%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM610+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 : Fri Sep 25 02:20:31 PM UTC 2026
% Result : Theorem 25.27s 3.66s
% Output : Proof 25.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 121 ( 29 unt; 2 def)
% Number of atoms : 940 ( 182 equ)
% Maximal formula atoms : 59 ( 7 avg)
% Number of connectives : 1270 ( 451 ~; 361 |; 386 &)
% ( 12 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-4 aty)
% Number of functors : 45 ( 45 usr; 17 con; 0-4 aty)
% Number of variables : 282 ( 6 sgn 154 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f13_nnf,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c18,plain,
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi11,axiom,
ifeq(aSet0(X0),true,ifeq(aSet0(X1),true,ifeq(aSet0(X2),true,ifeq(aSubsetOf0(X0,X1),true,ifeq(aSubsetOf0(X1,X2),true,aSubsetOf0(X0,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f103,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f103_nnf,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( ( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) ) )
& ! [W0] :
( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(nnf_transformation,[status(thm)],[f103]) ).
fof(f103_sk,plain,
! [W0] :
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ( W0 = szmzizndt0(xQ)
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,xP) )
& ( sdtlseqdt0(szmzizndt0(xQ),W0)
| ~ aElementOf0(W0,xQ) )
& aSet0(xP) ),
inference(skolemisation,[status(esa)],[f103_nnf]) ).
cnf(c1072,plain,
aSet0(xP),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(hi999,axiom,
aSet0(xP) = true,
inference(equality_encoding,[status(esa)],[c1072]) ).
fof(f98,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(f98_nnf,plain,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [W0] :
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c1054,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(hi982,axiom,
aSet0(xQ) = true,
inference(equality_encoding,[status(esa)],[c1054]) ).
fof(f95,hypothesis,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f95_nnf,plain,
( isCountable0(xO)
& aSet0(xO) ),
inference(nnf_transformation,[status(thm)],[f95]) ).
fof(f95_sk,plain,
( isCountable0(xO)
& aSet0(xO) ),
inference(skolemisation,[status(esa)],[f95_nnf]) ).
cnf(c1042,plain,
aSet0(xO),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(hi970,axiom,
aSet0(xO) = true,
inference(equality_encoding,[status(esa)],[c1042]) ).
fof(f106,hypothesis,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
fof(f106_nnf,plain,
( aSubsetOf0(xP,xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
| ~ aElementOf0(W0,xP) ) ),
inference(nnf_transformation,[status(thm)],[f106]) ).
fof(f106_sk,plain,
! [W0] :
( aSubsetOf0(xP,xQ)
& ( aElementOf0(W0,xQ)
| ~ aElementOf0(W0,xP) ) ),
inference(skolemisation,[status(esa)],[f106_nnf]) ).
cnf(c1083,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(esa)],[f106_sk]) ).
cnf(hi1009,axiom,
aSubsetOf0(xP,xQ) = true,
inference(equality_encoding,[status(esa)],[c1083]) ).
cnf(c1056,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(hi984,axiom,
aSubsetOf0(xQ,xO) = true,
inference(equality_encoding,[status(esa)],[c1056]) ).
cnf(h2257,plain,
aSubsetOf0(xP,xO) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi999,hi982,hi970,hi1009,hi984]) ).
fof(f107,conjecture,
( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f107_neg,negated_conjecture,
~ ( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f107_nnf,plain,
( ~ aSubsetOf0(xP,xO)
& ? [W0] :
( ~ aElementOf0(W0,xO)
& aElementOf0(W0,xP) ) ),
inference(nnf_transformation,[status(thm)],[f107_neg]) ).
fof(f107_sk,plain,
( ~ aSubsetOf0(xP,xO)
& ~ aElementOf0(sk48,xO)
& aElementOf0(sk48,xP) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk48])],[f107_nnf]) ).
cnf(c1086,plain,
~ aSubsetOf0(xP,xO),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(hi1048,negated_conjecture,
ifeq(aSubsetOf0(xP,xO),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c1086]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi1048,h2257]) ).
