TSTP Solution File: SEU156+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU156+3 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n009.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 10:57:49 EDT 2023
% Result : Theorem 245.71s 198.22s
% Output : CNFRefutation 245.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 134 ( 72 unt; 11 typ; 0 def)
% Number of atoms : 198 ( 192 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 136 ( 61 ~; 69 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 179 (; 179 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > unordered_pair > ordered_pair > #nlpp > singleton > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $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('#skF_4',type,
'#skF_4': $i ).
tff(f_58,axiom,
! [A] : ( unordered_pair(A,A) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
tff(f_30,axiom,
! [A,B] : ( ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
tff(f_28,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_56,negated_conjecture,
~ ! [A,B,C,D] :
( ( ordered_pair(A,B) = ordered_pair(C,D) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
tff(f_49,axiom,
! [A,B,C,D] :
~ ( ( unordered_pair(A,B) = unordered_pair(C,D) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
tff(f_66,axiom,
! [A,B,C] :
( ( singleton(A) = unordered_pair(B,C) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
tff(f_70,axiom,
! [A,B,C] :
( ( singleton(A) = unordered_pair(B,C) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
tff(c_20,plain,
! [A_13] : ( unordered_pair(A_13,A_13) = singleton(A_13) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_15751,plain,
! [A_386,B_387] : ( unordered_pair(unordered_pair(A_386,B_387),singleton(A_386)) = ordered_pair(A_386,B_387) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_15806,plain,
! [A_391] : ( unordered_pair(singleton(A_391),singleton(A_391)) = ordered_pair(A_391,A_391) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_15751]) ).
tff(c_15824,plain,
! [A_391] : ( singleton(singleton(A_391)) = ordered_pair(A_391,A_391) ),
inference(superposition,[status(thm),theory(equality)],[c_15806,c_20]) ).
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_15964,plain,
! [A_407,B_408] : ( unordered_pair(unordered_pair(A_407,B_408),singleton(B_408)) = ordered_pair(B_408,A_407) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15751]) ).
tff(c_15784,plain,
! [A_1,B_2] : ( unordered_pair(unordered_pair(A_1,B_2),singleton(B_2)) = ordered_pair(B_2,A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15751]) ).
tff(c_18075,plain,
! [B_532,A_533] : ( unordered_pair(ordered_pair(B_532,A_533),singleton(singleton(B_532))) = ordered_pair(singleton(B_532),unordered_pair(A_533,B_532)) ),
inference(superposition,[status(thm),theory(equality)],[c_15964,c_15784]) ).
tff(c_18210,plain,
! [A_391,A_533] : ( unordered_pair(ordered_pair(A_391,A_533),ordered_pair(A_391,A_391)) = ordered_pair(singleton(A_391),unordered_pair(A_533,A_391)) ),
inference(superposition,[status(thm),theory(equality)],[c_15824,c_18075]) ).
tff(c_16,plain,
( ( '#skF_6' != '#skF_4' )
| ( '#skF_5' != '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_28,plain,
'#skF_5' != '#skF_3',
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_18,plain,
ordered_pair('#skF_5','#skF_6') = ordered_pair('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_121,plain,
! [A_41,B_42] : ( unordered_pair(unordered_pair(A_41,B_42),singleton(A_41)) = ordered_pair(A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_154,plain,
! [A_41,B_42] : ( unordered_pair(singleton(A_41),unordered_pair(A_41,B_42)) = ordered_pair(A_41,B_42) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_121]) ).
tff(c_4,plain,
! [A_3,B_4] : ( unordered_pair(unordered_pair(A_3,B_4),singleton(A_3)) = ordered_pair(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_253,plain,
! [D_46,A_47,C_48,B_49] :
( ( D_46 = A_47 )
| ( C_48 = A_47 )
| ( unordered_pair(C_48,D_46) != unordered_pair(A_47,B_49) ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_837,plain,
! [A_105,A_106,B_107,B_108] :
( ( singleton(A_105) = A_106 )
| ( unordered_pair(A_105,B_107) = A_106 )
| ( unordered_pair(A_106,B_108) != ordered_pair(A_105,B_107) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_253]) ).
