TSTP Solution File: LCL326-3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL326-3 : TPTP v8.1.2. Released v2.3.0.
% 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:47:55 EDT 2023
% Result : Unsatisfiable 126.30s 99.98s
% Output : CNFRefutation 126.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 194 ( 77 unt; 8 typ; 0 def)
% Number of atoms : 327 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 285 ( 144 ~; 141 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 381 (; 381 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > equivalent > and > #nlpp > not > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(theorem,type,
theorem: $i > $o ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(equivalent,type,
equivalent: ( $i * $i ) > $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff(axiom,type,
axiom: $i > $o ).
tff(p,type,
p: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_56,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file(unknown,unknown) ).
tff(f_48,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_119,axiom,
! [P,Q] : ( equivalent(P,Q) = and(implies(P,Q),implies(Q,P)) ),
file(unknown,unknown) ).
tff(f_96,axiom,
! [P,Q] : ( and(P,Q) = not(or(not(P),not(Q))) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file(unknown,unknown) ).
tff(f_123,axiom,
~ theorem(not(equivalent(p,not(p)))),
file(unknown,unknown) ).
tff(c_12,plain,
! [X_12,Y_13] : ( or(not(X_12),Y_13) = implies(X_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_48,plain,
! [A_29,B_30] : axiom(implies(or(A_29,B_30),or(B_30,A_29))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_51,plain,
! [X_12,Y_13] : axiom(implies(implies(X_12,Y_13),or(Y_13,not(X_12)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_48]) ).
tff(c_4,plain,
! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_126,plain,
! [A_44,B_45,C_46] : axiom(implies(or(A_44,or(B_45,C_46)),or(B_45,or(A_44,C_46)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_139,plain,
! [X_12,B_45,Y_13] : axiom(implies(or(not(X_12),or(B_45,Y_13)),or(B_45,implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_126]) ).
tff(c_832,plain,
! [X_135,B_136,Y_137] : axiom(implies(implies(X_135,or(B_136,Y_137)),or(B_136,implies(X_135,Y_137)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_139]) ).
tff(c_55,plain,
! [Y_31,X_32] :
( ~ theorem(Y_31)
| ~ theorem(implies(Y_31,X_32))
| theorem(X_32) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_59,plain,
! [Y_31,X_32] :
( ~ theorem(Y_31)
| theorem(X_32)
| ~ axiom(implies(Y_31,X_32)) ),
inference(resolution,[status(thm)],[c_14,c_55]) ).
tff(c_850,plain,
! [X_135,B_136,Y_137] :
( ~ theorem(implies(X_135,or(B_136,Y_137)))
| theorem(or(B_136,implies(X_135,Y_137))) ),
inference(resolution,[status(thm)],[c_832,c_59]) ).
tff(c_6,plain,
! [A_4,B_5] : axiom(implies(or(A_4,B_5),or(B_5,A_4))),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_96,plain,
! [Y_38,X_39] :
( ~ theorem(Y_38)
| theorem(X_39)
| ~ axiom(implies(Y_38,X_39)) ),
inference(resolution,[status(thm)],[c_14,c_55]) ).
tff(c_115,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_96]) ).
tff(c_143,plain,
! [A_44,X_12,C_46] : axiom(implies(or(A_44,or(not(X_12),C_46)),implies(X_12,or(A_44,C_46)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_126]) ).
tff(c_593,plain,
! [A_98,X_99,C_100] : axiom(implies(or(A_98,implies(X_99,C_100)),implies(X_99,or(A_98,C_100)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_143]) ).
tff(c_1414,plain,
! [A_218,X_219,C_220] :
( ~ theorem(or(A_218,implies(X_219,C_220)))
| theorem(implies(X_219,or(A_218,C_220))) ),
inference(resolution,[status(thm)],[c_593,c_59]) ).
tff(c_1496,plain,
! [X_230,B_231,C_232] :
( theorem(implies(X_230,or(B_231,C_232)))
| ~ theorem(implies(X_230,C_232)) ),
inference(resolution,[status(thm)],[c_115,c_1414]) ).
tff(c_16,plain,
! [Y_16,X_15] :
( ~ theorem(Y_16)
| ~ theorem(implies(Y_16,X_15))
| theorem(X_15) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_1514,plain,
! [X_233,B_234,C_235] :
( ~ theorem(X_233)
| theorem(or(B_234,C_235))
| ~ theorem(implies(X_233,C_235)) ),
inference(resolution,[status(thm)],[c_1496,c_16]) ).
tff(c_1646,plain,
! [X_245,B_246,C_247] :
( ~ theorem(X_245)
| theorem(or(B_246,C_247))
| ~ axiom(implies(X_245,C_247)) ),
inference(resolution,[status(thm)],[c_14,c_1514]) ).
tff(c_2842,plain,
! [A_333,B_334,B_335] :
( ~ theorem(or(A_333,B_334))
| theorem(or(B_335,or(B_334,A_333))) ),
inference(resolution,[status(thm)],[c_6,c_1646]) ).
tff(c_144,plain,
! [A_44,B_45,C_46] :
( ~ theorem(or(A_44,or(B_45,C_46)))
| theorem(or(B_45,or(A_44,C_46))) ),
inference(resolution,[status(thm)],[c_126,c_59]) ).
