TSTP Solution File: NUM534+2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM534+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 10:52:01 EDT 2023
% Result : Theorem 18.48s 7.45s
% Output : CNFRefutation 18.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 130 ( 40 unt; 17 typ; 2 def)
% Number of atoms : 298 ( 70 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 317 ( 132 ~; 164 |; 9 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 60 (; 59 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > xx > xS > slcrc0 > #skF_6 > #skF_1 > #skF_4 > #skF_5 > #skF_3 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(xS,type,
xS: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(isCountable0,type,
isCountable0: $i > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(f_183,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xS,xx))
| ( W0 = xx ) ) ) ) )
=> ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_157,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
tff(f_52,definition,
! [W0] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(f_158,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).
tff(f_84,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_107,axiom,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
tff(c_98,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_100,plain,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_94,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_104,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_144,plain,
! [W0_66] :
( ( slcrc0 = W0_66 )
| aElementOf0('#skF_1'(W0_66),W0_66)
| ~ aSet0(W0_66) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_118,plain,
! [W0_55] :
( aElement0(W0_55)
| ~ aElementOf0(W0_55,sdtmndt0(xS,xx)) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_155,plain,
( aElement0('#skF_1'(sdtmndt0(xS,xx)))
| ( sdtmndt0(xS,xx) = slcrc0 )
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[c_144,c_118]) ).
tff(c_166,plain,
( aElement0('#skF_1'(sdtmndt0(xS,xx)))
| ( sdtmndt0(xS,xx) = slcrc0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_155]) ).
tff(c_213,plain,
sdtmndt0(xS,xx) = slcrc0,
inference(splitLeft,[status(thm)],[c_166]) ).
tff(c_219,plain,
sdtpldt0(slcrc0,xx) != xS,
inference(demodulation,[status(thm),theory(equality)],[c_213,c_98]) ).
tff(c_218,plain,
aSet0(sdtpldt0(slcrc0,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_100]) ).
tff(c_96,plain,
aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_439,plain,
! [W0_96,W1_97] :
( aElementOf0('#skF_2'(W0_96,W1_97),W1_97)
| aSubsetOf0(W1_97,W0_96)
| ~ aSet0(W1_97)
| ~ aSet0(W0_96) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_12,plain,
! [W1_10] : ~ aElementOf0(W1_10,slcrc0),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_106,plain,
! [W0_56] :
( ( xx = W0_56 )
| aElementOf0(W0_56,sdtmndt0(xS,xx))
| ~ aElementOf0(W0_56,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_381,plain,
! [W0_56] :
( ( xx = W0_56 )
| aElementOf0(W0_56,slcrc0)
| ~ aElementOf0(W0_56,sdtpldt0(slcrc0,xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_213,c_106]) ).
tff(c_382,plain,
! [W0_56] :
( ( xx = W0_56 )
| ~ aElementOf0(W0_56,sdtpldt0(slcrc0,xx)) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_381]) ).
tff(c_443,plain,
! [W0_96] :
( ( '#skF_2'(W0_96,sdtpldt0(slcrc0,xx)) = xx )
| aSubsetOf0(sdtpldt0(slcrc0,xx),W0_96)
| ~ aSet0(sdtpldt0(slcrc0,xx))
| ~ aSet0(W0_96) ),
inference(resolution,[status(thm)],[c_439,c_382]) ).
tff(c_899,plain,
! [W0_125] :
( ( '#skF_2'(W0_125,sdtpldt0(slcrc0,xx)) = xx )
| aSubsetOf0(sdtpldt0(slcrc0,xx),W0_125)
| ~ aSet0(W0_125) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_443]) ).
tff(c_6,plain,
! [W1_5,W0_3] :
( aElement0(W1_5)
| ~ aElementOf0(W1_5,W0_3)
| ~ aSet0(W0_3) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_481,plain,
! [W0_96,W1_97] :
( aElement0('#skF_2'(W0_96,W1_97))
| aSubsetOf0(W1_97,W0_96)
| ~ aSet0(W1_97)
| ~ aSet0(W0_96) ),
inference(resolution,[status(thm)],[c_439,c_6]) ).
tff(c_102,plain,
! [W0_55] :
( aElementOf0(W0_55,sdtmndt0(xS,xx))
| ( xx = W0_55 )
| ~ aElementOf0(W0_55,xS)
| ~ aElement0(W0_55) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_237,plain,
! [W0_55] :
( aElementOf0(W0_55,slcrc0)
| ( xx = W0_55 )
| ~ aElementOf0(W0_55,xS)
| ~ aElement0(W0_55) ),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_102]) ).
tff(c_238,plain,
! [W0_55] :
( ( xx = W0_55 )
| ~ aElementOf0(W0_55,xS)
| ~ aElement0(W0_55) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_237]) ).
