%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM545+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:20:19 PM UTC 2026
% Result : Theorem 92.19s 12.11s
% Output : Proof 92.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 21
% Syntax : Number of formulae : 164 ( 109 unt; 4 def)
% Number of atoms : 336 ( 151 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 297 ( 125 ~; 100 |; 56 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 125 ( 5 sgn 52 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(c55,plain,
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t140,plain,
ifeq(aElementOf0(X1,szNzAzT0),true,aElementOf0(szszuzczcdt0(X1),szNzAzT0),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t296,plain,
ifeq(aElementOf0(X1,szNzAzT0),true,aElementOf0(szszuzczcdt0(X1),szNzAzT0),true) = true,
inference(orient,[status(thm)],[t140]) ).
fof(f9,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/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(c12,plain,
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t207,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,ifeq(aElementOf0(X3,X2),true,aElementOf0(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t338,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,ifeq(aElementOf0(X3,X2),true,aElementOf0(X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t207]) ).
fof(f54,hypothesis,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(f54_nnf,plain,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c109,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(t8,plain,
aSubsetOf0(xS,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(t1867,plain,
aSubsetOf0(xS,szNzAzT0) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t1871,plain,
true = ifeq(aSet0(szNzAzT0),true,ifeq(true,true,ifeq(aElementOf0(X1,xS),true,aElementOf0(X1,szNzAzT0),true),true),true),
inference(cp,[status(thm)],[t338,t1867]) ).
fof(f22,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/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(t0,plain,
aSet0(szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t1253,plain,
aSet0(szNzAzT0) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t35687,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(aElementOf0(X1,xS),true,aElementOf0(X1,szNzAzT0),true),true),true),
inference(step,[status(thm)],[t1871,t1253]) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t36]) ).
cnf(t35688,plain,
true = ifeq(true,true,ifeq(aElementOf0(X1,xS),true,aElementOf0(X1,szNzAzT0),true),true),
inference(step,[status(thm)],[t35687,t256]) ).
cnf(t35689,plain,
true = ifeq(aElementOf0(X1,xS),true,aElementOf0(X1,szNzAzT0),true),
inference(step,[status(thm)],[t35688,t256]) ).
cnf(t32673,plain,
ifeq(aElementOf0(X1,xS),true,aElementOf0(X1,szNzAzT0),true) = true,
inference(orient,[status(thm)],[t35689]) ).
fof(f47,definition,
! [W0] :
( ( W0 != slcrc0
& isFinite0(W0)
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzazxdt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W2,W1) )
& aElementOf0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMax) ).
fof(f47_nnf,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ sdtlseqdt0(W2,W1)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzazxdt0(W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W2,W1)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzazxdt0(W0) ) )
| W0 = slcrc0
| ~ isFinite0(W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [W0,W1,W2] :
( ( ( ( ~ sdtlseqdt0(sk7(W0,W1),W1)
& aElementOf0(sk7(W0,W1),W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzazxdt0(W0) )
& ( ( ( sdtlseqdt0(W2,W1)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzazxdt0(W0) ) )
| W0 = slcrc0
| ~ isFinite0(W0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f47_nnf]) ).
cnf(c87,plain,
( aElementOf0(X1,X0)
| X1 != szmzazxdt0(X0)
| X0 = slcrc0
| ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(hi65,axiom,
ifeq(aSubsetOf0(X0,szNzAzT0),true,ifeq(isFinite0(X0),true,ifeq(X1,szmzazxdt0(X0),or(eq(X0,slcrc0),aElementOf0(X1,X0)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c87]) ).
cnf(hi84,axiom,
aSubsetOf0(xS,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(c110,plain,
isFinite0(xS),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi85,axiom,
isFinite0(xS) = true,
inference(equality_encoding,[status(esa)],[c110]) ).
cnf(hi105,axiom,
or(false,X0) = X0,
introduced(definition) ).
cnf(t147,plain,
or(eq(xS,slcrc0),aElementOf0(or(false,szmzazxdt0(xS)),xS)) = true,
inference(hyper_resolution,[status(thm)],[hi65,hi84,hi85,hi105]) ).
cnf(t13,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t265,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t33296,plain,
or(eq(xS,slcrc0),aElementOf0(szmzazxdt0(xS),xS)) = true,
inference(step,[status(thm)],[t147,t265]) ).
cnf(t385,plain,
or(eq(xS,slcrc0),aElementOf0(szmzazxdt0(xS),xS)) = true,
inference(orient,[status(thm)],[t33296]) ).
cnf(t70,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t2280,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t70]) ).
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]) ).
cnf(t135,plain,
or(not(eq(X1,slcrc0)),not(aElementOf0(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t398,plain,
or(not(eq(X1,slcrc0)),not(aElementOf0(X2,X1))) = true,
inference(orient,[status(thm)],[t135]) ).
cnf(c13,plain,
( aElementOf0(sk1(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t204,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(t307,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)],[t204]) ).
fof(f56,conjecture,
? [W0] :
( aSubsetOf0(xS,slbdtrb0(W0))
& aElementOf0(W0,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56_neg,negated_conjecture,
~ ? [W0] :
( aSubsetOf0(xS,slbdtrb0(W0))
& aElementOf0(W0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f56_nnf,plain,
! [W0] :
( ~ aSubsetOf0(xS,slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f56_neg]) ).