tff(c_3194,plain,
! [B_368,B_369,A_370] :
( theorem(or(B_368,or(B_369,A_370)))
| ~ theorem(or(A_370,B_368)) ),
inference(resolution,[status(thm)],[c_2842,c_144]) ).
tff(c_3259,plain,
! [B_373,X_374,Y_375] :
( theorem(or(B_373,implies(X_374,Y_375)))
| ~ theorem(or(Y_375,B_373)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_3194]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_116,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_96]) ).
tff(c_3751,plain,
! [X_415,Y_416] :
( theorem(implies(X_415,Y_416))
| ~ theorem(or(Y_416,implies(X_415,Y_416))) ),
inference(resolution,[status(thm)],[c_3259,c_116]) ).
tff(c_3995,plain,
! [X_427,Y_428] :
( theorem(implies(X_427,Y_428))
| ~ theorem(implies(X_427,or(Y_428,Y_428))) ),
inference(resolution,[status(thm)],[c_850,c_3751]) ).
tff(c_4100,plain,
! [X_431,Y_432] :
( theorem(implies(X_431,Y_432))
| ~ axiom(implies(X_431,or(Y_432,Y_432))) ),
inference(resolution,[status(thm)],[c_14,c_3995]) ).
tff(c_4139,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_4100]) ).
tff(c_20,plain,
! [P_19,Q_20] : ( and(implies(P_19,Q_20),implies(Q_20,P_19)) = equivalent(P_19,Q_20) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_18,plain,
! [P_17,Q_18] : ( not(or(not(P_17),not(Q_18))) = and(P_17,Q_18) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_69,plain,
! [P_35,Q_36] : ( not(implies(P_35,not(Q_36))) = and(P_35,Q_36) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_78,plain,
! [P_35,Q_36,Y_13] : ( implies(implies(P_35,not(Q_36)),Y_13) = or(and(P_35,Q_36),Y_13) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_12]) ).
tff(c_31,plain,
! [X_25,Y_26] : ( or(not(X_25),Y_26) = implies(X_25,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_41,plain,
! [X_25] : axiom(implies(implies(X_25,not(X_25)),not(X_25))),
inference(superposition,[status(thm),theory(equality)],[c_31,c_2]) ).
tff(c_416,plain,
! [X_75] : axiom(or(and(X_75,X_75),not(X_75))),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_41]) ).
tff(c_423,plain,
! [Q_20] : axiom(or(equivalent(Q_20,Q_20),not(implies(Q_20,Q_20)))),
inference(superposition,[status(thm),theory(equality)],[c_20,c_416]) ).
tff(c_269,plain,
! [Y_66,X_67] : axiom(implies(or(Y_66,not(X_67)),implies(X_67,Y_66))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_48]) ).
tff(c_298,plain,
! [Y_70,X_71] :
( ~ theorem(or(Y_70,not(X_71)))
| theorem(implies(X_71,Y_70)) ),
inference(resolution,[status(thm)],[c_269,c_59]) ).
tff(c_444,plain,
! [X_79,Y_80] :
( theorem(implies(X_79,Y_80))
| ~ axiom(or(Y_80,not(X_79))) ),
inference(resolution,[status(thm)],[c_14,c_298]) ).
tff(c_479,plain,
! [Q_83] : theorem(implies(implies(Q_83,Q_83),equivalent(Q_83,Q_83))),
inference(resolution,[status(thm)],[c_423,c_444]) ).
tff(c_491,plain,
! [Q_83] :
( ~ theorem(implies(Q_83,Q_83))
| theorem(equivalent(Q_83,Q_83)) ),
inference(resolution,[status(thm)],[c_479,c_16]) ).
tff(c_4353,plain,
! [Q_83] : theorem(equivalent(Q_83,Q_83)),
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_491]) ).
tff(c_23,plain,
! [P_17,Q_18] : ( not(implies(P_17,not(Q_18))) = and(P_17,Q_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_18]) ).
tff(c_2211,plain,
! [X_299,B_300,Y_301] :
( ~ theorem(implies(X_299,or(B_300,Y_301)))
| theorem(or(B_300,implies(X_299,Y_301))) ),
inference(resolution,[status(thm)],[c_832,c_59]) ).
tff(c_2234,plain,
! [X_299,X_12,Y_301] :
( ~ theorem(implies(X_299,or(not(X_12),Y_301)))
| theorem(implies(X_12,implies(X_299,Y_301))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_2211]) ).
tff(c_9925,plain,
! [X_653,X_654,Y_655] :
( ~ theorem(implies(X_653,implies(X_654,Y_655)))
| theorem(implies(X_654,implies(X_653,Y_655))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2234]) ).
tff(c_9986,plain,
! [X_654,Y_655] : theorem(implies(X_654,implies(implies(X_654,Y_655),Y_655))),
inference(resolution,[status(thm)],[c_4139,c_9925]) ).
tff(c_1683,plain,
! [A_2,B_246,B_3] :
( ~ theorem(A_2)
| theorem(or(B_246,or(B_3,A_2))) ),
inference(resolution,[status(thm)],[c_4,c_1646]) ).
