%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM538+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 1.95s 1.91s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 155 ( 32 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 208 ( 87 ~; 90 |; 16 &)
% ( 2 <=>; 13 =>; 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 : 56 ( 0 sgn 28 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__1522_02,hypothesis,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522_02) ).
fof(m__1522,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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,
! [X103,X104,X105,X106,X107,X108] :
( ( aSet0(X105)
| X105 != sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( aElement0(X106)
| ~ aElementOf0(X106,X105)
| X105 != sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( aElementOf0(X106,X103)
| ~ aElementOf0(X106,X105)
| X105 != sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( X106 != X104
| ~ aElementOf0(X106,X105)
| X105 != sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( ~ aElement0(X107)
| ~ aElementOf0(X107,X103)
| X107 = X104
| aElementOf0(X107,X105)
| X105 != sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( ~ aElementOf0(esk4_3(X103,X104,X108),X108)
| ~ aElement0(esk4_3(X103,X104,X108))
| ~ aElementOf0(esk4_3(X103,X104,X108),X103)
| esk4_3(X103,X104,X108) = X104
| ~ aSet0(X108)
| X108 = sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( aElement0(esk4_3(X103,X104,X108))
| aElementOf0(esk4_3(X103,X104,X108),X108)
| ~ aSet0(X108)
| X108 = sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( aElementOf0(esk4_3(X103,X104,X108),X103)
| aElementOf0(esk4_3(X103,X104,X108),X108)
| ~ aSet0(X108)
| X108 = sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) )
& ( esk4_3(X103,X104,X108) != X104
| aElementOf0(esk4_3(X103,X104,X108),X108)
| ~ aSet0(X108)
| X108 = sdtmndt0(X103,X104)
| ~ aSet0(X103)
| ~ aElement0(X104) ) ),
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,
! [X145,X146] :
( ~ aSet0(X145)
| ~ isFinite0(X145)
| ~ aElement0(X146)
| aElementOf0(X146,X145)
| sbrdtbr0(sdtpldt0(X145,X146)) = szszuzczcdt0(sbrdtbr0(X145)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X120,X121] :
( ~ aElement0(X120)
| ~ aSet0(X121)
| ~ isFinite0(X121)
| isFinite0(sdtmndt0(X121,X120)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,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_14,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(X1,X2),X3)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2)))
| aElementOf0(X3,sdtmndt0(X1,X2))
| ~ isFinite0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_18,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__1522]) ).
fof(c_0_19,plain,
! [X110,X111] :
( ~ aSet0(X110)
| ~ aElementOf0(X111,X110)
| sdtpldt0(sdtmndt0(X110,X111),X111) = X110 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).
fof(c_0_20,plain,
! [X75,X76] :
( ~ aSet0(X75)
| ~ aElementOf0(X76,X75)
| aElement0(X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_21,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_22,hypothesis,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,X1),X2)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,X1)))
| aElementOf0(X2,sdtmndt0(xS,X1))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_23,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
fof(c_0_26,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_27,plain,
( X1 != sdtmndt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,X1))) = sbrdtbr0(xS)
| aElementOf0(X1,sdtmndt0(xS,X1))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18])]) ).
cnf(c_0_29,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18])]) ).
cnf(c_0_30,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29])]),c_0_30]) ).
cnf(c_0_33,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM538+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n011.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:43:47 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.95/1.91 % Version : CSE_E---1.7
% 1.95/1.91 % Problem : theBenchmark.p
% 1.95/1.91 % SZS status Theorem for theBenchmark.p
% 1.95/1.91 % SZS output start CNFRefutation
% See solution above
% 1.95/1.91 % Total time : 1.371s
%------------------------------------------------------------------------------