%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n020.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 11:11:38 AM UTC 2026
% Result : Unsatisfiable 94.83s 74.71s
% Output : CNFRefutation 94.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 128 ( 65 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 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; 1 con; 0-2 aty)
% Number of variables : 189 ( 189 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(not,type,
not: $i > $i ).
tff(p,type,
p: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_40,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
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_42,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file(unknown,unknown) ).
tff(f_44,axiom,
~ is_a_theorem(not(not(implies(p,p)))),
file(unknown,unknown) ).
tff(c_6,plain,
! [X_6] : is_a_theorem(implies(implies(not(X_6),X_6),X_6)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_23,plain,
! [X_15,Y_16,Z_17] : is_a_theorem(implies(implies(X_15,Y_16),implies(implies(Y_16,Z_17),implies(X_15,Z_17)))),
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_40,plain,
! [Y_21,Z_22,X_23] :
( is_a_theorem(implies(implies(Y_21,Z_22),implies(X_23,Z_22)))
| ~ is_a_theorem(implies(X_23,Y_21)) ),
inference(resolution,[status(thm)],[c_23,c_2]) ).
tff(c_45,plain,
! [X_24,Z_25,Y_26] :
( is_a_theorem(implies(X_24,Z_25))
| ~ is_a_theorem(implies(Y_26,Z_25))
| ~ is_a_theorem(implies(X_24,Y_26)) ),
inference(resolution,[status(thm)],[c_40,c_2]) ).
tff(c_83,plain,
! [X_33,X_34] :
( is_a_theorem(implies(X_33,X_34))
| ~ is_a_theorem(implies(X_33,implies(not(X_34),X_34))) ),
inference(resolution,[status(thm)],[c_6,c_45]) ).
tff(c_107,plain,
! [X_34] : is_a_theorem(implies(implies(not(implies(not(X_34),X_34)),implies(not(X_34),X_34)),X_34)),
inference(resolution,[status(thm)],[c_6,c_83]) ).
tff(c_8,plain,
! [X_7,Y_8] : is_a_theorem(implies(X_7,implies(not(X_7),Y_8))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_70,plain,
! [X_30,X_31,Y_32] :
( is_a_theorem(implies(X_30,implies(not(X_31),Y_32)))
| ~ is_a_theorem(implies(X_30,X_31)) ),
inference(resolution,[status(thm)],[c_8,c_45]) ).
tff(c_44,plain,
! [X_23,Z_22,Y_21] :
( is_a_theorem(implies(X_23,Z_22))
| ~ is_a_theorem(implies(Y_21,Z_22))
| ~ is_a_theorem(implies(X_23,Y_21)) ),
inference(resolution,[status(thm)],[c_40,c_2]) ).
tff(c_1094,plain,
! [X_111,X_112,Y_113,X_114] :
( is_a_theorem(implies(X_111,implies(not(X_112),Y_113)))
| ~ is_a_theorem(implies(X_111,X_114))
| ~ is_a_theorem(implies(X_114,X_112)) ),
inference(resolution,[status(thm)],[c_70,c_44]) ).
tff(c_1552,plain,
! [X_139,X_140,Y_141,Y_142] :
( is_a_theorem(implies(X_139,implies(not(X_140),Y_141)))
| ~ is_a_theorem(implies(implies(not(X_139),Y_142),X_140)) ),
inference(resolution,[status(thm)],[c_8,c_1094]) ).
tff(c_1605,plain,
! [X_34,Y_141] : is_a_theorem(implies(implies(not(X_34),X_34),implies(not(X_34),Y_141))),
inference(resolution,[status(thm)],[c_107,c_1552]) ).
tff(c_27,plain,
! [Y_16,Z_17,X_15] :
( is_a_theorem(implies(implies(Y_16,Z_17),implies(X_15,Z_17)))
| ~ is_a_theorem(implies(X_15,Y_16)) ),
inference(resolution,[status(thm)],[c_23,c_2]) ).
