%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 07:58:04 AM UTC 2026
% Result : Unsatisfiable 15.42s 7.36s
% Output : CNFRefutation 15.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of formulae : 95 ( 49 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 98 ( 50 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 357 ( 0 sgn 6 !; 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(s_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(VAR_0,equivalent(VAR_0,equivalent(equivalent(equivalent(VAR_1,VAR_2),equivalent(VAR_3,VAR_2)),equivalent(VAR_1,VAR_3))))),
file('theBenchmark.p',s_3) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))))),
inference(clausify,[status(thm)],[s_3]) ).
fof(prove_lg_2,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('theBenchmark.p',prove_lg_2) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(clausify,[status(thm)],[prove_lg_2]) ).
cnf(c_7834,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))),equivalent(equivalent(equivalent(E,F),equivalent(V6,F)),equivalent(E,V6)))),
inference(resolve,[status(thm)],[c_7834,c_2]) ).
cnf(c_7835,plain,
( is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(V6,F)),equivalent(E,V6)))
| ~ is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_7835,c_2]) ).
cnf(c_7836,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C)),equivalent(equivalent(equivalent(D,E),equivalent(F,E)),equivalent(D,F)))),
inference(resolve,[status(thm)],[c_7836,c_5]) ).
cnf(c_7837,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E)),B)))),
inference(resolve,[status(thm)],[c_7837,c_4]) ).
cnf(c_7838,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(equivalent(A,D),equivalent(C,D)))),
inference(resolve,[status(thm)],[c_7838,c_6]) ).
cnf(c_7839,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_7839,c_8]) ).
cnf(c_7840,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,D)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E))),B))),
inference(resolve,[status(thm)],[c_7840,c_2]) ).
cnf(c_7841,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_7841,c_11]) ).
cnf(c_7842,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_18,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))),
inference(resolve,[status(thm)],[c_7842,c_16]) ).
cnf(c_7843,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,D)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_19,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))),
inference(resolve,[status(thm)],[c_7843,c_18]) ).
cnf(c_7844,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_20,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_7844,c_18]) ).
cnf(c_7845,plain,
( is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E)),B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),B),equivalent(equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E)),B))),
inference(resolve,[status(thm)],[c_7845,c_16]) ).
cnf(c_7846,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_20]) ).
cnf(c_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D),equivalent(equivalent(A,C),D))),
inference(resolve,[status(thm)],[c_7846,c_5]) ).
cnf(c_7847,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_37,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),C)),equivalent(equivalent(A,E),equivalent(D,E)))),
inference(resolve,[status(thm)],[c_7847,c_8]) ).
cnf(c_7848,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_40,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),C)),equivalent(A,D))),
inference(resolve,[status(thm)],[c_7848,c_5]) ).
cnf(c_7849,plain,
( is_a_theorem(equivalent(equivalent(A,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_43,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))),
inference(resolve,[status(thm)],[c_7849,c_32]) ).
cnf(c_7850,plain,
( is_a_theorem(equivalent(equivalent(A,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_47,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,C),D),equivalent(equivalent(B,C),D)))),
inference(resolve,[status(thm)],[c_7850,c_20]) ).
cnf(c_7851,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_58,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C)),equivalent(equivalent(A,E),equivalent(D,equivalent(E,B))))),
inference(resolve,[status(thm)],[c_7851,c_43]) ).
cnf(c_7852,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_62,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D),equivalent(equivalent(equivalent(A,C),E),equivalent(D,E)))),
inference(resolve,[status(thm)],[c_7852,c_32]) ).
cnf(c_7853,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E)),B))
| ~ is_a_theorem(equivalent(equivalent(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_26]) ).
cnf(c_279,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C)),equivalent(D,D))),
inference(resolve,[status(thm)],[c_7853,c_40]) ).
cnf(c_7854,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_288,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D),equivalent(equivalent(E,E),equivalent(D,equivalent(A,C))))),
inference(resolve,[status(thm)],[c_7854,c_279]) ).
cnf(c_7855,plain,
( is_a_theorem(equivalent(equivalent(E,E),equivalent(D,equivalent(A,C))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_288]) ).
cnf(c_324,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(equivalent(B,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_7855,c_5]) ).
cnf(c_7856,plain,
( is_a_theorem(equivalent(equivalent(E,E),equivalent(D,equivalent(A,C))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_288]) ).
cnf(c_327,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(equivalent(equivalent(B,C),equivalent(B,C)),equivalent(D,D)))),
inference(resolve,[status(thm)],[c_7856,c_324]) ).
cnf(c_7857,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(B,C)),equivalent(D,D)))
| ~ is_a_theorem(equivalent(A,A)) ),
inference(resolve,[status(thm)],[c_1,c_327]) ).
cnf(c_349,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),equivalent(C,C))),
inference(resolve,[status(thm)],[c_7857,c_327]) ).
cnf(c_7858,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(C,D),equivalent(E,D)),equivalent(C,E))),B))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_392,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))),A)),
inference(resolve,[status(thm)],[c_7858,c_16]) ).
cnf(c_7859,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,C),E),equivalent(D,E)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_62]) ).
cnf(c_401,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),B),equivalent(equivalent(C,C),B))),
inference(resolve,[status(thm)],[c_7859,c_349]) ).
