TSTP Solution File: SET600+3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n004.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 10:56:40 EDT 2023
% Result : Theorem 6.81s 2.72s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 160 ( 74 unt; 13 typ; 0 def)
% Number of atoms : 240 ( 102 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 181 ( 88 ~; 85 |; 2 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 142 (; 142 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > #nlpp > empty_set > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_8 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_82,negated_conjecture,
~ ! [B,C] :
( ( union(B,C) = empty_set )
<=> ( ( B = empty_set )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
tff(f_56,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_38,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_48,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_34,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
tff(f_45,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(f_66,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
tff(c_44,plain,
( ( empty_set = '#skF_6' )
| ( empty_set != '#skF_8' )
| ( empty_set != '#skF_7' ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_62,plain,
empty_set != '#skF_7',
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_191,plain,
! [B_49,C_50] :
( member('#skF_1'(B_49,C_50),B_49)
| subset(B_49,C_50) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_8,plain,
! [B_4] : ~ member(B_4,empty_set),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_216,plain,
! [C_50] : subset(empty_set,C_50),
inference(resolution,[status(thm)],[c_191,c_8]) ).
tff(c_16,plain,
! [C_8,B_7] : ( union(C_8,B_7) = union(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_52,plain,
( ( empty_set = '#skF_5' )
| ( union('#skF_7','#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_54,plain,
( ( empty_set = '#skF_5' )
| ( union('#skF_8','#skF_7') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_52]) ).
tff(c_106,plain,
union('#skF_8','#skF_7') = empty_set,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_112,plain,
! [D_31,C_32,B_33] :
( ~ member(D_31,C_32)
| member(D_31,union(B_33,C_32)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_118,plain,
! [D_31] :
( ~ member(D_31,'#skF_7')
| member(D_31,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_106,c_112]) ).
tff(c_126,plain,
! [D_31] : ~ member(D_31,'#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_8,c_118]) ).
tff(c_221,plain,
! [C_52] : subset('#skF_7',C_52),
inference(resolution,[status(thm)],[c_191,c_126]) ).
tff(c_10,plain,
! [C_6,B_5] :
( ( C_6 = B_5 )
| ~ subset(C_6,B_5)
| ~ subset(B_5,C_6) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_229,plain,
! [C_54] :
( ( C_54 = '#skF_7' )
| ~ subset(C_54,'#skF_7') ),
inference(resolution,[status(thm)],[c_221,c_10]) ).
tff(c_241,plain,
empty_set = '#skF_7',
inference(resolution,[status(thm)],[c_216,c_229]) ).
tff(c_252,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_241]) ).
tff(c_253,plain,
empty_set = '#skF_5',
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_254,plain,
union('#skF_8','#skF_7') != empty_set,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_269,plain,
union('#skF_8','#skF_7') != '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_253,c_254]) ).
tff(c_50,plain,
( ( empty_set = '#skF_6' )
| ( union('#skF_7','#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_53,plain,
( ( empty_set = '#skF_6' )
| ( union('#skF_8','#skF_7') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_50]) ).
tff(c_270,plain,
( ( '#skF_5' = '#skF_6' )
| ( union('#skF_8','#skF_7') = '#skF_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_253,c_253,c_53]) ).
tff(c_271,plain,
'#skF_5' = '#skF_6',
inference(negUnitSimplification,[status(thm)],[c_269,c_270]) ).
tff(c_272,plain,
union('#skF_8','#skF_7') != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_271,c_269]) ).
tff(c_276,plain,
empty_set = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_271,c_253]) ).
tff(c_48,plain,
( ( union('#skF_5','#skF_6') != empty_set )
| ( union('#skF_7','#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_56,plain,
( ( union('#skF_6','#skF_5') != empty_set )
| ( union('#skF_8','#skF_7') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_48]) ).
tff(c_285,plain,
( ( union('#skF_6','#skF_6') != '#skF_6' )
| ( union('#skF_8','#skF_7') = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_276,c_271,c_56]) ).
tff(c_286,plain,
union('#skF_6','#skF_6') != '#skF_6',
inference(splitLeft,[status(thm)],[c_285]) ).
tff(c_28,plain,
! [B_15] :
( empty(B_15)
| member('#skF_2'(B_15),B_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_469,plain,
! [D_92,C_93,B_94] :
( member(D_92,C_93)
| member(D_92,B_94)
| ~ member(D_92,union(B_94,C_93)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_498,plain,
! [B_94,C_93] :
( member('#skF_2'(union(B_94,C_93)),C_93)
| member('#skF_2'(union(B_94,C_93)),B_94)
| empty(union(B_94,C_93)) ),
inference(resolution,[status(thm)],[c_28,c_469]) ).