tff(c_216,plain,
! [X_47,Y_48,X_49] :
( is_a_theorem(implies(not(X_47),Y_48))
| ~ is_a_theorem(X_49)
| ~ is_a_theorem(implies(X_49,X_47)) ),
inference(resolution,[status(thm)],[c_70,c_2]) ).
tff(c_8856,plain,
! [X_441,Z_442,Y_443,Y_444] :
( is_a_theorem(implies(not(implies(X_441,Z_442)),Y_443))
| ~ is_a_theorem(implies(Y_444,Z_442))
| ~ is_a_theorem(implies(X_441,Y_444)) ),
inference(resolution,[status(thm)],[c_27,c_216]) ).
tff(c_9858,plain,
! [X_464,X_465,Y_466] :
( is_a_theorem(implies(not(implies(X_464,X_465)),Y_466))
| ~ is_a_theorem(implies(X_464,implies(not(X_465),X_465))) ),
inference(resolution,[status(thm)],[c_6,c_8856]) ).
tff(c_12492,plain,
! [Y_510,Y_511] : is_a_theorem(implies(not(implies(implies(not(Y_510),Y_510),Y_510)),Y_511)),
inference(resolution,[status(thm)],[c_1605,c_9858]) ).
tff(c_13,plain,
! [Y_12,X_13] :
( is_a_theorem(Y_12)
| ~ is_a_theorem(X_13)
| ~ is_a_theorem(implies(X_13,Y_12)) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_21,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(not(X_7),Y_8))
| ~ is_a_theorem(X_7) ),
inference(resolution,[status(thm)],[c_8,c_13]) ).
tff(c_127,plain,
! [X_36,X_37,Z_38,Y_39] :
( is_a_theorem(implies(X_36,implies(X_37,Z_38)))
| ~ is_a_theorem(implies(X_36,implies(Y_39,Z_38)))
| ~ is_a_theorem(implies(X_37,Y_39)) ),
inference(resolution,[status(thm)],[c_27,c_45]) ).
tff(c_194,plain,
! [X_44,X_45,Y_46] :
( is_a_theorem(implies(X_44,implies(X_45,Y_46)))
| ~ is_a_theorem(implies(X_45,not(X_44))) ),
inference(resolution,[status(thm)],[c_8,c_127]) ).
tff(c_244,plain,
! [X_50,X_51,Y_52] :
( is_a_theorem(implies(X_50,implies(not(X_51),Y_52)))
| ~ is_a_theorem(X_51) ),
inference(resolution,[status(thm)],[c_21,c_194]) ).
tff(c_59,plain,
! [X_24,X_6] :
( is_a_theorem(implies(X_24,X_6))
| ~ is_a_theorem(implies(X_24,implies(not(X_6),X_6))) ),
inference(resolution,[status(thm)],[c_6,c_45]) ).
tff(c_268,plain,
! [X_53,Y_54] :
( is_a_theorem(implies(X_53,Y_54))
| ~ is_a_theorem(Y_54) ),
inference(resolution,[status(thm)],[c_244,c_59]) ).
tff(c_296,plain,
! [X_53,X_6] :
( is_a_theorem(implies(X_53,X_6))
| ~ is_a_theorem(implies(not(X_6),X_6)) ),
inference(resolution,[status(thm)],[c_268,c_59]) ).
tff(c_12690,plain,
! [X_53,Y_510] : is_a_theorem(implies(X_53,implies(implies(not(Y_510),Y_510),Y_510))),
inference(resolution,[status(thm)],[c_12492,c_296]) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(implies(implies(X_3,Y_4),implies(implies(Y_4,Z_5),implies(X_3,Z_5)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_2147,plain,
! [X_174,Y_175,X_176,Z_177] :
( is_a_theorem(implies(implies(X_174,Y_175),implies(X_176,implies(X_174,Z_177))))
| ~ is_a_theorem(implies(X_176,implies(Y_175,Z_177))) ),
inference(resolution,[status(thm)],[c_4,c_127]) ).
