TSTP Solution File: SET931+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n015.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 10:57:22 EDT 2023
% Result : Theorem 4.33s 2.13s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 160 ( 104 unt; 14 typ; 0 def)
% Number of atoms : 246 ( 204 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 156 ( 56 ~; 91 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 80 (; 80 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > unordered_pair > set_difference > #nlpp > singleton > empty_set > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_53,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_57,axiom,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_73,negated_conjecture,
~ ! [A,B,C] :
( ( set_difference(A,unordered_pair(B,C)) = empty_set )
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
tff(f_30,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_46,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
tff(c_20,plain,
! [A_6] : subset(A_6,A_6),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_109,plain,
! [A_19,B_20] :
( ( set_difference(A_19,B_20) = empty_set )
| ~ subset(A_19,B_20) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_125,plain,
! [A_6] : ( set_difference(A_6,A_6) = empty_set ),
inference(resolution,[status(thm)],[c_20,c_109]) ).
tff(c_38,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( empty_set != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_126,plain,
empty_set != '#skF_6',
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_30,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( singleton('#skF_8') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_165,plain,
singleton('#skF_8') != '#skF_6',
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_34,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( singleton('#skF_7') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_190,plain,
singleton('#skF_7') != '#skF_6',
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_2,plain,
! [B_2,A_1] : ( unordered_pair(B_2,A_1) = unordered_pair(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_26,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( unordered_pair('#skF_7','#skF_8') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_46,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( unordered_pair('#skF_8','#skF_7') != '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26]) ).
tff(c_192,plain,
unordered_pair('#skF_8','#skF_7') != '#skF_6',
inference(splitLeft,[status(thm)],[c_46]) ).
tff(c_44,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( set_difference('#skF_6',unordered_pair('#skF_7','#skF_8')) = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_47,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( set_difference('#skF_6',unordered_pair('#skF_8','#skF_7')) = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_44]) ).
tff(c_259,plain,
set_difference('#skF_6',unordered_pair('#skF_8','#skF_7')) = empty_set,
inference(splitLeft,[status(thm)],[c_47]) ).
tff(c_22,plain,
! [A_8,B_9] :
( subset(A_8,B_9)
| ( set_difference(A_8,B_9) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_194,plain,
! [B_30,C_31,A_32] :
( ( unordered_pair(B_30,C_31) = A_32 )
| ( singleton(C_31) = A_32 )
| ( singleton(B_30) = A_32 )
| ( empty_set = A_32 )
| ~ subset(A_32,unordered_pair(B_30,C_31)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_264,plain,
! [B_36,C_37,A_38] :
( ( unordered_pair(B_36,C_37) = A_38 )
| ( singleton(C_37) = A_38 )
| ( singleton(B_36) = A_38 )
| ( empty_set = A_38 )
| ( set_difference(A_38,unordered_pair(B_36,C_37)) != empty_set ) ),
inference(resolution,[status(thm)],[c_22,c_194]) ).
tff(c_267,plain,
( ( unordered_pair('#skF_8','#skF_7') = '#skF_6' )
| ( singleton('#skF_7') = '#skF_6' )
| ( singleton('#skF_8') = '#skF_6' )
| ( empty_set = '#skF_6' ) ),
inference(superposition,[status(thm),theory(equality)],[c_259,c_264]) ).
tff(c_290,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_126,c_165,c_190,c_192,c_267]) ).
tff(c_291,plain,
( ( empty_set = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( unordered_pair('#skF_4','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_47]) ).
tff(c_293,plain,
unordered_pair('#skF_4','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_291]) ).
tff(c_42,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( set_difference('#skF_6',unordered_pair('#skF_7','#skF_8')) = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_48,plain,
( ( set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set )
| ( set_difference('#skF_6',unordered_pair('#skF_8','#skF_7')) = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_42]) ).
tff(c_193,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_294,plain,
set_difference('#skF_3','#skF_3') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_293,c_193]) ).
tff(c_297,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125,c_294]) ).
tff(c_298,plain,
( ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_291]) ).
tff(c_300,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_298]) ).
tff(c_14,plain,
! [B_4,C_5] : subset(empty_set,unordered_pair(B_4,C_5)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_124,plain,
! [B_4,C_5] : ( set_difference(empty_set,unordered_pair(B_4,C_5)) = empty_set ),
inference(resolution,[status(thm)],[c_14,c_109]) ).
tff(c_308,plain,
! [B_4,C_5] : ( set_difference('#skF_3',unordered_pair(B_4,C_5)) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_300,c_300,c_124]) ).
tff(c_304,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_300,c_193]) ).
tff(c_334,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_308,c_304]) ).
tff(c_335,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_298]) ).
tff(c_337,plain,
singleton('#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_335]) ).