tff(c_461,plain,
! [W0_96] :
( ( '#skF_2'(W0_96,xS) = xx )
| ~ aElement0('#skF_2'(W0_96,xS))
| aSubsetOf0(xS,W0_96)
| ~ aSet0(xS)
| ~ aSet0(W0_96) ),
inference(resolution,[status(thm)],[c_439,c_238]) ).
tff(c_632,plain,
! [W0_112] :
( ( '#skF_2'(W0_112,xS) = xx )
| ~ aElement0('#skF_2'(W0_112,xS))
| aSubsetOf0(xS,W0_112)
| ~ aSet0(W0_112) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_461]) ).
tff(c_636,plain,
! [W0_96] :
( ( '#skF_2'(W0_96,xS) = xx )
| aSubsetOf0(xS,W0_96)
| ~ aSet0(xS)
| ~ aSet0(W0_96) ),
inference(resolution,[status(thm)],[c_481,c_632]) ).
tff(c_640,plain,
! [W0_113] :
( ( '#skF_2'(W0_113,xS) = xx )
| aSubsetOf0(xS,W0_113)
| ~ aSet0(W0_113) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_636]) ).
tff(c_36,plain,
! [W1_29,W0_28] :
( ( W1_29 = W0_28 )
| ~ aSubsetOf0(W1_29,W0_28)
| ~ aSubsetOf0(W0_28,W1_29)
| ~ aSet0(W1_29)
| ~ aSet0(W0_28) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_650,plain,
! [W0_113] :
( ( xS = W0_113 )
| ~ aSubsetOf0(W0_113,xS)
| ~ aSet0(xS)
| ( '#skF_2'(W0_113,xS) = xx )
| ~ aSet0(W0_113) ),
inference(resolution,[status(thm)],[c_640,c_36]) ).
tff(c_668,plain,
! [W0_113] :
( ( xS = W0_113 )
| ~ aSubsetOf0(W0_113,xS)
| ( '#skF_2'(W0_113,xS) = xx )
| ~ aSet0(W0_113) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_650]) ).
tff(c_903,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
| ~ aSet0(sdtpldt0(slcrc0,xx))
| ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx )
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_899,c_668]) ).
tff(c_925,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
| ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx ) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_903]) ).
tff(c_926,plain,
( ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
| ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx ) ),
inference(negUnitSimplification,[status(thm)],[c_219,c_925]) ).
tff(c_966,plain,
'#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx,
inference(splitLeft,[status(thm)],[c_926]) ).
tff(c_28,plain,
! [W0_14,W1_20] :
( ~ aElementOf0('#skF_2'(W0_14,W1_20),W0_14)
| aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W1_20)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_973,plain,
( ~ aElementOf0(xx,xS)
| aSubsetOf0(sdtpldt0(slcrc0,xx),xS)
| ~ aSet0(sdtpldt0(slcrc0,xx))
| ~ aSet0(xS) ),
inference(superposition,[status(thm),theory(equality)],[c_966,c_28]) ).
tff(c_985,plain,
aSubsetOf0(sdtpldt0(slcrc0,xx),xS),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_96,c_973]) ).
tff(c_995,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
| ~ aSet0(sdtpldt0(slcrc0,xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_985,c_36]) ).
tff(c_1011,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_995]) ).
tff(c_1012,plain,
~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
inference(negUnitSimplification,[status(thm)],[c_219,c_1011]) ).
tff(c_136,plain,
! [W1_63,W0_64] :
( aElement0(W1_63)
| ~ aElementOf0(W1_63,W0_64)
| ~ aSet0(W0_64) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_139,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_96,c_136]) ).
tff(c_142,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_139]) ).
tff(c_110,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_195,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_110]) ).
tff(c_214,plain,
aElementOf0(xx,sdtpldt0(slcrc0,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_195]) ).
tff(c_993,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[c_985,c_668]) ).
tff(c_1007,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx ) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_993]) ).
tff(c_1008,plain,
'#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx,
inference(negUnitSimplification,[status(thm)],[c_219,c_1007]) ).
tff(c_1061,plain,
( ~ aElementOf0(xx,sdtpldt0(slcrc0,xx))
| aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(superposition,[status(thm),theory(equality)],[c_1008,c_28]) ).
tff(c_1071,plain,
aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_214,c_1061]) ).
tff(c_1073,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1012,c_1071]) ).
tff(c_1075,plain,
'#skF_2'(xS,sdtpldt0(slcrc0,xx)) != xx,
inference(splitRight,[status(thm)],[c_926]) ).
