%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL009-1 : 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 : n001.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 5.37s 3.00s
% Output : CNFRefutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 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(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(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
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_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_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_18,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_32,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_18]) ).
tff(c_40,plain,
! [X_22,Z_24,Y_9,Y_23] :
( is_a_theorem(equivalent(equivalent(equivalent(X_22,Z_24),Y_9),equivalent(X_22,Y_23)))
| ~ is_a_theorem(equivalent(equivalent(Z_24,Y_23),Y_9)) ),
inference(resolution,[status(thm)],[c_12,c_32]) ).
tff(c_41,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_32]) ).
tff(c_42,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_32]) ).
tff(c_24,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_18]) ).
tff(c_58,plain,
! [Z_27,Y_28,X_29] : is_a_theorem(equivalent(equivalent(equivalent(Z_27,Y_28),equivalent(X_29,Z_27)),equivalent(X_29,Y_28))),
inference(resolution,[status(thm)],[c_42,c_24]) ).
tff(c_74,plain,
! [X_30,Y_31,Z_32] :
( is_a_theorem(equivalent(X_30,Y_31))
| ~ is_a_theorem(equivalent(equivalent(Z_32,Y_31),equivalent(X_30,Z_32))) ),
inference(resolution,[status(thm)],[c_58,c_2]) ).
tff(c_82,plain,
! [Y_4] : is_a_theorem(equivalent(Y_4,Y_4)),
inference(resolution,[status(thm)],[c_41,c_74]) ).
tff(c_25,plain,
! [X_17,Z_18,Y_19,X_20] :
( is_a_theorem(equivalent(X_17,equivalent(Z_18,Y_19)))
| ~ is_a_theorem(equivalent(X_17,equivalent(X_20,Z_18)))
| ~ is_a_theorem(equivalent(X_20,Y_19)) ),
inference(resolution,[status(thm)],[c_12,c_18]) ).
tff(c_316,plain,
! [X_57,Y_58,Z_59,Y_60] :
( is_a_theorem(equivalent(equivalent(X_57,Y_58),equivalent(equivalent(X_57,Z_59),Y_60)))
| ~ is_a_theorem(equivalent(equivalent(Z_59,Y_58),Y_60)) ),
inference(resolution,[status(thm)],[c_4,c_25]) ).
tff(c_73,plain,
! [X_29,Y_28,Z_27] :
( is_a_theorem(equivalent(X_29,Y_28))
| ~ is_a_theorem(equivalent(equivalent(Z_27,Y_28),equivalent(X_29,Z_27))) ),
inference(resolution,[status(thm)],[c_58,c_2]) ).
tff(c_348,plain,
! [Y_61,Z_62,Y_63] :
( is_a_theorem(equivalent(equivalent(Y_61,Z_62),Y_63))
| ~ is_a_theorem(equivalent(equivalent(Z_62,Y_63),Y_61)) ),
inference(resolution,[status(thm)],[c_316,c_73]) ).
tff(c_383,plain,
! [Z_64,Y_65] : is_a_theorem(equivalent(equivalent(equivalent(Z_64,Y_65),Z_64),Y_65)),
inference(resolution,[status(thm)],[c_82,c_348]) ).
tff(c_446,plain,
! [Y_68,Z_69] :
( is_a_theorem(Y_68)
| ~ is_a_theorem(equivalent(equivalent(Z_69,Y_68),Z_69)) ),
inference(resolution,[status(thm)],[c_383,c_2]) ).
tff(c_548,plain,
! [Y_74,Y_75] :
( is_a_theorem(Y_74)
| ~ is_a_theorem(equivalent(equivalent(Y_75,Y_75),Y_74)) ),
inference(resolution,[status(thm)],[c_40,c_446]) ).
tff(c_641,plain,
! [Z_78,Y_79] : is_a_theorem(equivalent(equivalent(Z_78,Y_79),equivalent(Y_79,Z_78))),
inference(resolution,[status(thm)],[c_4,c_548]) ).
tff(c_343,plain,
! [Y_60,Z_59,Y_58] :
( is_a_theorem(equivalent(equivalent(Y_60,Z_59),Y_58))
| ~ is_a_theorem(equivalent(equivalent(Z_59,Y_58),Y_60)) ),
inference(resolution,[status(thm)],[c_316,c_73]) ).
tff(c_2037,plain,
! [Y_129,Z_130] : is_a_theorem(equivalent(equivalent(equivalent(Y_129,Z_130),Z_130),Y_129)),
inference(resolution,[status(thm)],[c_641,c_343]) ).
tff(c_2091,plain,
! [Y_129,Z_130] : is_a_theorem(equivalent(equivalent(Y_129,equivalent(Y_129,Z_130)),Z_130)),
inference(resolution,[status(thm)],[c_2037,c_343]) ).
tff(c_164,plain,
! [X_44,Z_45,Y_46,Y_47] :
( is_a_theorem(equivalent(equivalent(equivalent(X_44,Z_45),Y_46),equivalent(X_44,Y_47)))
| ~ is_a_theorem(equivalent(equivalent(Z_45,Y_47),Y_46)) ),
inference(resolution,[status(thm)],[c_12,c_32]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_193,plain,
~ is_a_theorem(equivalent(equivalent(b,equivalent(b,c)),c)),
inference(resolution,[status(thm)],[c_164,c_6]) ).
tff(c_2162,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2091,c_193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : 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
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 03:05:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 5.37/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.37/3.01
% 5.37/3.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------