tff(c_10,plain,
! [C_5,B_4] : subset(singleton(C_5),unordered_pair(B_4,C_5)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_122,plain,
! [C_5,B_4] : ( set_difference(singleton(C_5),unordered_pair(B_4,C_5)) = empty_set ),
inference(resolution,[status(thm)],[c_10,c_109]) ).
tff(c_344,plain,
! [B_4] : ( set_difference('#skF_3',unordered_pair(B_4,'#skF_5')) = empty_set ),
inference(superposition,[status(thm),theory(equality)],[c_337,c_122]) ).
tff(c_438,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_344,c_193]) ).
tff(c_439,plain,
singleton('#skF_4') = '#skF_3',
inference(splitRight,[status(thm)],[c_335]) ).
tff(c_12,plain,
! [B_4,C_5] : subset(singleton(B_4),unordered_pair(B_4,C_5)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_123,plain,
! [B_4,C_5] : ( set_difference(singleton(B_4),unordered_pair(B_4,C_5)) = empty_set ),
inference(resolution,[status(thm)],[c_12,c_109]) ).
tff(c_444,plain,
! [C_5] : ( set_difference('#skF_3',unordered_pair('#skF_4',C_5)) = empty_set ),
inference(superposition,[status(thm),theory(equality)],[c_439,c_123]) ).
tff(c_513,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_444,c_193]) ).
tff(c_514,plain,
set_difference('#skF_6',unordered_pair('#skF_8','#skF_7')) = empty_set,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_524,plain,
! [B_49,C_50,A_51] :
( ( unordered_pair(B_49,C_50) = A_51 )
| ( singleton(C_50) = A_51 )
| ( singleton(B_49) = A_51 )
| ( empty_set = A_51 )
| ~ subset(A_51,unordered_pair(B_49,C_50)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_590,plain,
! [B_55,C_56,A_57] :
( ( unordered_pair(B_55,C_56) = A_57 )
| ( singleton(C_56) = A_57 )
| ( singleton(B_55) = A_57 )
| ( empty_set = A_57 )
| ( set_difference(A_57,unordered_pair(B_55,C_56)) != empty_set ) ),
inference(resolution,[status(thm)],[c_22,c_524]) ).
tff(c_596,plain,
( ( unordered_pair('#skF_8','#skF_7') = '#skF_6' )
| ( singleton('#skF_7') = '#skF_6' )
| ( singleton('#skF_8') = '#skF_6' )
| ( empty_set = '#skF_6' ) ),
inference(superposition,[status(thm),theory(equality)],[c_514,c_590]) ).
tff(c_620,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_126,c_165,c_190,c_192,c_596]) ).
tff(c_622,plain,
unordered_pair('#skF_8','#skF_7') = '#skF_6',
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_28,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( unordered_pair('#skF_7','#skF_8') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_49,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( unordered_pair('#skF_8','#skF_7') != '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_28]) ).
tff(c_672,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_622,c_49]) ).
tff(c_673,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_672]) ).
tff(c_682,plain,
! [B_4,C_5] : ( set_difference('#skF_3',unordered_pair(B_4,C_5)) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_673,c_673,c_124]) ).
tff(c_621,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_675,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_673,c_621]) ).
tff(c_724,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_682,c_675]) ).
tff(c_725,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( unordered_pair('#skF_4','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_672]) ).
tff(c_727,plain,
unordered_pair('#skF_4','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_725]) ).
tff(c_728,plain,
set_difference('#skF_3','#skF_3') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_727,c_621]) ).
tff(c_731,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125,c_728]) ).
tff(c_732,plain,
( ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_725]) ).
tff(c_736,plain,
singleton('#skF_4') = '#skF_3',
inference(splitLeft,[status(thm)],[c_732]) ).
tff(c_766,plain,
! [C_62] : subset('#skF_3',unordered_pair('#skF_4',C_62)),
inference(superposition,[status(thm),theory(equality)],[c_736,c_12]) ).
tff(c_24,plain,
! [A_8,B_9] :
( ( set_difference(A_8,B_9) = empty_set )
| ~ subset(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_778,plain,
! [C_62] : ( set_difference('#skF_3',unordered_pair('#skF_4',C_62)) = empty_set ),
inference(resolution,[status(thm)],[c_766,c_24]) ).
tff(c_834,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_778,c_621]) ).
tff(c_835,plain,
singleton('#skF_5') = '#skF_3',
inference(splitRight,[status(thm)],[c_732]) ).
tff(c_866,plain,
! [B_67] : subset('#skF_3',unordered_pair(B_67,'#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_835,c_10]) ).
tff(c_878,plain,
! [B_67] : ( set_difference('#skF_3',unordered_pair(B_67,'#skF_5')) = empty_set ),
inference(resolution,[status(thm)],[c_866,c_24]) ).