tff(c_13339,plain,
! [X_523,Y_524,Z_525] :
( is_a_theorem(implies(implies(X_523,Y_524),implies(X_523,Z_525)))
| ~ is_a_theorem(implies(not(implies(X_523,Z_525)),implies(Y_524,Z_525))) ),
inference(resolution,[status(thm)],[c_2147,c_59]) ).
tff(c_13471,plain,
! [X_523,Y_510] : is_a_theorem(implies(implies(X_523,implies(not(Y_510),Y_510)),implies(X_523,Y_510))),
inference(resolution,[status(thm)],[c_12690,c_13339]) ).
tff(c_108,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_8,c_83]) ).
tff(c_359,plain,
! [X_61,Y_62,Z_63,X_64] :
( is_a_theorem(implies(X_61,implies(implies(Y_62,Z_63),implies(X_64,Z_63))))
| ~ is_a_theorem(implies(X_61,implies(X_64,Y_62))) ),
inference(resolution,[status(thm)],[c_4,c_45]) ).
tff(c_56,plain,
! [X_24,X_15,Z_17,Y_16] :
( is_a_theorem(implies(X_24,implies(X_15,Z_17)))
| ~ is_a_theorem(implies(X_24,implies(Y_16,Z_17)))
| ~ is_a_theorem(implies(X_15,Y_16)) ),
inference(resolution,[status(thm)],[c_27,c_45]) ).
tff(c_3603,plain,
! [X_263,Z_264,Y_261,X_265,X_262] :
( is_a_theorem(implies(X_265,implies(X_263,implies(X_262,Z_264))))
| ~ is_a_theorem(implies(X_263,implies(Y_261,Z_264)))
| ~ is_a_theorem(implies(X_265,implies(X_262,Y_261))) ),
inference(resolution,[status(thm)],[c_359,c_56]) ).
tff(c_6412,plain,
! [X_363,X_364,X_365,Y_366] :
( is_a_theorem(implies(X_363,implies(X_364,implies(X_365,Y_366))))
| ~ is_a_theorem(implies(X_363,implies(X_365,not(X_364)))) ),
inference(resolution,[status(thm)],[c_8,c_3603]) ).
tff(c_7010,plain,
! [X_381,X_382,Y_383] : is_a_theorem(implies(implies(X_381,not(X_382)),implies(X_382,implies(X_381,Y_383)))),
inference(resolution,[status(thm)],[c_108,c_6412]) ).
tff(c_2387,plain,
! [Y_194,Z_195,X_196,X_197] :
( is_a_theorem(implies(implies(Y_194,Z_195),implies(X_196,Z_195)))
| ~ is_a_theorem(implies(X_196,X_197))
| ~ is_a_theorem(implies(X_197,Y_194)) ),
inference(resolution,[status(thm)],[c_27,c_127]) ).
tff(c_2477,plain,
! [Y_194,Z_195,X_7,Y_8] :
( is_a_theorem(implies(implies(Y_194,Z_195),implies(X_7,Z_195)))
| ~ is_a_theorem(implies(implies(not(X_7),Y_8),Y_194)) ),
inference(resolution,[status(thm)],[c_8,c_2387]) ).
tff(c_152216,plain,
! [X_2233,X_2234,Y_2235,Z_2236] : is_a_theorem(implies(implies(implies(X_2233,implies(not(X_2234),Y_2235)),Z_2236),implies(X_2234,Z_2236))),
inference(resolution,[status(thm)],[c_7010,c_2477]) ).
tff(c_264,plain,
! [X_50,Y_52] :
( is_a_theorem(implies(X_50,Y_52))
| ~ is_a_theorem(Y_52) ),
inference(resolution,[status(thm)],[c_244,c_59]) ).