cnf(t3180,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f4_nnf,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( ( aElementOf0(sk0(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c5,plain,
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f7,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(f7_nnf,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f8_nnf,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( X0 != slcrc0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f15,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f15_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3)
& ~ aElementOf0(W3,W2) )
| ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ! [W3] :
( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( sk3(W0,W1,W2) != W1
& aElementOf0(sk3(W0,W1,W2),W0)
& aElement0(sk3(W0,W1,W2))
& ~ aElementOf0(sk3(W0,W1,W2),W2) )
| ( ( sk3(W0,W1,W2) = W1
| ~ aElementOf0(sk3(W0,W1,W2),W0)
| ~ aElement0(sk3(W0,W1,W2)) )
& aElementOf0(sk3(W0,W1,W2),W2) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f15_nnf]) ).
cnf(c36,plain,
( X3 != X1
| ~ aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f24,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f24_nnf,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c56,plain,
( szszuzczcdt0(X0) != sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f27,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f27_nnf,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c60,plain,
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f30,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(f30_nnf,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [W0] :
( ~ sdtlseqdt0(szszuzczcdt0(W0),sz00)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c63,plain,
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f76,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& ( aSubsetOf0(W1,szNzAzT0)
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,szNzAzT0) )
& aSet0(W1) ) ) )
=> ! [W2] :
( ( ( ( ! [W3] :
( aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2)))
<=> ? [W4] :
( sdtlpdtrp0(W2,W4) = W3
& aElementOf0(W4,szDzozmdt0(W2)) ) )
& aSet0(sdtlcdtrc0(W2,szDzozmdt0(W2))) )
=> ( aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
| ! [W3] :
( aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2)))
=> aElementOf0(W3,xT) ) ) )
& ( szDzozmdt0(W2) = slbdtsldtrb0(W1,W0)
| ! [W3] :
( ( ( sbrdtbr0(W3) = W0
& aSubsetOf0(W3,W1)
& ! [W4] :
( aElementOf0(W4,W3)
=> aElementOf0(W4,W1) )
& aSet0(W3) )
=> aElementOf0(W3,szDzozmdt0(W2)) )
& ( aElementOf0(W3,szDzozmdt0(W2))
=> ( sbrdtbr0(W3) = W0
& ( aSubsetOf0(W3,W1)
| ( ! [W4] :
( aElementOf0(W4,W3)
=> aElementOf0(W4,W1) )
& aSet0(W3) ) ) ) ) ) )
& aFunction0(W2) )
=> ( iLess0(W0,xK)
=> ? [W3] :
( ? [W4] :
( ! [W5] :
( ( aElementOf0(W5,slbdtsldtrb0(W4,W0))
| ( sbrdtbr0(W5) = W0
& ( aSubsetOf0(W5,W4)
| ( ! [W6] :
( aElementOf0(W6,W5)
=> aElementOf0(W6,W4) )
& aSet0(W5) ) ) ) )
=> sdtlpdtrp0(W2,W5) = W3 )
& isCountable0(W4)
& aSubsetOf0(W4,W1)
& ! [W5] :
( aElementOf0(W5,W4)
=> aElementOf0(W5,W1) )
& aSet0(W4) )
& aElementOf0(W3,xT) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3398) ).
fof(f76_nnf,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ? [W3] :
( ? [W4] :
( ! [W5] :
( sdtlpdtrp0(W2,W5) = W3
| ( ~ aElementOf0(W5,slbdtsldtrb0(W4,W0))
& ( sbrdtbr0(W5) != W0
| ( ~ aSubsetOf0(W5,W4)
& ( ? [W6] :
( ~ aElementOf0(W6,W4)
& aElementOf0(W6,W5) )
| ~ aSet0(W5) ) ) ) ) )
& isCountable0(W4)
& aSubsetOf0(W4,W1)
& ! [W5] :
( aElementOf0(W5,W1)
| ~ aElementOf0(W5,W4) )
& aSet0(W4) )
& aElementOf0(W3,xT) )
| ~ iLess0(W0,xK)
| ( ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
& ? [W3] :
( ~ aElementOf0(W3,xT)
& aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) )
& ! [W3] :
( ( ! [W4] :
( sdtlpdtrp0(W2,W4) != W3
| ~ aElementOf0(W4,szDzozmdt0(W2)) )
| aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) )
& ( ? [W4] :
( sdtlpdtrp0(W2,W4) = W3
& aElementOf0(W4,szDzozmdt0(W2)) )
| ~ aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) ) )
& aSet0(sdtlcdtrc0(W2,szDzozmdt0(W2))) )
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0)
& ? [W3] :
( ( ~ aElementOf0(W3,szDzozmdt0(W2))
& sbrdtbr0(W3) = W0
& aSubsetOf0(W3,W1)
& ! [W4] :
( aElementOf0(W4,W1)
| ~ aElementOf0(W4,W3) )
& aSet0(W3) )
| ( ( sbrdtbr0(W3) != W0
| ( ~ aSubsetOf0(W3,W1)
& ( ? [W4] :
( ~ aElementOf0(W4,W1)
& aElementOf0(W4,W3) )
| ~ aSet0(W3) ) ) )
& aElementOf0(W3,szDzozmdt0(W2)) ) ) )
| ~ aFunction0(W2) )
| ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,szNzAzT0)
& ( ? [W2] :
( ~ aElementOf0(W2,szNzAzT0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f76]) ).
