TSTP Solution File: LAT386+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Thu Aug 31 06:02:24 EDT 2023
% Result : Theorem 1.65s 1.73s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 57
% Syntax : Number of formulae : 139 ( 17 unt; 47 typ; 0 def)
% Number of atoms : 464 ( 18 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 530 ( 158 ~; 181 |; 140 &)
% ( 1 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 39 >; 29 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-3 aty)
% Number of variables : 126 ( 0 sgn; 72 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isEmpty0: $i > $o ).
tff(decl_26,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
aLowerBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
aUpperBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
aInfimumOfIn0: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
aSupremumOfIn0: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
aCompleteLattice0: $i > $o ).
tff(decl_33,type,
aFunction0: $i > $o ).
tff(decl_34,type,
szDzozmdt0: $i > $i ).
tff(decl_35,type,
szRzazndt0: $i > $i ).
tff(decl_36,type,
isOn0: ( $i * $i ) > $o ).
tff(decl_37,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(decl_38,type,
aFixedPointOf0: ( $i * $i ) > $o ).
tff(decl_39,type,
isMonotone0: $i > $o ).
tff(decl_40,type,
xU: $i ).
tff(decl_41,type,
xf: $i ).
tff(decl_42,type,
xS: $i ).
tff(decl_43,type,
cS1142: $i > $i ).
tff(decl_44,type,
xT: $i ).
tff(decl_45,type,
xP: $i ).
tff(decl_46,type,
cS1241: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
xp: $i ).
tff(decl_48,type,
epred1_1: $i > $o ).
tff(decl_49,type,
esk1_1: $i > $i ).
tff(decl_50,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk9_1: $i > $i ).
tff(decl_58,type,
esk10_1: $i > $i ).
tff(decl_59,type,
esk11_1: $i > $i ).
tff(decl_60,type,
esk12_1: $i > $i ).
tff(decl_61,type,
esk13_1: $i > $i ).
tff(decl_62,type,
esk14_1: $i > $i ).
tff(decl_63,type,
esk15_0: $i ).
tff(decl_64,type,
esk16_0: $i ).
tff(decl_65,type,
esk17_1: $i > $i ).
tff(decl_66,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk19_1: $i > $i ).
tff(decl_68,type,
esk20_2: ( $i * $i ) > $i ).
fof(m__1123,hypothesis,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> ? [X2] :
( aElementOf0(X2,xU)
& aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1123) ).
fof(m__1144,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ( aElementOf0(X1,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X1) = X1
& aFixedPointOf0(X1,xf) ) )
& ( ( ( aElementOf0(X1,szDzozmdt0(xf))
& sdtlpdtrp0(xf,X1) = X1 )
| aFixedPointOf0(X1,xf) )
=> aElementOf0(X1,xS) ) )
& xS = cS1142(xf) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1144) ).
fof(m__1173,hypothesis,
( aSet0(xT)
& ! [X1] :
( aElementOf0(X1,xT)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xT,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1173) ).
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X1) )
| aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) )
| aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1261,hypothesis,
( aElementOf0(xp,xU)
& aElementOf0(xp,xU)
& ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(xp,X1) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
=> sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1261) ).
fof(m__1244,hypothesis,
( aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
=> ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
& aUpperBoundOfIn0(X1,xT,xU) ) )
& ( ( aElementOf0(X1,xU)
& sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
& ( ! [X2] :
( aElementOf0(X2,xT)
=> sdtlseqdt0(X2,X1) )
| aUpperBoundOfIn0(X1,xT,xU) ) )
=> aElementOf0(X1,xP) ) )
& xP = cS1241(xU,xf,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1244) ).
fof(mImgSort,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgSort) ).
fof(mTrans,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTrans) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(c_0_9,plain,
! [X1] :
( epred1_1(X1)
<=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) ),
introduced(definition) ).
fof(c_0_10,hypothesis,
( aSet0(xU)
& ! [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xU) ) )
| aSubsetOf0(X1,xU) )
=> epred1_1(X1) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ! [X1,X2] :
( ( aElementOf0(X1,szDzozmdt0(xf))
& aElementOf0(X2,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(X1,X2)
=> sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2)) ) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[m__1123]),c_0_9]) ).
