%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:27 PM UTC 2026
% Result : Theorem 0.29s 0.51s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 332 ( 64 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 444 ( 168 ~; 190 |; 58 &)
% ( 13 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__617,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( ( X4 = X2
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).
fof(mSubASymm,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aSet0(X1) )
=> ( ( aSubsetOf0(X2,X1)
& aSubsetOf0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(c_0_8,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X17,X18,X19,X20] :
( ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| ~ aElementOf0(esk2_2(X17,X20),X17) )
& ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| aElementOf0(esk2_2(X17,X20),X20) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aElementOf0(X19,X17)
| ~ aElementOf0(X19,X18) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aSet0(X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_10,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( X1 != xx
& aElementOf0(X1,xS)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__617]) ).
fof(c_0_13,negated_conjecture,
! [X44,X45] :
( sdtpldt0(sdtmndt0(xS,xx),xx) != xS
& ( aElementOf0(X45,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X45)
| X45 != xx )
& ( aElementOf0(X45,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X45)
| ~ aElementOf0(X45,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X45,sdtpldt0(sdtmndt0(xS,xx),xx))
| X45 = xx
| aElementOf0(X45,sdtmndt0(xS,xx)) )
& ( ~ aElementOf0(X45,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElement0(X45) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ( aElementOf0(X44,sdtmndt0(xS,xx))
| X44 = xx
| ~ aElementOf0(X44,xS)
| ~ aElement0(X44) )
& ( ~ aElementOf0(X44,sdtmndt0(xS,xx))
| X44 != xx )
& ( ~ aElementOf0(X44,sdtmndt0(xS,xx))
| aElementOf0(X44,xS) )
& ( ~ aElementOf0(X44,sdtmndt0(xS,xx))
| aElement0(X44) )
& aSet0(sdtmndt0(xS,xx)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_14,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| aElementOf0(esk3_3(X30,X31,X35),X35)
| esk3_3(X30,X31,X35) = X31
| aElementOf0(esk3_3(X30,X31,X35),X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| aElementOf0(esk3_3(X30,X31,X35),X35)
| aElement0(esk3_3(X30,X31,X35)) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aElement0(esk3_3(X30,X31,X35))
| esk3_3(X30,X31,X35) != X31 )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aElement0(esk3_3(X30,X31,X35))
| ~ aElementOf0(esk3_3(X30,X31,X35),X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aElementOf0(X34,X32)
| ~ aElement0(X34)
| X34 != X31 )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aElementOf0(X34,X32)
| ~ aElement0(X34)
| ~ aElementOf0(X34,X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| ~ aElementOf0(X33,X32)
| X33 = X31
| aElementOf0(X33,X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| ~ aElementOf0(X33,X32)
| aElement0(X33) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aSet0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[mDefCons])])])])])])]) ).
fof(c_0_15,plain,
! [X7,X8] :
( aElement0(X8)
| ~ aElementOf0(X8,X7)
| ~ aSet0(X7) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_16,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,xS),xS)
| aSubsetOf0(xS,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtpldt0(X2,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( aElementOf0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS),xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,sdtpldt0(X2,X3)) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_24,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ aElementOf0(X1,xS)
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(xS,xx))
| X1 = xx ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( aElement0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_21]),c_0_12])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__617_02]) ).
cnf(c_0_28,negated_conjecture,
( ~ aElement0(X1)
| X1 != xx
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_29,plain,
! [X25,X26] :
( X25 = X26
| ~ aSubsetOf0(X26,X25)
| ~ aSubsetOf0(X25,X26)
| ~ aSet0(X26)
| ~ aSet0(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubASymm])])]) ).
cnf(c_0_30,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ aElementOf0(esk2_2(sdtpldt0(X2,X3),X1),X2)
| aSubsetOf0(X1,sdtpldt0(X2,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( aElementOf0(esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS),sdtmndt0(xS,xx))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_26]) ).
cnf(c_0_32,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_12])]) ).
cnf(c_0_33,negated_conjecture,
aSet0(sdtmndt0(xS,xx)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( ~ aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_37,negated_conjecture,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| esk2_2(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_12]),c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_32])]) ).
fof(c_0_39,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
cnf(c_0_40,negated_conjecture,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_41,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X1)
| X1 = X2 ),
inference(csr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_38]),c_0_12]),c_0_17])]) ).
cnf(c_0_43,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_44,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| esk4_3(X37,X38,X42) != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElementOf0(esk4_3(X37,X38,X42),X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElement0(esk4_3(X37,X38,X42)) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| esk4_3(X37,X38,X42) = X38
| ~ aElementOf0(esk4_3(X37,X38,X42),X37)
| ~ aElement0(esk4_3(X37,X38,X42))
| ~ aElementOf0(esk4_3(X37,X38,X42),X42) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aElementOf0(X41,X39)
| X41 = X38
| ~ aElementOf0(X41,X37)
| ~ aElement0(X41) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| X40 != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElementOf0(X40,X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElement0(X40) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aSet0(X39) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_39])])])])])])]) ).
cnf(c_0_45,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_46,hypothesis,
( aElementOf0(esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(spm,[status(thm)],[c_0_40,c_0_12]) ).
cnf(c_0_47,negated_conjecture,
~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_12])]),c_0_43]) ).