fof(f76_sk,plain,
! [W0,W1,W2,W4,W3,W5] :
( ( ( sdtlpdtrp0(W2,W5) = sk26(W0,W1,W2)
| ( ~ aElementOf0(W5,slbdtsldtrb0(sk27(W0,W1,W2),W0))
& ( sbrdtbr0(W5) != W0
| ( ~ aSubsetOf0(W5,sk27(W0,W1,W2))
& ( ( ~ aElementOf0(sk28(W0,W1,W2,W5),sk27(W0,W1,W2))
& aElementOf0(sk28(W0,W1,W2,W5),W5) )
| ~ aSet0(W5) ) ) ) ) )
& isCountable0(sk27(W0,W1,W2))
& aSubsetOf0(sk27(W0,W1,W2),W1)
& ( aElementOf0(W5,W1)
| ~ aElementOf0(W5,sk27(W0,W1,W2)) )
& aSet0(sk27(W0,W1,W2))
& aElementOf0(sk26(W0,W1,W2),xT) )
| ~ iLess0(W0,xK)
| ( ~ aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT)
& ~ aElementOf0(sk25(W0,W1,W2),xT)
& aElementOf0(sk25(W0,W1,W2),sdtlcdtrc0(W2,szDzozmdt0(W2)))
& ( sdtlpdtrp0(W2,W4) != W3
| ~ aElementOf0(W4,szDzozmdt0(W2))
| aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) )
& ( ( sdtlpdtrp0(W2,sk24(W0,W1,W2,W3)) = W3
& aElementOf0(sk24(W0,W1,W2,W3),szDzozmdt0(W2)) )
| ~ aElementOf0(W3,sdtlcdtrc0(W2,szDzozmdt0(W2))) )
& aSet0(sdtlcdtrc0(W2,szDzozmdt0(W2))) )
| ( szDzozmdt0(W2) != slbdtsldtrb0(W1,W0)
& ( ( ~ aElementOf0(sk22(W0,W1,W2),szDzozmdt0(W2))
& sbrdtbr0(sk22(W0,W1,W2)) = W0
& aSubsetOf0(sk22(W0,W1,W2),W1)
& ( aElementOf0(W4,W1)
| ~ aElementOf0(W4,sk22(W0,W1,W2)) )
& aSet0(sk22(W0,W1,W2)) )
| ( ( sbrdtbr0(sk22(W0,W1,W2)) != W0
| ( ~ aSubsetOf0(sk22(W0,W1,W2),W1)
& ( ( ~ aElementOf0(sk23(W0,W1,W2),W1)
& aElementOf0(sk23(W0,W1,W2),sk22(W0,W1,W2)) )
| ~ aSet0(sk22(W0,W1,W2)) ) ) )
& aElementOf0(sk22(W0,W1,W2),szDzozmdt0(W2)) ) ) )
| ~ aFunction0(W2)
| ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,szNzAzT0)
& ( ( ~ aElementOf0(sk21(W0,W1),szNzAzT0)
& aElementOf0(sk21(W0,W1),W1) )
| ~ aSet0(W1) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f76_nnf]) ).