tff(c_182,plain,
! [A_50,B_51,C_52] : axiom(implies(implies(A_50,B_51),implies(or(C_52,A_50),or(C_52,B_51)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_192,plain,
! [A_50,B_51,C_52] :
( ~ theorem(implies(A_50,B_51))
| theorem(implies(or(C_52,A_50),or(C_52,B_51))) ),
inference(resolution,[status(thm)],[c_182,c_59]) ).
tff(c_4064,plain,
! [B_429,A_430] :
( theorem(implies(or(B_429,A_430),B_429))
| ~ theorem(implies(A_430,B_429)) ),
inference(resolution,[status(thm)],[c_192,c_3995]) ).
tff(c_5691,plain,
! [B_499,A_500] :
( ~ theorem(or(B_499,A_500))
| theorem(B_499)
| ~ theorem(implies(A_500,B_499)) ),
inference(resolution,[status(thm)],[c_4064,c_16]) ).
tff(c_15781,plain,
! [B_945,B_946,A_947] :
( theorem(B_945)
| ~ theorem(implies(or(B_946,A_947),B_945))
| ~ theorem(A_947) ),
inference(resolution,[status(thm)],[c_1683,c_5691]) ).
tff(c_22041,plain,
! [B_1126,A_1127,Y_1128] :
( theorem(implies(implies(or(B_1126,A_1127),Y_1128),Y_1128))
| ~ theorem(A_1127) ),
inference(resolution,[status(thm)],[c_9986,c_15781]) ).
tff(c_320,plain,
! [X_12,X_71] :
( ~ theorem(implies(X_12,not(X_71)))
| theorem(implies(X_71,not(X_12))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_298]) ).
tff(c_22095,plain,
! [X_71,B_1126,A_1127] :
( theorem(implies(X_71,not(implies(or(B_1126,A_1127),not(X_71)))))
| ~ theorem(A_1127) ),
inference(resolution,[status(thm)],[c_22041,c_320]) ).
tff(c_28113,plain,
! [X_1271,B_1272,A_1273] :
( theorem(implies(X_1271,and(or(B_1272,A_1273),X_1271)))
| ~ theorem(A_1273) ),
inference(demodulation,[status(thm),theory(equality)],[c_23,c_22095]) ).
tff(c_36662,plain,
! [X_1478,X_1479,Y_1480] :
( theorem(implies(X_1478,and(implies(X_1479,Y_1480),X_1478)))
| ~ theorem(Y_1480) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_28113]) ).
tff(c_66457,plain,
! [Q_2107,P_2108] :
( theorem(implies(implies(Q_2107,P_2108),equivalent(P_2108,Q_2107)))
| ~ theorem(Q_2107) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_36662]) ).
tff(c_37,plain,
! [Y_26,X_25] : axiom(implies(Y_26,implies(X_25,Y_26))),
inference(superposition,[status(thm),theory(equality)],[c_31,c_4]) ).
tff(c_330,plain,
! [X_25] : axiom(or(and(X_25,X_25),not(X_25))),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_41]) ).
tff(c_459,plain,
! [X_25] : theorem(implies(X_25,and(X_25,X_25))),
inference(resolution,[status(thm)],[c_330,c_444]) ).
tff(c_191,plain,
! [A_50,Y_13,X_12] : axiom(implies(implies(A_50,Y_13),implies(or(not(X_12),A_50),implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_182]) ).
tff(c_512,plain,
! [A_85,Y_86,X_87] : axiom(implies(implies(A_85,Y_86),implies(implies(X_87,A_85),implies(X_87,Y_86)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_191]) ).
tff(c_2481,plain,
! [A_315,Y_316,X_317] :
( ~ theorem(implies(A_315,Y_316))
| theorem(implies(implies(X_317,A_315),implies(X_317,Y_316))) ),
inference(resolution,[status(thm)],[c_512,c_59]) ).
tff(c_10991,plain,
! [X_728,A_729,Y_730] :
( ~ theorem(implies(X_728,A_729))
| theorem(implies(X_728,Y_730))
| ~ theorem(implies(A_729,Y_730)) ),
inference(resolution,[status(thm)],[c_2481,c_16]) ).
tff(c_12455,plain,
! [X_812,Y_813] :
( theorem(implies(X_812,Y_813))
| ~ theorem(implies(and(X_812,X_812),Y_813)) ),
inference(resolution,[status(thm)],[c_459,c_10991]) ).
tff(c_12857,plain,
! [X_821,Y_822] :
( theorem(implies(X_821,Y_822))
| ~ axiom(implies(and(X_821,X_821),Y_822)) ),
inference(resolution,[status(thm)],[c_14,c_12455]) ).
tff(c_12911,plain,
! [X_824,X_825] : theorem(implies(X_824,implies(X_825,and(X_824,X_824)))),
inference(resolution,[status(thm)],[c_37,c_12857]) ).
tff(c_2241,plain,
! [X_299,X_12,Y_301] :
( ~ theorem(implies(X_299,implies(X_12,Y_301)))
| theorem(implies(X_12,implies(X_299,Y_301))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2234]) ).
