%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL033-1 : 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 : n004.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 07:57:48 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 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 : 66 ( 35 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(c0_CAMeredith,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(implies(implies(VAR_0,VAR_1),implies(VAR_2,falsehood)),VAR_3),VAR_4),implies(implies(VAR_4,VAR_0),implies(VAR_2,VAR_0)))),
file('theBenchmark.p',c0_CAMeredith) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E),implies(implies(E,A),implies(C,A)))),
inference(clausify,[status(thm)],[c0_CAMeredith]) ).
fof(prove_c0_2,axiom,
~ is_a_theorem(implies(a,implies(b,a))),
file('theBenchmark.p',prove_c0_2) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(clausify,[status(thm)],[prove_c0_2]) ).
cnf(c_31,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,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_31,c_2]) ).
cnf(c_32,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,implies(falsehood,B)),C),implies(D,C))),
inference(resolve,[status(thm)],[c_32,c_4]) ).
cnf(c_33,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(A,implies(falsehood,B)),C)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(B,implies(falsehood,C)))),
inference(resolve,[status(thm)],[c_33,c_6]) ).
cnf(c_34,plain,
( is_a_theorem(implies(B,implies(falsehood,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(falsehood,B))),
inference(resolve,[status(thm)],[c_34,c_14]) ).
cnf(c_35,plain,
( is_a_theorem(implies(implies(E,A),implies(C,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(C,falsehood)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_26,plain,
is_a_theorem(implies(implies(implies(falsehood,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_35,c_18]) ).
cnf(c_36,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_4]) ).
cnf(c_28,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_36,c_26]) ).
cnf(c_37,plain,
( is_a_theorem(implies(B,implies(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_28]) ).
cnf(c_29,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_37,c_28]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_29,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL033-1 : 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 : n004.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 21:44:51 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 30652 was started by sandbox2 on n004,
% 0.17/0.43 % Fri Sep 25 21:44:51 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 11.
% 0.17/0.45 % Level of proof is 8.
% 0.17/0.45 % Maximum clause weight is 20.000.
% 0.17/0.45 % Given clauses 13.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------