%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL104-1 : 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 : n015.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 07:57:59 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 34 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 9 !; 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(p_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(equivalent(equivalent(VAR_1,VAR_2),equivalent(VAR_1,VAR_3)),equivalent(VAR_2,VAR_3)),VAR_0))),
file('theBenchmark.p',p_4) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))),
inference(clausify,[status(thm)],[p_4]) ).
fof(q_3,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_1,VAR_0),VAR_2)),VAR_2)),
file('theBenchmark.p',q_3) ).
cnf(c_3,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C)),
inference(clausify,[status(thm)],[q_3]) ).
fof(prove_p_1,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('theBenchmark.p',prove_p_1) ).
cnf(c_4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(clausify,[status(thm)],[prove_p_1]) ).
cnf(c_155,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_155,c_2]) ).
cnf(c_156,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(A,equivalent(equivalent(D,B),equivalent(D,C))))),
inference(resolve,[status(thm)],[c_156,c_7]) ).
cnf(c_157,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),D))),equivalent(A,D))),
inference(resolve,[status(thm)],[c_157,c_3]) ).
cnf(c_158,plain,
( is_a_theorem(equivalent(A,D))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),D)))) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(resolve,[status(thm)],[c_158,c_12]) ).
cnf(c_159,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_62,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(C,D)))),
inference(resolve,[status(thm)],[c_159,c_46]) ).
cnf(c_160,plain,
( is_a_theorem(equivalent(A,equivalent(C,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_62]) ).
cnf(c_80,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D))),
inference(resolve,[status(thm)],[c_160,c_2]) ).
cnf(c_161,plain,
( is_a_theorem(equivalent(equivalent(B,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_80]) ).
cnf(c_153,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(resolve,[status(thm)],[c_161,c_80]) ).
cnf(c_154,plain,
$false,
inference(resolve,[status(thm)],[c_153,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 21:54:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2352792 was started by sandbox2 on n015,
% 0.11/0.37 % Fri Sep 25 21:54:28 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 12.
% 0.11/0.39 % Level of proof is 7.
% 0.11/0.39 % Maximum clause weight is 46.000.
% 0.11/0.39 % Given clauses 26.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------