cnf(c188,plain,
( ~ aElementOf0(sk21(X0,X1),szNzAzT0)
| ~ def0(X0,X1) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c194,plain,
( ~ aSubsetOf0(X1,szNzAzT0)
| ~ def2(X1,X0) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c200,plain,
( ~ aElementOf0(sk23(X0,X1,X2),X1)
| ~ def4(X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c206,plain,
( ~ aSubsetOf0(sk22(X0,X1,X2),X1)
| ~ def6(X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c227,plain,
( ~ aElementOf0(sk22(X0,X1,X2),szDzozmdt0(X2))
| ~ def13(X0,X1,X2,X4) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c233,plain,
( szDzozmdt0(X2) != slbdtsldtrb0(X1,X0)
| ~ def15(X0,X1,X2,X4) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c244,plain,
( sdtlpdtrp0(X2,X4) != X3
| ~ aElementOf0(X4,szDzozmdt0(X2))
| ~ def19(X4,X2,X3) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c257,plain,
( ~ aElementOf0(sk25(X0,X1,X2),xT)
| ~ def23(X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c260,plain,
( ~ aSubsetOf0(sdtlcdtrc0(X2,szDzozmdt0(X2)),xT)
| ~ def24(X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c281,plain,
( ~ aElementOf0(sk28(X0,X1,X2,X5),sk27(X0,X1,X2))
| ~ def31(X0,X1,X2,X5) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c287,plain,
( ~ aSubsetOf0(X5,sk27(X0,X1,X2))
| ~ def33(X5,X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
cnf(c293,plain,
( ~ aElementOf0(X5,slbdtsldtrb0(sk27(X0,X1,X2),X0))
| ~ def35(X5,X0,X1,X2) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42])],[f76_sk]) ).
fof(f77,hypothesis,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(f77_nnf,plain,
xK != sz00,
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
xK != sz00,
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c317,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
fof(f78,hypothesis,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3520) ).
fof(f78_nnf,plain,
xK != sz00,
inference(nnf_transformation,[status(thm)],[f78]) ).
fof(f78_sk,plain,
xK != sz00,
inference(skolemisation,[status(esa)],[f78_nnf]) ).
cnf(c318,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f78_sk]) ).
fof(f80,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f80_nnf,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ? [W1] :
( ~ aElementOf0(W1,szNzAzT0)
& aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [W0,W1] :
( ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ( ( ~ aElementOf0(sk29(W0),szNzAzT0)
& aElementOf0(sk29(W0),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk29])],[f80_nnf]) ).
cnf(c340,plain,
( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(sk29(X0),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
cnf(c351,plain,
( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
fof(f85,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ! [W1] :
( ( ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )
& aSet0(W1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) ) )
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
=> aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
=> ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) )
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).
fof(f85_nnf,plain,
( ! [W0] :
( ( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& ~ aElementOf0(W2,W1) )
| ~ aElement0(W2)
| aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) )
| ~ aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) ) ) )
& ! [W2] :
( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) ) ) )
& ( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
& ! [W1] :
( ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [W0,W1,W2] :
( ( ( ( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& ~ aElementOf0(W2,W1) )
| ~ aElement0(W2)
| aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| aElementOf0(W2,W1) )
& aElement0(W2) )
| ~ aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ~ aElementOf0(sk33(W0,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(sk33(W0,W1),W1) ) )
& ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ aSet0(W1) )
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
| sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ( ~ aElementOf0(sk32(W0,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(sk32(W0,W1),W1) )
| ~ aSet0(W1) ) ) )
& ( ( sbrdtbr0(W1) = xk
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) )
& ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| ~ aElement0(W1)
| aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) )
| ~ aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aFunction0(sdtlpdtrp0(xC,W0)) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk32,sk33])],[f85_nnf]) ).
cnf(c497,plain,
( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
fof(f87,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
=> ( ( ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W1) ) ) ) ) )
=> ! [W2] :
( ( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
| ( sbrdtbr0(W2) = xk
& ( aSubsetOf0(W2,W1)
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,W1) ) ) ) )
& aSet0(W2) )
=> ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4331) ).
fof(f87_nnf,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W3,W2) )
& ! [W3] :
( ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
& ( sbrdtbr0(W2) != xk
| ( ~ aSubsetOf0(W2,W1)
& ? [W3] :
( ~ aElementOf0(W3,W1)
& aElementOf0(W3,W2) ) ) ) )
| ~ aSet0(W2) )
| ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ? [W2] :
( ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ! [W2] :
( ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f87]) ).
