%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM612+3 : 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 : n025.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 04:58:02 PM UTC 2026
% Result : Theorem 2.78s 2.36s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 112 ( 22 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 113 ( 39 ~; 33 |; 30 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(m__5078,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(m__,conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(m__5195,hypothesis,
( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xQ) )
& aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(m__5164,hypothesis,
( aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
( aElementOf0(xp,xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(xp,X1) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(c_0_9,plain,
! [X325] :
( ( ~ aElementOf0(sbrdtbr0(X325),szNzAzT0)
| isFinite0(X325)
| ~ aSet0(X325) )
& ( ~ isFinite0(X325)
| aElementOf0(sbrdtbr0(X325),szNzAzT0)
| ~ aSet0(X325) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
fof(c_0_10,hypothesis,
! [X495] :
( aSet0(xQ)
& ( ~ aElementOf0(X495,xQ)
| aElementOf0(X495,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])]) ).
fof(c_0_11,negated_conjecture,
~ ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X270,X271] :
( ~ aSet0(X270)
| ~ isFinite0(X270)
| ~ aSubsetOf0(X271,X270)
| isFinite0(X271) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
fof(c_0_13,hypothesis,
! [X505] :
( ( ~ aElementOf0(X505,xP)
| aElementOf0(X505,xQ) )
& aSubsetOf0(xP,xQ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5195])])]) ).
cnf(c_0_14,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
sbrdtbr0(xQ) = xK,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_17,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,hypothesis,
isFinite0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
fof(c_0_22,hypothesis,
! [X502,X503] :
( aSet0(xP)
& ( ~ aElementOf0(X502,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X502) )
& ( aElement0(X503)
| ~ aElementOf0(X503,xP) )
& ( aElementOf0(X503,xQ)
| ~ aElementOf0(X503,xP) )
& ( X503 != szmzizndt0(xQ)
| ~ aElementOf0(X503,xP) )
& ( ~ aElement0(X503)
| ~ aElementOf0(X503,xQ)
| X503 = szmzizndt0(xQ)
| aElementOf0(X503,xP) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5164])])])]) ).
fof(c_0_23,hypothesis,
! [X501] :
( aElementOf0(xp,xQ)
& ( ~ aElementOf0(X501,xQ)
| sdtlseqdt0(xp,X501) )
& xp = szmzizndt0(xQ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])]) ).
cnf(c_0_24,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_17])]) ).
cnf(c_0_27,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X329,X330] :
( ~ aSet0(X329)
| ~ isFinite0(X329)
| ~ aElementOf0(X330,X329)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X329,X330))) = sbrdtbr0(X329) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_29,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( szszuzczcdt0(sbrdtbr0(xP)) != xK
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(rw,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_32,hypothesis,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_33,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
szszuzczcdt0(sbrdtbr0(xP)) != xK,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_15]),c_0_21]),c_0_17])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM612+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n025.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 00:50:58 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.78/2.36 % Version : CSE_E---1.7
% 2.78/2.36 % Problem : theBenchmark.p
% 2.78/2.36 % SZS status Theorem for theBenchmark.p
% 2.78/2.36 % SZS output start CNFRefutation
% See solution above
% 2.78/2.36 % Total time : 1.775s
%------------------------------------------------------------------------------