%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL047-1 : 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 : n006.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 11:11:08 AM UTC 2026
% Result : Unsatisfiable 80.56s 60.37s
% Output : CNFRefutation 80.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 104 ( 53 ~; 51 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 146 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > 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(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_44,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file(unknown,unknown) ).
tff(f_42,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file(unknown,unknown) ).
tff(f_48,axiom,
~ is_a_theorem(implies(a,implies(b,a))),
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_44]) ).
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_42]) ).
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_40]) ).
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_46]) ).
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_1233,plain,
! [X_122,X_123,Y_124,X_125] :
( is_a_theorem(implies(X_122,implies(not(X_123),Y_124)))
| ~ is_a_theorem(implies(X_122,X_125))
| ~ is_a_theorem(implies(X_125,X_123)) ),
inference(resolution,[status(thm)],[c_70,c_44]) ).
tff(c_2049,plain,
! [X_175,X_176,Y_177,Y_178] :
( is_a_theorem(implies(X_175,implies(not(X_176),Y_177)))
| ~ is_a_theorem(implies(implies(not(X_175),Y_178),X_176)) ),
inference(resolution,[status(thm)],[c_8,c_1233]) ).
tff(c_2122,plain,
! [X_34,Y_177] : is_a_theorem(implies(implies(not(X_34),X_34),implies(not(X_34),Y_177))),
inference(resolution,[status(thm)],[c_107,c_2049]) ).
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_10649,plain,
! [X_472,Z_473,Y_474,Y_475] :
( is_a_theorem(implies(not(implies(X_472,Z_473)),Y_474))
| ~ is_a_theorem(implies(Y_475,Z_473))
| ~ is_a_theorem(implies(X_472,Y_475)) ),
inference(resolution,[status(thm)],[c_27,c_216]) ).
tff(c_11489,plain,
! [X_490,X_491,Y_492] :
( is_a_theorem(implies(not(implies(X_490,X_491)),Y_492))
| ~ is_a_theorem(implies(X_490,implies(not(X_491),X_491))) ),
inference(resolution,[status(thm)],[c_6,c_10649]) ).
tff(c_14994,plain,
! [Y_555,Y_556] : is_a_theorem(implies(not(implies(implies(not(Y_555),Y_555),Y_555)),Y_556)),
inference(resolution,[status(thm)],[c_2122,c_11489]) ).
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_40]) ).
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_299,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_15226,plain,
! [X_557,Y_558] : is_a_theorem(implies(X_557,implies(implies(not(Y_558),Y_558),Y_558))),
inference(resolution,[status(thm)],[c_14994,c_299]) ).
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_42]) ).
tff(c_1930,plain,
! [X_163,Y_164,X_165,Z_166] :
( is_a_theorem(implies(implies(X_163,Y_164),implies(X_165,implies(X_163,Z_166))))
| ~ is_a_theorem(implies(X_165,implies(Y_164,Z_166))) ),
inference(resolution,[status(thm)],[c_4,c_127]) ).
tff(c_1965,plain,
! [X_163,Y_164,Z_166] :
( is_a_theorem(implies(implies(X_163,Y_164),implies(X_163,Z_166)))
| ~ is_a_theorem(implies(not(implies(X_163,Z_166)),implies(Y_164,Z_166))) ),
inference(resolution,[status(thm)],[c_1930,c_59]) ).
tff(c_15377,plain,
! [X_163,Y_558] : is_a_theorem(implies(implies(X_163,implies(not(Y_558),Y_558)),implies(X_163,Y_558))),
inference(resolution,[status(thm)],[c_15226,c_1965]) ).
tff(c_337,plain,
! [X_58,Y_59,Z_60,X_61] :
( is_a_theorem(implies(X_58,implies(implies(Y_59,Z_60),implies(X_61,Z_60))))
| ~ is_a_theorem(implies(X_58,implies(X_61,Y_59))) ),
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_3066,plain,
! [X_232,Z_231,X_234,X_235,Y_233] :
( is_a_theorem(implies(X_234,implies(X_232,implies(X_235,Z_231))))
| ~ is_a_theorem(implies(X_232,implies(Y_233,Z_231)))
| ~ is_a_theorem(implies(X_234,implies(X_235,Y_233))) ),
inference(resolution,[status(thm)],[c_337,c_56]) ).
