%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL035-1 : 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 07:57:48 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 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 : 48 ( 26 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_4,axiom,
~ is_a_theorem(implies(falsehood,a)),
file('theBenchmark.p',prove_c0_4) ).
cnf(c_3,plain,
~ is_a_theorem(implies(falsehood,a)),
inference(clausify,[status(thm)],[prove_c0_4]) ).
cnf(c_27,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_27,c_2]) ).
cnf(c_28,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_28,c_4]) ).
cnf(c_29,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_29,c_6]) ).
cnf(c_30,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_30,c_14]) ).
cnf(c_31,plain,
( is_a_theorem(implies(falsehood,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_25,plain,
is_a_theorem(implies(falsehood,A)),
inference(resolve,[status(thm)],[c_31,c_18]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 21:50:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 131171 was started by sandbox2 on n001,
% 0.09/0.35 % Fri Sep 25 21:50:55 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.14/0.37
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.37
% 0.14/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.37 % Length of proof is 9.
% 0.14/0.37 % Level of proof is 6.
% 0.14/0.37 % Maximum clause weight is 20.000.
% 0.14/0.37 % Given clauses 10.
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------