cnf(c_0_48,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
aElementOf0(esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(sr,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_52,hypothesis,
( aElementOf0(esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32]),c_0_33])]) ).
cnf(c_0_53,hypothesis,
( aElementOf0(esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_32]),c_0_12])]) ).
cnf(c_0_54,hypothesis,
esk2_2(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_53]),c_0_17]),c_0_12])]),c_0_47]) ).
cnf(c_0_55,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_54]),c_0_27]),c_0_17]),c_0_12])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:39:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.51 % Version: 3.5.1
% 0.29/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.51 % Starting sh5l with 300s (1) cores
% 0.29/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1814577 completed with status 0
% 0.29/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.29/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.51 % No SInE strategy applied
% 0.29/0.51 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.29/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/0.51 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.29/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.29/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.29/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1814585 completed with status 0
% 0.29/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.29/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.51 % No SInE strategy applied
% 0.29/0.51 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.29/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/0.51 % Preprocessing time : 0.002 s
% 0.29/0.51 % Presaturation interreduction done
% 0.29/0.51
% 0.29/0.51 % Proof found!
% 0.29/0.51 % SZS status Theorem
% 0.29/0.51 % SZS output start CNFRefutation
% See solution above
% 0.29/0.51 % Parsed axioms : 19
% 0.29/0.51 % Removed by relevancy pruning/SinE : 0
% 0.29/0.51 % Initial clauses : 50
% 0.29/0.51 % Removed in clause preprocessing : 4
% 0.29/0.51 % Initial clauses in saturation : 46
% 0.29/0.51 % Processed clauses : 489
% 0.29/0.51 % ...of these trivial : 1
% 0.29/0.51 % ...subsumed : 117
% 0.29/0.51 % ...remaining for further processing : 371
% 0.29/0.51 % Other redundant clauses eliminated : 17
% 0.29/0.51 % Clauses deleted for lack of memory : 0
% 0.29/0.51 % Backward-subsumed : 23
% 0.29/0.51 % Backward-rewritten : 21
% 0.29/0.51 % Generated clauses : 2321
% 0.29/0.51 % ...of the previous two non-redundant : 2195
% 0.29/0.51 % ...aggressively subsumed : 0
% 0.29/0.51 % Contextual simplify-reflections : 22
% 0.29/0.51 % Paramodulations : 2304
% 0.29/0.51 % Factorizations : 0
% 0.29/0.51 % NegExts : 0
% 0.29/0.51 % Equation resolutions : 17
% 0.29/0.51 % Disequality decompositions : 0
% 0.29/0.51 % Total rewrite steps : 556
% 0.29/0.51 % ...of those cached : 537
% 0.29/0.51 % Propositional unsat checks : 0
% 0.29/0.51 % Propositional check models : 0
% 0.29/0.51 % Propositional check unsatisfiable : 0
% 0.29/0.51 % Propositional clauses : 0
% 0.29/0.51 % Propositional clauses after purity: 0
% 0.29/0.51 % Propositional unsat core size : 0
% 0.29/0.51 % Propositional preprocessing time : 0.000
% 0.29/0.51 % Propositional encoding time : 0.000
% 0.29/0.51 % Propositional solver time : 0.000
% 0.29/0.51 % Success case prop preproc time : 0.000
% 0.29/0.51 % Success case prop encoding time : 0.000
% 0.29/0.51 % Success case prop solver time : 0.000
% 0.29/0.51 % Current number of processed clauses : 264
% 0.29/0.51 % Positive orientable unit clauses : 18
% 0.29/0.51 % Positive unorientable unit clauses: 0
% 0.29/0.51 % Negative unit clauses : 5
% 0.29/0.51 % Non-unit-clauses : 241
% 0.29/0.51 % Current number of unprocessed clauses: 1776
% 0.29/0.51 % ...number of literals in the above : 7676
% 0.29/0.51 % Current number of archived formulas : 0
% 0.29/0.51 % Current number of archived clauses : 92
% 0.29/0.51 % Clause-clause subsumption calls (NU) : 13057
% 0.29/0.51 % Rec. Clause-clause subsumption calls : 5029
% 0.29/0.51 % Non-unit clause-clause subsumptions : 145
% 0.29/0.51 % Unit Clause-clause subsumption calls : 774
% 0.29/0.51 % Rewrite failures with RHS unbound : 0
% 0.29/0.51 % BW rewrite match attempts : 9
% 0.29/0.51 % BW rewrite match successes : 9
% 0.29/0.51 % Condensation attempts : 0
% 0.29/0.51 % Condensation successes : 0
% 0.29/0.51 % Termbank termtop insertions : 64038
% 0.29/0.51 % Search garbage collected termcells : 1030
% 0.29/0.51
% 0.29/0.51 % -------------------------------------------------
% 0.29/0.51 % User time : 0.070 s
% 0.29/0.51 % System time : 0.011 s
% 0.29/0.51 % Total time : 0.081 s
% 0.29/0.51 % Maximum resident set size: 3652 pages
% 0.29/0.51
% 0.29/0.51 % -------------------------------------------------
% 0.29/0.51 % User time : 0.324 s
% 0.29/0.51 % System time : 0.034 s
% 0.29/0.51 % Total time : 0.358 s
% 0.29/0.51 % Maximum resident set size: 4608 pages
% 0.29/0.51 % E exiting
%------------------------------------------------------------------------------