tff(c_1404,plain,
! [B_200] :
( empty(union(B_200,B_200))
| member('#skF_2'(union(B_200,B_200)),B_200) ),
inference(factorization,[status(thm),theory(equality)],[c_498]) ).
tff(c_257,plain,
! [B_4] : ~ member(B_4,'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_253,c_8]) ).
tff(c_273,plain,
! [B_4] : ~ member(B_4,'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_271,c_257]) ).
tff(c_1425,plain,
empty(union('#skF_6','#skF_6')),
inference(resolution,[status(thm)],[c_1404,c_273]) ).
tff(c_22,plain,
! [B_9,C_10] :
( member('#skF_1'(B_9,C_10),B_9)
| subset(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( ~ member(D_3,C_2)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_376,plain,
! [B_78,C_79] :
( ~ member('#skF_1'(B_78,C_79),C_79)
| subset(B_78,C_79) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_832,plain,
! [B_131,B_132,C_133] :
( subset(B_131,union(B_132,C_133))
| ~ member('#skF_1'(B_131,union(B_132,C_133)),C_133) ),
inference(resolution,[status(thm)],[c_4,c_376]) ).
tff(c_859,plain,
! [B_134,B_135] : subset(B_134,union(B_135,B_134)),
inference(resolution,[status(thm)],[c_22,c_832]) ).
tff(c_294,plain,
! [B_57,C_58] :
( member('#skF_1'(B_57,C_58),B_57)
| subset(B_57,C_58) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_26,plain,
! [C_18,B_15] :
( ~ member(C_18,B_15)
| ~ empty(B_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_303,plain,
! [B_57,C_58] :
( ~ empty(B_57)
| subset(B_57,C_58) ),
inference(resolution,[status(thm)],[c_294,c_26]) ).
tff(c_339,plain,
! [C_74,B_75] :
( ( C_74 = B_75 )
| ~ subset(C_74,B_75)
| ~ subset(B_75,C_74) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_346,plain,
! [C_58,B_57] :
( ( C_58 = B_57 )
| ~ subset(C_58,B_57)
| ~ empty(B_57) ),
inference(resolution,[status(thm)],[c_303,c_339]) ).
tff(c_1195,plain,
! [B_173,B_174] :
( ( union(B_173,B_174) = B_174 )
| ~ empty(union(B_173,B_174)) ),
inference(resolution,[status(thm)],[c_859,c_346]) ).
tff(c_1198,plain,
! [B_7,C_8] :
( ( union(B_7,C_8) = C_8 )
| ~ empty(union(C_8,B_7)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1195]) ).
tff(c_1437,plain,
union('#skF_6','#skF_6') = '#skF_6',
inference(resolution,[status(thm)],[c_1425,c_1198]) ).
tff(c_1479,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_286,c_1437]) ).
tff(c_1480,plain,
union('#skF_8','#skF_7') = '#skF_6',
inference(splitRight,[status(thm)],[c_285]) ).
tff(c_1493,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_272,c_1480]) ).
tff(c_1495,plain,
empty_set = '#skF_7',
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_46,plain,
( ( empty_set = '#skF_5' )
| ( empty_set != '#skF_8' )
| ( empty_set != '#skF_7' ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_1503,plain,
( ( '#skF_7' = '#skF_5' )
| ( '#skF_7' != '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1495,c_1495,c_46]) ).
tff(c_1504,plain,
'#skF_7' != '#skF_8',
inference(splitLeft,[status(thm)],[c_1503]) ).
tff(c_1603,plain,
! [B_218,C_219] :
( member('#skF_1'(B_218,C_219),B_218)
| subset(B_218,C_219) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1539,plain,
! [B_205] :
( empty(B_205)
| member('#skF_2'(B_205),B_205) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1496,plain,
! [B_4] : ~ member(B_4,'#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_8]) ).
tff(c_1547,plain,
empty('#skF_7'),
inference(resolution,[status(thm)],[c_1539,c_1496]) ).
tff(c_1549,plain,
( ( '#skF_7' = '#skF_5' )
| ( union('#skF_8','#skF_7') = '#skF_7' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1495,c_54]) ).
tff(c_1550,plain,
union('#skF_8','#skF_7') = '#skF_7',
inference(splitLeft,[status(thm)],[c_1549]) ).