fof(c_0_11,hypothesis,
! [X75,X77,X78] :
( aSet0(xU)
& ( aElementOf0(esk12_1(X75),X75)
| ~ aSet0(X75)
| epred1_1(X75) )
& ( ~ aElementOf0(esk12_1(X75),xU)
| ~ aSet0(X75)
| epred1_1(X75) )
& ( ~ aSubsetOf0(X75,xU)
| epred1_1(X75) )
& aCompleteLattice0(xU)
& aFunction0(xf)
& ( ~ aElementOf0(X77,szDzozmdt0(xf))
| ~ aElementOf0(X78,szDzozmdt0(xf))
| ~ sdtlseqdt0(X77,X78)
| sdtlseqdt0(sdtlpdtrp0(xf,X77),sdtlpdtrp0(xf,X78)) )
& isMonotone0(xf)
& szDzozmdt0(xf) = szRzazndt0(xf)
& szRzazndt0(xf) = xU
& isOn0(xf,xU) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_12,hypothesis,
! [X79] :
( aSet0(xS)
& ( aElementOf0(X79,szDzozmdt0(xf))
| ~ aElementOf0(X79,xS) )
& ( sdtlpdtrp0(xf,X79) = X79
| ~ aElementOf0(X79,xS) )
& ( aFixedPointOf0(X79,xf)
| ~ aElementOf0(X79,xS) )
& ( ~ aElementOf0(X79,szDzozmdt0(xf))
| sdtlpdtrp0(xf,X79) != X79
| aElementOf0(X79,xS) )
& ( ~ aFixedPointOf0(X79,xf)
| aElementOf0(X79,xS) )
& xS = cS1142(xf) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1144])])])]) ).
cnf(c_0_13,hypothesis,
szDzozmdt0(xf) = szRzazndt0(xf),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
szRzazndt0(xf) = xU,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
( aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
szDzozmdt0(xf) = xU,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,hypothesis,
! [X80] :
( aSet0(xT)
& ( ~ aElementOf0(X80,xT)
| aElementOf0(X80,xS) )
& aSubsetOf0(xT,xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1173])])]) ).
fof(c_0_18,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(sdtlpdtrp0(xf,xp),X1) )
| aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(X1,sdtlpdtrp0(xf,xp)) )
| aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_19,hypothesis,
( aElementOf0(xp,xU)
& ! [X1] :
( aElementOf0(X1,xP)
=> sdtlseqdt0(xp,X1) )
& aLowerBoundOfIn0(xp,xP,xU)
& ! [X1] :
( ( ( aElementOf0(X1,xU)
& ! [X2] :
( aElementOf0(X2,xP)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xP,xU) )
=> sdtlseqdt0(X1,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(fof_simplification,[status(thm)],[m__1261]) ).
cnf(c_0_20,hypothesis,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,negated_conjecture,
( ( aElementOf0(esk16_0,xT)
| aElementOf0(esk15_0,xP) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| aElementOf0(esk15_0,xP) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| aElementOf0(esk15_0,xP) )
& ( aElementOf0(esk16_0,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) )
& ( aElementOf0(esk16_0,xT)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) )
& ( ~ aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)
| ~ aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_23,hypothesis,
! [X85,X86] :
( aElementOf0(xp,xU)
& ( ~ aElementOf0(X85,xP)
| sdtlseqdt0(xp,X85) )
& aLowerBoundOfIn0(xp,xP,xU)
& ( aElementOf0(esk14_1(X86),xP)
| ~ aElementOf0(X86,xU)
| sdtlseqdt0(X86,xp) )
& ( ~ sdtlseqdt0(X86,esk14_1(X86))
| ~ aElementOf0(X86,xU)
| sdtlseqdt0(X86,xp) )
& ( ~ aLowerBoundOfIn0(X86,xP,xU)
| sdtlseqdt0(X86,xp) )
& aInfimumOfIn0(xp,xP,xU) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).
