%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM612+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 : 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 : Tue May 5 04:58:01 PM UTC 2026
% Result : Theorem 1.43s 1.77s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 156 ( 33 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 189 ( 79 ~; 77 |; 21 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
fof(m__5164,hypothesis,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5093,hypothesis,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
fof(m__5078,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(m__5195,hypothesis,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
fof(c_0_14,negated_conjecture,
~ ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_15,plain,
! [X186,X187,X188,X189] :
( ( aSet0(X187)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(X188,X187)
| aElementOf0(X188,X186)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( aElementOf0(esk2_2(X186,X189),X189)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(esk2_2(X186,X189),X186)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) ) ),
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_16,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X246] :
( ( ~ aElementOf0(sbrdtbr0(X246),szNzAzT0)
| isFinite0(X246)
| ~ aSet0(X246) )
& ( ~ isFinite0(X246)
| aElementOf0(sbrdtbr0(X246),szNzAzT0)
| ~ aSet0(X246) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
fof(c_0_18,plain,
! [X250,X251] :
( ~ aSet0(X250)
| ~ isFinite0(X250)
| ~ aElementOf0(X251,X250)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X250,X251))) = sbrdtbr0(X250) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_19,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_20,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_21,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[m__5093]) ).
cnf(c_0_23,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
fof(c_0_24,plain,
! [X283,X284,X285,X286,X287,X288] :
( ( aSet0(X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( aSubsetOf0(X286,X283)
| ~ aElementOf0(X286,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( sbrdtbr0(X286) = X284
| ~ aElementOf0(X286,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( ~ aSubsetOf0(X287,X283)
| sbrdtbr0(X287) != X284
| aElementOf0(X287,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSubsetOf0(esk11_3(X283,X284,X288),X283)
| sbrdtbr0(esk11_3(X283,X284,X288)) != X284
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X283,X284,X288),X283)
| aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X283,X284,X288)) = X284
| aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,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_25,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_28,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
cnf(c_0_31,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_32,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X191,X192] :
( ~ aSet0(X191)
| ~ isFinite0(X191)
| ~ aSubsetOf0(X192,X191)
| isFinite0(X192) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
cnf(c_0_34,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ isFinite0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_35,hypothesis,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
| ~ isFinite0(xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31])]) ).
cnf(c_0_36,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(split_conjunct,[status(thm)],[m__5078]) ).
cnf(c_0_38,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_39,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[m__5195]) ).
cnf(c_0_41,negated_conjecture,
( ~ isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,hypothesis,
sbrdtbr0(xQ) = xK,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_23])]) ).
cnf(c_0_44,hypothesis,
~ isFinite0(xQ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31])]),c_0_41]) ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38]),c_0_31])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM612+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:50:50 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.43/1.77 % Version : CSE_E---1.7
% 1.43/1.77 % Problem : theBenchmark.p
% 1.43/1.77 % SZS status Theorem for theBenchmark.p
% 1.43/1.77 % SZS output start CNFRefutation
% See solution above
% 1.43/1.77 % Total time : 1.374s
%------------------------------------------------------------------------------