%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM537+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 : 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 04:57:44 PM UTC 2026
% Result : Theorem 11.36s 7.36s
% Output : CNFRefutation 11.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of formulae : 84 ( 12 unt; 0 def)
% Number of atoms : 386 ( 52 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 525 ( 223 ~; 256 |; 33 &)
% ( 5 <=>; 8 =>; 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 : 136 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(m__679,hypothesis,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X1)
& aSet0(X2)
& aSet0(X3) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X3) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
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(m__,conjecture,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__679_02,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
fof(c_0_8,plain,
! [X44,X45,X46,X47] :
( ( aSet0(X45)
| ~ aSubsetOf0(X45,X44)
| ~ aSet0(X44) )
& ( ~ aElementOf0(X46,X45)
| aElementOf0(X46,X44)
| ~ aSubsetOf0(X45,X44)
| ~ aSet0(X44) )
& ( aElementOf0(esk2_2(X44,X47),X47)
| ~ aSet0(X47)
| aSubsetOf0(X47,X44)
| ~ aSet0(X44) )
& ( ~ aElementOf0(esk2_2(X44,X47),X44)
| ~ aSet0(X47)
| aSubsetOf0(X47,X44)
| ~ aSet0(X44) ) ),
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])])])])])]) ).
fof(c_0_9,plain,
! [X57,X58,X59,X60,X61,X62] :
( ( aSet0(X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElement0(X60)
| ~ aElementOf0(X60,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElementOf0(X60,X57)
| X60 = X58
| ~ aElementOf0(X60,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( ~ aElementOf0(X61,X57)
| ~ aElement0(X61)
| aElementOf0(X61,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( X61 != X58
| ~ aElement0(X61)
| aElementOf0(X61,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( ~ aElementOf0(esk3_3(X57,X58,X62),X57)
| ~ aElement0(esk3_3(X57,X58,X62))
| ~ aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( esk3_3(X57,X58,X62) != X58
| ~ aElement0(esk3_3(X57,X58,X62))
| ~ aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElement0(esk3_3(X57,X58,X62))
| aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElementOf0(esk3_3(X57,X58,X62),X57)
| esk3_3(X57,X58,X62) = X58
| aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) ) ),
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)],[mDefCons])])])])])]) ).
cnf(c_0_10,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__679]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X36,X37] :
( ~ aSet0(X36)
| ~ aElementOf0(X37,X36)
| aElement0(X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_14,hypothesis,
( aSubsetOf0(xS,X1)
| aElementOf0(esk2_2(X1,xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| X3 != sdtpldt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
( aSubsetOf0(xS,sdtpldt0(X1,X2))
| aElementOf0(esk2_2(sdtpldt0(X1,X2),xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__679]) ).
fof(c_0_20,plain,
! [X54,X55,X56] :
( ~ aSet0(X54)
| ~ aSet0(X55)
| ~ aSet0(X56)
| ~ aSubsetOf0(X54,X55)
| ~ aSubsetOf0(X55,X56)
| aSubsetOf0(X54,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
cnf(c_0_21,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(X1,X2)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_23,hypothesis,
( aSubsetOf0(xS,sdtpldt0(X1,xx))
| aElementOf0(esk2_2(sdtpldt0(X1,xx),xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( aSubsetOf0(X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( aSubsetOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(esk2_2(sdtpldt0(X2,X3),X1),X2)
| ~ aElement0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15]) ).
cnf(c_0_27,hypothesis,
( aSubsetOf0(xS,sdtpldt0(xS,xx))
| aElementOf0(esk2_2(sdtpldt0(xS,xx),xS),xS) ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_29,hypothesis,
aSubsetOf0(xS,sdtpldt0(xS,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_11])]) ).
cnf(c_0_30,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X1,xS)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_32,hypothesis,
( aSubsetOf0(xS,xS)
| aElementOf0(esk2_2(xS,xS),xS) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
fof(c_0_33,plain,
! [X64,X65,X66,X67,X68,X69] :
( ( aSet0(X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElement0(X67)
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElementOf0(X67,X64)
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( X67 != X65
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( ~ aElement0(X68)
| ~ aElementOf0(X68,X64)
| X68 = X65
| aElementOf0(X68,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( ~ aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aElement0(esk4_3(X64,X65,X69))
| ~ aElementOf0(esk4_3(X64,X65,X69),X64)
| esk4_3(X64,X65,X69) = X65
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElement0(esk4_3(X64,X65,X69))
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElementOf0(esk4_3(X64,X65,X69),X64)
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( esk4_3(X64,X65,X69) != X65
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) ) ),
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])])])])])]) ).
cnf(c_0_34,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X2,xS)
| ~ aSubsetOf0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_15]),c_0_19]),c_0_11])]) ).
cnf(c_0_35,hypothesis,
aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_11])]) ).
