%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM538+2 : 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 : n007.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 04:57:44 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 173 ( 36 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 233 ( 94 ~; 93 |; 27 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardCons,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
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(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__,conjecture,
( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1522_02,hypothesis,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522_02) ).
fof(m__1522,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1522) ).
fof(c_0_8,plain,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
fof(c_0_9,plain,
! [X104,X105,X106,X107,X108,X109] :
( ( aSet0(X106)
| X106 != sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( aElement0(X107)
| ~ aElementOf0(X107,X106)
| X106 != sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( aElementOf0(X107,X104)
| ~ aElementOf0(X107,X106)
| X106 != sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( X107 != X105
| ~ aElementOf0(X107,X106)
| X106 != sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( ~ aElement0(X108)
| ~ aElementOf0(X108,X104)
| X108 = X105
| aElementOf0(X108,X106)
| X106 != sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( ~ aElementOf0(esk4_3(X104,X105,X109),X109)
| ~ aElement0(esk4_3(X104,X105,X109))
| ~ aElementOf0(esk4_3(X104,X105,X109),X104)
| esk4_3(X104,X105,X109) = X105
| ~ aSet0(X109)
| X109 = sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( aElement0(esk4_3(X104,X105,X109))
| aElementOf0(esk4_3(X104,X105,X109),X109)
| ~ aSet0(X109)
| X109 = sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( aElementOf0(esk4_3(X104,X105,X109),X104)
| aElementOf0(esk4_3(X104,X105,X109),X109)
| ~ aSet0(X109)
| X109 = sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) )
& ( esk4_3(X104,X105,X109) != X105
| aElementOf0(esk4_3(X104,X105,X109),X109)
| ~ aSet0(X109)
| X109 = sdtmndt0(X104,X105)
| ~ aSet0(X104)
| ~ aElement0(X105) ) ),
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_10,plain,
! [X146,X147] :
( ~ aSet0(X146)
| ~ isFinite0(X146)
| ~ aElement0(X147)
| aElementOf0(X147,X146)
| sbrdtbr0(sdtpldt0(X146,X147)) = szszuzczcdt0(sbrdtbr0(X146)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X111,X112] :
( ~ aSet0(X111)
| ~ aElementOf0(X112,X111)
| sdtpldt0(sdtmndt0(X111,X112),X112) = X111 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X76,X77] :
( ~ aSet0(X76)
| ~ aElementOf0(X77,X76)
| aElement0(X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_14,plain,
( aElementOf0(X2,X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X121,X122] :
( ~ aElement0(X121)
| ~ aSet0(X122)
| ~ isFinite0(X122)
| isFinite0(sdtmndt0(X122,X121)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).
fof(c_0_19,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_20,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| aElementOf0(X2,sdtmndt0(X1,X2))
| ~ isFinite0(sdtmndt0(X1,X2))
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_22,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,negated_conjecture,
! [X148] :
( aSet0(sdtmndt0(xS,xx))
& ( aElement0(X148)
| ~ aElementOf0(X148,sdtmndt0(xS,xx)) )
& ( aElementOf0(X148,xS)
| ~ aElementOf0(X148,sdtmndt0(xS,xx)) )
& ( X148 != xx
| ~ aElementOf0(X148,sdtmndt0(xS,xx)) )
& ( ~ aElement0(X148)
| ~ aElementOf0(X148,xS)
| X148 = xx
| aElementOf0(X148,sdtmndt0(xS,xx)) )
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_24,plain,
( X1 != sdtmndt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| aElementOf0(X2,sdtmndt0(X1,X2))
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_27,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_28,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__1522]) ).
cnf(c_0_29,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_32,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_28])]) ).
cnf(c_0_33,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM538+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:43:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------