TSTP Solution File: SET927+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET927+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 : n032.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 10:57:21 EDT 2023
% Result : Theorem 3.97s 1.97s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 149 ( 81 unt; 13 typ; 0 def)
% Number of atoms : 221 ( 90 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 167 ( 82 ~; 81 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 57 (; 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_difference > #nlpp > singleton > #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(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
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('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_48,negated_conjecture,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
tff(f_57,axiom,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
tff(f_28,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(c_20,plain,
( ~ in('#skF_3','#skF_5')
| ~ in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_73,plain,
~ in('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_14,plain,
( ~ in('#skF_3','#skF_5')
| ( '#skF_7' != '#skF_6' )
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_72,plain,
'#skF_7' != '#skF_6',
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_26,plain,
( ~ in('#skF_3','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_81,plain,
~ in('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_24,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_106,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6'),
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_119,plain,
! [B_20,A_21,C_22] :
( ( B_20 = A_21 )
| in(B_20,C_22)
| ( set_difference(unordered_pair(A_21,B_20),C_22) != singleton(A_21) ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_122,plain,
( ( '#skF_7' = '#skF_6' )
| in('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_106,c_119]) ).
tff(c_135,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_73,c_72,c_122]) ).
tff(c_136,plain,
( in('#skF_4','#skF_5')
| ( '#skF_3' = '#skF_4' ) ),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_138,plain,
'#skF_3' = '#skF_4',
inference(splitLeft,[status(thm)],[c_136]) ).
tff(c_139,plain,
~ in('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_81]) ).
tff(c_32,plain,
! [B_6,C_7] :
( ( set_difference(unordered_pair(B_6,B_6),C_7) = singleton(B_6) )
| in(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_137,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_24]) ).
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_28]) ).
tff(c_22,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != singleton('#skF_3') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_37,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22]) ).
tff(c_261,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_138,c_37]) ).
tff(c_262,plain,
set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_137,c_261]) ).
tff(c_271,plain,
in('#skF_4','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_32,c_262]) ).
tff(c_279,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_271]) ).
tff(c_280,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_136]) ).
tff(c_309,plain,
! [B_41,C_42,A_43] :
( ~ in(B_41,C_42)
| ( set_difference(unordered_pair(A_43,B_41),C_42) = singleton(A_43) )
| in(A_43,C_42) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_343,plain,
! [A_1,C_42,B_2] :
( ~ in(A_1,C_42)
| ( set_difference(unordered_pair(A_1,B_2),C_42) = singleton(B_2) )
| in(B_2,C_42) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_309]) ).
tff(c_400,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_137,c_37]) ).
tff(c_403,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_343,c_400]) ).
tff(c_409,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_403]) ).
tff(c_411,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_81,c_409]) ).
tff(c_412,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_455,plain,
! [B_52,A_53,C_54] :
( ( B_52 = A_53 )
| in(B_52,C_54)
| ( set_difference(unordered_pair(A_53,B_52),C_54) != singleton(A_53) ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_461,plain,
( ( '#skF_7' = '#skF_6' )
| in('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_412,c_455]) ).
tff(c_473,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_73,c_72,c_461]) ).
tff(c_474,plain,
( ~ in('#skF_3','#skF_5')
| in('#skF_6','#skF_8') ),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_479,plain,
~ in('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_474]) ).
tff(c_475,plain,
in('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| ~ in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_501,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_475,c_18]) ).
tff(c_502,plain,
in('#skF_6','#skF_8'),
inference(splitLeft,[status(thm)],[c_501]) ).
tff(c_530,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6'),
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_30,plain,
! [A_5,C_7,B_6] :
( ~ in(A_5,C_7)
| ( set_difference(unordered_pair(A_5,B_6),C_7) != singleton(A_5) ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_540,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_530,c_30]) ).
tff(c_551,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_502,c_540]) ).
tff(c_552,plain,
( in('#skF_4','#skF_5')
| ( '#skF_3' = '#skF_4' ) ),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_554,plain,
'#skF_3' = '#skF_4',
inference(splitLeft,[status(thm)],[c_552]) ).
tff(c_555,plain,
~ in('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_554,c_479]) ).
tff(c_553,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_678,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_554,c_554,c_37]) ).
tff(c_679,plain,
set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_553,c_678]) ).
tff(c_688,plain,
in('#skF_4','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_32,c_679]) ).
tff(c_696,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_555,c_688]) ).
tff(c_697,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_552]) ).
tff(c_714,plain,
! [B_81,C_82,A_83] :
( ~ in(B_81,C_82)
| ( set_difference(unordered_pair(A_83,B_81),C_82) = singleton(A_83) )
| in(A_83,C_82) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_748,plain,
! [A_1,C_82,B_2] :
( ~ in(A_1,C_82)
| ( set_difference(unordered_pair(A_1,B_2),C_82) = singleton(B_2) )
| in(B_2,C_82) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_714]) ).