cnf(c_0_36,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X2,xS)
| ~ aElementOf0(X1,X2)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,hypothesis,
( aSubsetOf0(xS,sdtmndt0(X1,X2))
| aElementOf0(esk2_2(sdtmndt0(X1,X2),xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_39]) ).
cnf(c_0_42,plain,
( X1 = X3
| aElementOf0(X1,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| X4 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,hypothesis,
( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aSubsetOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_15]),c_0_19]),c_0_11])]) ).
cnf(c_0_44,hypothesis,
( aSubsetOf0(xS,sdtmndt0(X1,xx))
| aElementOf0(esk2_2(sdtmndt0(X1,xx),xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_19]) ).
cnf(c_0_45,plain,
( X1 = X2
| aElementOf0(X1,sdtmndt0(X3,X2))
| ~ aElementOf0(X1,X3)
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_42,c_0_17])]) ).
cnf(c_0_46,hypothesis,
( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_47,hypothesis,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(X1,X2),xx))
| aElementOf0(esk2_2(sdtmndt0(sdtpldt0(X1,X2),xx),xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_15]) ).
cnf(c_0_48,hypothesis,
( X1 = X2
| aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),X2))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,hypothesis,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(X1,xx),xx))
| aElementOf0(esk2_2(sdtmndt0(sdtpldt0(X1,xx),xx),xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_50,hypothesis,
( X1 = X2
| aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),X2))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_15]),c_0_19]),c_0_11])]) ).
cnf(c_0_51,hypothesis,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS) ),
inference(spm,[status(thm)],[c_0_49,c_0_11]) ).
cnf(c_0_52,hypothesis,
( esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = X1
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,hypothesis,
( esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(spm,[status(thm)],[c_0_52,c_0_19]) ).
cnf(c_0_54,plain,
( aSubsetOf0(sdtmndt0(X1,X2),X3)
| aElementOf0(esk2_2(X3,sdtmndt0(X1,X2)),sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_39]) ).
cnf(c_0_55,hypothesis,
( esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_53]),c_0_11])]) ).
cnf(c_0_56,hypothesis,
( aSubsetOf0(sdtmndt0(X1,xx),X2)
| aElementOf0(esk2_2(X2,sdtmndt0(X1,xx)),sdtmndt0(X1,xx))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_19]) ).
fof(c_0_57,negated_conjecture,
~ ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_58,hypothesis,
( esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_39]),c_0_19])]) ).
fof(c_0_59,hypothesis,
~ aElementOf0(xx,xS),
inference(fof_simplification,[status(thm)],[m__679_02]) ).
cnf(c_0_60,hypothesis,
( aSubsetOf0(sdtmndt0(X1,xx),xS)
| aElementOf0(esk2_2(xS,sdtmndt0(X1,xx)),sdtmndt0(X1,xx))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_11]) ).
fof(c_0_61,negated_conjecture,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(fof_nnf,[status(thm)],[c_0_57]) ).
cnf(c_0_62,hypothesis,
( esk2_2(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_15]),c_0_19]),c_0_11])]) ).
cnf(c_0_63,hypothesis,
~ aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,hypothesis,
( aSubsetOf0(sdtmndt0(sdtpldt0(X1,X2),xx),xS)
| aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(X1,X2),xx)),sdtmndt0(sdtpldt0(X1,X2),xx))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_15]) ).
cnf(c_0_65,negated_conjecture,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,hypothesis,
aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_62]),c_0_63]) ).
cnf(c_0_67,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_68,hypothesis,
( aSubsetOf0(sdtmndt0(sdtpldt0(X1,xx),xx),xS)
| aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(X1,xx),xx)),sdtmndt0(sdtpldt0(X1,xx),xx))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_19]) ).
cnf(c_0_69,negated_conjecture,
~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_70,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_71,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_72,hypothesis,
aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_11]),c_0_69]) ).
cnf(c_0_73,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_74,hypothesis,
( aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_19])]) ).
cnf(c_0_75,hypothesis,
( esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_19]),c_0_11])]) ).
cnf(c_0_76,hypothesis,
( esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| aElementOf0(esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_15]),c_0_19]),c_0_11])]) ).
cnf(c_0_77,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_78,hypothesis,
( esk2_2(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_76]),c_0_11])]),c_0_69]) ).
cnf(c_0_79,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_77])]) ).
cnf(c_0_80,hypothesis,
( aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(spm,[status(thm)],[c_0_72,c_0_78]) ).
cnf(c_0_81,hypothesis,
( ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_19])]) ).
cnf(c_0_82,hypothesis,
~ aSet0(sdtpldt0(xS,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_39]),c_0_19])]) ).
cnf(c_0_83,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_15]),c_0_19]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM537+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
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:44:40 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 11.36/7.36 % Version : CSE_E---1.7
% 11.36/7.36 % Problem : theBenchmark.p
% 11.36/7.36 % SZS status Theorem for theBenchmark.p
% 11.36/7.36 % SZS output start CNFRefutation
% See solution above
% 11.46/7.40 % Total time : 5.368s
%------------------------------------------------------------------------------