tff(c_13024,plain,
! [X_828,X_829] : theorem(implies(X_828,implies(X_829,and(X_829,X_829)))),
inference(resolution,[status(thm)],[c_12911,c_2241]) ).
tff(c_1443,plain,
! [A_221,B_222,C_223] :
( ~ theorem(implies(A_221,B_222))
| theorem(implies(or(C_223,A_221),or(C_223,B_222))) ),
inference(resolution,[status(thm)],[c_182,c_59]) ).
tff(c_11838,plain,
! [C_788,A_789,B_790] :
( ~ theorem(or(C_788,A_789))
| theorem(or(C_788,B_790))
| ~ theorem(implies(A_789,B_790)) ),
inference(resolution,[status(thm)],[c_1443,c_16]) ).
tff(c_12009,plain,
! [B_3,B_790,A_2] :
( theorem(or(B_3,B_790))
| ~ theorem(implies(A_2,B_790))
| ~ theorem(A_2) ),
inference(resolution,[status(thm)],[c_115,c_11838]) ).
tff(c_13067,plain,
! [B_3,X_829,X_828] :
( theorem(or(B_3,implies(X_829,and(X_829,X_829))))
| ~ theorem(X_828) ),
inference(resolution,[status(thm)],[c_13024,c_12009]) ).
tff(c_14384,plain,
! [X_828] : ~ theorem(X_828),
inference(splitLeft,[status(thm)],[c_13067]) ).
tff(c_13058,plain,
! [P_35,Q_36,X_829] : theorem(or(and(P_35,Q_36),implies(X_829,and(X_829,X_829)))),
inference(superposition,[status(thm),theory(equality)],[c_78,c_13024]) ).
tff(c_14593,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14384,c_13058]) ).
tff(c_14596,plain,
! [B_900,X_901] : theorem(or(B_900,implies(X_901,and(X_901,X_901)))),
inference(splitRight,[status(thm)],[c_13067]) ).
tff(c_4099,plain,
! [B_429,A_430] :
( ~ theorem(or(B_429,A_430))
| theorem(B_429)
| ~ theorem(implies(A_430,B_429)) ),
inference(resolution,[status(thm)],[c_4064,c_16]) ).
tff(c_14671,plain,
! [B_900,X_901] :
( theorem(B_900)
| ~ theorem(implies(implies(X_901,and(X_901,X_901)),B_900)) ),
inference(resolution,[status(thm)],[c_14596,c_4099]) ).
tff(c_66517,plain,
! [Q_2109] :
( theorem(equivalent(and(Q_2109,Q_2109),Q_2109))
| ~ theorem(Q_2109) ),
inference(resolution,[status(thm)],[c_66457,c_14671]) ).
tff(c_331,plain,
! [P_72,Q_73,Y_74] : ( implies(implies(P_72,not(Q_73)),Y_74) = or(and(P_72,Q_73),Y_74) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_12]) ).
tff(c_352,plain,
! [P_72,Q_73] : axiom(or(and(P_72,Q_73),or(not(Q_73),not(P_72)))),
inference(superposition,[status(thm),theory(equality)],[c_331,c_51]) ).
tff(c_411,plain,
! [P_72,Q_73] : axiom(or(and(P_72,Q_73),implies(Q_73,not(P_72)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_352]) ).
tff(c_195,plain,
! [A_53,B_54] :
( ~ theorem(or(A_53,B_54))
| theorem(or(B_54,A_53)) ),
inference(resolution,[status(thm)],[c_6,c_96]) ).
tff(c_205,plain,
! [A_55,B_56] :
( theorem(or(A_55,B_56))
| ~ theorem(A_55) ),
inference(resolution,[status(thm)],[c_115,c_195]) ).
tff(c_214,plain,
! [X_12,Y_13] :
( theorem(implies(X_12,Y_13))
| ~ theorem(not(X_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_205]) ).
tff(c_7907,plain,
! [B_572,A_573] :
( theorem(B_572)
| ~ theorem(implies(A_573,B_572))
| ~ axiom(or(B_572,A_573)) ),
inference(resolution,[status(thm)],[c_14,c_5691]) ).
tff(c_8105,plain,
! [Y_576,X_577] :
( theorem(Y_576)
| ~ axiom(or(Y_576,X_577))
| ~ theorem(not(X_577)) ),
inference(resolution,[status(thm)],[c_214,c_7907]) ).
tff(c_8121,plain,
! [P_72,Q_73] :
( theorem(and(P_72,Q_73))
| ~ theorem(not(implies(Q_73,not(P_72)))) ),
inference(resolution,[status(thm)],[c_411,c_8105]) ).
tff(c_8137,plain,
! [P_578,Q_579] :
( theorem(and(P_578,Q_579))
| ~ theorem(and(Q_579,P_578)) ),
inference(demodulation,[status(thm),theory(equality)],[c_23,c_8121]) ).
tff(c_8147,plain,
! [Q_20,P_19] :
( theorem(and(implies(Q_20,P_19),implies(P_19,Q_20)))
| ~ theorem(equivalent(P_19,Q_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_8137]) ).
tff(c_8155,plain,
! [Q_20,P_19] :
( theorem(equivalent(Q_20,P_19))
| ~ theorem(equivalent(P_19,Q_20)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_8147]) ).
