%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM558+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 May 5 04:57:49 PM UTC 2026
% Result : Theorem 1.42s 1.77s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 274 ( 53 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 381 ( 156 ~; 169 |; 42 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(m__2227,hypothesis,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
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/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__2378,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2378) ).
fof(m__2357,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(m__,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_14,plain,
! [X119,X120,X121,X122] :
( ( aSet0(X120)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(X121,X120)
| aElementOf0(X121,X119)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( aElementOf0(esk2_2(X119,X122),X122)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(esk2_2(X119,X122),X119)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) ) ),
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])])])])])]) ).
fof(c_0_15,plain,
! [X216,X217,X218,X219,X220,X221] :
( ( aSet0(X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(X219,X216)
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(X219) = X217
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aSubsetOf0(X220,X216)
| sbrdtbr0(X220) != X217
| aElementOf0(X220,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSubsetOf0(esk11_3(X216,X217,X221),X216)
| sbrdtbr0(esk11_3(X216,X217,X221)) != X217
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X216,X217,X221),X216)
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X216,X217,X221)) = X217
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) ) ),
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)],[mDefSel])])])])])]) ).
cnf(c_0_16,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,hypothesis,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(split_conjunct,[status(thm)],[m__2227]) ).
cnf(c_0_18,plain,
( aSet0(X1)
| X1 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
( aElementOf0(X1,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( aSet0(slbdtsldtrb0(X1,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_23,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_24,plain,
! [X132,X133,X134,X135,X136,X137] :
( ( aSet0(X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElement0(X135)
| ~ aElementOf0(X135,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElementOf0(X135,X132)
| X135 = X133
| ~ aElementOf0(X135,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( ~ aElementOf0(X136,X132)
| ~ aElement0(X136)
| aElementOf0(X136,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( X136 != X133
| ~ aElement0(X136)
| aElementOf0(X136,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( ~ aElementOf0(esk3_3(X132,X133,X137),X132)
| ~ aElement0(esk3_3(X132,X133,X137))
| ~ aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( esk3_3(X132,X133,X137) != X133
| ~ aElement0(esk3_3(X132,X133,X137))
| ~ aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElement0(esk3_3(X132,X133,X137))
| aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElementOf0(esk3_3(X132,X133,X137),X132)
| esk3_3(X132,X133,X137) = X133
| aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) ) ),
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])])])])])]) ).
fof(c_0_25,plain,
! [X111,X112] :
( ~ aSet0(X111)
| ~ aElementOf0(X112,X111)
| aElement0(X112) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_26,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
( aElementOf0(X1,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_28,plain,
( aElementOf0(X1,X3)
| X1 != X2
| ~ aElement0(X1)
| X3 != sdtpldt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_31,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_32,plain,
! [X139,X140,X141,X142,X143,X144] :
( ( aSet0(X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElement0(X142)
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElementOf0(X142,X139)
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( X142 != X140
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( ~ aElement0(X143)
| ~ aElementOf0(X143,X139)
| X143 = X140
| aElementOf0(X143,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( ~ aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aElement0(esk4_3(X139,X140,X144))
| ~ aElementOf0(esk4_3(X139,X140,X144),X139)
| esk4_3(X139,X140,X144) = X140
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElement0(esk4_3(X139,X140,X144))
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElementOf0(esk4_3(X139,X140,X144),X139)
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( esk4_3(X139,X140,X144) != X140
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) ) ),
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_33,hypothesis,
( aSubsetOf0(X1,xT)
| ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_23])]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2378]) ).
cnf(c_0_35,plain,
( aElementOf0(X1,sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])]) ).
cnf(c_0_36,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[m__2357]) ).
cnf(c_0_37,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_38,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,hypothesis,
aSubsetOf0(xP,xT),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(xx,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_41,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_42,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_43,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
fof(c_0_44,negated_conjecture,
~ aElementOf0(xx,xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_45,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_39]),c_0_23])]) ).
cnf(c_0_46,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
~ aElementOf0(xx,xT),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM558+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:45:06 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.42/1.77 % Version : CSE_E---1.7
% 1.42/1.77 % Problem : theBenchmark.p
% 1.42/1.77 % SZS status Theorem for theBenchmark.p
% 1.42/1.77 % SZS output start CNFRefutation
% See solution above
% 1.42/1.77 % Total time : 1.370s
%------------------------------------------------------------------------------