tff(c_950,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_878,c_621]) ).
tff(c_952,plain,
singleton('#skF_7') = '#skF_6',
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_36,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( singleton('#skF_7') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1041,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_952,c_36]) ).
tff(c_1042,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_1041]) ).
tff(c_1049,plain,
! [B_4,C_5] : ( set_difference('#skF_3',unordered_pair(B_4,C_5)) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_1042,c_1042,c_124]) ).
tff(c_951,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_1045,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_1042,c_951]) ).
tff(c_1075,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1049,c_1045]) ).
tff(c_1076,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( unordered_pair('#skF_4','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1041]) ).
tff(c_1083,plain,
unordered_pair('#skF_4','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1076]) ).
tff(c_1084,plain,
set_difference('#skF_3','#skF_3') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_1083,c_951]) ).
tff(c_1087,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125,c_1084]) ).
tff(c_1088,plain,
( ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1076]) ).
tff(c_1090,plain,
singleton('#skF_4') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1088]) ).
tff(c_1121,plain,
! [C_80] : subset('#skF_3',unordered_pair('#skF_4',C_80)),
inference(superposition,[status(thm),theory(equality)],[c_1090,c_12]) ).
tff(c_1133,plain,
! [C_80] : ( set_difference('#skF_3',unordered_pair('#skF_4',C_80)) = empty_set ),
inference(resolution,[status(thm)],[c_1121,c_24]) ).
tff(c_1140,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1133,c_951]) ).
tff(c_1141,plain,
singleton('#skF_5') = '#skF_3',
inference(splitRight,[status(thm)],[c_1088]) ).
tff(c_1159,plain,
! [B_81] : subset('#skF_3',unordered_pair(B_81,'#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_1141,c_10]) ).
tff(c_1171,plain,
! [B_81] : ( set_difference('#skF_3',unordered_pair(B_81,'#skF_5')) = empty_set ),
inference(resolution,[status(thm)],[c_1159,c_24]) ).
tff(c_1207,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1171,c_951]) ).
tff(c_1209,plain,
singleton('#skF_8') = '#skF_6',
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_32,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( singleton('#skF_8') != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1327,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1209,c_32]) ).
tff(c_1328,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_1327]) ).
tff(c_1335,plain,
! [B_4,C_5] : ( set_difference('#skF_3',unordered_pair(B_4,C_5)) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_1328,c_1328,c_124]) ).
tff(c_1208,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_1332,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_1328,c_1208]) ).
tff(c_1361,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1335,c_1332]) ).
tff(c_1362,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( unordered_pair('#skF_4','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1327]) ).
tff(c_1365,plain,
unordered_pair('#skF_4','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1362]) ).
tff(c_1366,plain,
set_difference('#skF_3','#skF_3') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_1365,c_1208]) ).
tff(c_1369,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125,c_1366]) ).
tff(c_1370,plain,
( ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1362]) ).
tff(c_1372,plain,
singleton('#skF_4') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1370]) ).
tff(c_1402,plain,
! [C_94] : subset('#skF_3',unordered_pair('#skF_4',C_94)),
inference(superposition,[status(thm),theory(equality)],[c_1372,c_12]) ).
tff(c_1414,plain,
! [C_94] : ( set_difference('#skF_3',unordered_pair('#skF_4',C_94)) = empty_set ),
inference(resolution,[status(thm)],[c_1402,c_24]) ).
tff(c_1423,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1414,c_1208]) ).
tff(c_1424,plain,
singleton('#skF_5') = '#skF_3',
inference(splitRight,[status(thm)],[c_1370]) ).
tff(c_1457,plain,
! [B_96] : subset('#skF_3',unordered_pair(B_96,'#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_1424,c_10]) ).
tff(c_1469,plain,
! [B_96] : ( set_difference('#skF_3',unordered_pair(B_96,'#skF_5')) = empty_set ),
inference(resolution,[status(thm)],[c_1457,c_24]) ).
tff(c_1493,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1469,c_1208]) ).
tff(c_1495,plain,
empty_set = '#skF_6',
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_1510,plain,
! [A_6] : ( set_difference(A_6,A_6) = '#skF_6' ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_125]) ).
tff(c_40,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( empty_set = '#skF_3' )
| ( empty_set != '#skF_6' ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1602,plain,
( ( unordered_pair('#skF_4','#skF_5') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' )
| ( '#skF_6' = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1495,c_40]) ).
tff(c_1603,plain,
'#skF_6' = '#skF_3',
inference(splitLeft,[status(thm)],[c_1602]) ).