tff(c_66802,plain,
! [Q_2117] :
( theorem(equivalent(Q_2117,and(Q_2117,Q_2117)))
| ~ theorem(Q_2117) ),
inference(resolution,[status(thm)],[c_66517,c_8155]) ).
tff(c_66844,plain,
! [Q_20] :
( theorem(equivalent(implies(Q_20,Q_20),equivalent(Q_20,Q_20)))
| ~ theorem(implies(Q_20,Q_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_66802]) ).
tff(c_66855,plain,
! [Q_20] : theorem(equivalent(implies(Q_20,Q_20),equivalent(Q_20,Q_20))),
inference(demodulation,[status(thm),theory(equality)],[c_4139,c_66844]) ).
tff(c_9481,plain,
! [X_635,Y_636] :
( theorem(not(X_635))
| ~ axiom(implies(X_635,Y_636))
| ~ theorem(not(Y_636)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_8105]) ).
tff(c_9530,plain,
! [Y_637,X_638] :
( theorem(not(Y_637))
| ~ theorem(not(implies(X_638,Y_637))) ),
inference(resolution,[status(thm)],[c_37,c_9481]) ).
tff(c_10323,plain,
! [Q_681,P_682] :
( theorem(not(not(Q_681)))
| ~ theorem(and(P_682,Q_681)) ),
inference(superposition,[status(thm),theory(equality)],[c_23,c_9530]) ).
tff(c_69968,plain,
! [Q_2170,P_2171] :
( theorem(not(not(implies(Q_2170,P_2171))))
| ~ theorem(equivalent(P_2171,Q_2170)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_10323]) ).
tff(c_204,plain,
! [B_54,A_53] :
( theorem(or(B_54,A_53))
| ~ axiom(or(A_53,B_54)) ),
inference(resolution,[status(thm)],[c_14,c_195]) ).
tff(c_17064,plain,
! [B_986,A_987] :
( theorem(B_986)
| ~ theorem(implies(A_987,B_986))
| ~ axiom(or(A_987,B_986)) ),
inference(resolution,[status(thm)],[c_204,c_5691]) ).
tff(c_17316,plain,
! [Y_989,X_990] :
( theorem(Y_989)
| ~ axiom(or(X_990,Y_989))
| ~ theorem(not(X_990)) ),
inference(resolution,[status(thm)],[c_214,c_17064]) ).
tff(c_33403,plain,
! [Y_1394,X_1395] :
( theorem(Y_1394)
| ~ axiom(implies(X_1395,Y_1394))
| ~ theorem(not(not(X_1395))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_17316]) ).
tff(c_33459,plain,
! [B_3,A_2] :
( theorem(or(B_3,A_2))
| ~ theorem(not(not(A_2))) ),
inference(resolution,[status(thm)],[c_4,c_33403]) ).
tff(c_142318,plain,
! [B_3109,Q_3110,P_3111] :
( theorem(or(B_3109,implies(Q_3110,P_3111)))
| ~ theorem(equivalent(P_3111,Q_3110)) ),
inference(resolution,[status(thm)],[c_69968,c_33459]) ).
tff(c_1904,plain,
! [A_273,B_274,C_275] :
( ~ theorem(or(A_273,or(B_274,C_275)))
| theorem(or(B_274,or(A_273,C_275))) ),
inference(resolution,[status(thm)],[c_126,c_59]) ).
tff(c_2052,plain,
! [B_288,B_289,C_290] :
( theorem(or(B_288,or(B_289,C_290)))
| ~ theorem(or(B_288,C_290)) ),
inference(resolution,[status(thm)],[c_115,c_1904]) ).
tff(c_113,plain,
! [A_4,B_5] :
( ~ theorem(or(A_4,B_5))
| theorem(or(B_5,A_4)) ),
inference(resolution,[status(thm)],[c_6,c_96]) ).
tff(c_2073,plain,
! [B_289,C_290,B_288] :
( theorem(or(or(B_289,C_290),B_288))
| ~ theorem(or(B_288,C_290)) ),
inference(resolution,[status(thm)],[c_2052,c_113]) ).
tff(c_7661,plain,
! [Y_555] : theorem(implies(or(or(Y_555,Y_555),or(Y_555,Y_555)),Y_555)),
inference(resolution,[status(thm)],[c_2,c_4100]) ).
tff(c_5873,plain,
! [B_3,A_2] :
( theorem(B_3)
| ~ theorem(implies(A_2,B_3))
| ~ theorem(A_2) ),
inference(resolution,[status(thm)],[c_115,c_5691]) ).
tff(c_19595,plain,
! [Y_1056] :
( theorem(Y_1056)
| ~ theorem(or(or(Y_1056,Y_1056),or(Y_1056,Y_1056))) ),
inference(resolution,[status(thm)],[c_7661,c_5873]) ).
tff(c_19761,plain,
! [C_290] :
( theorem(C_290)
| ~ theorem(or(or(C_290,C_290),C_290)) ),
inference(resolution,[status(thm)],[c_2073,c_19595]) ).
