%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:20:23 PM UTC 2026
% Result : Theorem 70.74s 24.49s
% Output : Proof 70.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 23
% Syntax : Number of formulae : 150 ( 99 unt; 4 def)
% Number of atoms : 342 ( 154 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 326 ( 134 ~; 105 |; 70 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 147 ( 12 sgn 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f56_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0)
& ~ aElementOf0(W3,W2) )
| ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( sbrdtbr0(sk10(W0,W1,W2)) = W1
& aSubsetOf0(sk10(W0,W1,W2),W0)
& ~ aElementOf0(sk10(W0,W1,W2),W2) )
| ( ( sbrdtbr0(sk10(W0,W1,W2)) != W1
| ~ aSubsetOf0(sk10(W0,W1,W2),W0) )
& aElementOf0(sk10(W0,W1,W2),W2) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f56_nnf]) ).
cnf(c115,plain,
( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t218,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),ifeq(aSubsetOf0(X4,X1),true,ifeq(sbrdtbr0(X4),X2,aElementOf0(X4,X3),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(t319,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(X2,szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,X2),ifeq(aSubsetOf0(X4,X1),true,ifeq(sbrdtbr0(X4),X2,aElementOf0(X4,X3),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t218]) ).
cnf(t60,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t60]) ).
cnf(t321,plain,
true = ifeq(aSet0(X1),true,ifeq(aElementOf0(sbrdtbr0(X2),szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,sbrdtbr0(X2)),ifeq(aSubsetOf0(X2,X1),true,aElementOf0(X2,X3),true),true),true),true),
inference(cp,[status(thm)],[t319,t256]) ).
cnf(t19143,plain,
ifeq(aSet0(X1),true,ifeq(aElementOf0(sbrdtbr0(X2),szNzAzT0),true,ifeq(X3,slbdtsldtrb0(X1,sbrdtbr0(X2)),ifeq(aSubsetOf0(X2,X1),true,aElementOf0(X2,X3),true),true),true),true) = true,
inference(orient,[status(thm)],[t321]) ).
fof(f9,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f9_nnf,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [W0,W1,W2] :
( ( ( ( ~ aElementOf0(sk1(W0,W1),W0)
& aElementOf0(sk1(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f9_nnf]) ).
cnf(c13,plain,
( aElementOf0(sk1(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t161,plain,
ifeq(aSet0(X1),true,ifeq(aSet0(X2),true,or(aSubsetOf0(X2,X1),aElementOf0(sk1(X1,X2),X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t334,plain,
ifeq(aSet0(X1),true,ifeq(aSet0(X2),true,or(aSubsetOf0(X2,X1),aElementOf0(sk1(X1,X2),X2)),true),true) = true,
inference(orient,[status(thm)],[t161]) ).
cnf(t76,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t2484,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t76]) ).
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/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]) ).
cnf(t109,plain,
or(not(eq(X1,slcrc0)),not(aElementOf0(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t843,plain,
or(not(eq(X1,slcrc0)),not(aElementOf0(X2,X1))) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t14,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t1561,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t1562,plain,
true = or(not(true),not(aElementOf0(X1,slcrc0))),
inference(cp,[status(thm)],[t843,t1561]) ).
cnf(t9,plain,
not(true) = false,
introduced(definition) ).
cnf(t2754,plain,
not(true) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t20760,plain,
true = or(false,not(aElementOf0(X1,slcrc0))),
inference(step,[status(thm)],[t1562,t2754]) ).
cnf(t19,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t274,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t19]) ).
cnf(t20761,plain,
true = not(aElementOf0(X1,slcrc0)),
inference(step,[status(thm)],[t20760,t274]) ).
cnf(t6333,plain,
not(aElementOf0(X1,slcrc0)) = true,
inference(orient,[status(thm)],[t20761]) ).
cnf(t6334,plain,
false = ifeq(true,true,aElementOf0(X1,slcrc0),false),
inference(cp,[status(thm)],[t2484,t6333]) ).
cnf(t20762,plain,
false = aElementOf0(X1,slcrc0),
inference(step,[status(thm)],[t6334,t256]) ).
cnf(t6335,plain,
aElementOf0(X1,slcrc0) = false,
inference(orient,[status(thm)],[t20762]) ).
cnf(t6350,plain,
true = ifeq(aSet0(X1),true,ifeq(aSet0(slcrc0),true,or(aSubsetOf0(slcrc0,X1),false),true),true),
inference(cp,[status(thm)],[t334,t6335]) ).
