%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL029-1 : 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 : n026.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 07:57:47 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 19 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 64 ( 13 sgn 10 !; 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(c0_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',c0_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[c0_1]) ).
fof(c0_2,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',c0_2) ).
cnf(c_3,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[c0_2]) ).
fof(c0_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_0),VAR_0)),
file('theBenchmark.p',c0_3) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(clausify,[status(thm)],[c0_3]) ).
fof(c0_4,axiom,
! [VAR_0] : is_a_theorem(implies(falsehood,VAR_0)),
file('theBenchmark.p',c0_4) ).
cnf(c_5,plain,
is_a_theorem(implies(falsehood,A)),
inference(clausify,[status(thm)],[c0_4]) ).
fof(prove_c0_5,axiom,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
file('theBenchmark.p',prove_c0_5) ).
cnf(c_6,plain,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
inference(clausify,[status(thm)],[prove_c0_5]) ).
cnf(c_254,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_254,c_2]) ).
cnf(c_255,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_13,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_255,c_5]) ).
cnf(c_256,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_256,c_4]) ).
cnf(c_257,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_24,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_257,c_13]) ).
cnf(c_258,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_60,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),B)),
inference(resolve,[status(thm)],[c_258,c_24]) ).
cnf(c_259,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_65,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))),
inference(resolve,[status(thm)],[c_259,c_60]) ).
cnf(c_260,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_70,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,falsehood),C))),
inference(resolve,[status(thm)],[c_260,c_65]) ).
cnf(c_261,plain,
( is_a_theorem(implies(implies(A,falsehood),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_70]) ).
cnf(c_252,plain,
is_a_theorem(implies(implies(implies(A,B),falsehood),A)),
inference(resolve,[status(thm)],[c_261,c_4]) ).
cnf(c_253,plain,
$false,
inference(resolve,[status(thm)],[c_252,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 21:47:39 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3525785 was started by sandbox2 on n026,
% 0.17/0.43 % Fri Sep 25 21:47:39 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.03) seconds.
% 0.17/0.50 % Length of proof is 15.
% 0.17/0.50 % Level of proof is 7.
% 0.17/0.50 % Maximum clause weight is 41.000.
% 0.17/0.50 % Given clauses 37.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------