%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:58:02 AM UTC 2026
% Result : Unsatisfiable 0.03s 5.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 32 ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 5 !; 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(wo,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,equivalent(VAR_1,VAR_2)),equivalent(VAR_2,equivalent(VAR_1,VAR_0)))),
file('theBenchmark.p',wo) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,equivalent(B,A)))),
inference(clausify,[status(thm)],[wo]) ).
fof(prove_yqm,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
file('theBenchmark.p',prove_yqm) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))),
inference(clausify,[status(thm)],[prove_yqm]) ).
cnf(c_145,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(B,equivalent(A,C))))),
inference(resolve,[status(thm)],[c_145,c_2]) ).
cnf(c_146,plain,
( is_a_theorem(equivalent(C,equivalent(B,equivalent(A,C))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(C,D)),equivalent(equivalent(D,equivalent(C,B)),A)))),
inference(resolve,[status(thm)],[c_146,c_2]) ).
cnf(c_147,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),D),equivalent(equivalent(C,equivalent(B,A)),D))),
inference(resolve,[status(thm)],[c_147,c_6]) ).
cnf(c_148,plain,
( is_a_theorem(equivalent(equivalent(C,equivalent(B,A)),D))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_25,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(D,equivalent(equivalent(B,A),equivalent(C,D))))),
inference(resolve,[status(thm)],[c_148,c_4]) ).
cnf(c_149,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_47,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,D)),equivalent(D,equivalent(B,equivalent(A,C))))),
inference(resolve,[status(thm)],[c_149,c_25]) ).
cnf(c_150,plain,
( is_a_theorem(equivalent(D,equivalent(B,equivalent(A,C))))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_58,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_150,c_2]) ).
cnf(c_151,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_143,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(C,A)))),
inference(resolve,[status(thm)],[c_151,c_58]) ).
cnf(c_144,plain,
$false,
inference(resolve,[status(thm)],[c_143,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL118-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.31 % Computer : n012.cluster.edu
% 0.03/5.31 % Model : x86_64 x86_64
% 0.03/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.31 % Memory : 8046.5625MB
% 0.03/5.31 % OS : Linux 6.8.0-71-generic
% 0.03/5.31 % CPULimit : 300
% 0.03/5.31 % WCLimit : 300
% 0.03/5.31 % DateTime : Fri Sep 25 21:53:14 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/5.31 % Process 3140502 was started by sandbox on n012,
% 0.03/5.31 % Fri Sep 25 21:53:14 2026
% 0.03/5.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/5.31
% 0.03/5.31 % From the command line: assign(max_seconds, 300).
% 0.03/5.32
% 0.03/5.32 % SZS status Unsatisfiable for theBenchmark
% 0.03/5.32
% 0.03/5.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/5.32 % Length of proof is 11.
% 0.03/5.32 % Level of proof is 8.
% 0.03/5.32 % Maximum clause weight is 46.000.
% 0.03/5.32 % Given clauses 16.
% 0.03/5.32
% 0.03/5.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------