%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL096-1 : 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 : n002.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 14.73s 2.32s
% Output : CNFRefutation 14.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 72 ( 0 sgn 16 !; 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(lg_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),VAR_2),VAR_3),equivalent(equivalent(equivalent(VAR_0,VAR_4),VAR_2),equivalent(equivalent(VAR_1,VAR_4),VAR_3)))),
file('theBenchmark.p',lg_4) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),D),equivalent(equivalent(equivalent(A,E),C),equivalent(equivalent(B,E),D)))),
inference(clausify,[status(thm)],[lg_4]) ).
fof(prove_lg_1,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
file('theBenchmark.p',prove_lg_1) ).
cnf(c_5,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(clausify,[status(thm)],[prove_lg_1]) ).
cnf(c_6520,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,E),C),equivalent(equivalent(B,E),D)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),E),F),equivalent(equivalent(equivalent(equivalent(B,C),D),E),F))),
inference(resolve,[status(thm)],[c_6520,c_3]) ).
cnf(c_6521,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,E),C),equivalent(equivalent(B,E),D)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),E),equivalent(equivalent(equivalent(B,C),D),E))),
inference(resolve,[status(thm)],[c_6521,c_2]) ).
cnf(c_6522,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),D),E),F))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),E),F)) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_92,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C))),E),E)),
inference(resolve,[status(thm)],[c_6522,c_3]) ).
cnf(c_6523,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,C),D),E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),E)) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_6518,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,B),A)),C),C)),
inference(resolve,[status(thm)],[c_6523,c_92]) ).
cnf(c_6519,plain,
$false,
inference(resolve,[status(thm)],[c_6518,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 21:53:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 68608 was started by sandbox2 on n002,
% 0.10/0.37 % Fri Sep 25 21:53:35 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 14.73/2.32
% 14.73/2.32 % SZS status Unsatisfiable for theBenchmark
% 14.73/2.32
% 14.73/2.32 % Proof 1 at 1.62 (+ 0.29) seconds.
% 14.73/2.32 % Length of proof is 10.
% 14.73/2.32 % Level of proof is 4.
% 14.73/2.32 % Maximum clause weight is 59.000.
% 14.73/2.32 % Given clauses 190.
% 14.73/2.32
% 14.73/2.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------