%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL094-1 : 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 : n009.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 07:57:57 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.74s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 194 ( 82 sgn 7 !; 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(ic_JLukasiewicz_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,VAR_3)),implies(VAR_4,implies(implies(VAR_3,VAR_0),implies(VAR_2,VAR_0))))),
file('theBenchmark.p',ic_JLukasiewicz_4) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A))))),
inference(clausify,[status(thm)],[ic_JLukasiewicz_4]) ).
fof(prove_ic_5,axiom,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
file('theBenchmark.p',prove_ic_5) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(clausify,[status(thm)],[prove_ic_5]) ).
cnf(c_467,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))),
inference(resolve,[status(thm)],[c_467,c_2]) ).
cnf(c_468,plain,
( is_a_theorem(implies(implies(implies(implies(B,C),implies(D,C)),implies(C,E)),implies(F,implies(C,E))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_468,c_4]) ).
cnf(c_469,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(C,implies(B,C))))),
inference(resolve,[status(thm)],[c_469,c_5]) ).
cnf(c_470,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),implies(D,C))))),
inference(resolve,[status(thm)],[c_470,c_2]) ).
cnf(c_471,plain,
( is_a_theorem(implies(implies(B,C),implies(C,implies(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(A,B),implies(B,implies(A,B)))),
inference(resolve,[status(thm)],[c_471,c_7]) ).
cnf(c_472,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(C,B)))),
inference(resolve,[status(thm)],[c_472,c_10]) ).
cnf(c_473,plain,
( is_a_theorem(implies(B,implies(implies(B,C),implies(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_17,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_473,c_9]) ).
cnf(c_474,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(implies(implies(implies(B,C),implies(D,C)),E),implies(B,E)))),
inference(resolve,[status(thm)],[c_474,c_9]) ).
cnf(c_475,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_28,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolve,[status(thm)],[c_475,c_12]) ).
cnf(c_476,plain,
( is_a_theorem(implies(E,implies(B,D)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(B,D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_33,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_476,c_28]) ).
cnf(c_477,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_51,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_477,c_33]) ).
cnf(c_478,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_57,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(D,B)))),
inference(resolve,[status(thm)],[c_478,c_51]) ).
cnf(c_479,plain,
( is_a_theorem(implies(implies(implies(implies(B,C),implies(D,C)),E),implies(B,E)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_76,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))),
inference(resolve,[status(thm)],[c_479,c_18]) ).
cnf(c_480,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(D,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_57]) ).
cnf(c_125,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_480,c_57]) ).
cnf(c_481,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_125]) ).
cnf(c_128,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_481,c_125]) ).
cnf(c_482,plain,
( is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))
| ~ is_a_theorem(implies(implies(A,B),implies(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_130,plain,
is_a_theorem(implies(A,implies(implies(B,implies(B,C)),implies(D,implies(B,C))))),
inference(resolve,[status(thm)],[c_482,c_125]) ).
cnf(c_483,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_128]) ).
cnf(c_142,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_483,c_128]) ).
cnf(c_484,plain,
( is_a_theorem(implies(implies(A,B),implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_147,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_484,c_142]) ).
cnf(c_485,plain,
( is_a_theorem(implies(implies(B,implies(B,C)),implies(D,implies(B,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_130]) ).
cnf(c_316,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_485,c_130]) ).
cnf(c_486,plain,
( is_a_theorem(implies(A,D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_76]) ).
cnf(c_325,plain,
is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))),
inference(resolve,[status(thm)],[c_486,c_316]) ).
cnf(c_487,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_316]) ).
cnf(c_329,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_487,c_147]) ).
cnf(c_488,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_316]) ).
cnf(c_331,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_488,c_125]) ).
cnf(c_489,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_316]) ).
cnf(c_343,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_489,c_325]) ).
cnf(c_490,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_329]) ).
cnf(c_396,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_490,c_329]) ).
cnf(c_491,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_396]) ).
cnf(c_441,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_491,c_331]) ).
cnf(c_492,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_441]) ).
cnf(c_465,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_492,c_343]) ).
cnf(c_466,plain,
$false,
inference(resolve,[status(thm)],[c_465,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL094-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.64 % Computer : n009.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Fri Sep 25 21:50:45 UTC 2026
% 0.17/0.64 % CPUTime :
% 0.17/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.64 % Process 2633151 was started by sandbox2 on n009,
% 0.17/0.64 % Fri Sep 25 21:50:45 2026
% 0.17/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.65
% 0.17/0.65 % From the command line: assign(max_seconds, 300).
% 0.21/0.74
% 0.21/0.74 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.74
% 0.21/0.74 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.21/0.74 % Length of proof is 30.
% 0.21/0.74 % Level of proof is 18.
% 0.21/0.74 % Maximum clause weight is 50.000.
% 0.21/0.74 % Given clauses 57.
% 0.21/0.74
% 0.21/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------