tff(c_13318,plain,
! [A_357,A_356,B_358,B_359] :
( ( singleton(A_357) = singleton(A_356) )
| ( unordered_pair(A_357,B_358) = singleton(A_356) )
| ( ordered_pair(A_357,B_358) != ordered_pair(A_356,B_359) ) ),
inference(superposition,[status(thm),theory(equality)],[c_154,c_837]) ).
tff(c_13352,plain,
! [A_356,B_359] :
( ( singleton(A_356) = singleton('#skF_5') )
| ( unordered_pair('#skF_5','#skF_6') = singleton(A_356) )
| ( ordered_pair(A_356,B_359) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_13318]) ).
tff(c_13363,plain,
! [A_356,B_359] :
( ( singleton(A_356) = singleton('#skF_5') )
| ( unordered_pair('#skF_6','#skF_5') = singleton(A_356) )
| ( ordered_pair(A_356,B_359) != ordered_pair('#skF_3','#skF_4') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13352]) ).
tff(c_14906,plain,
( ( singleton('#skF_5') = singleton('#skF_3') )
| ( unordered_pair('#skF_6','#skF_5') = singleton('#skF_3') ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_13363]) ).
tff(c_14928,plain,
unordered_pair('#skF_6','#skF_5') = singleton('#skF_3'),
inference(splitLeft,[status(thm)],[c_14906]) ).
tff(c_85,plain,
! [B_30,A_31,C_32] :
( ( B_30 = A_31 )
| ( unordered_pair(B_30,C_32) != singleton(A_31) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_91,plain,
! [B_2,A_31,A_1] :
( ( B_2 = A_31 )
| ( unordered_pair(A_1,B_2) != singleton(A_31) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_85]) ).
tff(c_15088,plain,
! [A_31] :
( ( A_31 = '#skF_5' )
| ( singleton(A_31) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_14928,c_91]) ).
tff(c_15116,plain,
'#skF_5' = '#skF_3',
inference(reflexivity,[status(thm),theory(equality)],[c_15088]) ).
tff(c_15118,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_15116]) ).
tff(c_15119,plain,
singleton('#skF_5') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_14906]) ).
tff(c_94,plain,
! [A_31,A_13] :
( ( A_31 = A_13 )
| ( singleton(A_31) != singleton(A_13) ) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_85]) ).
tff(c_15329,plain,
! [A_31] :
( ( A_31 = '#skF_5' )
| ( singleton(A_31) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_15119,c_94]) ).
tff(c_15655,plain,
'#skF_5' = '#skF_3',
inference(reflexivity,[status(thm),theory(equality)],[c_15329]) ).
tff(c_15657,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_15655]) ).
tff(c_15659,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_15664,plain,
ordered_pair('#skF_3','#skF_6') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15659,c_18]) ).
tff(c_18219,plain,
unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(singleton('#skF_3'))) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_6','#skF_3')),
inference(superposition,[status(thm),theory(equality)],[c_15664,c_18075]) ).
tff(c_18230,plain,
unordered_pair(ordered_pair('#skF_3','#skF_4'),ordered_pair('#skF_3','#skF_3')) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_15824,c_2,c_18219]) ).
tff(c_23028,plain,
ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_18210,c_18230]) ).
tff(c_26,plain,
! [C_21,B_20,A_19] :
( ( C_21 = B_20 )
| ( unordered_pair(B_20,C_21) != singleton(A_19) ) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_16211,plain,
! [A_420,B_421,A_422] :
( ( unordered_pair(A_420,B_421) = singleton(A_420) )
| ( singleton(A_422) != ordered_pair(A_420,B_421) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15751,c_26]) ).
tff(c_16216,plain,
! [A_422] :
( ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') )
| ( singleton(A_422) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_15664,c_16211]) ).
tff(c_16222,plain,
! [A_423] : ( singleton(A_423) != ordered_pair('#skF_3','#skF_4') ),
inference(splitLeft,[status(thm)],[c_16216]) ).
tff(c_16224,plain,
! [A_391] : ( ordered_pair(A_391,A_391) != ordered_pair('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_15824,c_16222]) ).
tff(c_18323,plain,
! [A_19] :
( ( ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4') )
| ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_18230,c_26]) ).