tff(c_173,plain,
! [Y_42,Z_43] :
( is_a_theorem(implies(implies(Y_42,Z_43),Z_43))
| ~ is_a_theorem(implies(not(Z_43),Y_42)) ),
inference(resolution,[status(thm)],[c_27,c_83]) ).
tff(c_604,plain,
! [Z_89,Y_90] :
( is_a_theorem(Z_89)
| ~ is_a_theorem(implies(Y_90,Z_89))
| ~ is_a_theorem(implies(not(Z_89),Y_90)) ),
inference(resolution,[status(thm)],[c_173,c_2]) ).
tff(c_656,plain,
! [Z_89,Y_52] :
( is_a_theorem(Z_89)
| ~ is_a_theorem(implies(Y_52,Z_89))
| ~ is_a_theorem(Y_52) ),
inference(resolution,[status(thm)],[c_264,c_604]) ).
tff(c_170730,plain,
! [X_2373,Z_2374,X_2375,Y_2376] :
( is_a_theorem(implies(X_2373,Z_2374))
| ~ is_a_theorem(implies(implies(X_2375,implies(not(X_2373),Y_2376)),Z_2374)) ),
inference(resolution,[status(thm)],[c_152216,c_656]) ).
tff(c_172759,plain,
! [Y_2383,X_2384] : is_a_theorem(implies(Y_2383,implies(X_2384,Y_2383))),
inference(resolution,[status(thm)],[c_13471,c_170730]) ).
tff(c_3725,plain,
! [X_265,X_7,X_262,Y_8] :
( is_a_theorem(implies(X_265,implies(X_7,implies(X_262,Y_8))))
| ~ is_a_theorem(implies(X_265,implies(X_262,not(X_7)))) ),
inference(resolution,[status(thm)],[c_8,c_3603]) ).
tff(c_176462,plain,
! [X_2414,X_2415,Y_2416] : is_a_theorem(implies(not(X_2414),implies(X_2414,implies(X_2415,Y_2416)))),
inference(resolution,[status(thm)],[c_172759,c_3725]) ).
tff(c_185570,plain,
! [X_2490,Y_2491] : is_a_theorem(implies(not(not(implies(X_2490,Y_2491))),implies(X_2490,Y_2491))),
inference(resolution,[status(thm)],[c_176462,c_59]) ).
tff(c_215,plain,
! [X_44,Y_46] : is_a_theorem(implies(X_44,implies(implies(not(not(X_44)),not(X_44)),Y_46))),
inference(resolution,[status(thm)],[c_6,c_194]) ).
tff(c_8030,plain,
! [X_417,Z_418,Y_419] :
( is_a_theorem(implies(X_417,Z_418))
| ~ is_a_theorem(implies(X_417,implies(Y_419,Z_418)))
| ~ is_a_theorem(implies(not(Z_418),Y_419)) ),
inference(resolution,[status(thm)],[c_173,c_44]) ).
tff(c_8208,plain,
! [X_44,Y_46] :
( is_a_theorem(implies(X_44,Y_46))
| ~ is_a_theorem(implies(not(Y_46),implies(not(not(X_44)),not(X_44)))) ),
inference(resolution,[status(thm)],[c_215,c_8030]) ).
tff(c_190345,plain,
! [X_2517] : is_a_theorem(implies(X_2517,not(implies(not(not(X_2517)),not(X_2517))))),
inference(resolution,[status(thm)],[c_185570,c_8208]) ).
tff(c_1613,plain,
! [X_139,Y_142,Y_141] : is_a_theorem(implies(X_139,implies(not(implies(not(X_139),Y_142)),Y_141))),
inference(resolution,[status(thm)],[c_108,c_1552]) ).
tff(c_8203,plain,
! [X_139,Y_141,Y_142] :
( is_a_theorem(implies(X_139,Y_141))
| ~ is_a_theorem(implies(not(Y_141),not(implies(not(X_139),Y_142)))) ),
inference(resolution,[status(thm)],[c_1613,c_8030]) ).