tff(c_142457,plain,
! [Q_3112,P_3113] :
( theorem(implies(Q_3112,P_3113))
| ~ theorem(equivalent(P_3113,Q_3112)) ),
inference(resolution,[status(thm)],[c_142318,c_19761]) ).
tff(c_532,plain,
! [P_35,Q_36,X_87] : axiom(or(and(P_35,Q_36),implies(implies(X_87,P_35),implies(X_87,not(Q_36))))),
inference(superposition,[status(thm),theory(equality)],[c_78,c_512]) ).
tff(c_4354,plain,
! [A_436] : theorem(implies(A_436,A_436)),
inference(resolution,[status(thm)],[c_4,c_4100]) ).
tff(c_4384,plain,
! [X_71] : theorem(implies(X_71,not(not(X_71)))),
inference(resolution,[status(thm)],[c_4354,c_320]) ).
tff(c_4724,plain,
! [P_454,Q_455,Y_456] :
( ~ theorem(implies(P_454,not(Q_455)))
| theorem(Y_456)
| ~ axiom(or(and(P_454,Q_455),Y_456)) ),
inference(superposition,[status(thm),theory(equality)],[c_331,c_59]) ).
tff(c_5655,plain,
! [Y_497,X_498] :
( theorem(Y_497)
| ~ axiom(or(and(X_498,not(X_498)),Y_497)) ),
inference(resolution,[status(thm)],[c_4384,c_4724]) ).
tff(c_36827,plain,
! [X_1482,P_1483] : theorem(implies(implies(X_1482,P_1483),implies(X_1482,not(not(P_1483))))),
inference(resolution,[status(thm)],[c_532,c_5655]) ).
tff(c_51594,plain,
! [X_1833,P_1834] : theorem(implies(X_1833,implies(implies(X_1833,P_1834),not(not(P_1834))))),
inference(resolution,[status(thm)],[c_36827,c_2241]) ).
tff(c_82154,plain,
! [X_2403,P_2404] :
( theorem(implies(implies(X_2403,P_2404),not(not(P_2404))))
| ~ theorem(X_2403) ),
inference(resolution,[status(thm)],[c_51594,c_5873]) ).
tff(c_82261,plain,
! [P_2404,X_2403] :
( theorem(not(not(P_2404)))
| ~ theorem(implies(X_2403,P_2404))
| ~ theorem(X_2403) ),
inference(resolution,[status(thm)],[c_82154,c_5873]) ).
tff(c_216994,plain,
! [P_4013,Q_4014] :
( theorem(not(not(P_4013)))
| ~ theorem(Q_4014)
| ~ theorem(equivalent(P_4013,Q_4014)) ),
inference(resolution,[status(thm)],[c_142457,c_82261]) ).
tff(c_217108,plain,
! [Q_20] :
( theorem(not(not(implies(Q_20,Q_20))))
| ~ theorem(equivalent(Q_20,Q_20)) ),
inference(resolution,[status(thm)],[c_66855,c_216994]) ).
tff(c_217270,plain,
! [Q_4018] : theorem(not(not(implies(Q_4018,Q_4018)))),
inference(demodulation,[status(thm),theory(equality)],[c_4353,c_217108]) ).
tff(c_217373,plain,
! [B_4019,Q_4020] : theorem(or(B_4019,implies(Q_4020,Q_4020))),
inference(resolution,[status(thm)],[c_217270,c_33459]) ).
tff(c_10,plain,
! [A_9,B_10,C_11] : axiom(implies(implies(A_9,B_10),implies(or(C_11,A_9),or(C_11,B_10)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_362,plain,
! [P_72,Q_73,C_11] : axiom(or(and(P_72,Q_73),implies(or(C_11,P_72),or(C_11,not(Q_73))))),
inference(superposition,[status(thm),theory(equality)],[c_331,c_10]) ).
tff(c_33827,plain,
! [C_1423,P_1424] : theorem(implies(or(C_1423,P_1424),or(C_1423,not(not(P_1424))))),
inference(resolution,[status(thm)],[c_362,c_5655]) ).
tff(c_59263,plain,
! [C_1998,P_1999] :
( theorem(or(C_1998,not(not(P_1999))))
| ~ theorem(or(C_1998,P_1999)) ),
inference(resolution,[status(thm)],[c_33827,c_5873]) ).
tff(c_280,plain,
! [Y_66,X_67] :
( ~ theorem(or(Y_66,not(X_67)))
| theorem(implies(X_67,Y_66)) ),
inference(resolution,[status(thm)],[c_269,c_59]) ).
tff(c_59376,plain,
! [P_2000,C_2001] :
( theorem(implies(not(P_2000),C_2001))
| ~ theorem(or(C_2001,P_2000)) ),
inference(resolution,[status(thm)],[c_59263,c_280]) ).
tff(c_5871,plain,
! [B_54,A_53] :
( theorem(B_54)
| ~ theorem(implies(A_53,B_54))
| ~ axiom(or(A_53,B_54)) ),
inference(resolution,[status(thm)],[c_204,c_5691]) ).
tff(c_59439,plain,
! [C_2001,P_2000] :
( theorem(C_2001)
| ~ axiom(or(not(P_2000),C_2001))
| ~ theorem(or(C_2001,P_2000)) ),
inference(resolution,[status(thm)],[c_59376,c_5871]) ).
