%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL103-1 : 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 : n014.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 15.53s 2.44s
% Output : CNFRefutation 15.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 23 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 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 : 144 ( 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_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),VAR_2),equivalent(equivalent(VAR_3,VAR_1),equivalent(equivalent(VAR_0,VAR_3),VAR_2)))),
file('theBenchmark.p',p_1) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(clausify,[status(thm)],[p_1]) ).
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_lg_2,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(b,c)),e),e)),
file('theBenchmark.p',prove_lg_2) ).
cnf(c_4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(b,c)),e),e)),
inference(clausify,[status(thm)],[prove_lg_2]) ).
cnf(c_3204,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_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,D),A),equivalent(equivalent(E,D),equivalent(equivalent(C,E),B))))),
inference(resolve,[status(thm)],[c_3204,c_2]) ).
cnf(c_3205,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_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),D)),equivalent(equivalent(equivalent(C,B),A),D))),
inference(resolve,[status(thm)],[c_3205,c_3]) ).
cnf(c_3206,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_3206,c_5]) ).
cnf(c_3207,plain,
( is_a_theorem(equivalent(equivalent(equivalent(C,B),A),D))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),D))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(A,equivalent(equivalent(C,B),D))),D)),
inference(resolve,[status(thm)],[c_3207,c_6]) ).
cnf(c_3208,plain,
( is_a_theorem(equivalent(equivalent(equivalent(C,B),A),D))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),D))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),D)),equivalent(equivalent(C,B),D))),
inference(resolve,[status(thm)],[c_3208,c_2]) ).
cnf(c_3209,plain,
( is_a_theorem(equivalent(equivalent(equivalent(C,B),A),D))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),D))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(resolve,[status(thm)],[c_3209,c_7]) ).
cnf(c_3210,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_19,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),D)),equivalent(A,equivalent(equivalent(E,C),equivalent(equivalent(B,E),D))))),
inference(resolve,[status(thm)],[c_3210,c_2]) ).
cnf(c_3211,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_2]) ).
cnf(c_23,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(equivalent(B,D),A),equivalent(D,C)))),
inference(resolve,[status(thm)],[c_3211,c_14]) ).
cnf(c_3212,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_24,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,B),A))),
inference(resolve,[status(thm)],[c_3212,c_2]) ).
cnf(c_3213,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_2]) ).
cnf(c_53,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,D),E))),equivalent(equivalent(equivalent(B,equivalent(D,C)),A),E))),
inference(resolve,[status(thm)],[c_3213,c_8]) ).
cnf(c_3214,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_122,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(D,B),E))),equivalent(A,equivalent(equivalent(D,C),E)))),
inference(resolve,[status(thm)],[c_3214,c_12]) ).
cnf(c_3215,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(E,C),equivalent(equivalent(B,E),D))))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),D))) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_381,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
inference(resolve,[status(thm)],[c_3215,c_24]) ).
cnf(c_3216,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,D),A),equivalent(D,C)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_23]) ).
cnf(c_607,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),D),equivalent(C,equivalent(equivalent(B,A),D)))),
inference(resolve,[status(thm)],[c_3216,c_381]) ).
cnf(c_3217,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(D,C),E)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(D,B),E)))) ),
inference(resolve,[status(thm)],[c_1,c_122]) ).
cnf(c_2680,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D))),
inference(resolve,[status(thm)],[c_3217,c_607]) ).
cnf(c_3218,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(B,A),D)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_607]) ).
cnf(c_2916,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(equivalent(D,C),A)))),
inference(resolve,[status(thm)],[c_3218,c_2680]) ).
cnf(c_3219,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(D,C)),A),E))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,D),E)))) ),
inference(resolve,[status(thm)],[c_1,c_53]) ).
cnf(c_3202,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),D),D)),
inference(resolve,[status(thm)],[c_3219,c_2916]) ).
cnf(c_3203,plain,
$false,
inference(resolve,[status(thm)],[c_3202,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL103-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 21:51:17 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1186088 was started by sandbox2 on n014,
% 0.16/0.43 % Fri Sep 25 21:51:17 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 15.53/2.44
% 15.53/2.44 % SZS status Unsatisfiable for theBenchmark
% 15.53/2.44
% 15.53/2.44 % Proof 1 at 1.28 (+ 0.62) seconds.
% 15.53/2.44 % Length of proof is 21.
% 15.53/2.44 % Level of proof is 10.
% 15.53/2.44 % Maximum clause weight is 90.000.
% 15.53/2.44 % Given clauses 234.
% 15.53/2.44
% 15.53/2.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------