.62/4.36
% 29.62/4.36 % Proof 1 at 2.62 (+ 0.95) seconds.
% 29.62/4.36 % Length of proof is 33.
% 29.62/4.36 % Level of proof is 15.
% 29.62/4.36 % Maximum clause weight is 94.000.
% 29.62/4.36 % Given clauses 347.
% 29.62/4.36
% 29.62/4.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------