%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM535+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 01:49:28 PM UTC 2026
% Result : Theorem 153.30s 22.92s
% Output : CNFRefutation 153.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 9 unt; 0 def)
% Number of atoms : 378 ( 71 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 548 ( 235 ~; 266 |; 33 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 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 : 149 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(m__617,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_7,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])])])]) ).
fof(c_0_8,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])])])])])])]) ).
cnf(c_0_9,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__617_02]) ).
cnf(c_0_11,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__617]) ).
cnf(c_0_12,plain,
( ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3)
| X3 = sdtpldt0(X1,X2)
| aElementOf0(esk3_3(X1,X2,X3),X3)
| esk3_3(X1,X2,X3) = X2
| aElementOf0(esk3_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_14,hypothesis,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(esk3_3(X1,xx,X2),X1)
| aElementOf0(esk3_3(X1,xx,X2),X2)
| X2 = sdtpldt0(X1,xx)
| esk3_3(X1,xx,X2) = xx ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_15,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_16,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtpldt0(X2,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3)
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aElement0(esk3_3(X1,X2,X3))
| ~ aElementOf0(esk3_3(X1,X2,X3),X1)
| X3 = sdtpldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk3_3(X1,xx,xS),X1)
| aElementOf0(esk3_3(X1,xx,xS),xS)
| sdtpldt0(X1,xx) = xS
| esk3_3(X1,xx,xS) = xx ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
fof(c_0_19,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_15])])])])])])]) ).
fof(c_0_20,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])])])])])])]) ).
cnf(c_0_21,plain,
( ~ aSet0(X3)
| ~ aElement0(X4)
| ~ aElementOf0(X1,X3)
| X2 != sdtpldt0(X3,X4)
| aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_22,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3)
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aElement0(esk3_3(X1,X2,X3))
| esk3_3(X1,X2,X3) != X2
| X3 = sdtpldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ aElementOf0(esk3_3(X2,X3,X1),X2)
| ~ aElementOf0(esk3_3(X2,X3,X1),X1)
| X1 = sdtpldt0(X2,X3) ),
inference(csr,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_25,hypothesis,
( aElementOf0(esk3_3(xS,xx,xS),xS)
| sdtpldt0(xS,xx) = xS
| esk3_3(xS,xx,xS) = xx ),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_26,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtmndt0(X2,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| aElementOf0(X1,X4)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,sdtpldt0(X2,X3)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ aElementOf0(esk3_3(X2,X3,X1),X1)
| esk3_3(X2,X3,X1) != X3
| X1 = sdtpldt0(X2,X3) ),
inference(csr,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_32,hypothesis,
( sdtpldt0(xS,xx) = xS
| esk3_3(xS,xx,xS) = xx ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_13]),c_0_11])]),c_0_25]) ).
cnf(c_0_33,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_36,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
( ~ aSet0(X4)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X4)
| X3 != sdtmndt0(X4,X2)
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(csr,[status(thm)],[c_0_27,c_0_9]) ).
cnf(c_0_38,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_28,c_0_29]),c_0_30]) ).
cnf(c_0_39,hypothesis,
sdtpldt0(xS,xx) = xS,
inference(cn,[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_10]),c_0_13]),c_0_11])]) ).
cnf(c_0_40,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElement0(X3)
| aElementOf0(esk2_2(X1,sdtpldt0(X2,X3)),X2)
| aSubsetOf0(sdtpldt0(X2,X3),X1)
| esk2_2(X1,sdtpldt0(X2,X3)) = X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]) ).
cnf(c_0_42,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( ~ aElement0(X4)
| ~ aSet0(X3)
| X2 != sdtpldt0(X3,X4)
| ~ aElementOf0(X1,X2)
| aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_44,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,sdtmndt0(X3,X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_37]) ).
fof(c_0_45,negated_conjecture,
~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_46,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(esk2_2(xS,X1),xS)
| aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_13]),c_0_11])]) ).