tff(c_1556,plain,
! [D_206,C_207,B_208] :
( ~ member(D_206,C_207)
| member(D_206,union(B_208,C_207)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_1572,plain,
! [B_209,C_210,D_211] :
( ~ empty(union(B_209,C_210))
| ~ member(D_211,C_210) ),
inference(resolution,[status(thm)],[c_1556,c_26]) ).
tff(c_1581,plain,
! [C_212,B_213,D_214] :
( ~ empty(union(C_212,B_213))
| ~ member(D_214,C_212) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1572]) ).
tff(c_1583,plain,
! [D_214] :
( ~ empty('#skF_7')
| ~ member(D_214,'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_1550,c_1581]) ).
tff(c_1589,plain,
! [D_214] : ~ member(D_214,'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_1547,c_1583]) ).
tff(c_1615,plain,
! [C_219] : subset('#skF_8',C_219),
inference(resolution,[status(thm)],[c_1603,c_1589]) ).
tff(c_1618,plain,
! [C_220] : subset('#skF_7',C_220),
inference(resolution,[status(thm)],[c_1603,c_1496]) ).
tff(c_1632,plain,
! [C_224] :
( ( C_224 = '#skF_7' )
| ~ subset(C_224,'#skF_7') ),
inference(resolution,[status(thm)],[c_1618,c_10]) ).
tff(c_1640,plain,
'#skF_7' = '#skF_8',
inference(resolution,[status(thm)],[c_1615,c_1632]) ).
tff(c_1653,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1504,c_1640]) ).
tff(c_1654,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_1549]) ).
tff(c_1655,plain,
union('#skF_8','#skF_7') != '#skF_7',
inference(splitRight,[status(thm)],[c_1549]) ).
tff(c_1675,plain,
union('#skF_8','#skF_5') != '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_1654,c_1654,c_1655]) ).
tff(c_1659,plain,
empty_set = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_1654,c_1495]) ).
tff(c_1676,plain,
( ( '#skF_5' = '#skF_6' )
| ( union('#skF_8','#skF_5') = '#skF_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1659,c_1654,c_1659,c_53]) ).
tff(c_1677,plain,
'#skF_5' = '#skF_6',
inference(negUnitSimplification,[status(thm)],[c_1675,c_1676]) ).
tff(c_1678,plain,
union('#skF_8','#skF_6') != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1677,c_1675]) ).
tff(c_1683,plain,
'#skF_7' = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1654]) ).
tff(c_1681,plain,
empty_set = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1659]) ).
tff(c_1771,plain,
( ( union('#skF_6','#skF_6') != '#skF_6' )
| ( union('#skF_8','#skF_6') = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1683,c_1681,c_1681,c_1677,c_56]) ).
tff(c_1772,plain,
union('#skF_6','#skF_6') != '#skF_6',
inference(negUnitSimplification,[status(thm)],[c_1678,c_1771]) ).
tff(c_1836,plain,
! [D_257,C_258,B_259] :
( member(D_257,C_258)
| member(D_257,B_259)
| ~ member(D_257,union(B_259,C_258)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_1860,plain,
! [B_259,C_258] :
( member('#skF_2'(union(B_259,C_258)),C_258)
| member('#skF_2'(union(B_259,C_258)),B_259)
| empty(union(B_259,C_258)) ),
inference(resolution,[status(thm)],[c_28,c_1836]) ).
tff(c_2878,plain,
! [C_376] :
( empty(union(C_376,C_376))
| member('#skF_2'(union(C_376,C_376)),C_376) ),
inference(factorization,[status(thm),theory(equality)],[c_1860]) ).
tff(c_1658,plain,
! [B_4] : ~ member(B_4,'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1654,c_1496]) ).
tff(c_1680,plain,
! [B_4] : ~ member(B_4,'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1658]) ).
tff(c_2899,plain,
empty(union('#skF_6','#skF_6')),
inference(resolution,[status(thm)],[c_2878,c_1680]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( ~ member(D_3,B_1)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_1744,plain,
! [B_241,C_242] :
( ~ member('#skF_1'(B_241,C_242),C_242)
| subset(B_241,C_242) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_2207,plain,
! [B_297,B_298,C_299] :
( subset(B_297,union(B_298,C_299))
| ~ member('#skF_1'(B_297,union(B_298,C_299)),B_298) ),
inference(resolution,[status(thm)],[c_6,c_1744]) ).
tff(c_2234,plain,
! [B_300,C_301] : subset(B_300,union(B_300,C_301)),
inference(resolution,[status(thm)],[c_22,c_2207]) ).
