TSTP Solution File: SEU156+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n028.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 10:57:48 EDT 2023
% Result : Theorem 232.78s 186.35s
% Output : CNFRefutation 232.78s
% 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_59,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_57,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_50,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_67,axiom,
! [A,B,C] :
( ( singleton(A) = unordered_pair(B,C) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
tff(f_71,axiom,
! [A,B,C] :
( ( singleton(A) = unordered_pair(B,C) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
tff(c_26,plain,
! [A_13] : ( unordered_pair(A_13,A_13) = singleton(A_13) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_15757,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_15812,plain,
! [A_391] : ( unordered_pair(singleton(A_391),singleton(A_391)) = ordered_pair(A_391,A_391) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_15757]) ).
tff(c_15830,plain,
! [A_391] : ( singleton(singleton(A_391)) = ordered_pair(A_391,A_391) ),
inference(superposition,[status(thm),theory(equality)],[c_15812,c_26]) ).
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_15970,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_15757]) ).
tff(c_15790,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_15757]) ).
tff(c_18081,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_15970,c_15790]) ).
tff(c_18216,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_15830,c_18081]) ).
tff(c_22,plain,
( ( '#skF_6' != '#skF_4' )
| ( '#skF_5' != '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_34,plain,
'#skF_5' != '#skF_3',
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_24,plain,
ordered_pair('#skF_5','#skF_6') = ordered_pair('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_127,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_160,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_127]) ).
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_259,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_50]) ).
tff(c_843,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_259]) ).
tff(c_13324,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_160,c_843]) ).
tff(c_13358,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_24,c_13324]) ).
tff(c_13369,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_13358]) ).
tff(c_14912,plain,
( ( singleton('#skF_5') = singleton('#skF_3') )
| ( unordered_pair('#skF_6','#skF_5') = singleton('#skF_3') ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_13369]) ).
tff(c_14934,plain,
unordered_pair('#skF_6','#skF_5') = singleton('#skF_3'),
inference(splitLeft,[status(thm)],[c_14912]) ).
tff(c_91,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_67]) ).
tff(c_97,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_91]) ).
tff(c_15094,plain,
! [A_31] :
( ( A_31 = '#skF_5' )
| ( singleton(A_31) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_14934,c_97]) ).
tff(c_15122,plain,
'#skF_5' = '#skF_3',
inference(reflexivity,[status(thm),theory(equality)],[c_15094]) ).
tff(c_15124,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_15122]) ).
tff(c_15125,plain,
singleton('#skF_5') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_14912]) ).
tff(c_100,plain,
! [A_31,A_13] :
( ( A_31 = A_13 )
| ( singleton(A_31) != singleton(A_13) ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_91]) ).
tff(c_15335,plain,
! [A_31] :
( ( A_31 = '#skF_5' )
| ( singleton(A_31) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_15125,c_100]) ).
tff(c_15661,plain,
'#skF_5' = '#skF_3',
inference(reflexivity,[status(thm),theory(equality)],[c_15335]) ).
tff(c_15663,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_15661]) ).
tff(c_15665,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_15670,plain,
ordered_pair('#skF_3','#skF_6') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15665,c_24]) ).
tff(c_18225,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_15670,c_18081]) ).
tff(c_18236,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_15830,c_2,c_18225]) ).
tff(c_23034,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_18216,c_18236]) ).
tff(c_32,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_71]) ).
tff(c_16217,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_15757,c_32]) ).
tff(c_16222,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_15670,c_16217]) ).
tff(c_16228,plain,
! [A_423] : ( singleton(A_423) != ordered_pair('#skF_3','#skF_4') ),
inference(splitLeft,[status(thm)],[c_16222]) ).
tff(c_16230,plain,
! [A_391] : ( ordered_pair(A_391,A_391) != ordered_pair('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_15830,c_16228]) ).
tff(c_18329,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_18236,c_32]) ).