cnf(c_7860,plain,
( is_a_theorem(equivalent(equivalent(A,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_406,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(B,B))),
inference(resolve,[status(thm)],[c_7860,c_349]) ).
cnf(c_7861,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,C),D),equivalent(equivalent(B,C),D)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_415,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,A),B),C),equivalent(equivalent(equivalent(D,D),B),C))),
inference(resolve,[status(thm)],[c_7861,c_406]) ).
cnf(c_7862,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_416,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,C),equivalent(B,A)))),
inference(resolve,[status(thm)],[c_7862,c_406]) ).
cnf(c_7863,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,C),E),equivalent(D,E)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_62]) ).
cnf(c_436,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(D,D),equivalent(B,A)),C))),
inference(resolve,[status(thm)],[c_7863,c_401]) ).
cnf(c_7864,plain,
( is_a_theorem(equivalent(equivalent(equivalent(D,D),B),C))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_415]) ).
cnf(c_552,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),equivalent(B,B)),equivalent(C,C))),
inference(resolve,[status(thm)],[c_7864,c_406]) ).
cnf(c_7865,plain,
( is_a_theorem(equivalent(equivalent(equivalent(D,D),equivalent(B,A)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_436]) ).
cnf(c_766,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),equivalent(equivalent(B,B),equivalent(C,C))),equivalent(D,D))),
inference(resolve,[status(thm)],[c_7865,c_552]) ).
cnf(c_7866,plain,
( is_a_theorem(equivalent(equivalent(A,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_1469,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),equivalent(A,equivalent(B,D)))),
inference(resolve,[status(thm)],[c_7866,c_392]) ).
cnf(c_7867,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_392]) ).
cnf(c_1477,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(A,equivalent(equivalent(B,D),equivalent(C,D))))),
inference(resolve,[status(thm)],[c_7867,c_15]) ).
cnf(c_7868,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_1469]) ).
cnf(c_1499,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(B,D))),equivalent(A,C))),
inference(resolve,[status(thm)],[c_7868,c_1469]) ).
cnf(c_7869,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_1469]) ).
cnf(c_1536,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(D,B)),equivalent(A,equivalent(D,C)))),
inference(resolve,[status(thm)],[c_7869,c_1477]) ).
cnf(c_7870,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_1499]) ).
cnf(c_1602,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,B)),A)),
inference(resolve,[status(thm)],[c_7870,c_1477]) ).
cnf(c_7871,plain,
( is_a_theorem(equivalent(equivalent(C,C),equivalent(B,A)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_416]) ).
cnf(c_1613,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(B,equivalent(B,equivalent(C,C))))),
inference(resolve,[status(thm)],[c_7871,c_1602]) ).
cnf(c_7872,plain,
( is_a_theorem(equivalent(B,equivalent(B,equivalent(C,C))))
| ~ is_a_theorem(equivalent(A,A)) ),
inference(resolve,[status(thm)],[c_1,c_1613]) ).
cnf(c_1720,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(B,B)))),
inference(resolve,[status(thm)],[c_7872,c_766]) ).
cnf(c_7873,plain,
( is_a_theorem(equivalent(equivalent(A,E),equivalent(D,E)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),C))) ),
inference(resolve,[status(thm)],[c_1,c_37]) ).
cnf(c_1741,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,equivalent(C,C)),B))),
inference(resolve,[status(thm)],[c_7873,c_1720]) ).
cnf(c_7874,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_1469]) ).
cnf(c_2132,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,C))),equivalent(A,B))),
inference(resolve,[status(thm)],[c_7874,c_1741]) ).
cnf(c_7875,plain,
( is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,C)))) ),
inference(resolve,[status(thm)],[c_1,c_2132]) ).
cnf(c_3453,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),A)),
inference(resolve,[status(thm)],[c_7875,c_1536]) ).
cnf(c_7876,plain,
( is_a_theorem(equivalent(equivalent(A,E),equivalent(D,equivalent(E,B))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_58]) ).
cnf(c_3521,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),D),equivalent(A,equivalent(D,equivalent(C,B))))),
inference(resolve,[status(thm)],[c_7876,c_3453]) ).
cnf(c_7877,plain,
( is_a_theorem(equivalent(A,equivalent(D,equivalent(C,B))))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_3521]) ).
cnf(c_7832,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))),
inference(resolve,[status(thm)],[c_7877,c_392]) ).
cnf(c_7833,plain,
$false,
inference(resolve,[status(thm)],[c_7832,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n012.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Fri Sep 25 21:53:59 UTC 2026
% 0.08/5.35 % CPUTime :
% 0.08/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.35 % Process 3141270 was started by sandbox2 on n012,
% 0.08/5.35 % Fri Sep 25 21:53:59 2026
% 0.08/5.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.36
% 0.08/5.36 % From the command line: assign(max_seconds, 300).
% 15.42/7.36
% 15.42/7.36 % SZS status Unsatisfiable for theBenchmark
% 15.42/7.36
% 15.42/7.36 % Proof 1 at 1.64 (+ 0.33) seconds.
% 15.42/7.36 % Length of proof is 48.
% 15.42/7.36 % Level of proof is 25.
% 15.42/7.36 % Maximum clause weight is 87.000.
% 15.42/7.36 % Given clauses 194.
% 15.42/7.36
% 15.42/7.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
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