%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL081-1 : 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 : n027.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 11:11:12 AM UTC 2026
% Result : Unsatisfiable 4.91s 2.74s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 97 ( 97 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_38,axiom,
! [X,Y,Z,U] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_40,axiom,
~ is_a_theorem(implies(a,a)),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5,U_6] : is_a_theorem(implies(implies(implies(X_3,Y_4),Z_5),implies(implies(Z_5,X_3),implies(U_6,X_3)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_8,plain,
! [X_9,Y_10,Z_11,U_12] : is_a_theorem(implies(implies(implies(X_9,Y_10),Z_11),implies(implies(Z_11,X_9),implies(U_12,X_9)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(X_1)
| ~ is_a_theorem(implies(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_13,plain,
! [Z_13,X_14,U_15,Y_16] :
( is_a_theorem(implies(implies(Z_13,X_14),implies(U_15,X_14)))
| ~ is_a_theorem(implies(implies(X_14,Y_16),Z_13)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_17,plain,
! [X_18,U_20,U_17,Y_21,Z_19] : is_a_theorem(implies(implies(implies(implies(Z_19,X_18),implies(U_20,X_18)),implies(X_18,Y_21)),implies(U_17,implies(X_18,Y_21)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_12,plain,
! [Z_11,X_9,U_12,Y_10] :
( is_a_theorem(implies(implies(Z_11,X_9),implies(U_12,X_9)))
| ~ is_a_theorem(implies(implies(X_9,Y_10),Z_11)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_119,plain,
! [X_51,U_50,Z_53,Y_48,U_49,U_52] : is_a_theorem(implies(implies(implies(U_52,implies(X_51,Y_48)),implies(implies(Z_53,X_51),implies(U_49,X_51))),implies(U_50,implies(implies(Z_53,X_51),implies(U_49,X_51))))),
inference(resolution,[status(thm)],[c_17,c_12]) ).
tff(c_24,plain,
! [X_18,U_20,U_17,Y_21,Z_19] :
( is_a_theorem(implies(U_17,implies(X_18,Y_21)))
| ~ is_a_theorem(implies(implies(implies(Z_19,X_18),implies(U_20,X_18)),implies(X_18,Y_21))) ),
inference(resolution,[status(thm)],[c_17,c_2]) ).
tff(c_131,plain,
! [U_54,U_55,Z_56] : is_a_theorem(implies(U_54,implies(implies(U_55,U_55),implies(implies(Z_56,U_55),implies(U_55,U_55))))),
inference(resolution,[status(thm)],[c_119,c_24]) ).
tff(c_149,plain,
! [U_55,Z_56,U_54] :
( is_a_theorem(implies(implies(U_55,U_55),implies(implies(Z_56,U_55),implies(U_55,U_55))))
| ~ is_a_theorem(U_54) ),
inference(resolution,[status(thm)],[c_131,c_2]) ).
tff(c_150,plain,
! [U_54] : ~ is_a_theorem(U_54),
inference(splitLeft,[status(thm)],[c_149]) ).
tff(c_128,plain,
! [U_17,U_49,Z_53] : is_a_theorem(implies(U_17,implies(implies(U_49,U_49),implies(implies(Z_53,U_49),implies(U_49,U_49))))),
inference(resolution,[status(thm)],[c_119,c_24]) ).
tff(c_165,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_150,c_128]) ).
tff(c_202,plain,
! [U_61,Z_62] : is_a_theorem(implies(implies(U_61,U_61),implies(implies(Z_62,U_61),implies(U_61,U_61)))),
inference(splitRight,[status(thm)],[c_149]) ).
tff(c_208,plain,
! [Z_62,U_61,U_12] : is_a_theorem(implies(implies(implies(implies(Z_62,U_61),implies(U_61,U_61)),U_61),implies(U_12,U_61))),
inference(resolution,[status(thm)],[c_202,c_12]) ).
