%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM609+1 : 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 : 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 1.53s 1.79s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 135 ( 23 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 174 ( 71 ~; 76 |; 19 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__5164,hypothesis,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(m__5182,hypothesis,
aElementOf0(xp,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5182) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(m__5093,hypothesis,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(m__,conjecture,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_9,plain,
! [X206,X207,X208,X209,X210,X211] :
( ( aSet0(X208)
| X208 != sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( aElement0(X209)
| ~ aElementOf0(X209,X208)
| X208 != sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( aElementOf0(X209,X206)
| ~ aElementOf0(X209,X208)
| X208 != sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( X209 != X207
| ~ aElementOf0(X209,X208)
| X208 != sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( ~ aElement0(X210)
| ~ aElementOf0(X210,X206)
| X210 = X207
| aElementOf0(X210,X208)
| X208 != sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( ~ aElementOf0(esk4_3(X206,X207,X211),X211)
| ~ aElement0(esk4_3(X206,X207,X211))
| ~ aElementOf0(esk4_3(X206,X207,X211),X206)
| esk4_3(X206,X207,X211) = X207
| ~ aSet0(X211)
| X211 = sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( aElement0(esk4_3(X206,X207,X211))
| aElementOf0(esk4_3(X206,X207,X211),X211)
| ~ aSet0(X211)
| X211 = sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( aElementOf0(esk4_3(X206,X207,X211),X206)
| aElementOf0(esk4_3(X206,X207,X211),X211)
| ~ aSet0(X211)
| X211 = sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) )
& ( esk4_3(X206,X207,X211) != X207
| aElementOf0(esk4_3(X206,X207,X211),X211)
| ~ aSet0(X211)
| X211 = sdtmndt0(X206,X207)
| ~ aSet0(X206)
| ~ aElement0(X207) ) ),
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,
! [X178,X179] :
( ~ aSet0(X178)
| ~ aElementOf0(X179,X178)
| aElement0(X179) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_11,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])])])])])]) ).
cnf(c_0_12,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_14,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_15,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xp,xO),
inference(split_conjunct,[status(thm)],[m__5182]) ).
cnf(c_0_17,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
cnf(c_0_18,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[m__5093]) ).
cnf(c_0_20,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_23,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]) ).
cnf(c_0_24,hypothesis,
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_25,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[m__5164]) ).
fof(c_0_27,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,hypothesis,
( aSubsetOf0(xP,X1)
| aElementOf0(esk2_2(X1,xP),xQ)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_23])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM609+1 : 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:50:35 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.53/1.79 % Version : CSE_E---1.7
% 1.53/1.79 % Problem : theBenchmark.p
% 1.53/1.79 % SZS status Theorem for theBenchmark.p
% 1.53/1.79 % SZS output start CNFRefutation
% See solution above
% 1.53/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------