%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM545+2 : 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 : n021.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 04:57:46 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 140 ( 16 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 162 ( 53 ~; 54 |; 42 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 30 ( 2 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( ( aSet0(slbdtrb0(X1))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X1) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) )
| aSubsetOf0(xS,slbdtrb0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2035,hypothesis,
( ~ ( ~ ? [X1] : aElementOf0(X1,xS)
& xS = slcrc0 )
=> ( aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,szmzazxdt0(xS)) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) ) )
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
fof(m__1986,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( ( aSet0(slbdtrb0(X1))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X1) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) )
| aSubsetOf0(xS,slbdtrb0(X1)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,hypothesis,
! [X209,X210,X211,X212] :
( ( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X209,xS) )
& ( ~ aElementOf0(X210,xS)
| sdtlseqdt0(X210,szmzazxdt0(xS))
| ~ aElementOf0(X209,xS) )
& ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( aElementOf0(X211,szNzAzT0)
| ~ aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( sdtlseqdt0(szszuzczcdt0(X211),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( ~ aElementOf0(X211,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X211),szszuzczcdt0(szmzazxdt0(xS)))
| aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( ~ aElementOf0(X212,xS)
| aElementOf0(X212,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X209,xS) )
& ( aElementOf0(szmzazxdt0(xS),xS)
| xS = slcrc0 )
& ( ~ aElementOf0(X210,xS)
| sdtlseqdt0(X210,szmzazxdt0(xS))
| xS = slcrc0 )
& ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( aElementOf0(X211,szNzAzT0)
| ~ aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( sdtlseqdt0(szszuzczcdt0(X211),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( ~ aElementOf0(X211,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X211),szszuzczcdt0(szmzazxdt0(xS)))
| aElementOf0(X211,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( ~ aElementOf0(X212,xS)
| aElementOf0(X212,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 )
& ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2035])])])]) ).
fof(c_0_9,negated_conjecture,
! [X213,X214,X215] :
( ( aSet0(slbdtrb0(X213))
| ~ aElementOf0(X213,szNzAzT0) )
& ( aElementOf0(X214,szNzAzT0)
| ~ aElementOf0(X214,slbdtrb0(X213))
| ~ aElementOf0(X213,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X214),X213)
| ~ aElementOf0(X214,slbdtrb0(X213))
| ~ aElementOf0(X213,szNzAzT0) )
& ( ~ aElementOf0(X215,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X215),X213)
| aElementOf0(X215,slbdtrb0(X213))
| ~ aElementOf0(X213,szNzAzT0) )
& ( aElementOf0(esk10_1(X213),xS)
| ~ aElementOf0(X213,szNzAzT0) )
& ( ~ aElementOf0(esk10_1(X213),slbdtrb0(X213))
| ~ aElementOf0(X213,szNzAzT0) )
& ( ~ aSubsetOf0(xS,slbdtrb0(X213))
| ~ aElementOf0(X213,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)],[c_0_7])])])])])]) ).
cnf(c_0_10,hypothesis,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( aElementOf0(esk10_1(X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,hypothesis,
! [X208] :
( aSet0(xS)
& ( ~ aElementOf0(X208,xS)
| aElementOf0(X208,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1986])])]) ).
cnf(c_0_13,negated_conjecture,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_15,negated_conjecture,
( ~ aSubsetOf0(xS,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,plain,
! [X153] :
( ( aElementOf0(szszuzczcdt0(X153),szNzAzT0)
| ~ aElementOf0(X153,szNzAzT0) )
& ( szszuzczcdt0(X153) != sz00
| ~ aElementOf0(X153,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
aElementOf0(szmzazxdt0(xS),xS),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_21,negated_conjecture,
( slcrc0 = xS
| ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_14])]) ).
cnf(c_0_25,negated_conjecture,
slcrc0 = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_26,plain,
! [X121] :
( ~ aSet0(X121)
| aSubsetOf0(X121,X121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
cnf(c_0_27,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM545+2 : 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
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % 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 00:46:10 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------