tff(c_59545,plain,
! [C_2001,P_2000] :
( theorem(C_2001)
| ~ axiom(implies(P_2000,C_2001))
| ~ theorem(or(C_2001,P_2000)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_59439]) ).
tff(c_222232,plain,
! [B_4071,Q_4072] :
( theorem(B_4071)
| ~ axiom(implies(implies(Q_4072,Q_4072),B_4071)) ),
inference(resolution,[status(thm)],[c_217373,c_59545]) ).
tff(c_222318,plain,
! [Y_13] : theorem(or(Y_13,not(Y_13))),
inference(resolution,[status(thm)],[c_51,c_222232]) ).
tff(c_3854,plain,
! [X_135,Y_137] :
( theorem(implies(X_135,Y_137))
| ~ theorem(implies(X_135,or(Y_137,Y_137))) ),
inference(resolution,[status(thm)],[c_850,c_3751]) ).
tff(c_33866,plain,
! [P_1424] : theorem(implies(or(not(not(P_1424)),P_1424),not(not(P_1424)))),
inference(resolution,[status(thm)],[c_33827,c_3854]) ).
tff(c_33920,plain,
! [P_1425] : theorem(implies(implies(not(P_1425),P_1425),not(not(P_1425)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_33866]) ).
tff(c_34012,plain,
! [P_1425] : theorem(implies(not(P_1425),not(implies(not(P_1425),P_1425)))),
inference(resolution,[status(thm)],[c_33920,c_320]) ).
tff(c_222327,plain,
! [Y_4073] : theorem(or(Y_4073,not(Y_4073))),
inference(resolution,[status(thm)],[c_51,c_222232]) ).
tff(c_1458,plain,
! [C_223,A_221,B_222] :
( ~ theorem(or(C_223,A_221))
| theorem(or(C_223,B_222))
| ~ theorem(implies(A_221,B_222)) ),
inference(resolution,[status(thm)],[c_1443,c_16]) ).
tff(c_244888,plain,
! [Y_4305,B_4306] :
( theorem(or(Y_4305,B_4306))
| ~ theorem(implies(not(Y_4305),B_4306)) ),
inference(resolution,[status(thm)],[c_222327,c_1458]) ).
tff(c_249064,plain,
! [P_4345] : theorem(or(P_4345,not(implies(not(P_4345),P_4345)))),
inference(resolution,[status(thm)],[c_34012,c_244888]) ).
tff(c_249211,plain,
! [P_4345] : theorem(implies(implies(not(P_4345),P_4345),P_4345)),
inference(resolution,[status(thm)],[c_249064,c_280]) ).
tff(c_194,plain,
! [A_50,Y_13,X_12] : axiom(implies(implies(A_50,Y_13),implies(implies(X_12,A_50),implies(X_12,Y_13)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_191]) ).
tff(c_18944,plain,
! [B_1040,X_1041] :
( theorem(B_1040)
| ~ theorem(implies(implies(X_1041,and(X_1041,X_1041)),B_1040)) ),
inference(resolution,[status(thm)],[c_14596,c_4099]) ).
tff(c_21957,plain,
! [B_1120,X_1121] :
( theorem(B_1120)
| ~ axiom(implies(implies(X_1121,and(X_1121,X_1121)),B_1120)) ),
inference(resolution,[status(thm)],[c_14,c_18944]) ).
tff(c_38355,plain,
! [X_1514,A_1515] : theorem(implies(implies(X_1514,A_1515),implies(X_1514,and(A_1515,A_1515)))),
inference(resolution,[status(thm)],[c_194,c_21957]) ).
tff(c_38447,plain,
! [X_1514,A_1515] :
( theorem(implies(X_1514,and(A_1515,A_1515)))
| ~ theorem(implies(X_1514,A_1515)) ),
inference(resolution,[status(thm)],[c_38355,c_5873]) ).
tff(c_5029,plain,
! [P_474,Q_475,Y_476] :
( ~ theorem(implies(P_474,not(Q_475)))
| ~ theorem(or(and(P_474,Q_475),Y_476))
| theorem(Y_476) ),
inference(superposition,[status(thm),theory(equality)],[c_331,c_16]) ).
tff(c_30785,plain,
! [P_1317,Q_1318,Y_1319] :
( ~ theorem(implies(implies(P_1317,Q_1318),not(implies(Q_1318,P_1317))))
| ~ theorem(or(equivalent(P_1317,Q_1318),Y_1319))
| theorem(Y_1319) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_5029]) ).
tff(c_258773,plain,
! [Q_4498,P_4499,Y_4500] :
( ~ theorem(implies(implies(not(Q_4498),P_4499),and(P_4499,Q_4498)))
| ~ theorem(or(equivalent(not(Q_4498),P_4499),Y_4500))
| theorem(Y_4500) ),
inference(superposition,[status(thm),theory(equality)],[c_23,c_30785]) ).
