%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL108-1 : 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 : n020.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 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% 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 : 8 ( 2 avg)
% Maximal term depth : 8 ( 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 : 105 ( 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(lg_27_1690,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),VAR_2),equivalent(equivalent(VAR_3,VAR_4),equivalent(equivalent(equivalent(VAR_5,VAR_4),equivalent(VAR_5,VAR_3)),VAR_6))),equivalent(VAR_2,equivalent(equivalent(VAR_1,VAR_0),VAR_6)))),
file('theBenchmark.p',lg_27_1690) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),V6))),equivalent(C,equivalent(equivalent(B,A),V6)))),
inference(clausify,[status(thm)],[lg_27_1690]) ).
fof(prove_q_3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
file('theBenchmark.p',prove_q_3) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
inference(clausify,[status(thm)],[prove_q_3]) ).
cnf(c_28,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(B,A),V6)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),V6)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,B),equivalent(C,A)),D)),equivalent(equivalent(equivalent(E,F),equivalent(equivalent(V6,E),equivalent(V6,F))),D))),
inference(resolve,[status(thm)],[c_28,c_2]) ).
cnf(c_29,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(B,A),V6)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),V6)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(equivalent(equivalent(D,equivalent(equivalent(E,F),equivalent(E,V6))),equivalent(D,equivalent(F,V6))),V7)),equivalent(equivalent(B,C),V7))),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_30,plain,
( is_a_theorem(equivalent(equivalent(B,C),V7))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(equivalent(equivalent(D,equivalent(equivalent(E,F),equivalent(E,V6))),equivalent(D,equivalent(F,V6))),V7))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,D)),equivalent(B,equivalent(C,E)))),equivalent(A,equivalent(D,E))),F),F)),
inference(resolve,[status(thm)],[c_30,c_5]) ).
cnf(c_31,plain,
( is_a_theorem(F)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,D)),equivalent(B,equivalent(C,E)))),equivalent(A,equivalent(D,E))),F)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(D,equivalent(E,A)),equivalent(D,equivalent(E,equivalent(B,F))))),equivalent(C,F))),
inference(resolve,[status(thm)],[c_31,c_6]) ).
cnf(c_32,plain,
( is_a_theorem(F)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,D)),equivalent(B,equivalent(C,E)))),equivalent(A,equivalent(D,E))),F)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,D),equivalent(C,E)))),equivalent(A,equivalent(B,F))),equivalent(equivalent(D,E),F))),
inference(resolve,[status(thm)],[c_32,c_2]) ).
cnf(c_33,plain,
( is_a_theorem(equivalent(C,F))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(D,equivalent(E,A)),equivalent(D,equivalent(E,equivalent(B,F)))))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(equivalent(equivalent(D,B),equivalent(D,C)),E))),E)),
inference(resolve,[status(thm)],[c_33,c_4]) ).
cnf(c_34,plain,
( is_a_theorem(equivalent(equivalent(D,E),F))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,D),equivalent(C,E)))),equivalent(A,equivalent(B,F)))) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,A),C)),C)),
inference(resolve,[status(thm)],[c_34,c_20]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL108-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n020.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Fri Sep 25 21:52:18 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.42 % Process 3874768 was started by sandbox on n020,
% 0.09/0.42 % Fri Sep 25 21:52:18 2026
% 0.09/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.42
% 0.09/0.42 % From the command line: assign(max_seconds, 300).
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45
% 0.09/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.45 % Length of proof is 11.
% 0.09/0.45 % Level of proof is 7.
% 0.09/0.45 % Maximum clause weight is 72.000.
% 0.09/0.45 % Given clauses 10.
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------