tff(c_2263,plain,
! [B_302,C_303] : subset(B_302,union(C_303,B_302)),
inference(superposition,[status(thm),theory(equality)],[c_16,c_2234]) ).
tff(c_1755,plain,
! [B_243,C_244] :
( member('#skF_1'(B_243,C_244),B_243)
| subset(B_243,C_244) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1777,plain,
! [B_246,C_247] :
( ~ empty(B_246)
| subset(B_246,C_247) ),
inference(resolution,[status(thm)],[c_1755,c_26]) ).
tff(c_1780,plain,
! [C_247,B_246] :
( ( C_247 = B_246 )
| ~ subset(C_247,B_246)
| ~ empty(B_246) ),
inference(resolution,[status(thm)],[c_1777,c_10]) ).
tff(c_2507,plain,
! [C_332,B_333] :
( ( union(C_332,B_333) = B_333 )
| ~ empty(union(C_332,B_333)) ),
inference(resolution,[status(thm)],[c_2263,c_1780]) ).
tff(c_2513,plain,
! [C_8,B_7] :
( ( union(C_8,B_7) = B_7 )
| ~ empty(union(B_7,C_8)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_2507]) ).
tff(c_2919,plain,
union('#skF_6','#skF_6') = '#skF_6',
inference(resolution,[status(thm)],[c_2899,c_2513]) ).
tff(c_2960,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1772,c_2919]) ).
tff(c_2962,plain,
'#skF_7' = '#skF_8',
inference(splitRight,[status(thm)],[c_1503]) ).
tff(c_2961,plain,
'#skF_7' = '#skF_5',
inference(splitRight,[status(thm)],[c_1503]) ).
tff(c_2999,plain,
'#skF_5' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_2962,c_2961]) ).
tff(c_2994,plain,
empty_set = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_2961,c_1495]) ).
tff(c_3016,plain,
empty_set = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_2999,c_2994]) ).
tff(c_1494,plain,
( ( empty_set != '#skF_8' )
| ( empty_set = '#skF_6' ) ),
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_2963,plain,
( ( '#skF_7' != '#skF_8' )
| ( '#skF_7' = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1495,c_1494]) ).
tff(c_2964,plain,
'#skF_7' != '#skF_8',
inference(splitLeft,[status(thm)],[c_2963]) ).
tff(c_2990,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2962,c_2964]) ).
tff(c_2991,plain,
'#skF_7' = '#skF_6',
inference(splitRight,[status(thm)],[c_2963]) ).
tff(c_3004,plain,
'#skF_6' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_2962,c_2991]) ).
tff(c_3009,plain,
( ( empty_set = '#skF_8' )
| ( union('#skF_8','#skF_8') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2962,c_3004,c_53]) ).
tff(c_3010,plain,
union('#skF_8','#skF_8') = empty_set,
inference(splitLeft,[status(thm)],[c_3009]) ).
tff(c_3023,plain,
union('#skF_8','#skF_8') = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_3016,c_3010]) ).
tff(c_42,plain,
( ( union('#skF_5','#skF_6') != empty_set )
| ( empty_set != '#skF_8' )
| ( empty_set != '#skF_7' ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_55,plain,
( ( union('#skF_6','#skF_5') != empty_set )
| ( empty_set != '#skF_8' )
| ( empty_set != '#skF_7' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_42]) ).
tff(c_3073,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3016,c_2962,c_3016,c_3023,c_3016,c_2999,c_3004,c_55]) ).
tff(c_3074,plain,
empty_set = '#skF_8',
inference(splitRight,[status(thm)],[c_3009]) ).
tff(c_3075,plain,
union('#skF_8','#skF_8') != empty_set,
inference(splitRight,[status(thm)],[c_3009]) ).
tff(c_3088,plain,
union('#skF_8','#skF_8') != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_3074,c_3075]) ).
tff(c_3267,plain,
! [D_415,C_416,B_417] :
( member(D_415,C_416)
| member(D_415,B_417)
| ~ member(D_415,union(B_417,C_416)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_3291,plain,
! [B_417,C_416] :
( member('#skF_2'(union(B_417,C_416)),C_416)
| member('#skF_2'(union(B_417,C_416)),B_417)
| empty(union(B_417,C_416)) ),
inference(resolution,[status(thm)],[c_28,c_3267]) ).
tff(c_4309,plain,
! [C_534] :
( empty(union(C_534,C_534))
| member('#skF_2'(union(C_534,C_534)),C_534) ),
inference(factorization,[status(thm),theory(equality)],[c_3291]) ).
tff(c_2993,plain,
! [B_4] : ~ member(B_4,'#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_2961,c_1496]) ).