cnf(c_0_47,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElement0(X4)
| ~ aElement0(X3)
| aElementOf0(esk2_2(X1,sdtpldt0(sdtmndt0(X2,X3),X4)),X2)
| aSubsetOf0(sdtpldt0(sdtmndt0(X2,X3),X4),X1)
| esk2_2(X1,sdtpldt0(sdtmndt0(X2,X3),X4)) = X4 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtpldt0(X2,X3))
| aElement0(X1) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
( ~ aSet0(X1)
| ~ aSet0(X4)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(esk2_2(sdtpldt0(sdtmndt0(X1,X2),X3),X4),X1)
| aSubsetOf0(X4,sdtpldt0(sdtmndt0(X1,X2),X3))
| esk2_2(sdtpldt0(sdtmndt0(X1,X2),X3),X4) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_42]) ).
cnf(c_0_50,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtpldt0(X4,X2)
| ~ aElement0(X1)
| X1 != X2
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_51,negated_conjecture,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])]) ).
cnf(c_0_52,hypothesis,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,X1),X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,X1),X2),xS)
| esk2_2(xS,sdtpldt0(sdtmndt0(xS,X1),X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_11])]) ).
cnf(c_0_53,hypothesis,
( ~ aElementOf0(X1,xS)
| aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_13]),c_0_11])]) ).
cnf(c_0_54,plain,
( ~ aSet0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(X1,X2),X3))
| ~ aElement0(X2)
| ~ aElement0(X3)
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(X1,X2),X3))
| esk2_2(sdtpldt0(sdtmndt0(X1,X2),X3),X1) = X2 ),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_55,plain,
( ~ aSet0(X3)
| ~ aElement0(X1)
| X2 != sdtpldt0(X3,X1)
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,hypothesis,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,X1),X2))
| ~ aElement0(X1)
| ~ aElementOf0(X2,xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,X1),X2),xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_52]),c_0_11])]),c_0_53]) ).
cnf(c_0_58,plain,
( ~ aSet0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(X1,X2),X3))
| ~ aElement0(X3)
| ~ aElementOf0(X2,sdtpldt0(sdtmndt0(X1,X2),X3))
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_54]),c_0_9]) ).
cnf(c_0_59,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X2,X1)) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_10]),c_0_13])]) ).
cnf(c_0_61,plain,
( ~ aSet0(X1)
| ~ aSet0(sdtpldt0(sdtmndt0(X1,X2),X2))
| ~ aElement0(X2)
| aSubsetOf0(X1,sdtpldt0(sdtmndt0(X1,X2),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42]) ).
cnf(c_0_62,negated_conjecture,
~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_13]),c_0_11])]) ).
cnf(c_0_63,negated_conjecture,
~ aSet0(sdtmndt0(xS,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_30]),c_0_13])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_42]),c_0_13]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:39:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 153.30/22.92 % Version: 3.5.1
% 153.30/22.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 153.30/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 153.30/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 153.30/22.92 % Starting new_bool_3 with 300s (1) cores
% 153.30/22.92 % Starting new_bool_1 with 300s (1) cores
% 153.30/22.92 % Starting sh5l with 300s (1) cores
% 153.30/22.92 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1814606 completed with status 0
% 153.30/22.92 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 153.30/22.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 153.30/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 153.30/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 153.30/22.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 153.30/22.92 % No SInE strategy applied
% 153.30/22.92 % Search class: FGHSF-FFMS32-SFFFFFNN
% 153.30/22.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 153.30/22.92 % Starting SubtermCWHack with 136s (1) cores
% 153.30/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 153.30/22.92 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 153.30/22.92 % Starting new_bool_3 with 136s (1) cores
% 153.30/22.92 % Starting new_bool_1 with 136s (1) cores
% 153.30/22.92 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1814612 completed with status 0
% 153.30/22.92 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 153.30/22.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 153.30/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 153.30/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 153.30/22.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 153.30/22.92 % No SInE strategy applied
% 153.30/22.92 % Search class: FGHSF-FFMS32-SFFFFFNN
% 153.30/22.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 153.30/22.92 % Starting SubtermCWHack with 136s (1) cores
% 153.30/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 153.30/22.92 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 153.30/22.92 % Preprocessing time : 0.003 s
% 153.30/22.92
% 153.30/22.92 % Proof found!