tff(c_18350,plain,
! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) ),
inference(negUnitSimplification,[status(thm)],[c_16230,c_18329]) ).
tff(c_23228,plain,
! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_23034,c_18350]) ).
tff(c_15796,plain,
! [A_13] : ( unordered_pair(singleton(A_13),singleton(A_13)) = ordered_pair(A_13,A_13) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_15757]) ).
tff(c_16058,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_15757,c_2]) ).
tff(c_16103,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_15796,c_16058]) ).
tff(c_16808,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_15830,c_16103]) ).
tff(c_16949,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_15830,c_16808]) ).
tff(c_17016,plain,
! [A_474] : ( singleton(singleton(singleton(A_474))) = singleton(ordered_pair(A_474,A_474)) ),
inference(superposition,[status(thm),theory(equality)],[c_16949,c_26]) ).
tff(c_16127,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_16058]) ).
tff(c_18919,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_15830,c_16127]) ).
tff(c_19053,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_15790,c_18919]) ).
tff(c_15664,plain,
'#skF_6' != '#skF_4',
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_15899,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_50]) ).
tff(c_16411,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_15899]) ).
tff(c_16417,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_15790,c_16411]) ).
tff(c_56139,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_16417]) ).
tff(c_56195,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_15670,c_56139]) ).
tff(c_57108,plain,
unordered_pair('#skF_3','#skF_6') != singleton('#skF_3'),
inference(splitLeft,[status(thm)],[c_56195]) ).
tff(c_16227,plain,
! [A_422] : ( singleton(A_422) != ordered_pair('#skF_3','#skF_4') ),
inference(splitLeft,[status(thm)],[c_16222]) ).
tff(c_16517,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_15757]) ).
tff(c_16612,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_15670,c_16517]) ).
tff(c_15908,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_15899]) ).
tff(c_16638,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_16612,c_15908]) ).
tff(c_16690,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_16227,c_16638]) ).
tff(c_28321,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_16690]) ).
tff(c_16246,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_15899]) ).
tff(c_16261,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_15790,c_16246]) ).
tff(c_389655,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_28321,c_16261]) ).
tff(c_392996,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_389655,c_16612]) ).
tff(c_16609,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_16517]) ).
tff(c_393836,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_392996,c_16609]) ).
tff(c_394834,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_393836]) ).
tff(c_394835,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_57108,c_394834]) ).
tff(c_16362,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_15899]) ).
tff(c_17849,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_15790,c_16362]) ).
tff(c_17861,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_16612,c_17849]) ).
tff(c_17892,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_16227,c_17861]) ).
tff(c_394971,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_394835,c_17892]) ).
tff(c_404074,plain,
singleton(unordered_pair('#skF_3','#skF_6')) = singleton(unordered_pair('#skF_4','#skF_3')),
inference(reflexivity,[status(thm),theory(equality)],[c_394971]) ).
tff(c_15731,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_67]) ).
tff(c_15740,plain,
! [A_379,A_13] :
( ( A_379 = A_13 )
| ( singleton(A_379) != singleton(A_13) ) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_15731]) ).
tff(c_405558,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_404074,c_15740]) ).
tff(c_406425,plain,
unordered_pair('#skF_3','#skF_6') = unordered_pair('#skF_4','#skF_3'),
inference(reflexivity,[status(thm),theory(equality)],[c_405558]) ).
tff(c_15923,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_15899]) ).
tff(c_407223,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_406425,c_15923]) ).
tff(c_419402,plain,
( ( '#skF_6' = '#skF_3' )
| ( '#skF_6' = '#skF_4' ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_407223]) ).
tff(c_419403,plain,
'#skF_6' = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_15664,c_419402]) ).
tff(c_407244,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_406425,c_15790]) ).
tff(c_419857,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_419403,c_419403,c_407244]) ).
tff(c_419871,plain,
ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15790,c_419857]) ).
tff(c_419873,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16230,c_419871]) ).
