%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL023-1 : 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 : n015.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 11:11:05 AM UTC 2026
% Result : Unsatisfiable 5.88s 3.12s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 29 ~; 26 |; 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 : 89 ( 89 !; 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(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
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(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,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_34]) ).
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_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(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_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_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_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_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_191,plain,
! [X_48,Y_49,Z_50] :
( is_a_theorem(equivalent(X_48,Y_49))
| ~ is_a_theorem(equivalent(equivalent(Z_50,equivalent(X_48,Z_50)),Y_49)) ),
inference(resolution,[status(thm)],[c_164,c_73]) ).
tff(c_217,plain,
! [X_51,Z_52] : is_a_theorem(equivalent(X_51,equivalent(Z_52,equivalent(X_51,Z_52)))),
inference(resolution,[status(thm)],[c_82,c_191]) ).
tff(c_238,plain,
! [Z_52,X_51] :
( is_a_theorem(equivalent(Z_52,equivalent(X_51,Z_52)))
| ~ is_a_theorem(X_51) ),
inference(resolution,[status(thm)],[c_217,c_2]) ).
tff(c_302,plain,
! [X_57,X_58,Z_59] :
( is_a_theorem(equivalent(X_57,equivalent(X_58,Z_59)))
| ~ is_a_theorem(equivalent(X_58,equivalent(X_57,Z_59))) ),
inference(resolution,[status(thm)],[c_12,c_191]) ).
tff(c_324,plain,
! [X_51,Z_52] :
( is_a_theorem(equivalent(X_51,equivalent(Z_52,Z_52)))
| ~ is_a_theorem(X_51) ),
inference(resolution,[status(thm)],[c_238,c_302]) ).
tff(c_363,plain,
! [X_62,Z_63] : is_a_theorem(equivalent(X_62,equivalent(equivalent(X_62,Z_63),Z_63))),
inference(resolution,[status(thm)],[c_82,c_302]) ).
tff(c_614,plain,
! [Z_76,Y_77] : is_a_theorem(equivalent(equivalent(equivalent(Z_76,Y_77),Z_76),Y_77)),
inference(resolution,[status(thm)],[c_363,c_73]) ).
tff(c_436,plain,
! [X_66,Z_67] :
( is_a_theorem(equivalent(equivalent(X_66,Z_67),Z_67))
| ~ is_a_theorem(X_66) ),
inference(resolution,[status(thm)],[c_363,c_2]) ).
tff(c_472,plain,
! [Z_67,X_66] :
( is_a_theorem(Z_67)
| ~ is_a_theorem(equivalent(X_66,Z_67))
| ~ is_a_theorem(X_66) ),
inference(resolution,[status(thm)],[c_436,c_2]) ).
tff(c_738,plain,
! [Y_85,Z_86] :
( is_a_theorem(Y_85)
| ~ is_a_theorem(equivalent(equivalent(Z_86,Y_85),Z_86)) ),
inference(resolution,[status(thm)],[c_614,c_472]) ).
tff(c_770,plain,
! [Y_87,Z_88] :
( is_a_theorem(Y_87)
| ~ is_a_theorem(equivalent(equivalent(Z_88,Z_88),Y_87)) ),
inference(resolution,[status(thm)],[c_324,c_738]) ).
tff(c_1206,plain,
! [Z_103,Y_104] : is_a_theorem(equivalent(equivalent(Z_103,Y_104),equivalent(Y_104,Z_103))),
inference(resolution,[status(thm)],[c_4,c_770]) ).
tff(c_215,plain,
! [X_48,X_8,Z_10] :
( is_a_theorem(equivalent(X_48,equivalent(X_8,Z_10)))
| ~ is_a_theorem(equivalent(X_8,equivalent(X_48,Z_10))) ),
inference(resolution,[status(thm)],[c_12,c_191]) ).
tff(c_1901,plain,
! [Y_126,Z_127] : is_a_theorem(equivalent(Y_126,equivalent(equivalent(Z_127,Y_126),Z_127))),
inference(resolution,[status(thm)],[c_1206,c_215]) ).
tff(c_1956,plain,
! [Z_127,Y_28] : is_a_theorem(equivalent(equivalent(Z_127,equivalent(Z_127,Y_28)),Y_28)),
inference(resolution,[status(thm)],[c_1901,c_73]) ).
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_473,plain,
! [X_68,Y_69,Z_70,Y_71] :
( is_a_theorem(equivalent(equivalent(X_68,Y_69),equivalent(equivalent(X_68,Z_70),Y_71)))
| ~ is_a_theorem(equivalent(equivalent(Z_70,Y_69),Y_71)) ),
inference(resolution,[status(thm)],[c_4,c_25]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_510,plain,
~ is_a_theorem(equivalent(equivalent(b,equivalent(b,c)),c)),
inference(resolution,[status(thm)],[c_473,c_6]) ).
tff(c_2383,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1956,c_510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL023-1 : 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
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 5 18:44:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 5.88/3.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.22/3.13
% 6.22/3.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------