tff(c_18344,plain,
! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) ),
inference(negUnitSimplification,[status(thm)],[c_16224,c_18323]) ).
tff(c_23222,plain,
! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_23028,c_18344]) ).
tff(c_15790,plain,
! [A_13] : ( unordered_pair(singleton(A_13),singleton(A_13)) = ordered_pair(A_13,A_13) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_15751]) ).
tff(c_16052,plain,
! [A_412,B_413] : ( unordered_pair(singleton(A_412),unordered_pair(A_412,B_413)) = ordered_pair(A_412,B_413) ),
inference(superposition,[status(thm),theory(equality)],[c_15751,c_2]) ).
tff(c_16097,plain,
! [A_13] : ( unordered_pair(singleton(singleton(A_13)),ordered_pair(A_13,A_13)) = ordered_pair(singleton(A_13),singleton(A_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_15790,c_16052]) ).
tff(c_16802,plain,
! [A_466] : ( unordered_pair(singleton(singleton(A_466)),ordered_pair(A_466,A_466)) = singleton(singleton(singleton(A_466))) ),
inference(demodulation,[status(thm),theory(equality)],[c_15824,c_16097]) ).
tff(c_16943,plain,
! [A_474] : ( unordered_pair(ordered_pair(A_474,A_474),ordered_pair(A_474,A_474)) = singleton(singleton(singleton(A_474))) ),
inference(superposition,[status(thm),theory(equality)],[c_15824,c_16802]) ).
tff(c_17010,plain,
! [A_474] : ( singleton(singleton(singleton(A_474))) = singleton(ordered_pair(A_474,A_474)) ),
inference(superposition,[status(thm),theory(equality)],[c_16943,c_20]) ).
tff(c_16121,plain,
! [B_415,A_416] : ( unordered_pair(singleton(B_415),unordered_pair(A_416,B_415)) = ordered_pair(B_415,A_416) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_16052]) ).
tff(c_18913,plain,
! [A_548,A_549] : ( unordered_pair(ordered_pair(A_548,A_548),unordered_pair(A_549,singleton(A_548))) = ordered_pair(singleton(A_548),A_549) ),
inference(superposition,[status(thm),theory(equality)],[c_15824,c_16121]) ).
tff(c_19047,plain,
! [B_2,A_1] : ( unordered_pair(ordered_pair(B_2,B_2),ordered_pair(B_2,A_1)) = ordered_pair(singleton(B_2),unordered_pair(A_1,B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_15784,c_18913]) ).
tff(c_15658,plain,
'#skF_6' != '#skF_4',
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_15893,plain,
! [D_394,A_395,C_396,B_397] :
( ( D_394 = A_395 )
| ( C_396 = A_395 )
| ( unordered_pair(C_396,D_394) != unordered_pair(A_395,B_397) ) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_16405,plain,
! [A_443,A_444,B_445,B_446] :
( ( singleton(A_443) = A_444 )
| ( unordered_pair(A_443,B_445) = A_444 )
| ( unordered_pair(A_444,B_446) != ordered_pair(A_443,B_445) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15893]) ).
tff(c_16411,plain,
! [A_1,B_2,A_443,B_445] :
( ( unordered_pair(A_1,B_2) = singleton(A_443) )
| ( unordered_pair(A_443,B_445) = unordered_pair(A_1,B_2) )
| ( ordered_pair(B_2,A_1) != ordered_pair(A_443,B_445) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15784,c_16405]) ).
tff(c_56133,plain,
! [B_923,A_924,A_925,B_926] :
( ( ordered_pair(B_923,A_924) != ordered_pair(A_925,B_926) )
| ( unordered_pair(A_924,B_923) = singleton(A_925) )
| ( unordered_pair(A_925,B_926) != singleton(A_925) ) ),
inference(factorization,[status(thm),theory(equality)],[c_16411]) ).
tff(c_56189,plain,
! [B_923,A_924] :
( ( ordered_pair(B_923,A_924) != ordered_pair('#skF_3','#skF_4') )
| ( unordered_pair(A_924,B_923) = singleton('#skF_3') )
| ( unordered_pair('#skF_3','#skF_6') != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_15664,c_56133]) ).
tff(c_57102,plain,
unordered_pair('#skF_3','#skF_6') != singleton('#skF_3'),
inference(splitLeft,[status(thm)],[c_56189]) ).
