%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL097-1 : 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 : n005.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 07:57:58 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(equivalent(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(lg_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),equivalent(VAR_1,VAR_2)),VAR_3),VAR_3)),
file('theBenchmark.p',lg_2) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),D),D)),
inference(clausify,[status(thm)],[lg_2]) ).
fof(lg_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),VAR_3),equivalent(equivalent(VAR_1,VAR_2),VAR_3)),VAR_4),VAR_4)),
file('theBenchmark.p',lg_3) ).
cnf(c_3,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E)),
inference(clausify,[status(thm)],[lg_3]) ).
fof(prove_lg_4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('theBenchmark.p',prove_lg_4) ).
cnf(c_4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(clausify,[status(thm)],[prove_lg_4]) ).
cnf(c_287,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(resolve,[status(thm)],[c_287,c_3]) ).
cnf(c_288,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_288,c_2]) ).
cnf(c_289,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),equivalent(C,E)),A),equivalent(equivalent(D,E),B)))),
inference(resolve,[status(thm)],[c_289,c_5]) ).
cnf(c_290,plain,
( is_a_theorem(equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_290,c_6]) ).
cnf(c_291,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E)),equivalent(A,equivalent(equivalent(C,D),E)))),
inference(resolve,[status(thm)],[c_291,c_11]) ).
cnf(c_292,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(C,D),E)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,D)),E))) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_285,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),D),equivalent(equivalent(equivalent(A,E),C),equivalent(equivalent(B,E),D)))),
inference(resolve,[status(thm)],[c_292,c_8]) ).
cnf(c_286,plain,
$false,
inference(resolve,[status(thm)],[c_285,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL097-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 21:50:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 332142 was started by sandbox2 on n005,
% 0.17/0.44 % Fri Sep 25 21:50:32 2026
% 0.17/0.44 % 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 (+ 0.02) seconds.
% 0.17/0.50 % Length of proof is 11.
% 0.17/0.50 % Level of proof is 5.
% 0.17/0.50 % Maximum clause weight is 95.000.
% 0.17/0.50 % Given clauses 33.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------