%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL008-1 : 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 : n026.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 3.30s 2.29s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > 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(f_35,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
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(a,b),equivalent(b,a))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(equivalent(X_3,Y_4),equivalent(equivalent(Z_5,Y_4),equivalent(X_3,Z_5)))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_8,plain,
! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(equivalent(X_8,Y_9),equivalent(equivalent(Z_10,Y_9),equivalent(X_8,Z_10)))),
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,
! [Z_11,Y_12,X_13] :
( is_a_theorem(equivalent(equivalent(Z_11,Y_12),equivalent(X_13,Z_11)))
| ~ is_a_theorem(equivalent(X_13,Y_12)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_22,plain,
! [X_14,Z_15,Y_16] :
( is_a_theorem(equivalent(X_14,Z_15))
| ~ is_a_theorem(equivalent(Z_15,Y_16))
| ~ is_a_theorem(equivalent(X_14,Y_16)) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_36,plain,
! [X_21,X_22,Y_23,Z_24] :
( is_a_theorem(equivalent(X_21,equivalent(X_22,Y_23)))
| ~ is_a_theorem(equivalent(X_21,equivalent(equivalent(Z_24,Y_23),equivalent(X_22,Z_24)))) ),
inference(resolution,[status(thm)],[c_4,c_22]) ).
tff(c_45,plain,
! [X_3,Y_4] : is_a_theorem(equivalent(equivalent(X_3,Y_4),equivalent(X_3,Y_4))),
inference(resolution,[status(thm)],[c_4,c_36]) ).
tff(c_46,plain,
! [X_25,Y_26] : is_a_theorem(equivalent(equivalent(X_25,Y_26),equivalent(X_25,Y_26))),
inference(resolution,[status(thm)],[c_4,c_36]) ).
tff(c_28,plain,
! [X_14,X_3,Y_4,Z_5] :
( is_a_theorem(equivalent(X_14,equivalent(X_3,Y_4)))
| ~ is_a_theorem(equivalent(X_14,equivalent(equivalent(Z_5,Y_4),equivalent(X_3,Z_5)))) ),
inference(resolution,[status(thm)],[c_4,c_22]) ).
tff(c_98,plain,
! [Z_34,Y_35,X_36] : is_a_theorem(equivalent(equivalent(equivalent(Z_34,Y_35),equivalent(X_36,Z_34)),equivalent(X_36,Y_35))),
inference(resolution,[status(thm)],[c_46,c_28]) ).
tff(c_133,plain,
! [X_40,Y_41,Z_42] :
( is_a_theorem(equivalent(X_40,Y_41))
| ~ is_a_theorem(equivalent(equivalent(Z_42,Y_41),equivalent(X_40,Z_42))) ),
inference(resolution,[status(thm)],[c_98,c_2]) ).
tff(c_151,plain,
! [Y_4] : is_a_theorem(equivalent(Y_4,Y_4)),
inference(resolution,[status(thm)],[c_45,c_133]) ).
tff(c_12,plain,
! [Z_10,Y_9,X_8] :
( is_a_theorem(equivalent(equivalent(Z_10,Y_9),equivalent(X_8,Z_10)))
| ~ is_a_theorem(equivalent(X_8,Y_9)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_27,plain,
! [X_14,Z_10,Y_9,X_8] :
( is_a_theorem(equivalent(X_14,equivalent(Z_10,Y_9)))
| ~ is_a_theorem(equivalent(X_14,equivalent(X_8,Z_10)))
| ~ is_a_theorem(equivalent(X_8,Y_9)) ),
inference(resolution,[status(thm)],[c_12,c_22]) ).
tff(c_78,plain,
! [X_31,Y_32,Y_33] :
( is_a_theorem(equivalent(equivalent(X_31,Y_32),equivalent(Y_32,Y_33)))
| ~ is_a_theorem(equivalent(X_31,Y_33)) ),
inference(resolution,[status(thm)],[c_46,c_27]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_97,plain,
~ is_a_theorem(equivalent(a,a)),
inference(resolution,[status(thm)],[c_78,c_6]) ).
tff(c_182,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_151,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL008-1 : 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
% 0.11/0.36 % Computer : n026.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 4 22:45:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 3.30/2.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/2.30
% 3.30/2.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------