tff(c_16221,plain,
! [A_422] : ( singleton(A_422) != ordered_pair('#skF_3','#skF_4') ),
inference(splitLeft,[status(thm)],[c_16216]) ).
tff(c_16511,plain,
! [A_459,B_460] : ( unordered_pair(ordered_pair(A_459,B_460),singleton(unordered_pair(A_459,B_460))) = ordered_pair(unordered_pair(A_459,B_460),singleton(A_459)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15751]) ).
tff(c_16606,plain,
unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(unordered_pair('#skF_3','#skF_6'))) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')),
inference(superposition,[status(thm),theory(equality)],[c_15664,c_16511]) ).
tff(c_15902,plain,
! [A_3,A_395,B_4,B_397] :
( ( singleton(A_3) = A_395 )
| ( unordered_pair(A_3,B_4) = A_395 )
| ( unordered_pair(A_395,B_397) != ordered_pair(A_3,B_4) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15893]) ).
tff(c_16632,plain,
! [A_3,B_4] :
( ( singleton(A_3) = ordered_pair('#skF_3','#skF_4') )
| ( unordered_pair(A_3,B_4) = ordered_pair('#skF_3','#skF_4') )
| ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(A_3,B_4) ) ),
inference(superposition,[status(thm),theory(equality)],[c_16606,c_15902]) ).
tff(c_16684,plain,
! [A_3,B_4] :
( ( unordered_pair(A_3,B_4) = ordered_pair('#skF_3','#skF_4') )
| ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(A_3,B_4) ) ),
inference(negUnitSimplification,[status(thm)],[c_16221,c_16632]) ).
tff(c_28315,plain,
unordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_4'),
inference(reflexivity,[status(thm),theory(equality)],[c_16684]) ).
tff(c_16240,plain,
! [B_427,A_428,A_429,B_430] :
( ( B_427 = A_428 )
| ( A_429 = A_428 )
| ( unordered_pair(B_427,A_429) != unordered_pair(A_428,B_430) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).
tff(c_16255,plain,
! [A_1,B_2,A_428,B_430] :
( ( unordered_pair(A_1,B_2) = A_428 )
| ( singleton(B_2) = A_428 )
| ( unordered_pair(A_428,B_430) != ordered_pair(B_2,A_1) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15784,c_16240]) ).
tff(c_389649,plain,
! [A_2018,B_2019] :
( ( unordered_pair(A_2018,B_2019) = unordered_pair('#skF_3','#skF_6') )
| ( unordered_pair('#skF_3','#skF_6') = singleton(B_2019) )
| ( ordered_pair(B_2019,A_2018) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_28315,c_16255]) ).
tff(c_392990,plain,
! [A_2020,B_2021] :
( ( unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(unordered_pair(A_2020,B_2021))) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) )
| ( unordered_pair('#skF_3','#skF_6') = singleton(B_2021) )
| ( ordered_pair(B_2021,A_2020) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_389649,c_16606]) ).
tff(c_16603,plain,
! [B_2,A_1] : ( unordered_pair(ordered_pair(B_2,A_1),singleton(unordered_pair(A_1,B_2))) = ordered_pair(unordered_pair(B_2,A_1),singleton(B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_16511]) ).
tff(c_393830,plain,
( ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_3','#skF_4'),singleton('#skF_3')) )
| ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_392990,c_16603]) ).
tff(c_394828,plain,
( ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) )
| ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_393830]) ).
tff(c_394829,plain,
ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_57102,c_394828]) ).
tff(c_16356,plain,
! [D_439,B_440,C_441,A_442] :
( ( D_439 = B_440 )
| ( C_441 = B_440 )
| ( unordered_pair(C_441,D_439) != unordered_pair(A_442,B_440) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).
tff(c_17843,plain,
! [B_520,D_521,C_522,A_523] :
( ( singleton(B_520) = D_521 )
| ( singleton(B_520) = C_522 )
| ( unordered_pair(C_522,D_521) != ordered_pair(B_520,A_523) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15784,c_16356]) ).
