%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL101-1 : 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 : n003.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 10 !; 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(p_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(equivalent(equivalent(VAR_1,VAR_2),equivalent(VAR_1,VAR_3)),equivalent(VAR_2,VAR_3)),VAR_0))),
file('theBenchmark.p',p_4) ).
cnf(c_3,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))),
inference(clausify,[status(thm)],[p_4]) ).
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_4,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_55,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_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),equivalent(equivalent(equivalent(D,E),equivalent(D,F)),equivalent(E,F)))),
inference(resolve,[status(thm)],[c_55,c_3]) ).
cnf(c_56,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_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(resolve,[status(thm)],[c_56,c_5]) ).
cnf(c_57,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_57,c_5]) ).
cnf(c_58,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_58,c_7]) ).
cnf(c_59,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)),equivalent(D,D))),
inference(resolve,[status(thm)],[c_59,c_8]) ).
cnf(c_60,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_60,c_10]) ).
cnf(c_61,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_14,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(C,D)))),
inference(resolve,[status(thm)],[c_61,c_11]) ).
cnf(c_62,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_14]) ).
cnf(c_30,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D))),
inference(resolve,[status(thm)],[c_62,c_3]) ).
cnf(c_63,plain,
( is_a_theorem(equivalent(equivalent(B,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_30]) ).
cnf(c_53,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(resolve,[status(thm)],[c_63,c_30]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL101-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 21:52:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1188452 was started by sandbox2 on n003,
% 0.11/0.36 % Fri Sep 25 21:52:39 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 14.
% 0.13/0.38 % Level of proof is 10.
% 0.13/0.38 % Maximum clause weight is 99.000.
% 0.13/0.38 % Given clauses 21.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------