%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL106-1 : 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 : n011.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 0.09s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 8 !; 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(q_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(VAR_1,VAR_2),equivalent(equivalent(VAR_2,VAR_1),VAR_0)))),
file('theBenchmark.p',q_1) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
inference(clausify,[status(thm)],[q_1]) ).
fof(q_4,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),equivalent(VAR_1,VAR_2))),
file('theBenchmark.p',q_4) ).
cnf(c_3,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(clausify,[status(thm)],[q_4]) ).
fof(prove_q_2,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
file('theBenchmark.p',prove_q_2) ).
cnf(c_4,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
inference(clausify,[status(thm)],[prove_q_2]) ).
cnf(c_26,plain,
( is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,A),equivalent(C,equivalent(equivalent(D,E),equivalent(equivalent(E,D),C)))))),
inference(resolve,[status(thm)],[c_26,c_2]) ).
cnf(c_27,plain,
( is_a_theorem(equivalent(equivalent(B,A),equivalent(C,equivalent(equivalent(D,E),equivalent(equivalent(E,D),C)))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B))),equivalent(D,equivalent(equivalent(E,F),equivalent(equivalent(F,E),D))))),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_28,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_19,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(equivalent(D,E),equivalent(equivalent(E,D),equivalent(B,C))))),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_29,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_24,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL106-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n011.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 21:51:19 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 2993207 was started by sandbox2 on n011,
% 0.09/5.38 % Fri Sep 25 21:51:19 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.40
% 0.09/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.40
% 0.09/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.40 % Length of proof is 9.
% 0.09/5.40 % Level of proof is 5.
% 0.09/5.40 % Maximum clause weight is 24.000.
% 0.09/5.40 % Given clauses 8.
% 0.09/5.40
% 0.09/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------