cnf(c4,plain,
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi1,axiom,
ifeq(X0,slcrc0,aSet0(X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(hi163,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(t28,plain,
aSet0(or(false,slcrc0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi163]) ).
cnf(t20496,plain,
aSet0(slcrc0) = true,
inference(step,[status(thm)],[t28,t274]) ).
cnf(t850,plain,
aSet0(slcrc0) = true,
inference(orient,[status(thm)],[t20496]) ).
cnf(t21023,plain,
true = ifeq(aSet0(X1),true,ifeq(true,true,or(aSubsetOf0(slcrc0,X1),false),true),true),
inference(step,[status(thm)],[t6350,t850]) ).
cnf(t21024,plain,
true = ifeq(aSet0(X1),true,or(aSubsetOf0(slcrc0,X1),false),true),
inference(step,[status(thm)],[t21023,t256]) ).
cnf(t17,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t273,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t17]) ).
cnf(t21025,plain,
true = ifeq(aSet0(X1),true,aSubsetOf0(slcrc0,X1),true),
inference(step,[status(thm)],[t21024,t273]) ).
cnf(t9542,plain,
ifeq(aSet0(X1),true,aSubsetOf0(slcrc0,X1),true) = true,
inference(orient,[status(thm)],[t21025]) ).
cnf(c11,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t135,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,aSet0(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t336,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,aSet0(X2),true),true) = true,
inference(orient,[status(thm)],[t135]) ).
fof(f74,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f74_nnf,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c168,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(t13,plain,
aSubsetOf0(xS,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c168]) ).
cnf(t1531,plain,
aSubsetOf0(xS,szNzAzT0) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t1532,plain,
true = ifeq(aSet0(szNzAzT0),true,ifeq(true,true,aSet0(xS),true),true),
inference(cp,[status(thm)],[t336,t1531]) ).
fof(f22,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f22_nnf,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c52,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t2,plain,
aSet0(szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t1289,plain,
aSet0(szNzAzT0) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t20550,plain,
true = ifeq(true,true,ifeq(true,true,aSet0(xS),true),true),
inference(step,[status(thm)],[t1532,t1289]) ).
cnf(t20551,plain,
true = ifeq(true,true,aSet0(xS),true),
inference(step,[status(thm)],[t20550,t256]) ).
cnf(t20552,plain,
true = aSet0(xS),
inference(step,[status(thm)],[t20551,t256]) ).
cnf(t2855,plain,
aSet0(xS) = true,
inference(orient,[status(thm)],[t20552]) ).
cnf(t9550,plain,
true = ifeq(true,true,aSubsetOf0(slcrc0,xS),true),
inference(cp,[status(thm)],[t9542,t2855]) ).
cnf(t21026,plain,
true = aSubsetOf0(slcrc0,xS),
inference(step,[status(thm)],[t9550,t256]) ).
cnf(t9555,plain,
aSubsetOf0(slcrc0,xS) = true,
inference(orient,[status(thm)],[t21026]) ).
cnf(t19300,plain,
true = ifeq(aSet0(xS),true,ifeq(aElementOf0(sbrdtbr0(slcrc0),szNzAzT0),true,ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),true),true),
inference(cp,[status(thm)],[t19143,t9555]) ).
cnf(t21944,plain,
true = ifeq(true,true,ifeq(aElementOf0(sbrdtbr0(slcrc0),szNzAzT0),true,ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),true),true),
inference(step,[status(thm)],[t19300,t2855]) ).
cnf(t21945,plain,
true = ifeq(aElementOf0(sbrdtbr0(slcrc0),szNzAzT0),true,ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),true),
inference(step,[status(thm)],[t21944,t256]) ).
cnf(h251,plain,
aSet0(or(false,slcrc0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi163]) ).
fof(f41,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f41_nnf,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c77,plain,
( X0 != slcrc0
| sbrdtbr0(X0) = sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(hi55,axiom,
ifeq(aSet0(X0),true,ifeq(X0,slcrc0,sbrdtbr0(X0),sz00),sz00) = sz00,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(t44,plain,
sbrdtbr0(or(false,slcrc0)) = sz00,
inference(hyper_resolution,[status(thm)],[hi55,h251,hi163]) ).
cnf(t20536,plain,
sbrdtbr0(slcrc0) = sz00,
inference(step,[status(thm)],[t44,t274]) ).