tff(c_809,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_553,c_37]) ).
tff(c_812,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_748,c_809]) ).
tff(c_818,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_697,c_812]) ).
tff(c_820,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_479,c_818]) ).
tff(c_821,plain,
( in('#skF_4','#skF_5')
| ( '#skF_3' = '#skF_4' ) ),
inference(splitRight,[status(thm)],[c_501]) ).
tff(c_823,plain,
'#skF_3' = '#skF_4',
inference(splitLeft,[status(thm)],[c_821]) ).
tff(c_824,plain,
~ in('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_823,c_479]) ).
tff(c_822,plain,
~ in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_501]) ).
tff(c_16,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != singleton('#skF_3') )
| ~ in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_35,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| ~ in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16]) ).
tff(c_857,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4') )
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_475,c_823,c_823,c_35]) ).
tff(c_858,plain,
set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_822,c_857]) ).
tff(c_861,plain,
in('#skF_4','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_32,c_858]) ).
tff(c_865,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_824,c_861]) ).
tff(c_866,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_821]) ).
tff(c_912,plain,
! [B_102,C_103,A_104] :
( ~ in(B_102,C_103)
| ( set_difference(unordered_pair(A_104,B_102),C_103) = singleton(A_104) )
| in(A_104,C_103) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_954,plain,
! [B_105,C_106,A_107] :
( ~ in(B_105,C_106)
| ( set_difference(unordered_pair(B_105,A_107),C_106) = singleton(A_107) )
| in(A_107,C_106) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_912]) ).
tff(c_910,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_475,c_35]) ).
tff(c_911,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_822,c_910]) ).
tff(c_963,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_954,c_911]) ).
tff(c_998,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_866,c_963]) ).
tff(c_1000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_479,c_998]) ).
tff(c_1001,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_474]) ).
tff(c_1002,plain,
in('#skF_3','#skF_5'),
inference(splitRight,[status(thm)],[c_474]) ).
tff(c_1031,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = singleton('#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_1002,c_26]) ).
tff(c_1035,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_1031,c_30]) ).
tff(c_1041,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1001,c_1035]) ).
tff(c_1042,plain,
( ~ in('#skF_3','#skF_5')
| in('#skF_6','#skF_8') ),
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_1048,plain,
~ in('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_1042]) ).
tff(c_1043,plain,
'#skF_7' = '#skF_6',
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_12,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| ( '#skF_7' != '#skF_6' )
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_1059,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_12]) ).
tff(c_1060,plain,
in('#skF_6','#skF_8'),
inference(splitLeft,[status(thm)],[c_1059]) ).
tff(c_1092,plain,
( ( '#skF_3' = '#skF_4' )
| in('#skF_4','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_24]) ).
tff(c_1093,plain,
set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') = singleton('#skF_6'),
inference(splitLeft,[status(thm)],[c_1092]) ).
tff(c_1051,plain,
! [A_113,C_114,B_115] :
( ~ in(A_113,C_114)
| ( set_difference(unordered_pair(A_113,B_115),C_114) != singleton(A_113) ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1054,plain,
! [A_1,C_114,B_2] :
( ~ in(A_1,C_114)
| ( set_difference(unordered_pair(B_2,A_1),C_114) != singleton(A_1) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1051]) ).
tff(c_1097,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_1093,c_1054]) ).
tff(c_1112,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1060,c_1097]) ).
tff(c_1113,plain,
( in('#skF_4','#skF_5')
| ( '#skF_3' = '#skF_4' ) ),
inference(splitRight,[status(thm)],[c_1092]) ).
tff(c_1115,plain,
'#skF_3' = '#skF_4',
inference(splitLeft,[status(thm)],[c_1113]) ).
tff(c_1116,plain,
~ in('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1115,c_1048]) ).
tff(c_1114,plain,
set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') != singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_1092]) ).
tff(c_1252,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4') )
| ( set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_1115,c_1115,c_37]) ).
tff(c_1253,plain,
set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_1114,c_1252]) ).
tff(c_1262,plain,
in('#skF_4','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_32,c_1253]) ).
tff(c_1270,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1116,c_1262]) ).
tff(c_1271,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_1113]) ).
tff(c_1293,plain,
! [B_139,C_140,A_141] :
( ~ in(B_139,C_140)
| ( set_difference(unordered_pair(A_141,B_139),C_140) = singleton(A_141) )
| in(A_141,C_140) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1357,plain,
! [B_145,C_146,A_147] :
( ~ in(B_145,C_146)
| ( set_difference(unordered_pair(B_145,A_147),C_146) = singleton(A_147) )
| in(A_147,C_146) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1293]) ).
