%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL070-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:57:53 AM UTC 2026
% Result : Unsatisfiable 4.45s 1.63s
% Output : CNFRefutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 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 : 105 ( 19 sgn 12 !; 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_60,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(implies(implies(VAR_0,implies(not(VAR_1),VAR_2)),implies(VAR_0,implies(implies(VAR_3,VAR_2),implies(implies(VAR_1,VAR_3),VAR_2))))),
file('theBenchmark.p',cn_60) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C))))),
inference(clausify,[status(thm)],[cn_60]) ).
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_3071,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_3071,c_2]) ).
cnf(c_3072,plain,
( is_a_theorem(implies(A,implies(implies(D,C),implies(implies(B,D),C))))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,C),implies(implies(A,D),C)))),
inference(resolve,[status(thm)],[c_3072,c_3]) ).
cnf(c_3073,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_17,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_3073,c_6]) ).
cnf(c_3074,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_102,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_3074,c_6]) ).
cnf(c_3075,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_105,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(D,B),A),implies(B,C)))),
inference(resolve,[status(thm)],[c_3075,c_2]) ).
cnf(c_3076,plain,
( is_a_theorem(implies(implies(implies(D,B),A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_105]) ).
cnf(c_143,plain,
is_a_theorem(implies(implies(implies(A,B),implies(implies(C,B),D)),implies(B,D))),
inference(resolve,[status(thm)],[c_3076,c_2]) ).
cnf(c_3077,plain,
( is_a_theorem(implies(B,D))
| ~ is_a_theorem(implies(implies(A,B),implies(implies(C,B),D))) ),
inference(resolve,[status(thm)],[c_1,c_143]) ).
cnf(c_208,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_3077,c_2]) ).
cnf(c_3078,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_215,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(B,A),implies(B,C)))),
inference(resolve,[status(thm)],[c_3078,c_208]) ).
cnf(c_3079,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_215]) ).
cnf(c_274,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_3079,c_17]) ).
cnf(c_3080,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_102]) ).
cnf(c_1597,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_3080,c_274]) ).
cnf(c_3081,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1597]) ).
cnf(c_2431,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_3081,c_274]) ).
cnf(c_3082,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_102]) ).
cnf(c_3069,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_3082,c_2431]) ).
cnf(c_3070,plain,
$false,
inference(resolve,[status(thm)],[c_3069,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL070-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n009.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Fri Sep 25 21:48:44 UTC 2026
% 0.08/0.39 % CPUTime :
% 0.08/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.39 % Process 2628136 was started by sandbox on n009,
% 0.08/0.39 % Fri Sep 25 21:48:44 2026
% 0.08/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 4.45/1.63
% 4.45/1.63 % SZS status Unsatisfiable for theBenchmark
% 4.45/1.64
% 4.45/1.64 % Proof 1 at 0.39 (+ 0.19) seconds.
% 4.45/1.64 % Length of proof is 18.
% 4.45/1.64 % Level of proof is 10.
% 4.45/1.64 % Maximum clause weight is 49.000.
% 4.45/1.64 % Given clauses 209.
% 4.45/1.64
% 4.45/1.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------