fof(f77,hypothesis,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f77_nnf,plain,
xK = sz00,
inference(nnf_transformation,[status(thm)],[f77]) ).
cnf(c177,plain,
xK = sz00,
inference(cnf_transformation,[status(esa)],[f77_nnf]) ).
cnf(t0,plain,
xK = sz00,
inference(equality_encoding,[status(esa)],[c177]) ).
cnf(t2680,plain,
sz00 = xK,
inference(orient,[status(thm)],[t0]) ).
cnf(t20537,plain,
sbrdtbr0(slcrc0) = xK,
inference(step,[status(thm)],[t20536,t2680]) ).
cnf(t2699,plain,
sbrdtbr0(slcrc0) = xK,
inference(orient,[status(thm)],[t20537]) ).
cnf(t21946,plain,
true = ifeq(aElementOf0(xK,szNzAzT0),true,ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),true),
inference(step,[status(thm)],[t21945,t2699]) ).
fof(f73,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f73_nnf,plain,
aElementOf0(xK,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f73]) ).
cnf(c167,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f73_nnf]) ).
cnf(t12,plain,
aElementOf0(xK,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c167]) ).
cnf(t710,plain,
aElementOf0(xK,szNzAzT0) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t21947,plain,
true = ifeq(true,true,ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),true),
inference(step,[status(thm)],[t21946,t710]) ).
cnf(t21948,plain,
true = ifeq(X1,slbdtsldtrb0(xS,sbrdtbr0(slcrc0)),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),
inference(step,[status(thm)],[t21947,t256]) ).
cnf(t21949,plain,
true = ifeq(X1,slbdtsldtrb0(xS,xK),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),
inference(step,[status(thm)],[t21948,t2699]) ).
fof(f75,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f75_nnf,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c171,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t52,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(equality_encoding,[status(esa)],[c171]) ).
cnf(t2801,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(orient,[status(thm)],[t52]) ).
cnf(t21950,plain,
true = ifeq(X1,szDzozmdt0(xc),ifeq(true,true,aElementOf0(slcrc0,X1),true),true),
inference(step,[status(thm)],[t21949,t2801]) ).
cnf(t21951,plain,
true = ifeq(X1,szDzozmdt0(xc),aElementOf0(slcrc0,X1),true),
inference(step,[status(thm)],[t21950,t256]) ).
cnf(t20344,plain,
ifeq(X1,szDzozmdt0(xc),aElementOf0(slcrc0,X1),true) = true,
inference(orient,[status(thm)],[t21951]) ).
cnf(t20345,plain,
true = aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(cp,[status(thm)],[t20344,t256]) ).
fof(f78,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f78_neg,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(negated_conjecture,[status(cth)],[f78]) ).
fof(f78_nnf,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(nnf_transformation,[status(thm)],[f78_neg]) ).
fof(f78_sk,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(skolemisation,[status(esa)],[f78_nnf]) ).
cnf(c178,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[status(esa)],[f78_sk]) ).
cnf(t55,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) = false,
inference(equality_encoding,[status(esa)],[c178]) ).
cnf(t2485,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) = false,
inference(orient,[status(thm)],[t55]) ).
cnf(t20516,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) = false,
inference(step,[status(thm)],[t2485,t2680]) ).
cnf(t2681,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)) = false,
inference(rw,[status(thm)],[t20516]) ).
cnf(t20619,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)) = false,
inference(step,[status(thm)],[t2681,t2801]) ).
cnf(t4280,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)) = false,
inference(orient,[status(thm)],[t20619]) ).
cnf(t21952,plain,
true = false,
inference(step,[status(thm)],[t20345,t4280]) ).
cnf(t20351,plain,
false = true,
inference(orient,[status(thm)],[t21952]) ).
fof(f7,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c178]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t20351]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/15.41 % Computer : n002.cluster.edu
% 0.11/15.41 % Model : x86_64 x86_64
% 0.11/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.41 % Memory : 8046.5625MB
% 0.11/15.41 % OS : Linux 6.8.0-71-generic
% 0.11/15.41 % CPULimit : 300
% 0.11/15.41 % WCLimit : 300
% 0.11/15.41 % DateTime : Thu Sep 24 04:42:08 UTC 2026
% 0.11/15.41 % CPUTime :
% 0.11/15.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 70.74/24.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.74/24.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------