tff(c_190885,plain,
! [Y_2518] : is_a_theorem(implies(not(not(Y_2518)),Y_2518)),
inference(resolution,[status(thm)],[c_190345,c_8203]) ).
tff(c_105,plain,
! [Y_16,Z_17] :
( is_a_theorem(implies(implies(Y_16,Z_17),Z_17))
| ~ is_a_theorem(implies(not(Z_17),Y_16)) ),
inference(resolution,[status(thm)],[c_27,c_83]) ).
tff(c_10063,plain,
! [Y_467,Y_468] : is_a_theorem(implies(not(implies(Y_467,Y_467)),Y_468)),
inference(resolution,[status(thm)],[c_8,c_9858]) ).
tff(c_1620,plain,
! [X_143,Y_144] : is_a_theorem(implies(implies(not(X_143),X_143),implies(not(X_143),Y_144))),
inference(resolution,[status(thm)],[c_107,c_1552]) ).
tff(c_82,plain,
! [X_31,Y_32,X_30] :
( is_a_theorem(implies(not(X_31),Y_32))
| ~ is_a_theorem(X_30)
| ~ is_a_theorem(implies(X_30,X_31)) ),
inference(resolution,[status(thm)],[c_70,c_2]) ).
tff(c_1655,plain,
! [X_143,Y_144,Y_32] :
( is_a_theorem(implies(not(implies(not(X_143),Y_144)),Y_32))
| ~ is_a_theorem(implies(not(X_143),X_143)) ),
inference(resolution,[status(thm)],[c_1620,c_82]) ).
tff(c_13519,plain,
! [Y_526,Y_527,Y_528] : is_a_theorem(implies(not(implies(not(implies(Y_526,Y_526)),Y_527)),Y_528)),
inference(resolution,[status(thm)],[c_10063,c_1655]) ).
tff(c_1194,plain,
! [X_120,X_121,Y_122] :
( is_a_theorem(implies(implies(not(X_120),X_120),implies(not(X_121),Y_122)))
| ~ is_a_theorem(implies(X_120,X_121)) ),
inference(resolution,[status(thm)],[c_6,c_1094]) ).
tff(c_1275,plain,
! [X_125,Y_126] :
( is_a_theorem(implies(implies(not(X_125),X_125),Y_126))
| ~ is_a_theorem(implies(X_125,Y_126)) ),
inference(resolution,[status(thm)],[c_1194,c_59]) ).
tff(c_1311,plain,
! [Y_126,X_125] :
( is_a_theorem(Y_126)
| ~ is_a_theorem(implies(not(X_125),X_125))
| ~ is_a_theorem(implies(X_125,Y_126)) ),
inference(resolution,[status(thm)],[c_1275,c_656]) ).
tff(c_20688,plain,
! [Y_650,Y_651,Y_652] :
( is_a_theorem(Y_650)
| ~ is_a_theorem(implies(implies(not(implies(Y_651,Y_651)),Y_652),Y_650)) ),
inference(resolution,[status(thm)],[c_13519,c_1311]) ).
tff(c_21044,plain,
! [Z_17,Y_651] :
( is_a_theorem(Z_17)
| ~ is_a_theorem(implies(not(Z_17),not(implies(Y_651,Y_651)))) ),
inference(resolution,[status(thm)],[c_105,c_20688]) ).
tff(c_191259,plain,
! [Y_651] : is_a_theorem(not(not(implies(Y_651,Y_651)))),
inference(resolution,[status(thm)],[c_190885,c_21044]) ).
tff(c_10,plain,
~ is_a_theorem(not(not(implies(p,p)))),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_191716,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_191259,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 23:27:12 UTC 2026
% 0.13/0.36 % CPUTime :
% 94.83/74.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.83/74.73
% 94.83/74.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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