tff(c_3086,plain,
! [B_4] : ~ member(B_4,'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_2999,c_2993]) ).
tff(c_4330,plain,
empty(union('#skF_8','#skF_8')),
inference(resolution,[status(thm)],[c_4309,c_3086]) ).
tff(c_3226,plain,
! [B_407,C_408] :
( ~ member('#skF_1'(B_407,C_408),C_408)
| subset(B_407,C_408) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_3675,plain,
! [B_459,B_460,C_461] :
( subset(B_459,union(B_460,C_461))
| ~ member('#skF_1'(B_459,union(B_460,C_461)),B_460) ),
inference(resolution,[status(thm)],[c_6,c_3226]) ).
tff(c_3702,plain,
! [B_462,C_463] : subset(B_462,union(B_462,C_463)),
inference(resolution,[status(thm)],[c_22,c_3675]) ).
tff(c_3735,plain,
! [B_464,C_465] : subset(B_464,union(C_465,B_464)),
inference(superposition,[status(thm),theory(equality)],[c_16,c_3702]) ).
tff(c_3157,plain,
! [B_394,C_395] :
( member('#skF_1'(B_394,C_395),B_394)
| subset(B_394,C_395) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_3166,plain,
! [B_394,C_395] :
( ~ empty(B_394)
| subset(B_394,C_395) ),
inference(resolution,[status(thm)],[c_3157,c_26]) ).
tff(c_3169,plain,
! [C_399,B_400] :
( ( C_399 = B_400 )
| ~ subset(C_399,B_400)
| ~ subset(B_400,C_399) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_3176,plain,
! [C_395,B_394] :
( ( C_395 = B_394 )
| ~ subset(C_395,B_394)
| ~ empty(B_394) ),
inference(resolution,[status(thm)],[c_3166,c_3169]) ).
tff(c_4035,plain,
! [C_499,B_500] :
( ( union(C_499,B_500) = B_500 )
| ~ empty(union(C_499,B_500)) ),
inference(resolution,[status(thm)],[c_3735,c_3176]) ).
tff(c_4041,plain,
! [C_8,B_7] :
( ( union(C_8,B_7) = B_7 )
| ~ empty(union(B_7,C_8)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_4035]) ).
tff(c_4344,plain,
union('#skF_8','#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_4330,c_4041]) ).
tff(c_4387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3088,c_4344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.13 % 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
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 16:10:26 EDT 2023
% 0.14/0.34 % CPUTime :
% 6.81/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.81/2.74
% 6.81/2.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.32/2.79
% 7.32/2.79 Inference rules
% 7.32/2.79 ----------------------
% 7.32/2.79 #Ref : 0
% 7.32/2.79 #Sup : 1019
% 7.32/2.79 #Fact : 6
% 7.32/2.79 #Define : 0
% 7.32/2.79 #Split : 7
% 7.32/2.79 #Chain : 0
% 7.32/2.79 #Close : 0
% 7.32/2.79
% 7.32/2.79 Ordering : KBO
% 7.32/2.79
% 7.32/2.79 Simplification rules
% 7.32/2.79 ----------------------
% 7.32/2.79 #Subsume : 281
% 7.32/2.79 #Demod : 174
% 7.32/2.79 #Tautology : 216
% 7.32/2.79 #SimpNegUnit : 14
% 7.32/2.79 #BackRed : 26
% 7.32/2.79
% 7.32/2.79 #Partial instantiations: 0
% 7.32/2.79 #Strategies tried : 1
% 7.32/2.79
% 7.32/2.79 Timing (in seconds)
% 7.32/2.79 ----------------------
% 7.32/2.79 Preprocessing : 0.50
% 7.32/2.79 Parsing : 0.25
% 7.32/2.79 CNF conversion : 0.04
% 7.32/2.79 Main loop : 1.20
% 7.32/2.79 Inferencing : 0.47
% 7.32/2.79 Reduction : 0.33
% 7.32/2.79 Demodulation : 0.24
% 7.32/2.79 BG Simplification : 0.04
% 7.32/2.79 Subsumption : 0.26
% 7.32/2.79 Abstraction : 0.05
% 7.32/2.79 MUC search : 0.00
% 7.32/2.79 Cooper : 0.00
% 7.32/2.79 Total : 1.78
% 7.32/2.79 Index Insertion : 0.00
% 7.32/2.79 Index Deletion : 0.00
% 7.32/2.79 Index Matching : 0.00
% 7.32/2.79 BG Taut test : 0.00
%------------------------------------------------------------------------------