fof(c_0_24,hypothesis,
! [X81,X82,X83] :
( aSet0(xP)
& ( aElementOf0(X81,xU)
| ~ aElementOf0(X81,xP) )
& ( sdtlseqdt0(sdtlpdtrp0(xf,X81),X81)
| ~ aElementOf0(X81,xP) )
& ( ~ aElementOf0(X82,xT)
| sdtlseqdt0(X82,X81)
| ~ aElementOf0(X81,xP) )
& ( aUpperBoundOfIn0(X81,xT,xU)
| ~ aElementOf0(X81,xP) )
& ( aElementOf0(esk13_1(X83),xT)
| ~ aElementOf0(X83,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X83),X83)
| aElementOf0(X83,xP) )
& ( ~ sdtlseqdt0(esk13_1(X83),X83)
| ~ aElementOf0(X83,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X83),X83)
| aElementOf0(X83,xP) )
& ( ~ aUpperBoundOfIn0(X83,xT,xU)
| ~ aElementOf0(X83,xU)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,X83),X83)
| aElementOf0(X83,xP) )
& xP = cS1241(xU,xf,xT) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1244])])])])])]) ).
cnf(c_0_25,hypothesis,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xT) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( aElementOf0(esk16_0,xT)
| aElementOf0(esk15_0,xP) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ aElementOf0(X1,szDzozmdt0(xf))
| ~ aElementOf0(X2,szDzozmdt0(xf))
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk14_1(X1))
| ~ aElementOf0(X1,xU) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X1,xT)
| ~ aElementOf0(X2,xP) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
( aElementOf0(esk14_1(X1),xP)
| sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xU) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( aElementOf0(esk15_0,xP)
| aElementOf0(esk16_0,xU) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_32,plain,
! [X1] :
( epred1_1(X1)
=> ? [X2] :
( aElementOf0(X2,xU)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aLowerBoundOfIn0(X2,X1,xU)
& ! [X3] :
( ( ( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X3,X4) ) )
| aLowerBoundOfIn0(X3,X1,xU) )
=> sdtlseqdt0(X3,X2) )
& aInfimumOfIn0(X2,X1,xU)
& ? [X3] :
( aElementOf0(X3,xU)
& ! [X4] :
( aElementOf0(X4,X1)
=> sdtlseqdt0(X4,X3) )
& aUpperBoundOfIn0(X3,X1,xU)
& ! [X4] :
( ( ( aElementOf0(X4,xU)
& ! [X5] :
( aElementOf0(X5,X1)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,X1,xU) )
=> sdtlseqdt0(X3,X4) )
& aSupremumOfIn0(X3,X1,xU) ) ) ),
inference(split_equiv,[status(thm)],[c_0_9]) ).
cnf(c_0_33,hypothesis,
( aElementOf0(esk12_1(X1),X1)
| epred1_1(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_35,plain,
! [X66,X67] :
( ~ aFunction0(X66)
| ~ aElementOf0(X67,szDzozmdt0(X66))
| aElementOf0(sdtlpdtrp0(X66,X67),szRzazndt0(X66)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgSort])])]) ).
cnf(c_0_36,hypothesis,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xU) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_16]),c_0_16]) ).
cnf(c_0_37,hypothesis,
( sdtlpdtrp0(xf,X1) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(esk14_1(X1),xP)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]) ).