tff(c_16,plain,
! [X_3,Z_5,U_15,U_6,Y_4] : is_a_theorem(implies(implies(implies(implies(Z_5,X_3),implies(U_6,X_3)),implies(X_3,Y_4)),implies(U_15,implies(X_3,Y_4)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_526,plain,
! [U_101,Y_102,U_103,X_105,Z_106,U_104] :
( is_a_theorem(implies(U_101,implies(implies(Z_106,X_105),implies(U_104,X_105))))
| ~ is_a_theorem(implies(implies(U_103,implies(X_105,Y_102)),implies(implies(Z_106,X_105),implies(U_104,X_105)))) ),
inference(resolution,[status(thm)],[c_119,c_2]) ).
tff(c_578,plain,
! [U_107,Z_108,Y_109] : is_a_theorem(implies(U_107,implies(implies(Z_108,Y_109),implies(Y_109,Y_109)))),
inference(resolution,[status(thm)],[c_16,c_526]) ).
tff(c_616,plain,
! [Z_108,Y_109,U_107] :
( is_a_theorem(implies(implies(Z_108,Y_109),implies(Y_109,Y_109)))
| ~ is_a_theorem(U_107) ),
inference(resolution,[status(thm)],[c_578,c_2]) ).
tff(c_618,plain,
! [U_107] : ~ is_a_theorem(U_107),
inference(splitLeft,[status(thm)],[c_616]) ).
tff(c_576,plain,
! [U_101,X_3,Y_102,U_6] : is_a_theorem(implies(U_101,implies(implies(implies(X_3,Y_102),X_3),implies(U_6,X_3)))),
inference(resolution,[status(thm)],[c_4,c_526]) ).
tff(c_687,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_618,c_576]) ).
tff(c_689,plain,
! [Z_114,Y_115] : is_a_theorem(implies(implies(Z_114,Y_115),implies(Y_115,Y_115))),
inference(splitRight,[status(thm)],[c_616]) ).
tff(c_710,plain,
! [Y_116,Z_117] :
( is_a_theorem(implies(Y_116,Y_116))
| ~ is_a_theorem(implies(Z_117,Y_116)) ),
inference(resolution,[status(thm)],[c_689,c_2]) ).
tff(c_768,plain,
! [U_12,U_61] : is_a_theorem(implies(implies(U_12,U_61),implies(U_12,U_61))),
inference(resolution,[status(thm)],[c_208,c_710]) ).
tff(c_853,plain,
! [Y_124,Z_125,U_126] : is_a_theorem(implies(implies(implies(Y_124,Y_124),Z_125),implies(U_126,Z_125))),
inference(resolution,[status(thm)],[c_689,c_12]) ).
tff(c_1019,plain,
! [U_134,Z_135,Y_136] :
( is_a_theorem(implies(U_134,Z_135))
| ~ is_a_theorem(implies(implies(Y_136,Y_136),Z_135)) ),
inference(resolution,[status(thm)],[c_853,c_2]) ).
tff(c_1084,plain,
! [U_137,U_138] : is_a_theorem(implies(U_137,implies(U_138,U_138))),
inference(resolution,[status(thm)],[c_768,c_1019]) ).
tff(c_1127,plain,
! [U_138,U_137] :
( is_a_theorem(implies(U_138,U_138))
| ~ is_a_theorem(U_137) ),
inference(resolution,[status(thm)],[c_1084,c_2]) ).
tff(c_1128,plain,
! [U_137] : ~ is_a_theorem(U_137),
inference(splitLeft,[status(thm)],[c_1127]) ).
tff(c_1069,plain,
! [U_134,U_61] : is_a_theorem(implies(U_134,implies(U_61,U_61))),
inference(resolution,[status(thm)],[c_768,c_1019]) ).
tff(c_1156,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1128,c_1069]) ).
tff(c_1157,plain,
! [U_138] : is_a_theorem(implies(U_138,U_138)),
inference(splitRight,[status(thm)],[c_1127]) ).
tff(c_6,plain,
~ is_a_theorem(implies(a,a)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_1164,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1157,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL081-1 : 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
% 0.11/0.36 % Computer : n027.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 : Sat Sep 5 13:00:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 4.91/2.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/2.75
% 4.91/2.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------