tff(c_471,plain,
! [W0_96] :
( ( '#skF_2'(W0_96,sdtpldt0(slcrc0,xx)) = xx )
| aSubsetOf0(sdtpldt0(slcrc0,xx),W0_96)
| ~ aSet0(W0_96) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_443]) ).
tff(c_1074,plain,
'#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx,
inference(splitRight,[status(thm)],[c_926]) ).
tff(c_1079,plain,
( ~ aElementOf0(xx,sdtpldt0(slcrc0,xx))
| aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(superposition,[status(thm),theory(equality)],[c_1074,c_28]) ).
tff(c_1089,plain,
aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_214,c_1079]) ).
tff(c_1099,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(slcrc0,xx)) ),
inference(resolution,[status(thm)],[c_1089,c_36]) ).
tff(c_1114,plain,
( ( sdtpldt0(slcrc0,xx) = xS )
| ~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_1099]) ).
tff(c_1115,plain,
~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS),
inference(negUnitSimplification,[status(thm)],[c_219,c_1114]) ).
tff(c_1127,plain,
( ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx )
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_471,c_1115]) ).
tff(c_1130,plain,
'#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx,
inference(demodulation,[status(thm),theory(equality)],[c_94,c_1127]) ).
tff(c_1131,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1075,c_1130]) ).
tff(c_1133,plain,
sdtmndt0(xS,xx) != slcrc0,
inference(splitRight,[status(thm)],[c_166]) ).
tff(c_116,plain,
! [W0_55] :
( aElementOf0(W0_55,xS)
| ~ aElementOf0(W0_55,sdtmndt0(xS,xx)) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_148,plain,
( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS)
| ( sdtmndt0(xS,xx) = slcrc0 )
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[c_144,c_116]) ).
tff(c_162,plain,
( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS)
| ( sdtmndt0(xS,xx) = slcrc0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_148]) ).
tff(c_1134,plain,
aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS),
inference(negUnitSimplification,[status(thm)],[c_1133,c_162]) ).
tff(c_1157,plain,
! [W2_132,W0_133,W1_134] :
( aElementOf0(W2_132,W0_133)
| ~ aElementOf0(W2_132,W1_134)
| ~ aSubsetOf0(W1_134,W0_133)
| ~ aSet0(W0_133) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_1168,plain,
! [W0_133] :
( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),W0_133)
| ~ aSubsetOf0(xS,W0_133)
| ~ aSet0(W0_133) ),
inference(resolution,[status(thm)],[c_1134,c_1157]) ).
tff(c_1506,plain,
! [W0_159] :
( ( xx = W0_159 )
| aElementOf0(W0_159,sdtmndt0(xS,xx))
| ~ aElementOf0(W0_159,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_1521,plain,
( ( '#skF_1'(sdtmndt0(xS,xx)) = xx )
| aElementOf0('#skF_1'(sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c_1168,c_1506]) ).
tff(c_1542,plain,
( ( '#skF_1'(sdtmndt0(xS,xx)) = xx )
| aElementOf0('#skF_1'(sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_1521]) ).
tff(c_3184,plain,
~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(splitLeft,[status(thm)],[c_1542]) ).
tff(c_1312,plain,
! [W0_148,W1_149] :
( aElementOf0('#skF_2'(W0_148,W1_149),W1_149)
| aSubsetOf0(W1_149,W0_148)
| ~ aSet0(W1_149)
| ~ aSet0(W0_148) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_1361,plain,
! [W0_148,W1_149] :
( aElement0('#skF_2'(W0_148,W1_149))
| aSubsetOf0(W1_149,W0_148)
| ~ aSet0(W1_149)
| ~ aSet0(W0_148) ),
inference(resolution,[status(thm)],[c_1312,c_6]) ).
tff(c_30,plain,
! [W0_14,W1_20] :
( aElementOf0('#skF_2'(W0_14,W1_20),W1_20)
| aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W1_20)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_1402,plain,
! [W0_154] :
( ~ aElementOf0(W0_154,sdtmndt0(xS,xx))
| aElementOf0(W0_154,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(W0_154) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_1406,plain,
! [W1_20] :
( aSubsetOf0(W1_20,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(W1_20)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_20),sdtmndt0(xS,xx))
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_20)) ),
inference(resolution,[status(thm)],[c_1402,c_28]) ).
tff(c_24586,plain,
! [W1_760] :
( aSubsetOf0(W1_760,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(W1_760)
| ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_760),sdtmndt0(xS,xx))
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_760)) ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_1406]) ).
tff(c_25058,plain,
! [W1_767] :
( aSubsetOf0(W1_767,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(W1_767)
| ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767) = xx )
| ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767),xS)
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767)) ),
inference(resolution,[status(thm)],[c_102,c_24586]) ).
tff(c_25086,plain,
( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c_30,c_25058]) ).
tff(c_25107,plain,
( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25086]) ).