cnf(c_0_39,negated_conjecture,
( sdtlseqdt0(esk16_0,xp)
| aElementOf0(esk14_1(esk16_0),xP)
| aElementOf0(esk15_0,xP) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_40,plain,
! [X90,X92,X93,X96,X97] :
( ( aElementOf0(esk17_1(X90),xU)
| ~ epred1_1(X90) )
& ( ~ aElementOf0(X92,X90)
| sdtlseqdt0(esk17_1(X90),X92)
| ~ epred1_1(X90) )
& ( aLowerBoundOfIn0(esk17_1(X90),X90,xU)
| ~ epred1_1(X90) )
& ( aElementOf0(esk18_2(X90,X93),X90)
| ~ aElementOf0(X93,xU)
| sdtlseqdt0(X93,esk17_1(X90))
| ~ epred1_1(X90) )
& ( ~ sdtlseqdt0(X93,esk18_2(X90,X93))
| ~ aElementOf0(X93,xU)
| sdtlseqdt0(X93,esk17_1(X90))
| ~ epred1_1(X90) )
& ( ~ aLowerBoundOfIn0(X93,X90,xU)
| sdtlseqdt0(X93,esk17_1(X90))
| ~ epred1_1(X90) )
& ( aInfimumOfIn0(esk17_1(X90),X90,xU)
| ~ epred1_1(X90) )
& ( aElementOf0(esk19_1(X90),xU)
| ~ epred1_1(X90) )
& ( ~ aElementOf0(X96,X90)
| sdtlseqdt0(X96,esk19_1(X90))
| ~ epred1_1(X90) )
& ( aUpperBoundOfIn0(esk19_1(X90),X90,xU)
| ~ epred1_1(X90) )
& ( aElementOf0(esk20_2(X90,X97),X90)
| ~ aElementOf0(X97,xU)
| sdtlseqdt0(esk19_1(X90),X97)
| ~ epred1_1(X90) )
& ( ~ sdtlseqdt0(esk20_2(X90,X97),X97)
| ~ aElementOf0(X97,xU)
| sdtlseqdt0(esk19_1(X90),X97)
| ~ epred1_1(X90) )
& ( ~ aUpperBoundOfIn0(X97,X90,xU)
| sdtlseqdt0(esk19_1(X90),X97)
| ~ epred1_1(X90) )
& ( aSupremumOfIn0(esk19_1(X90),X90,xU)
| ~ epred1_1(X90) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])]) ).
cnf(c_0_41,hypothesis,
( epred1_1(xT)
| aElementOf0(esk12_1(xT),xT) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_42,plain,
! [X19,X20,X21] :
( ~ aElement0(X19)
| ~ aElement0(X20)
| ~ aElement0(X21)
| ~ sdtlseqdt0(X19,X20)
| ~ sdtlseqdt0(X20,X21)
| sdtlseqdt0(X19,X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTrans])]) ).
fof(c_0_43,plain,
! [X6,X7] :
( ~ aSet0(X6)
| ~ aElementOf0(X7,X6)
| aElement0(X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_44,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),szRzazndt0(X1))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,hypothesis,
aFunction0(xf),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_46,negated_conjecture,
( aElementOf0(esk15_0,xP)
| ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,hypothesis,
( sdtlseqdt0(X1,sdtlpdtrp0(xf,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xU)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20]) ).
cnf(c_0_48,hypothesis,
aElementOf0(xp,xU),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_49,negated_conjecture,
( sdtlseqdt0(esk16_0,xp)
| aElementOf0(esk15_0,xP) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]) ).
cnf(c_0_50,plain,
( aElementOf0(esk19_1(X1),xU)
| ~ epred1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,hypothesis,
( epred1_1(X1)
| ~ aElementOf0(esk12_1(X1),xU)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_52,hypothesis,
( epred1_1(xT)
| aElementOf0(esk12_1(xT),xU) ),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_53,plain,
( sdtlseqdt0(X1,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,hypothesis,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X1)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,hypothesis,
( aElementOf0(sdtlpdtrp0(xf,X1),xU)
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_14]),c_0_45]),c_0_16])]) ).
cnf(c_0_57,hypothesis,
aSet0(xU),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_58,negated_conjecture,
( aElementOf0(esk15_0,xP)
| ~ aElementOf0(esk16_0,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_59,plain,
( sdtlseqdt0(esk19_1(X2),X1)
| ~ aUpperBoundOfIn0(X1,X2,xU)
| ~ epred1_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_60,plain,
( sdtlseqdt0(esk19_1(X1),xp)
| aElementOf0(esk14_1(esk19_1(X1)),xP)
| ~ epred1_1(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_61,hypothesis,
epred1_1(xT),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34])]) ).
