%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM611+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 : n019.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 4.15s 3.56s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 124 ( 30 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 122 ( 41 ~; 38 |; 30 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 24 !; 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__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(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(mSuccEquSucc,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
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(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(m__,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_11,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_12,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_13,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_14,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])])]) ).
fof(c_0_15,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_16,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_17,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
sbrdtbr0(xQ) = xK,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_20,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X305,X306] :
( ~ aElementOf0(X305,szNzAzT0)
| ~ aElementOf0(X306,szNzAzT0)
| szszuzczcdt0(X305) != szszuzczcdt0(X306)
| X305 = X306 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEquSucc])]) ).
fof(c_0_22,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_23,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,hypothesis,
aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,hypothesis,
isFinite0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_30,hypothesis,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_31,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_34,plain,
( aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,hypothesis,
isFinite0(xP),
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_20])]) ).
cnf(c_0_36,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_37,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_38,hypothesis,
( X1 = xk
| szszuzczcdt0(X1) != xK
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_39,hypothesis,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
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_31,c_0_32]),c_0_33]),c_0_18]),c_0_27]),c_0_20])]) ).
cnf(c_0_40,hypothesis,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM611+3 : 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
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:51:14 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 4.15/3.56 % Version : CSE_E---1.7
% 4.15/3.56 % Problem : theBenchmark.p
% 4.15/3.56 % SZS status Theorem for theBenchmark.p
% 4.15/3.56 % SZS output start CNFRefutation
% See solution above
% 4.15/3.57 % Total time : 2.828s
%------------------------------------------------------------------------------