tff(c_3418,plain,
! [X_248,X_249,X_250,Y_251] :
( is_a_theorem(implies(X_248,implies(X_249,implies(X_250,Y_251))))
| ~ is_a_theorem(implies(X_248,implies(X_250,not(X_249)))) ),
inference(resolution,[status(thm)],[c_8,c_3066]) ).
tff(c_3542,plain,
! [X_7,X_249,Y_251] : is_a_theorem(implies(X_7,implies(X_249,implies(not(X_7),Y_251)))),
inference(resolution,[status(thm)],[c_8,c_3418]) ).
tff(c_149,plain,
! [X_3,Y_4,X_37,Z_5] :
( is_a_theorem(implies(implies(X_3,Y_4),implies(X_37,implies(X_3,Z_5))))
| ~ is_a_theorem(implies(X_37,implies(Y_4,Z_5))) ),
inference(resolution,[status(thm)],[c_4,c_127]) ).
tff(c_2232,plain,
! [Y_187,Z_188,X_189,X_190] :
( is_a_theorem(implies(implies(Y_187,Z_188),implies(X_189,Z_188)))
| ~ is_a_theorem(X_190)
| ~ is_a_theorem(implies(X_190,implies(X_189,Y_187))) ),
inference(resolution,[status(thm)],[c_337,c_2]) ).
tff(c_40923,plain,
! [Z_966,X_967,Y_969,Z_968,X_965] :
( is_a_theorem(implies(implies(implies(X_967,Z_968),Z_966),implies(X_965,Z_966)))
| ~ is_a_theorem(implies(X_967,Y_969))
| ~ is_a_theorem(implies(X_965,implies(Y_969,Z_968))) ),
inference(resolution,[status(thm)],[c_149,c_2232]) ).
tff(c_44071,plain,
! [Z_1057,Z_1056,X_1059,X_1058,Y_1055] :
( is_a_theorem(implies(implies(implies(X_1058,Z_1057),Z_1056),implies(X_1059,Z_1056)))
| ~ is_a_theorem(implies(X_1059,implies(implies(not(X_1058),Y_1055),Z_1057))) ),
inference(resolution,[status(thm)],[c_8,c_40923]) ).
tff(c_146755,plain,
! [X_2156,X_2157,Y_2158,Z_2159] : is_a_theorem(implies(implies(implies(X_2156,implies(not(X_2157),Y_2158)),Z_2159),implies(X_2157,Z_2159))),
inference(resolution,[status(thm)],[c_3542,c_44071]) ).
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_556,plain,
! [Z_80,Y_81] :
( is_a_theorem(Z_80)
| ~ is_a_theorem(implies(Y_81,Z_80))
| ~ is_a_theorem(implies(not(Z_80),Y_81)) ),
inference(resolution,[status(thm)],[c_173,c_2]) ).
tff(c_599,plain,
! [Z_80,Y_52] :
( is_a_theorem(Z_80)
| ~ is_a_theorem(implies(Y_52,Z_80))
| ~ is_a_theorem(Y_52) ),
inference(resolution,[status(thm)],[c_264,c_556]) ).
tff(c_162773,plain,
! [X_2291,Z_2292,X_2293,Y_2294] :
( is_a_theorem(implies(X_2291,Z_2292))
| ~ is_a_theorem(implies(implies(X_2293,implies(not(X_2291),Y_2294)),Z_2292)) ),
inference(resolution,[status(thm)],[c_146755,c_599]) ).
tff(c_163854,plain,
! [Y_558,X_163] : is_a_theorem(implies(Y_558,implies(X_163,Y_558))),
inference(resolution,[status(thm)],[c_15377,c_162773]) ).
tff(c_10,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_163969,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_163854,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % 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
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 4 22:05:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 80.56/60.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.56/60.38
% 80.56/60.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------