fof(f87_sk,plain,
! [W0,W2,W1,W3] :
( ( aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W3,W2) )
& ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
& ( sbrdtbr0(W2) != xk
| ( ~ aSubsetOf0(W2,W1)
& ~ aElementOf0(sk36(W0,W1,W2),W1)
& aElementOf0(sk36(W0,W1,W2),W2) ) ) )
| ~ aSet0(W2)
| ~ isCountable0(W1)
| ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( ( ~ aElementOf0(sk35(W0,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& aElementOf0(sk35(W0,W1),W1) )
| ~ aSet0(W1) )
& ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| ~ aElement0(W2)
| aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) )
| ~ aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2)
| ~ aElementOf0(W2,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk35,sk36])],[f87_nnf]) ).
cnf(c805,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aElementOf0(sk36(X0,X1,X2),X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| X2 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c815,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| X2 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c825,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk))
| ~ aSet0(X2)
| ~ isCountable0(X1)
| X2 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c925,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aElementOf0(sk36(X0,X1,X2),X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aElementOf0(sk35(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c935,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aElementOf0(sk35(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c945,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk))
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aElementOf0(sk35(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c965,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aElementOf0(sk36(X0,X1,X2),X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c975,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X2) != xk
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(c985,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,slbdtsldtrb0(X1,xk))
| ~ aSet0(X2)
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
fof(f88,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( ? [W2] :
( ! [W3] :
( ( ( aElementOf0(W3,slbdtsldtrb0(W2,xk))
| ( sbrdtbr0(W3) = xk
& ( aSubsetOf0(W3,W2)
| ! [W4] :
( aElementOf0(W4,W3)
=> aElementOf0(W4,W2) ) ) ) )
& aSet0(W3) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 )
& isCountable0(W2)
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(W2)
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
& aElementOf0(W1,xT) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4411) ).
fof(f88_nnf,plain,
! [W0] :
( ? [W1] :
( ? [W2] :
( ! [W3] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1
| ( ~ aElementOf0(W3,slbdtsldtrb0(W2,xk))
& ( sbrdtbr0(W3) != xk
| ( ~ aSubsetOf0(W3,W2)
& ? [W4] :
( ~ aElementOf0(W4,W2)
& aElementOf0(W4,W3) ) ) ) )
| ~ aSet0(W3) )
& isCountable0(W2)
& aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W3,W2) )
& aSet0(W2)
& ! [W3] :
( ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) )
& aElementOf0(W1,xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f88]) ).
fof(f88_sk,plain,
! [W0,W3] :
( ( ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = sk37(W0)
| ( ~ aElementOf0(W3,slbdtsldtrb0(sk38(W0),xk))
& ( sbrdtbr0(W3) != xk
| ( ~ aSubsetOf0(W3,sk38(W0))
& ~ aElementOf0(sk39(W0,W3),sk38(W0))
& aElementOf0(sk39(W0,W3),W3) ) ) )
| ~ aSet0(W3) )
& isCountable0(sk38(W0))
& aSubsetOf0(sk38(W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
| ~ aElementOf0(W3,sk38(W0)) )
& aSet0(sk38(W0))
& ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
| ~ aElement0(W3)
| aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ( ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W3,sdtlpdtrp0(xN,W0))
& aElement0(W3) )
| ~ aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3)
| ~ aElementOf0(W3,sdtlpdtrp0(xN,W0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& aElementOf0(sk37(W0),xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk37,sk38,sk39])],[f88_nnf]) ).
cnf(c996,plain,
( X3 != szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
fof(f99,hypothesis,
( ~ ( xQ = slcrc0
| ~ ? [W0] : aElementOf0(W0,xQ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f99_nnf,plain,
( xQ != slcrc0
& ? [W0] : aElementOf0(W0,xQ)
& ! [W0] :
( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) ) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [W0] :
( xQ != slcrc0
& aElementOf0(sk46,xQ)
& ( aElementOf0(W0,xO)
| ~ aElementOf0(W0,xQ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk46])],[f99_nnf]) ).
cnf(c1061,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(c1076,plain,
( X0 != szmzizndt0(xQ)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(esa)],[f103_sk]) ).
cnf(c1085,plain,
~ aElementOf0(sk48,xO),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c188,c194,c200,c206,c227,c233,c244,c257,c260,c281,c287,c293,c317,c318,c340,c351,c497,c805,c815,c825,c925,c935,c945,c965,c975,c985,c996,c1061,c1076,c1085,c1086]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3180]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM610+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n003.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 : Thu Sep 24 04:56:06 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.27/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.27/3.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------