cnf(c_0_62,hypothesis,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X1,sdtlpdtrp0(xf,X2))
| ~ aElementOf0(X2,xP)
| ~ aElement0(sdtlpdtrp0(xf,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_63,hypothesis,
( aElement0(sdtlpdtrp0(xf,X1))
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_64,hypothesis,
( aElementOf0(X1,xU)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_65,hypothesis,
aElementOf0(esk15_0,xP),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_21]),c_0_26]) ).
cnf(c_0_66,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_67,hypothesis,
( sdtlseqdt0(esk19_1(X1),xp)
| ~ epred1_1(X1)
| ~ aUpperBoundOfIn0(esk14_1(esk19_1(X1)),X1,xU) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_59]),c_0_50]) ).
cnf(c_0_68,hypothesis,
( aUpperBoundOfIn0(X1,xT,xU)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_69,hypothesis,
( sdtlseqdt0(esk19_1(xT),xp)
| aElementOf0(esk14_1(esk19_1(xT)),xP) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,hypothesis,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,xP)
| ~ aElementOf0(X1,xU)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_36]),c_0_63]),c_0_63]),c_0_64]) ).
cnf(c_0_71,hypothesis,
aElement0(esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_65]),c_0_66])]) ).
cnf(c_0_72,hypothesis,
sdtlseqdt0(esk19_1(xT),xp),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_61])]),c_0_69]) ).
cnf(c_0_73,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_57])]) ).
cnf(c_0_74,negated_conjecture,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_75,hypothesis,
( sdtlseqdt0(sdtlpdtrp0(xf,X1),esk15_0)
| ~ sdtlseqdt0(X1,esk15_0)
| ~ aElementOf0(X1,xU) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_65]),c_0_71])]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk19_1(xT))
| ~ aElement0(esk19_1(xT))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_72]),c_0_73])]) ).
cnf(c_0_77,plain,
( aElement0(esk19_1(X1))
| ~ epred1_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_57])]) ).
cnf(c_0_78,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_79,negated_conjecture,
( aElementOf0(esk16_0,xT)
| ~ sdtlseqdt0(sdtlpdtrp0(xf,xp),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_80,negated_conjecture,
( ~ sdtlseqdt0(esk16_0,sdtlpdtrp0(xf,xp))
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_48])]) ).
cnf(c_0_81,plain,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,esk19_1(xT))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_61])]) ).
cnf(c_0_82,plain,
( sdtlseqdt0(X1,esk19_1(X2))
| ~ aElementOf0(X1,X2)
| ~ epred1_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_83,hypothesis,
( aElement0(X1)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_21]),c_0_78])]) ).
cnf(c_0_84,negated_conjecture,
( aElementOf0(esk16_0,xT)
| ~ sdtlseqdt0(xp,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_75]),c_0_48])]) ).
cnf(c_0_85,hypothesis,
( sdtlseqdt0(xp,X1)
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_86,hypothesis,
( ~ sdtlseqdt0(xp,esk15_0)
| ~ sdtlseqdt0(esk16_0,xp)
| ~ aElementOf0(esk16_0,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_47]),c_0_48])]) ).
cnf(c_0_87,plain,
( sdtlseqdt0(X1,xp)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_61])]),c_0_83]) ).
cnf(c_0_88,hypothesis,
aElementOf0(esk16_0,xT),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_65])]) ).
cnf(c_0_89,plain,
( ~ sdtlseqdt0(xp,esk15_0)
| ~ aElementOf0(esk16_0,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_90,hypothesis,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_85]),c_0_65])]) ).
cnf(c_0_91,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_21]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT386+4 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 07:44:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.54/0.57 start to proof: theBenchmark
% 1.65/1.73 % Version : CSE_E---1.5
% 1.65/1.73 % Problem : theBenchmark.p
% 1.65/1.73 % Proof found
% 1.65/1.73 % SZS status Theorem for theBenchmark.p
% 1.65/1.73 % SZS output start Proof
% See solution above
% 1.65/1.74 % Total time : 1.151000 s
% 1.65/1.74 % SZS output end Proof
% 1.65/1.74 % Total time : 1.154000 s
%------------------------------------------------------------------------------