%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL102-1 : 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 : n019.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 3.87s 1.01s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 36 ( 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 : 7 ( 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 : 80 ( 0 sgn 12 !; 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_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),equivalent(VAR_1,VAR_2)),VAR_3),VAR_3)),
file('theBenchmark.p',lg_2) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),D),D)),
inference(clausify,[status(thm)],[lg_2]) ).
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_3,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
inference(clausify,[status(thm)],[q_1]) ).
fof(q_2,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_2,VAR_0),equivalent(VAR_2,VAR_1)))),
file('theBenchmark.p',q_2) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B)))),
inference(clausify,[status(thm)],[q_2]) ).
fof(prove_p_1,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('theBenchmark.p',prove_p_1) ).
cnf(c_5,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(clausify,[status(thm)],[prove_p_1]) ).
cnf(c_1281,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(C,D)))),
inference(resolve,[status(thm)],[c_1281,c_4]) ).
cnf(c_1282,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,equivalent(equivalent(C,D),equivalent(equivalent(D,C),B))))),
inference(resolve,[status(thm)],[c_1282,c_3]) ).
cnf(c_1283,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),E)),equivalent(A,E))),
inference(resolve,[status(thm)],[c_1283,c_2]) ).
cnf(c_1284,plain,
( is_a_theorem(equivalent(A,equivalent(C,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_57,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),D),equivalent(C,equivalent(equivalent(B,A),D)))),
inference(resolve,[status(thm)],[c_1284,c_11]) ).
cnf(c_1285,plain,
( is_a_theorem(equivalent(A,E))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),E))) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_110,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(D,A),equivalent(D,B)),C))),
inference(resolve,[status(thm)],[c_1285,c_4]) ).
cnf(c_1286,plain,
( is_a_theorem(equivalent(A,equivalent(C,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_321,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),D)),equivalent(equivalent(C,B),D))),
inference(resolve,[status(thm)],[c_1286,c_110]) ).
cnf(c_1287,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_57]) ).
cnf(c_1279,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(resolve,[status(thm)],[c_1287,c_321]) ).
cnf(c_1280,plain,
$false,
inference(resolve,[status(thm)],[c_1279,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL102-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n019.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 21:51:33 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 3814108 was started by sandbox on n019,
% 0.19/0.44 % Fri Sep 25 21:51:33 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 3.87/1.01
% 3.87/1.01 % SZS status Unsatisfiable for theBenchmark
% 3.87/1.01
% 3.87/1.01 % Proof 1 at 0.37 (+ 0.17) seconds.
% 3.87/1.01 % Length of proof is 13.
% 3.87/1.01 % Level of proof is 5.
% 3.87/1.01 % Maximum clause weight is 95.000.
% 3.87/1.01 % Given clauses 135.
% 3.87/1.01
% 3.87/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------