%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Mon Sep 7 11:11:04 AM UTC 2026
% Result : Unsatisfiable 2.51s 2.01s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 22 ( 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(b,type,
b: $i ).
tff(equivalent,type,
equivalent: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_35,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y)))),
file(unknown,unknown) ).
tff(f_32,axiom,
! [X,Y] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_38,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(X_3,equivalent(equivalent(Y_4,equivalent(X_3,Z_5)),equivalent(Z_5,Y_4)))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_8,plain,
! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(X_8,equivalent(equivalent(Y_9,equivalent(X_8,Z_10)),equivalent(Z_10,Y_9)))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(X_1)
| ~ is_a_theorem(equivalent(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_13,plain,
! [Y_11,X_12,Z_13] :
( is_a_theorem(equivalent(equivalent(Y_11,equivalent(X_12,Z_13)),equivalent(Z_13,Y_11)))
| ~ is_a_theorem(X_12) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_18,plain,
! [Z_14,Y_15,X_16] :
( is_a_theorem(equivalent(Z_14,Y_15))
| ~ is_a_theorem(equivalent(Y_15,equivalent(X_16,Z_14)))
| ~ is_a_theorem(X_16) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_36,plain,
! [Z_20,Y_21,X_22] :
( is_a_theorem(equivalent(equivalent(Z_20,Y_21),X_22))
| ~ is_a_theorem(equivalent(Y_21,equivalent(X_22,Z_20))) ),
inference(resolution,[status(thm)],[c_4,c_18]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_43,plain,
~ is_a_theorem(equivalent(c,equivalent(equivalent(b,equivalent(c,a)),equivalent(a,b)))),
inference(resolution,[status(thm)],[c_36,c_6]) ).
tff(c_51,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.36 % Computer : n019.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 4 14:00:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 2.51/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.51/2.01
% 2.51/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------