%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL089-1 : 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 : n001.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 5.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 73 ( 38 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 238 ( 95 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_4,axiom,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('theBenchmark.p',prove_ic_4) ).
cnf(c_3,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(clausify,[status(thm)],[prove_ic_4]) ).
cnf(c_802,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_802,c_2]) ).
cnf(c_803,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_803,c_4]) ).
cnf(c_804,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_804,c_5]) ).
cnf(c_805,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_805,c_2]) ).
cnf(c_806,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_806,c_7]) ).
cnf(c_807,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_807,c_10]) ).
cnf(c_808,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_808,c_9]) ).
cnf(c_809,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_809,c_9]) ).
cnf(c_810,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_32,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolve,[status(thm)],[c_810,c_12]) ).
cnf(c_811,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_37,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_811,c_32]) ).
cnf(c_812,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_37]) ).
cnf(c_52,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_812,c_37]) ).
cnf(c_813,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_55,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),D),implies(C,D)))),
inference(resolve,[status(thm)],[c_813,c_37]) ).
cnf(c_814,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_58,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),implies(D,B)))),
inference(resolve,[status(thm)],[c_814,c_52]) ).
cnf(c_815,plain,
( is_a_theorem(implies(implies(implies(B,C),D),implies(C,D)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_55]) ).
cnf(c_68,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_815,c_55]) ).
cnf(c_816,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_73,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(A,D))),
inference(resolve,[status(thm)],[c_816,c_18]) ).
cnf(c_817,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_68]) ).
cnf(c_79,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(implies(B,D),implies(A,D))))),
inference(resolve,[status(thm)],[c_817,c_2]) ).
cnf(c_818,plain,
( is_a_theorem(implies(implies(implies(B,C),B),implies(D,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_58]) ).
cnf(c_126,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(C,A))),
inference(resolve,[status(thm)],[c_818,c_58]) ).
cnf(c_819,plain,
( is_a_theorem(implies(C,A))
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_126]) ).
cnf(c_129,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_819,c_126]) ).
cnf(c_820,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_131,plain,
is_a_theorem(implies(A,implies(implies(B,implies(B,C)),implies(D,implies(B,C))))),
inference(resolve,[status(thm)],[c_820,c_126]) ).
cnf(c_821,plain,
( is_a_theorem(implies(B,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_129]) ).
cnf(c_134,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_821,c_129]) ).
cnf(c_822,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_145,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_822,c_134]) ).
cnf(c_823,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_131]) ).
cnf(c_451,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_823,c_131]) ).
cnf(c_824,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_451]) ).
cnf(c_459,plain,
is_a_theorem(implies(A,implies(implies(B,implies(B,C)),implies(B,C)))),
inference(resolve,[status(thm)],[c_824,c_451]) ).
cnf(c_825,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_73]) ).
cnf(c_461,plain,
is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))),
inference(resolve,[status(thm)],[c_825,c_451]) ).
cnf(c_826,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_451]) ).
cnf(c_466,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_826,c_145]) ).
cnf(c_827,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_451]) ).
cnf(c_468,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_827,c_126]) ).
cnf(c_828,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_451]) ).
cnf(c_481,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_828,c_461]) ).
cnf(c_829,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_466]) ).
cnf(c_572,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_829,c_466]) ).
cnf(c_830,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_572]) ).
cnf(c_586,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_830,c_468]) ).
cnf(c_831,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(implies(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_586]) ).
cnf(c_606,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_831,c_481]) ).
cnf(c_832,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_606]) ).
cnf(c_672,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)),
inference(resolve,[status(thm)],[c_832,c_52]) ).
cnf(c_833,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_1,c_672]) ).
cnf(c_782,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_833,c_459]) ).
cnf(c_834,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_782]) ).
cnf(c_800,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_834,c_79]) ).
cnf(c_801,plain,
$false,
inference(resolve,[status(thm)],[c_800,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL089-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n001.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Fri Sep 25 21:56:16 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 146585 was started by sandbox2 on n001,
% 0.17/5.45 % Fri Sep 25 21:56:16 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 0.21/5.61
% 0.21/5.61 % SZS status Unsatisfiable for theBenchmark
% 0.21/5.61
% 0.21/5.61 % Proof 1 at 0.09 (+ 0.05) seconds.
% 0.21/5.61 % Length of proof is 37.
% 0.21/5.61 % Level of proof is 21.
% 0.21/5.61 % Maximum clause weight is 20.000.
% 0.21/5.61 % Given clauses 82.
% 0.21/5.61
% 0.21/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------