TSTP Solution File: NUM536+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM536+1 : 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 : 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 : Thu Aug 31 10:38:30 EDT 2023
% Result : Theorem 5.60s 5.69s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 52 ( 10 unt; 15 typ; 0 def)
% Number of atoms : 235 ( 56 equ)
% Maximal formula atoms : 54 ( 6 avg)
% Number of connectives : 338 ( 140 ~; 166 |; 24 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 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 : 69 ( 0 sgn; 24 !; 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,
xx: $i ).
tff(decl_32,type,
xS: $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(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(m__679,hypothesis,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__679_02,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679_02) ).
fof(c_0_6,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])])])])])]) ).
cnf(c_0_7,plain,
( aElementOf0(esk4_3(X1,X2,X3),X1)
| aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__679]) ).
fof(c_0_9,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( aSet0(X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElement0(X29)
| ~ aElementOf0(X29,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElementOf0(X29,X26)
| X29 = X27
| ~ aElementOf0(X29,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( ~ aElementOf0(X30,X26)
| ~ aElement0(X30)
| aElementOf0(X30,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( X30 != X27
| ~ aElement0(X30)
| aElementOf0(X30,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( ~ aElementOf0(esk3_3(X26,X27,X31),X26)
| ~ aElement0(esk3_3(X26,X27,X31))
| ~ aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( esk3_3(X26,X27,X31) != X27
| ~ aElement0(esk3_3(X26,X27,X31))
| ~ aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElement0(esk3_3(X26,X27,X31))
| aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElementOf0(esk3_3(X26,X27,X31),X26)
| esk3_3(X26,X27,X31) = X27
| aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) ) ),
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)],[mDefCons])])])])])]) ).
cnf(c_0_10,hypothesis,
( X1 = sdtmndt0(X2,xx)
| aElementOf0(esk4_3(X2,xx,X1),X1)
| aElementOf0(esk4_3(X2,xx,X1),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__679]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
( sdtmndt0(X1,xx) = xS
| aElementOf0(esk4_3(X1,xx,xS),xS)
| aElementOf0(esk4_3(X1,xx,xS),X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
( sdtmndt0(sdtpldt0(X1,X2),xx) = xS
| aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),sdtpldt0(X1,X2))
| aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,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])])]) ).
cnf(c_0_19,hypothesis,
( esk4_3(sdtpldt0(X1,X2),xx,xS) = X2
| sdtmndt0(sdtpldt0(X1,X2),xx) = xS
| aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),xS)
| aElementOf0(esk4_3(sdtpldt0(X1,X2),xx,xS),X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_20,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_21,plain,
( esk4_3(X1,X2,X3) = X2
| X3 = sdtmndt0(X1,X2)
| ~ aElementOf0(esk4_3(X1,X2,X3),X3)
| ~ aElement0(esk4_3(X1,X2,X3))
| ~ aElementOf0(esk4_3(X1,X2,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
( esk4_3(sdtpldt0(X1,xx),xx,xS) = xx
| sdtmndt0(sdtpldt0(X1,xx),xx) = xS
| aElementOf0(esk4_3(sdtpldt0(X1,xx),xx,xS),xS)
| aElementOf0(esk4_3(sdtpldt0(X1,xx),xx,xS),X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_24,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| X3 != sdtpldt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( esk4_3(X1,X2,X3) = X2
| X3 = sdtmndt0(X1,X2)
| ~ aElementOf0(esk4_3(X1,X2,X3),X3)
| ~ aElementOf0(esk4_3(X1,X2,X3),X1)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,hypothesis,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_11]),c_0_24]) ).
cnf(c_0_28,plain,
( aElementOf0(X1,X2)
| X2 != sdtpldt0(X3,X4)
| ~ aElementOf0(X1,X3)
| ~ aElement0(X4)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_29,hypothesis,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| ~ aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_8]),c_0_11])]),c_0_24]) ).
cnf(c_0_30,plain,
( aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(X1,X2)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_28]) ).
fof(c_0_31,hypothesis,
~ aElementOf0(xx,xS),
inference(fof_simplification,[status(thm)],[m__679_02]) ).
cnf(c_0_32,plain,
( aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| esk4_3(X1,X2,X3) != X2
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_33,hypothesis,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_8]),c_0_11])]),c_0_27]) ).
cnf(c_0_34,hypothesis,
~ aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,hypothesis,
~ aSet0(sdtpldt0(xS,xx)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_8]),c_0_11])]),c_0_24]),c_0_34]) ).
cnf(c_0_36,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_15]),c_0_8]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM536+1 : 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 : n028.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 15:17:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 5.60/5.69 % Version : CSE_E---1.5
% 5.60/5.69 % Problem : theBenchmark.p
% 5.60/5.69 % Proof found
% 5.60/5.69 % SZS status Theorem for theBenchmark.p
% 5.60/5.69 % SZS output start Proof
% See solution above
% 5.60/5.69 % Total time : 5.131000 s
% 5.60/5.69 % SZS output end Proof
% 5.60/5.69 % Total time : 5.133000 s
%------------------------------------------------------------------------------