tff(c_419875,plain,
unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_56195]) ).
tff(c_24770,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_16058]) ).
tff(c_25033,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_15670,c_24770]) ).
tff(c_419911,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_419875,c_419875,c_25033]) ).
tff(c_419954,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_17016,c_15830,c_19053,c_15830,c_419911]) ).
tff(c_419956,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23228,c_419954]) ).
tff(c_419957,plain,
unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
inference(splitRight,[status(thm)],[c_16222]) ).
tff(c_420045,plain,
! [A_19] :
( ( '#skF_6' = '#skF_3' )
| ( singleton(A_19) != singleton('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_419957,c_32]) ).
tff(c_420084,plain,
! [A_19] : ( singleton(A_19) != singleton('#skF_3') ),
inference(splitLeft,[status(thm)],[c_420045]) ).
tff(c_420089,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_420084]) ).
tff(c_420090,plain,
'#skF_6' = '#skF_3',
inference(splitRight,[status(thm)],[c_420045]) ).
tff(c_420093,plain,
'#skF_3' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_420090,c_15664]) ).
tff(c_15775,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_15757,c_2]) ).
tff(c_420024,plain,
unordered_pair(singleton('#skF_3'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_419957,c_15775]) ).
tff(c_420051,plain,
ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_15670,c_15796,c_420024]) ).
tff(c_420296,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_15970,c_32]) ).
tff(c_421272,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_15830,c_420296]) ).
tff(c_421437,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_420051,c_421272]) ).
tff(c_421531,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_421437,c_32]) ).
tff(c_422235,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_421531]) ).
tff(c_422248,plain,
'#skF_3' = '#skF_4',
inference(reflexivity,[status(thm),theory(equality)],[c_422235]) ).
tff(c_422250,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_420093,c_422248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU156+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % 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
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 12:15:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 232.78/186.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.78/186.37
% 232.78/186.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 232.78/186.41
% 232.78/186.41 Inference rules
% 232.78/186.41 ----------------------
% 232.78/186.41 #Ref : 129
% 232.78/186.41 #Sup : 126084
% 232.78/186.41 #Fact : 32
% 232.78/186.41 #Define : 0
% 232.78/186.41 #Split : 16
% 232.78/186.41 #Chain : 0
% 232.78/186.41 #Close : 0
% 232.78/186.41
% 232.78/186.41 Ordering : KBO
% 232.78/186.41
% 232.78/186.41 Simplification rules
% 232.78/186.41 ----------------------
% 232.78/186.41 #Subsume : 20040
% 232.78/186.41 #Demod : 88495
% 232.78/186.41 #Tautology : 5253
% 232.78/186.41 #SimpNegUnit : 5419
% 232.78/186.41 #BackRed : 326
% 232.78/186.41
% 232.78/186.41 #Partial instantiations: 0
% 232.78/186.41 #Strategies tried : 1
% 232.78/186.41
% 232.78/186.41 Timing (in seconds)
% 232.78/186.41 ----------------------
% 232.78/186.42 Preprocessing : 0.47
% 232.78/186.42 Parsing : 0.25
% 232.78/186.42 CNF conversion : 0.03
% 232.78/186.42 Main loop : 184.87
% 232.78/186.42 Inferencing : 8.33
% 232.78/186.42 Reduction : 76.16
% 232.78/186.42 Demodulation : 67.92
% 232.78/186.42 BG Simplification : 1.74
% 232.78/186.42 Subsumption : 82.49
% 232.78/186.42 Abstraction : 3.22
% 232.78/186.42 MUC search : 0.00
% 232.78/186.42 Cooper : 0.00
% 232.78/186.42 Total : 185.41
% 232.78/186.42 Index Insertion : 0.00
% 232.78/186.42 Index Deletion : 0.00
% 232.78/186.42 Index Matching : 0.00
% 232.78/186.42 BG Taut test : 0.00
%------------------------------------------------------------------------------