tff(c_258850,plain,
! [A_1515,Y_4500] :
( ~ theorem(or(equivalent(not(A_1515),A_1515),Y_4500))
| theorem(Y_4500)
| ~ theorem(implies(implies(not(A_1515),A_1515),A_1515)) ),
inference(resolution,[status(thm)],[c_38447,c_258773]) ).
tff(c_270984,plain,
! [A_4611,Y_4612] :
( ~ theorem(or(equivalent(not(A_4611),A_4611),Y_4612))
| theorem(Y_4612) ),
inference(demodulation,[status(thm),theory(equality)],[c_249211,c_258850]) ).
tff(c_271630,plain,
! [A_4613] : theorem(not(equivalent(not(A_4613),A_4613))),
inference(resolution,[status(thm)],[c_222318,c_270984]) ).
tff(c_38459,plain,
! [Q_1516,P_1517] :
( theorem(implies(Q_1516,not(P_1517)))
| ~ theorem(not(and(P_1517,Q_1516))) ),
inference(resolution,[status(thm)],[c_411,c_17316]) ).
tff(c_4596,plain,
! [X_447] : theorem(implies(X_447,not(not(X_447)))),
inference(resolution,[status(thm)],[c_4354,c_320]) ).
tff(c_4624,plain,
! [P_17,Q_18] : theorem(implies(implies(P_17,not(Q_18)),not(and(P_17,Q_18)))),
inference(superposition,[status(thm),theory(equality)],[c_23,c_4596]) ).
tff(c_7145,plain,
! [P_543,Q_544] : theorem(or(and(P_543,Q_544),not(and(P_543,Q_544)))),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_4624]) ).
tff(c_385,plain,
! [P_72,Q_73,Y_74] :
( ~ theorem(implies(P_72,not(Q_73)))
| ~ theorem(or(and(P_72,Q_73),Y_74))
| theorem(Y_74) ),
inference(superposition,[status(thm),theory(equality)],[c_331,c_16]) ).
tff(c_7174,plain,
! [P_543,Q_544] :
( ~ theorem(implies(P_543,not(Q_544)))
| theorem(not(and(P_543,Q_544))) ),
inference(resolution,[status(thm)],[c_7145,c_385]) ).
tff(c_62972,plain,
! [Q_2029,P_2030] :
( theorem(not(and(Q_2029,P_2030)))
| ~ theorem(not(and(P_2030,Q_2029))) ),
inference(resolution,[status(thm)],[c_38459,c_7174]) ).
tff(c_63028,plain,
! [Q_20,P_19] :
( theorem(not(and(implies(Q_20,P_19),implies(P_19,Q_20))))
| ~ theorem(not(equivalent(P_19,Q_20))) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_62972]) ).
tff(c_63069,plain,
! [Q_20,P_19] :
( theorem(not(equivalent(Q_20,P_19)))
| ~ theorem(not(equivalent(P_19,Q_20))) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_63028]) ).
tff(c_271707,plain,
! [A_4613] : theorem(not(equivalent(A_4613,not(A_4613)))),
inference(resolution,[status(thm)],[c_271630,c_63069]) ).
tff(c_22,plain,
~ theorem(not(equivalent(p,not(p)))),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_272160,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_271707,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL326-3 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 14:18:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 126.30/99.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 126.30/100.00
% 126.30/100.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 126.30/100.06
% 126.30/100.06 Inference rules
% 126.30/100.06 ----------------------
% 126.30/100.06 #Ref : 0
% 126.30/100.06 #Sup : 65426
% 126.30/100.06 #Fact : 0
% 126.30/100.06 #Define : 0
% 126.30/100.06 #Split : 3
% 126.30/100.06 #Chain : 0
% 126.30/100.06 #Close : 0
% 126.30/100.06
% 126.30/100.06 Ordering : KBO
% 126.30/100.06
% 126.30/100.06 Simplification rules
% 126.30/100.06 ----------------------
% 126.30/100.06 #Subsume : 18026
% 126.30/100.06 #Demod : 36526
% 126.30/100.06 #Tautology : 9402
% 126.30/100.06 #SimpNegUnit : 285
% 126.30/100.06 #BackRed : 103
% 126.30/100.06
% 126.30/100.06 #Partial instantiations: 0
% 126.30/100.06 #Strategies tried : 1
% 126.30/100.06
% 126.30/100.06 Timing (in seconds)
% 126.30/100.06 ----------------------
% 126.30/100.07 Preprocessing : 0.43
% 126.30/100.07 Parsing : 0.24
% 126.30/100.07 CNF conversion : 0.02
% 126.30/100.07 Main loop : 98.52
% 126.30/100.07 Inferencing : 7.75
% 126.70/100.07 Reduction : 42.66
% 126.70/100.07 Demodulation : 33.12
% 126.70/100.07 BG Simplification : 0.31
% 126.70/100.07 Subsumption : 40.61
% 126.70/100.07 Abstraction : 0.61
% 126.70/100.07 MUC search : 0.00
% 126.70/100.07 Cooper : 0.00
% 126.70/100.07 Total : 99.06
% 126.70/100.07 Index Insertion : 0.00
% 126.70/100.07 Index Deletion : 0.00
% 126.70/100.07 Index Matching : 0.00
% 126.70/100.07 BG Taut test : 0.00
%------------------------------------------------------------------------------