%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL023-1 : 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 07:57:46 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.71s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 73 ( 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(yql,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_2,VAR_1),equivalent(VAR_0,VAR_2)))),
file('theBenchmark.p',yql) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(clausify,[status(thm)],[yql]) ).
fof(prove_ec_2,axiom,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
file('theBenchmark.p',prove_ec_2) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
inference(clausify,[status(thm)],[prove_ec_2]) ).
cnf(c_460,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B))),equivalent(equivalent(D,C),A))),
inference(resolve,[status(thm)],[c_460,c_2]) ).
cnf(c_461,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(equivalent(D,B),equivalent(C,D))))),
inference(resolve,[status(thm)],[c_461,c_4]) ).
cnf(c_462,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_462,c_2]) ).
cnf(c_463,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(C,A),B))),
inference(resolve,[status(thm)],[c_463,c_5]) ).
cnf(c_464,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),A),B)),
inference(resolve,[status(thm)],[c_464,c_7]) ).
cnf(c_465,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_27,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,A)),B)),
inference(resolve,[status(thm)],[c_465,c_22]) ).
cnf(c_466,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_32,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_466,c_27]) ).
cnf(c_467,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_38,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_467,c_32]) ).
cnf(c_468,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_43,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,B),A))),
inference(resolve,[status(thm)],[c_468,c_38]) ).
cnf(c_469,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_38]) ).
cnf(c_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(B,C),A))),
inference(resolve,[status(thm)],[c_469,c_8]) ).
cnf(c_470,plain,
( is_a_theorem(equivalent(equivalent(C,B),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_458,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_470,c_46]) ).
cnf(c_459,plain,
$false,
inference(resolve,[status(thm)],[c_458,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.60 % Computer : n020.cluster.edu
% 0.08/0.60 % Model : x86_64 x86_64
% 0.08/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.60 % Memory : 8046.5625MB
% 0.08/0.60 % OS : Linux 6.8.0-71-generic
% 0.08/0.60 % CPULimit : 300
% 0.08/0.60 % WCLimit : 300
% 0.08/0.60 % DateTime : Fri Sep 25 21:45:04 UTC 2026
% 0.08/0.60 % CPUTime :
% 0.08/0.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.61 % Process 3852282 was started by sandbox on n020,
% 0.08/0.61 % Fri Sep 25 21:45:04 2026
% 0.08/0.61 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.61
% 0.08/0.61 % From the command line: assign(max_seconds, 300).
% 0.14/0.71
% 0.14/0.71 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.71
% 0.14/0.71 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.71 % Length of proof is 15.
% 0.14/0.71 % Level of proof is 10.
% 0.14/0.71 % Maximum clause weight is 71.000.
% 0.14/0.71 % Given clauses 36.
% 0.14/0.71
% 0.14/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------