tff(c_17855,plain,
! [B_520,A_523] :
( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
| ( singleton(B_520) = ordered_pair('#skF_3','#skF_4') )
| ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
inference(superposition,[status(thm),theory(equality)],[c_16606,c_17843]) ).
tff(c_17886,plain,
! [B_520,A_523] :
( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
| ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
inference(negUnitSimplification,[status(thm)],[c_16221,c_17855]) ).
tff(c_394965,plain,
! [B_520,A_523] :
( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
| ( ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_394829,c_17886]) ).
tff(c_404068,plain,
singleton(unordered_pair('#skF_3','#skF_6')) = singleton(unordered_pair('#skF_4','#skF_3')),
inference(reflexivity,[status(thm),theory(equality)],[c_394965]) ).
tff(c_15725,plain,
! [B_378,A_379,C_380] :
( ( B_378 = A_379 )
| ( unordered_pair(B_378,C_380) != singleton(A_379) ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_15734,plain,
! [A_379,A_13] :
( ( A_379 = A_13 )
| ( singleton(A_379) != singleton(A_13) ) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_15725]) ).
tff(c_405552,plain,
! [A_379] :
( ( unordered_pair('#skF_3','#skF_6') = A_379 )
| ( singleton(unordered_pair('#skF_4','#skF_3')) != singleton(A_379) ) ),
inference(superposition,[status(thm),theory(equality)],[c_404068,c_15734]) ).
tff(c_406419,plain,
unordered_pair('#skF_3','#skF_6') = unordered_pair('#skF_4','#skF_3'),
inference(reflexivity,[status(thm),theory(equality)],[c_405552]) ).
tff(c_15917,plain,
! [D_394,B_2,C_396,A_1] :
( ( D_394 = B_2 )
| ( C_396 = B_2 )
| ( unordered_pair(C_396,D_394) != unordered_pair(A_1,B_2) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).
tff(c_407217,plain,
! [D_394,C_396] :
( ( D_394 = '#skF_6' )
| ( C_396 = '#skF_6' )
| ( unordered_pair(C_396,D_394) != unordered_pair('#skF_4','#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_406419,c_15917]) ).
tff(c_419396,plain,
( ( '#skF_6' = '#skF_3' )
| ( '#skF_6' = '#skF_4' ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_407217]) ).
tff(c_419397,plain,
'#skF_6' = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_15658,c_419396]) ).
tff(c_407238,plain,
unordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_6')) = ordered_pair('#skF_6','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_406419,c_15784]) ).
tff(c_419851,plain,
unordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_419397,c_419397,c_407238]) ).
tff(c_419865,plain,
ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15784,c_419851]) ).
tff(c_419867,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16224,c_419865]) ).
tff(c_419869,plain,
unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_56189]) ).
tff(c_24764,plain,
! [A_643,B_644] : ( unordered_pair(singleton(unordered_pair(A_643,B_644)),ordered_pair(A_643,B_644)) = ordered_pair(unordered_pair(A_643,B_644),singleton(A_643)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_16052]) ).
tff(c_25027,plain,
unordered_pair(singleton(unordered_pair('#skF_3','#skF_6')),ordered_pair('#skF_3','#skF_4')) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')),
inference(superposition,[status(thm),theory(equality)],[c_15664,c_24764]) ).
tff(c_419905,plain,
unordered_pair(singleton(singleton('#skF_3')),ordered_pair('#skF_3','#skF_4')) = ordered_pair(singleton('#skF_3'),singleton('#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_419869,c_419869,c_25027]) ).
tff(c_419948,plain,
ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')) = singleton(ordered_pair('#skF_3','#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_17010,c_15824,c_19047,c_15824,c_419905]) ).
tff(c_419950,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23222,c_419948]) ).
tff(c_419951,plain,
unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_16216]) ).
tff(c_420039,plain,
! [A_19] :
( ( '#skF_6' = '#skF_3' )
| ( singleton(A_19) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_419951,c_26]) ).
tff(c_420078,plain,
! [A_19] : ( singleton(A_19) != singleton('#skF_3') ),
inference(splitLeft,[status(thm)],[c_420039]) ).
tff(c_420083,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_420078]) ).
tff(c_420084,plain,
'#skF_6' = '#skF_3',
inference(splitRight,[status(thm)],[c_420039]) ).
