%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL067-1 : 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 : n006.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 07:57:53 AM UTC 2026
% Result : Unsatisfiable 3.17s 0.90s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 30 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 147 ( 29 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(cn_19,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(VAR_1,VAR_2))),
file('theBenchmark.p',cn_19) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(clausify,[status(thm)],[cn_19]) ).
fof(cn_37,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(not(VAR_0),VAR_2))),
file('theBenchmark.p',cn_37) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(clausify,[status(thm)],[cn_37]) ).
fof(cn_59,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(not(VAR_0),VAR_1),implies(implies(VAR_2,VAR_1),implies(implies(VAR_0,VAR_2),VAR_1)))),
file('theBenchmark.p',cn_59) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(C,B),implies(implies(A,C),B)))),
inference(clausify,[status(thm)],[cn_59]) ).
fof(prove_cn_1,axiom,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('theBenchmark.p',prove_cn_1) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(clausify,[status(thm)],[prove_cn_1]) ).
cnf(c_1780,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_1780,c_2]) ).
cnf(c_1781,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_7,plain,
is_a_theorem(implies(not(implies(A,B)),implies(not(A),C))),
inference(resolve,[status(thm)],[c_1781,c_3]) ).
cnf(c_1782,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_13,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1782,c_6]) ).
cnf(c_1783,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_1783,c_6]) ).
cnf(c_1784,plain,
( is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_19,plain,
is_a_theorem(implies(implies(A,implies(not(B),C)),implies(implies(implies(B,D),A),implies(not(B),C)))),
inference(resolve,[status(thm)],[c_1784,c_7]) ).
cnf(c_1785,plain,
( is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_23,plain,
is_a_theorem(implies(implies(A,implies(B,implies(C,not(D)))),implies(implies(D,A),implies(B,implies(C,not(D)))))),
inference(resolve,[status(thm)],[c_1785,c_14]) ).
cnf(c_1786,plain,
( is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(A,implies(B,implies(C,D))),implies(implies(C,A),implies(B,implies(C,D))))),
inference(resolve,[status(thm)],[c_1786,c_13]) ).
cnf(c_1787,plain,
( is_a_theorem(implies(implies(implies(B,D),A),implies(not(B),C)))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_108,plain,
is_a_theorem(implies(implies(implies(A,B),not(C)),implies(not(A),implies(C,D)))),
inference(resolve,[status(thm)],[c_1787,c_13]) ).
cnf(c_1788,plain,
( is_a_theorem(implies(implies(D,A),implies(B,implies(C,not(D)))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,not(D))))) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_158,plain,
is_a_theorem(implies(implies(A,not(B)),implies(C,implies(B,not(A))))),
inference(resolve,[status(thm)],[c_1788,c_13]) ).
cnf(c_1789,plain,
( is_a_theorem(implies(implies(D,A),implies(B,implies(C,not(D)))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,not(D))))) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_174,plain,
is_a_theorem(implies(implies(A,implies(A,not(B))),implies(C,implies(B,not(A))))),
inference(resolve,[status(thm)],[c_1789,c_158]) ).
cnf(c_1790,plain,
( is_a_theorem(implies(C,implies(B,not(A))))
| ~ is_a_theorem(implies(A,implies(A,not(B)))) ),
inference(resolve,[status(thm)],[c_1,c_174]) ).
cnf(c_225,plain,
is_a_theorem(implies(A,implies(B,not(not(B))))),
inference(resolve,[status(thm)],[c_1790,c_6]) ).
cnf(c_1791,plain,
( is_a_theorem(implies(C,implies(B,not(A))))
| ~ is_a_theorem(implies(A,implies(A,not(B)))) ),
inference(resolve,[status(thm)],[c_1,c_174]) ).
cnf(c_227,plain,
is_a_theorem(implies(A,implies(not(B),not(B)))),
inference(resolve,[status(thm)],[c_1791,c_225]) ).
cnf(c_1792,plain,
( is_a_theorem(implies(not(B),not(B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_227]) ).
cnf(c_292,plain,
is_a_theorem(implies(not(A),not(A))),
inference(resolve,[status(thm)],[c_1792,c_227]) ).
cnf(c_1793,plain,
( is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_301,plain,
is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_1793,c_292]) ).
cnf(c_1794,plain,
( is_a_theorem(implies(implies(B,A),not(B)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_301]) ).
cnf(c_309,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(resolve,[status(thm)],[c_1794,c_292]) ).
cnf(c_1795,plain,
( is_a_theorem(implies(not(A),implies(C,D)))
| ~ is_a_theorem(implies(implies(A,B),not(C))) ),
inference(resolve,[status(thm)],[c_1,c_108]) ).
cnf(c_316,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_1795,c_309]) ).
cnf(c_1796,plain,
( is_a_theorem(implies(implies(C,B),implies(implies(A,C),B)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_329,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(B,A),implies(B,C)))),
inference(resolve,[status(thm)],[c_1796,c_316]) ).
cnf(c_1797,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_329]) ).
cnf(c_1358,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_1797,c_14]) ).
cnf(c_1798,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_1425,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1798,c_1358]) ).
cnf(c_1799,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1425]) ).
cnf(c_1565,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_1799,c_1358]) ).
cnf(c_1800,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_1778,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_1800,c_1565]) ).
cnf(c_1779,plain,
$false,
inference(resolve,[status(thm)],[c_1778,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n006.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Fri Sep 25 21:48:11 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3828414 was started by sandbox2 on n006,
% 0.20/0.45 % Fri Sep 25 21:48:11 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.45
% 0.20/0.45 % From the command line: assign(max_seconds, 300).
% 3.17/0.90
% 3.17/0.90 % SZS status Unsatisfiable for theBenchmark
% 3.17/0.90
% 3.17/0.90 % Proof 1 at 0.27 (+ 0.16) seconds.
% 3.17/0.90 % Length of proof is 27.
% 3.17/0.90 % Level of proof is 17.
% 3.17/0.90 % Maximum clause weight is 50.000.
% 3.17/0.90 % Given clauses 123.
% 3.17/0.90
% 3.17/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------