tff(c_1351,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| ( set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') = singleton('#skF_6') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_37]) ).
tff(c_1352,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_1114,c_1351]) ).
tff(c_1363,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_1357,c_1352]) ).
tff(c_1404,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1271,c_1363]) ).
tff(c_1406,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1048,c_1404]) ).
tff(c_1407,plain,
( in('#skF_4','#skF_5')
| ( '#skF_3' = '#skF_4' ) ),
inference(splitRight,[status(thm)],[c_1059]) ).
tff(c_1409,plain,
'#skF_3' = '#skF_4',
inference(splitLeft,[status(thm)],[c_1407]) ).
tff(c_1410,plain,
~ in('#skF_4','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1409,c_1048]) ).
tff(c_1408,plain,
~ in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_1059]) ).
tff(c_10,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != singleton('#skF_3') )
| ( '#skF_7' != '#skF_6' )
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_36,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| ( '#skF_7' != '#skF_6' )
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10]) ).
tff(c_1456,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4') )
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_1409,c_1409,c_36]) ).
tff(c_1457,plain,
set_difference(unordered_pair('#skF_4','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_1408,c_1456]) ).
tff(c_1460,plain,
in('#skF_4','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_32,c_1457]) ).
tff(c_1464,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1410,c_1460]) ).
tff(c_1465,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_1407]) ).
tff(c_1527,plain,
! [B_167,C_168,A_169] :
( ~ in(B_167,C_168)
| ( set_difference(unordered_pair(A_169,B_167),C_168) = singleton(A_169) )
| in(A_169,C_168) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1569,plain,
! [B_170,C_171,A_172] :
( ~ in(B_170,C_171)
| ( set_difference(unordered_pair(B_170,A_172),C_171) = singleton(A_172) )
| in(A_172,C_171) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1527]) ).
tff(c_1511,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3') )
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_36]) ).
tff(c_1512,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_1408,c_1511]) ).
tff(c_1581,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_1569,c_1512]) ).
tff(c_1614,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1465,c_1581]) ).
tff(c_1616,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1048,c_1614]) ).
tff(c_1617,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_1042]) ).
tff(c_1618,plain,
in('#skF_3','#skF_5'),
inference(splitRight,[status(thm)],[c_1042]) ).
tff(c_1635,plain,
set_difference(unordered_pair('#skF_6','#skF_6'),'#skF_8') = singleton('#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_1618,c_26]) ).
tff(c_1639,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_1635,c_30]) ).
tff(c_1645,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1617,c_1639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % 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
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Aug 3 16:59:06 EDT 2023
% 0.12/0.32 % CPUTime :
% 3.97/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.99
% 3.97/1.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.97/2.03
% 3.97/2.03 Inference rules
% 3.97/2.03 ----------------------
% 3.97/2.03 #Ref : 0
% 3.97/2.03 #Sup : 386
% 3.97/2.03 #Fact : 0
% 3.97/2.03 #Define : 0
% 3.97/2.03 #Split : 17
% 3.97/2.03 #Chain : 0
% 3.97/2.03 #Close : 0
% 3.97/2.03
% 3.97/2.03 Ordering : KBO
% 3.97/2.03
% 3.97/2.03 Simplification rules
% 3.97/2.03 ----------------------
% 3.97/2.03 #Subsume : 94
% 3.97/2.03 #Demod : 108
% 3.97/2.03 #Tautology : 191
% 3.97/2.03 #SimpNegUnit : 43
% 3.97/2.03 #BackRed : 5
% 3.97/2.03
% 3.97/2.03 #Partial instantiations: 0
% 3.97/2.03 #Strategies tried : 1
% 3.97/2.03
% 3.97/2.03 Timing (in seconds)
% 3.97/2.03 ----------------------
% 3.97/2.03 Preprocessing : 0.47
% 3.97/2.03 Parsing : 0.24
% 3.97/2.03 CNF conversion : 0.03
% 3.97/2.03 Main loop : 0.60
% 3.97/2.03 Inferencing : 0.23
% 3.97/2.03 Reduction : 0.16
% 3.97/2.03 Demodulation : 0.12
% 3.97/2.03 BG Simplification : 0.03
% 3.97/2.03 Subsumption : 0.13
% 3.97/2.03 Abstraction : 0.03
% 3.97/2.03 MUC search : 0.00
% 3.97/2.03 Cooper : 0.00
% 3.97/2.03 Total : 1.14
% 3.97/2.03 Index Insertion : 0.00
% 3.97/2.03 Index Deletion : 0.00
% 3.97/2.03 Index Matching : 0.00
% 3.97/2.03 BG Taut test : 0.00
%------------------------------------------------------------------------------