TSTP Solution File: NUM534+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM534+2 : 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 : n020.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 10:38:29 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 61 ( 11 unt; 15 typ; 0 def)
% Number of atoms : 244 ( 47 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 324 ( 126 ~; 142 |; 38 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn; 31 !; 0 ?; 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,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
xS: $i ).
tff(decl_32,type,
xx: $i ).
tff(decl_33,type,
esk1_1: $i > $i ).
tff(decl_34,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk4_3: ( $i * $i * $i ) > $i ).
fof(m__,conjecture,
( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| X1 = xx ) ) ) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).
fof(m__617,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
fof(mSubASymm,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
fof(c_0_7,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| X1 = xx ) ) ) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( aSet0(X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElement0(X36)
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElementOf0(X36,X33)
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( X36 != X34
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( ~ aElement0(X37)
| ~ aElementOf0(X37,X33)
| X37 = X34
| aElementOf0(X37,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( ~ aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aElement0(esk4_3(X33,X34,X38))
| ~ aElementOf0(esk4_3(X33,X34,X38),X33)
| esk4_3(X33,X34,X38) = X34
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElement0(esk4_3(X33,X34,X38))
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElementOf0(esk4_3(X33,X34,X38),X33)
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( esk4_3(X33,X34,X38) != X34
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) ) ),
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)],[mDefDiff])])])])])]) ).
fof(c_0_9,plain,
! [X5,X6] :
( ~ aSet0(X5)
| ~ aElementOf0(X6,X5)
| aElement0(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_10,negated_conjecture,
! [X40,X41] :
( aSet0(sdtmndt0(xS,xx))
& ( aElement0(X40)
| ~ aElementOf0(X40,sdtmndt0(xS,xx)) )
& ( aElementOf0(X40,xS)
| ~ aElementOf0(X40,sdtmndt0(xS,xx)) )
& ( X40 != xx
| ~ aElementOf0(X40,sdtmndt0(xS,xx)) )
& ( ~ aElement0(X40)
| ~ aElementOf0(X40,xS)
| X40 = xx
| aElementOf0(X40,sdtmndt0(xS,xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ( aElement0(X41)
| ~ aElementOf0(X41,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( aElementOf0(X41,sdtmndt0(xS,xx))
| X41 = xx
| ~ aElementOf0(X41,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( ~ aElementOf0(X41,sdtmndt0(xS,xx))
| ~ aElement0(X41)
| aElementOf0(X41,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ( X41 != xx
| ~ aElement0(X41)
| aElementOf0(X41,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& sdtpldt0(sdtmndt0(xS,xx),xx) != xS ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
( X1 = X3
| aElementOf0(X1,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| X4 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X13,X14,X15,X16] :
( ( aSet0(X14)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(X15,X14)
| aElementOf0(X15,X13)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( aElementOf0(esk2_2(X13,X16),X16)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(esk2_2(X13,X16),X13)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) ) ),
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)],[mDefSub])])])])])]) ).
cnf(c_0_14,negated_conjecture,
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(xS,xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( X1 = X2
| aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X4)
| ~ aElement0(X2)
| ~ aSet0(X4) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__617_02]) ).
cnf(c_0_18,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__617]) ).
cnf(c_0_19,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X1,sdtmndt0(xS,xx)) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( X1 = X2
| aElementOf0(X1,sdtmndt0(X3,X2))
| ~ aElementOf0(X1,X3)
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_18])]) ).
cnf(c_0_24,negated_conjecture,
( aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),X1),sdtmndt0(xS,xx))
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( X1 = xx
| aElement0(X1)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_22]),c_0_23]),c_0_18])]) ).
fof(c_0_27,plain,
! [X21,X22] :
( ~ aSet0(X21)
| ~ aSet0(X22)
| ~ aSubsetOf0(X21,X22)
| ~ aSubsetOf0(X22,X21)
| X21 = X22 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubASymm])]) ).
cnf(c_0_28,negated_conjecture,
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| X1 != xx
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,negated_conjecture,
( esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),X1) = xx
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),X1),xS)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( aElementOf0(X1,sdtmndt0(xS,xx))
| X1 = xx
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( aSubsetOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),X1) != xx
| ~ aElement0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),X1))
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_21])]) ).
cnf(c_0_36,negated_conjecture,
( esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_18]),c_0_21])]) ).
cnf(c_0_37,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( esk2_2(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| aElementOf0(esk2_2(X1,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_21])]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23]),c_0_18])]) ).
cnf(c_0_41,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_42,negated_conjecture,
( esk2_2(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1)
| aElementOf0(esk2_2(X1,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]),c_0_18])]) ).
cnf(c_0_43,negated_conjecture,
~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_18])]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_42]),c_0_21]),c_0_18])]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_44]),c_0_17]),c_0_21]),c_0_18])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM534+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:09:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.64 % Version : CSE_E---1.5
% 0.19/0.64 % Problem : theBenchmark.p
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark.p
% 0.19/0.64 % SZS output start Proof
% See solution above
% 0.19/0.65 % Total time : 0.067000 s
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time : 0.069000 s
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