tff(c_420087,plain,
'#skF_3' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_420084,c_15658]) ).
tff(c_15769,plain,
! [A_386,B_387] : ( unordered_pair(singleton(A_386),unordered_pair(A_386,B_387)) = ordered_pair(A_386,B_387) ),
inference(superposition,[status(thm),theory(equality)],[c_15751,c_2]) ).
tff(c_420018,plain,
unordered_pair(singleton('#skF_3'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_419951,c_15769]) ).
tff(c_420045,plain,
ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15664,c_15790,c_420018]) ).
tff(c_420290,plain,
! [A_2092,B_2093,A_2094] :
( ( unordered_pair(A_2092,B_2093) = singleton(B_2093) )
| ( singleton(A_2094) != ordered_pair(B_2093,A_2092) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15964,c_26]) ).
tff(c_421266,plain,
! [A_2134,B_2135,A_2136] :
( ( unordered_pair(A_2134,B_2135) = singleton(B_2135) )
| ( ordered_pair(B_2135,A_2134) != ordered_pair(A_2136,A_2136) ) ),
inference(superposition,[status(thm),theory(equality)],[c_15824,c_420290]) ).
tff(c_421431,plain,
! [A_2139,B_2140] :
( ( unordered_pair(A_2139,B_2140) = singleton(B_2140) )
| ( ordered_pair(B_2140,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_420045,c_421266]) ).
tff(c_421525,plain,
! [B_2140,A_2139,A_19] :
( ( B_2140 = A_2139 )
| ( singleton(B_2140) != singleton(A_19) )
| ( ordered_pair(B_2140,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_421431,c_26]) ).
tff(c_422229,plain,
! [A_2139,A_19] :
( ( A_2139 = A_19 )
| ( ordered_pair(A_19,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_421525]) ).
tff(c_422242,plain,
'#skF_3' = '#skF_4',
inference(reflexivity,[status(thm),theory(equality)],[c_422229]) ).
tff(c_422244,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_420087,c_422242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU156+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.18/0.35 % Computer : n009.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 11:34:09 EDT 2023
% 0.18/0.35 % CPUTime :
% 245.71/198.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 245.93/198.29
% 245.93/198.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 245.93/198.33
% 245.93/198.33 Inference rules
% 245.93/198.33 ----------------------
% 245.93/198.33 #Ref : 129
% 245.93/198.33 #Sup : 126084
% 245.93/198.33 #Fact : 32
% 245.93/198.33 #Define : 0
% 245.93/198.33 #Split : 16
% 245.93/198.33 #Chain : 0
% 245.93/198.33 #Close : 0
% 245.93/198.33
% 245.93/198.33 Ordering : KBO
% 245.93/198.33
% 245.93/198.33 Simplification rules
% 245.93/198.33 ----------------------
% 245.93/198.33 #Subsume : 20040
% 245.93/198.33 #Demod : 88495
% 245.93/198.33 #Tautology : 5250
% 245.93/198.33 #SimpNegUnit : 5419
% 245.93/198.33 #BackRed : 326
% 245.93/198.33
% 245.93/198.33 #Partial instantiations: 0
% 245.93/198.33 #Strategies tried : 1
% 245.93/198.33
% 245.93/198.33 Timing (in seconds)
% 245.93/198.33 ----------------------
% 245.93/198.34 Preprocessing : 0.49
% 245.93/198.34 Parsing : 0.27
% 245.93/198.34 CNF conversion : 0.03
% 245.93/198.34 Main loop : 196.66
% 245.93/198.34 Inferencing : 8.31
% 245.93/198.34 Reduction : 77.93
% 245.93/198.34 Demodulation : 69.45
% 245.93/198.34 BG Simplification : 1.70
% 245.93/198.34 Subsumption : 85.65
% 245.93/198.34 Abstraction : 3.14
% 245.93/198.34 MUC search : 0.00
% 245.93/198.34 Cooper : 0.00
% 245.93/198.34 Total : 197.27
% 245.93/198.34 Index Insertion : 0.00
% 245.93/198.34 Index Deletion : 0.00
% 245.93/198.34 Index Matching : 0.00
% 245.93/198.34 BG Taut test : 0.00
%------------------------------------------------------------------------------