tff(c_1519,plain,
! [B_4,C_5] : ( set_difference('#skF_6',unordered_pair(B_4,C_5)) = '#skF_6' ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1495,c_124]) ).
tff(c_1608,plain,
! [B_4,C_5] : ( set_difference('#skF_3',unordered_pair(B_4,C_5)) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_1603,c_1603,c_1519]) ).
tff(c_1494,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != empty_set,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_1518,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1494]) ).
tff(c_1609,plain,
set_difference('#skF_3',unordered_pair('#skF_4','#skF_5')) != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_1603,c_1518]) ).
tff(c_1638,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1608,c_1609]) ).
tff(c_1639,plain,
( ( singleton('#skF_4') = '#skF_3' )
| ( singleton('#skF_5') = '#skF_3' )
| ( unordered_pair('#skF_4','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1602]) ).
tff(c_1645,plain,
unordered_pair('#skF_4','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1639]) ).
tff(c_1646,plain,
set_difference('#skF_3','#skF_3') != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1645,c_1518]) ).
tff(c_1649,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1510,c_1646]) ).
tff(c_1650,plain,
( ( singleton('#skF_5') = '#skF_3' )
| ( singleton('#skF_4') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_1639]) ).
tff(c_1652,plain,
singleton('#skF_4') = '#skF_3',
inference(splitLeft,[status(thm)],[c_1650]) ).
tff(c_1682,plain,
! [C_115] : subset('#skF_3',unordered_pair('#skF_4',C_115)),
inference(superposition,[status(thm),theory(equality)],[c_1652,c_12]) ).
tff(c_1496,plain,
! [A_8,B_9] :
( ( set_difference(A_8,B_9) = '#skF_6' )
| ~ subset(A_8,B_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_24]) ).
tff(c_1694,plain,
! [C_115] : ( set_difference('#skF_3',unordered_pair('#skF_4',C_115)) = '#skF_6' ),
inference(resolution,[status(thm)],[c_1682,c_1496]) ).
tff(c_1718,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1694,c_1518]) ).
tff(c_1719,plain,
singleton('#skF_5') = '#skF_3',
inference(splitRight,[status(thm)],[c_1650]) ).
tff(c_1559,plain,
! [C_5,B_4] : ( set_difference(singleton(C_5),unordered_pair(B_4,C_5)) = '#skF_6' ),
inference(demodulation,[status(thm),theory(equality)],[c_1495,c_122]) ).
tff(c_1727,plain,
! [B_4] : ( set_difference('#skF_3',unordered_pair(B_4,'#skF_5')) = '#skF_6' ),
inference(superposition,[status(thm),theory(equality)],[c_1719,c_1559]) ).
tff(c_1772,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1727,c_1518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.15 % 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
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 17:03:14 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.33/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.33/2.14
% 4.33/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.75/2.18
% 4.75/2.18 Inference rules
% 4.75/2.18 ----------------------
% 4.75/2.18 #Ref : 0
% 4.75/2.18 #Sup : 385
% 4.75/2.18 #Fact : 0
% 4.75/2.18 #Define : 0
% 4.75/2.18 #Split : 23
% 4.75/2.18 #Chain : 0
% 4.75/2.18 #Close : 0
% 4.75/2.18
% 4.75/2.18 Ordering : KBO
% 4.75/2.18
% 4.75/2.18 Simplification rules
% 4.75/2.18 ----------------------
% 4.75/2.18 #Subsume : 33
% 4.75/2.18 #Demod : 257
% 4.75/2.18 #Tautology : 273
% 4.75/2.18 #SimpNegUnit : 22
% 4.75/2.18 #BackRed : 84
% 4.75/2.18
% 4.75/2.18 #Partial instantiations: 0
% 4.75/2.18 #Strategies tried : 1
% 4.75/2.18
% 4.75/2.18 Timing (in seconds)
% 4.75/2.18 ----------------------
% 4.75/2.19 Preprocessing : 0.48
% 4.75/2.19 Parsing : 0.24
% 4.75/2.19 CNF conversion : 0.03
% 4.75/2.19 Main loop : 0.62
% 4.75/2.19 Inferencing : 0.20
% 4.75/2.19 Reduction : 0.21
% 4.75/2.19 Demodulation : 0.16
% 4.75/2.19 BG Simplification : 0.03
% 4.75/2.19 Subsumption : 0.12
% 4.75/2.19 Abstraction : 0.03
% 4.75/2.19 MUC search : 0.00
% 4.75/2.19 Cooper : 0.00
% 4.75/2.19 Total : 1.18
% 4.75/2.19 Index Insertion : 0.00
% 4.75/2.19 Index Deletion : 0.00
% 4.75/2.19 Index Matching : 0.00
% 4.75/2.19 BG Taut test : 0.00
%------------------------------------------------------------------------------