tff(c_25108,plain,
( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
| ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS)) ),
inference(negUnitSimplification,[status(thm)],[c_3184,c_25107]) ).
tff(c_25109,plain,
~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS)),
inference(splitLeft,[status(thm)],[c_25108]) ).
tff(c_25112,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c_1361,c_25109]) ).
tff(c_25115,plain,
aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25112]) ).
tff(c_25117,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3184,c_25115]) ).
tff(c_25118,plain,
'#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx,
inference(splitRight,[status(thm)],[c_25108]) ).
tff(c_25165,plain,
( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(superposition,[status(thm),theory(equality)],[c_25118,c_28]) ).
tff(c_25211,plain,
aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_195,c_25165]) ).
tff(c_25213,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3184,c_25211]) ).
tff(c_25215,plain,
aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(splitRight,[status(thm)],[c_1542]) ).
tff(c_25230,plain,
( ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c_25215,c_36]) ).
tff(c_25261,plain,
( ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25230]) ).
tff(c_25262,plain,
~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
inference(negUnitSimplification,[status(thm)],[c_98,c_25261]) ).
tff(c_1517,plain,
! [W0_14] :
( ( '#skF_2'(W0_14,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
| aElementOf0('#skF_2'(W0_14,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_14)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(W0_14) ),
inference(resolution,[status(thm)],[c_30,c_1506]) ).
tff(c_49179,plain,
! [W0_1302] :
( ( '#skF_2'(W0_1302,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
| aElementOf0('#skF_2'(W0_1302,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_1302)
| ~ aSet0(W0_1302) ),
inference(demodulation,[status(thm),theory(equality)],[c_100,c_1517]) ).
tff(c_49360,plain,
! [W0_1303] :
( aElementOf0('#skF_2'(W0_1303,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| ( '#skF_2'(W0_1303,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_1303)
| ~ aSet0(W0_1303) ),
inference(resolution,[status(thm)],[c_49179,c_116]) ).
tff(c_49374,plain,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ( '#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_49360,c_28]) ).
tff(c_49399,plain,
( ( '#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_100,c_49374]) ).
tff(c_49400,plain,
'#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx,
inference(negUnitSimplification,[status(thm)],[c_25262,c_49399]) ).
tff(c_49465,plain,
( ~ aElementOf0(xx,xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(superposition,[status(thm),theory(equality)],[c_49400,c_28]) ).
tff(c_49520,plain,
aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_100,c_96,c_49465]) ).
tff(c_49522,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25262,c_49520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM534+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.17/0.35 % Computer : n025.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 15:20:19 EDT 2023
% 0.17/0.36 % CPUTime :
% 18.48/7.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.48/7.47
% 18.48/7.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.64/7.51
% 18.64/7.51 Inference rules
% 18.64/7.51 ----------------------
% 18.64/7.51 #Ref : 0
% 18.64/7.51 #Sup : 10256
% 18.64/7.51 #Fact : 0
% 18.64/7.51 #Define : 0
% 18.64/7.51 #Split : 63
% 18.64/7.51 #Chain : 0
% 18.64/7.51 #Close : 0
% 18.64/7.51
% 18.64/7.51 Ordering : KBO
% 18.64/7.51
% 18.64/7.51 Simplification rules
% 18.64/7.51 ----------------------
% 18.64/7.51 #Subsume : 4674
% 18.64/7.51 #Demod : 10609
% 18.64/7.51 #Tautology : 2005
% 18.64/7.51 #SimpNegUnit : 1060
% 18.64/7.51 #BackRed : 88
% 18.64/7.51
% 18.64/7.51 #Partial instantiations: 0
% 18.64/7.51 #Strategies tried : 1
% 18.64/7.51
% 18.64/7.51 Timing (in seconds)
% 18.64/7.51 ----------------------
% 18.64/7.51 Preprocessing : 0.58
% 18.64/7.51 Parsing : 0.29
% 18.64/7.51 CNF conversion : 0.05
% 18.64/7.51 Main loop : 5.83
% 18.64/7.51 Inferencing : 1.57
% 18.64/7.51 Reduction : 2.04
% 18.64/7.51 Demodulation : 1.43
% 18.64/7.51 BG Simplification : 0.11
% 18.64/7.51 Subsumption : 1.81
% 18.64/7.51 Abstraction : 0.20
% 18.64/7.51 MUC search : 0.00
% 18.64/7.51 Cooper : 0.00
% 18.64/7.51 Total : 6.48
% 18.64/7.51 Index Insertion : 0.00
% 18.64/7.51 Index Deletion : 0.00
% 18.64/7.51 Index Matching : 0.00
% 18.64/7.51 BG Taut test : 0.00
%------------------------------------------------------------------------------