%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL120-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 11:11:18 AM UTC 2026
% Result : Unsatisfiable 7.62s 3.17s
% Output : CNFRefutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 42 ( 42 !; 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_34,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Z,Y))),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X,Y] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_37,axiom,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(equivalent(equivalent(X_3,Y_4),equivalent(X_3,Z_5)),equivalent(Z_5,Y_4))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_8,plain,
! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(equivalent(equivalent(X_8,Y_9),equivalent(X_8,Z_10)),equivalent(Z_10,Y_9))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
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_31]) ).
tff(c_13,plain,
! [Z_11,Y_12,X_13] :
( is_a_theorem(equivalent(Z_11,Y_12))
| ~ is_a_theorem(equivalent(equivalent(X_13,Y_12),equivalent(X_13,Z_11))) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_18,plain,
! [Y_4,X_3] : is_a_theorem(equivalent(Y_4,equivalent(X_3,equivalent(X_3,Y_4)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_19,plain,
! [Y_14,X_15] : is_a_theorem(equivalent(Y_14,equivalent(X_15,equivalent(X_15,Y_14)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_40,plain,
! [X_18,Y_19] :
( is_a_theorem(equivalent(X_18,equivalent(X_18,Y_19)))
| ~ is_a_theorem(Y_19) ),
inference(resolution,[status(thm)],[c_19,c_2]) ).
tff(c_66,plain,
! [X_23,Y_24] :
( is_a_theorem(equivalent(X_23,Y_24))
| ~ is_a_theorem(X_23)
| ~ is_a_theorem(Y_24) ),
inference(resolution,[status(thm)],[c_40,c_2]) ).
tff(c_12,plain,
! [Z_10,Y_9,X_8] :
( is_a_theorem(equivalent(Z_10,Y_9))
| ~ is_a_theorem(equivalent(equivalent(X_8,Y_9),equivalent(X_8,Z_10))) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_84,plain,
! [Z_25,Y_26,X_27] :
( is_a_theorem(equivalent(Z_25,Y_26))
| ~ is_a_theorem(equivalent(X_27,Y_26))
| ~ is_a_theorem(equivalent(X_27,Z_25)) ),
inference(resolution,[status(thm)],[c_66,c_12]) ).
tff(c_309,plain,
! [Z_46,X_47,Y_48] :
( is_a_theorem(equivalent(Z_46,equivalent(X_47,equivalent(X_47,Y_48))))
| ~ is_a_theorem(equivalent(Y_48,Z_46)) ),
inference(resolution,[status(thm)],[c_18,c_84]) ).
tff(c_1373,plain,
! [X_102,Y_103,Y_104] :
( is_a_theorem(equivalent(equivalent(X_102,Y_103),Y_104))
| ~ is_a_theorem(equivalent(Y_103,equivalent(X_102,Y_104))) ),
inference(resolution,[status(thm)],[c_309,c_12]) ).
tff(c_2891,plain,
! [Z_159,Y_160,X_161] :
( is_a_theorem(equivalent(Z_159,Y_160))
| ~ is_a_theorem(equivalent(Y_160,equivalent(X_161,equivalent(X_161,Z_159)))) ),
inference(resolution,[status(thm)],[c_1373,c_12]) ).
tff(c_3029,plain,
! [Z_159,X_3,Z_5] : is_a_theorem(equivalent(Z_159,equivalent(equivalent(X_3,equivalent(Z_5,Z_159)),equivalent(X_3,Z_5)))),
inference(resolution,[status(thm)],[c_4,c_2891]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_4752,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3029,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 20:41:43 UTC 2026
% 0.11/0.38 % CPUTime :
% 7.62/3.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.62/3.18
% 7.62/3.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------