% 153.30/22.92 % SZS status Theorem
% 153.30/22.92 % SZS output start CNFRefutation
% See solution above
% 153.30/22.92 % Parsed axioms : 19
% 153.30/22.92 % Removed by relevancy pruning/SinE : 0
% 153.30/22.92 % Initial clauses : 40
% 153.30/22.92 % Removed in clause preprocessing : 4
% 153.30/22.92 % Initial clauses in saturation : 36
% 153.30/22.92 % Processed clauses : 13244
% 153.30/22.92 % ...of these trivial : 176
% 153.30/22.92 % ...subsumed : 9294
% 153.30/22.92 % ...remaining for further processing : 3774
% 153.30/22.92 % Other redundant clauses eliminated : 47
% 153.30/22.92 % Clauses deleted for lack of memory : 0
% 153.30/22.92 % Backward-subsumed : 508
% 153.30/22.92 % Backward-rewritten : 63
% 153.30/22.92 % Generated clauses : 311371
% 153.30/22.92 % ...of the previous two non-redundant : 302857
% 153.30/22.92 % ...aggressively subsumed : 0
% 153.30/22.92 % Contextual simplify-reflections : 1210
% 153.30/22.92 % Paramodulations : 311154
% 153.30/22.92 % Factorizations : 36
% 153.30/22.92 % NegExts : 0
% 153.30/22.92 % Equation resolutions : 178
% 153.30/22.92 % Disequality decompositions : 0
% 153.30/22.92 % Total rewrite steps : 88377
% 153.30/22.92 % ...of those cached : 88349
% 153.30/22.92 % Propositional unsat checks : 0
% 153.30/22.92 % Propositional check models : 0
% 153.30/22.92 % Propositional check unsatisfiable : 0
% 153.30/22.92 % Propositional clauses : 0
% 153.30/22.92 % Propositional clauses after purity: 0
% 153.30/22.92 % Propositional unsat core size : 0
% 153.30/22.92 % Propositional preprocessing time : 0.000
% 153.30/22.92 % Propositional encoding time : 0.000
% 153.30/22.92 % Propositional solver time : 0.000
% 153.30/22.92 % Success case prop preproc time : 0.000
% 153.30/22.92 % Success case prop encoding time : 0.000
% 153.30/22.92 % Success case prop solver time : 0.000
% 153.30/22.92 % Current number of processed clauses : 3198
% 153.30/22.92 % Positive orientable unit clauses : 28
% 153.30/22.92 % Positive unorientable unit clauses: 0
% 153.30/22.92 % Negative unit clauses : 10
% 153.30/22.92 % Non-unit-clauses : 3160
% 153.30/22.92 % Current number of unprocessed clauses: 287157
% 153.30/22.92 % ...number of literals in the above : 2915806
% 153.30/22.92 % Current number of archived formulas : 0
% 153.30/22.92 % Current number of archived clauses : 574
% 153.30/22.92 % Clause-clause subsumption calls (NU) : 4211497
% 153.30/22.92 % Rec. Clause-clause subsumption calls : 135614
% 153.30/22.92 % Non-unit clause-clause subsumptions : 8753
% 153.30/22.92 % Unit Clause-clause subsumption calls : 12598
% 153.30/22.92 % Rewrite failures with RHS unbound : 0
% 153.30/22.92 % BW rewrite match attempts : 270
% 153.30/22.92 % BW rewrite match successes : 21
% 153.30/22.92 % Condensation attempts : 0
% 153.30/22.92 % Condensation successes : 0
% 153.30/22.92 % Termbank termtop insertions : 12787092
% 153.30/22.92 % Search garbage collected termcells : 852
% 153.30/22.92
% 153.30/22.92 % -------------------------------------------------
% 153.30/22.92 % User time : 21.255 s
% 153.30/22.92 % System time : 0.504 s
% 153.30/22.92 % Total time : 21.759 s
% 153.30/22.92 % Maximum resident set size: 3392 pages
% 153.30/22.92
% 153.30/22.92 % -------------------------------------------------
% 153.30/22.92 % User time : 105.736 s
% 153.30/22.92 % System time : 3.329 s
% 153.30/22.92 % Total time : 109.065 s
% 153.30/22.92 % Maximum resident set size: 4608 pages
% 153.30/22.92 % E exiting
%------------------------------------------------------------------------------