fof(f56_sk,plain,
! [W0] :
( ~ aSubsetOf0(xS,slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c112,plain,
( ~ aSubsetOf0(xS,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t152,plain,
or(not(aElementOf0(X1,szNzAzT0)),not(aSubsetOf0(xS,slbdtrb0(X1)))) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t394,plain,
or(not(aElementOf0(X1,szNzAzT0)),not(aSubsetOf0(xS,slbdtrb0(X1)))) = true,
inference(orient,[status(thm)],[t152]) ).
fof(f51,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegZero) ).
fof(f51_nnf,plain,
slbdtrb0(sz00) = slcrc0,
inference(nnf_transformation,[status(thm)],[f51]) ).
cnf(c103,plain,
slbdtrb0(sz00) = slcrc0,
inference(cnf_transformation,[status(esa)],[f51_nnf]) ).
cnf(t6,plain,
slbdtrb0(sz00) = slcrc0,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(t2530,plain,
slbdtrb0(sz00) = slcrc0,
inference(orient,[status(thm)],[t6]) ).
cnf(t2531,plain,
true = or(not(aElementOf0(sz00,szNzAzT0)),not(aSubsetOf0(xS,slcrc0))),
inference(cp,[status(thm)],[t394,t2530]) ).
fof(f23,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f23_nnf,plain,
aElementOf0(sz00,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c54,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(t7,plain,
aElementOf0(sz00,szNzAzT0) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(t569,plain,
aElementOf0(sz00,szNzAzT0) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t33378,plain,
true = or(not(true),not(aSubsetOf0(xS,slcrc0))),
inference(step,[status(thm)],[t2531,t569]) ).
cnf(t5,plain,
not(true) = false,
introduced(definition) ).
cnf(t2513,plain,
not(true) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t33379,plain,
true = or(false,not(aSubsetOf0(xS,slcrc0))),
inference(step,[status(thm)],[t33378,t2513]) ).
cnf(t33380,plain,
true = not(aSubsetOf0(xS,slcrc0)),
inference(step,[status(thm)],[t33379,t265]) ).
cnf(t2914,plain,
not(aSubsetOf0(xS,slcrc0)) = true,
inference(orient,[status(thm)],[t33380]) ).
cnf(t2915,plain,
false = ifeq(true,true,aSubsetOf0(xS,slcrc0),false),
inference(cp,[status(thm)],[t2280,t2914]) ).
cnf(t33381,plain,
false = aSubsetOf0(xS,slcrc0),
inference(step,[status(thm)],[t2915,t256]) ).
cnf(t2916,plain,
aSubsetOf0(xS,slcrc0) = false,
inference(orient,[status(thm)],[t33381]) ).
cnf(t2921,plain,
true = ifeq(aSet0(slcrc0),true,ifeq(aSet0(xS),true,or(false,aElementOf0(sk1(slcrc0,xS),xS)),true),true),
inference(cp,[status(thm)],[t307,t2916]) ).
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(t19,plain,
aSet0(or(false,slcrc0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi105]) ).
cnf(t33307,plain,
aSet0(slcrc0) = true,
inference(step,[status(thm)],[t19,t265]) ).
cnf(t750,plain,
aSet0(slcrc0) = true,
inference(orient,[status(thm)],[t33307]) ).
cnf(t33448,plain,
true = ifeq(true,true,ifeq(aSet0(xS),true,or(false,aElementOf0(sk1(slcrc0,xS),xS)),true),true),
inference(step,[status(thm)],[t2921,t750]) ).
cnf(t33449,plain,
true = ifeq(aSet0(xS),true,or(false,aElementOf0(sk1(slcrc0,xS),xS)),true),
inference(step,[status(thm)],[t33448,t256]) ).
cnf(c11,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t178,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,aSet0(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t339,plain,
ifeq(aSet0(X1),true,ifeq(aSubsetOf0(X2,X1),true,aSet0(X2),true),true) = true,
inference(orient,[status(thm)],[t178]) ).
cnf(t1868,plain,
true = ifeq(aSet0(szNzAzT0),true,ifeq(true,true,aSet0(xS),true),true),
inference(cp,[status(thm)],[t339,t1867]) ).
cnf(t33359,plain,
true = ifeq(true,true,ifeq(true,true,aSet0(xS),true),true),
inference(step,[status(thm)],[t1868,t1253]) ).
cnf(t33360,plain,
true = ifeq(true,true,aSet0(xS),true),
inference(step,[status(thm)],[t33359,t256]) ).
cnf(t33361,plain,
true = aSet0(xS),
inference(step,[status(thm)],[t33360,t256]) ).
cnf(t2550,plain,
aSet0(xS) = true,
inference(orient,[status(thm)],[t33361]) ).
cnf(t33450,plain,
true = ifeq(true,true,or(false,aElementOf0(sk1(slcrc0,xS),xS)),true),
inference(step,[status(thm)],[t33449,t2550]) ).
cnf(t33451,plain,
true = or(false,aElementOf0(sk1(slcrc0,xS),xS)),
inference(step,[status(thm)],[t33450,t256]) ).
cnf(t33452,plain,
true = aElementOf0(sk1(slcrc0,xS),xS),
inference(step,[status(thm)],[t33451,t265]) ).
cnf(t3526,plain,
aElementOf0(sk1(slcrc0,xS),xS) = true,
inference(orient,[status(thm)],[t33452]) ).
cnf(t3528,plain,
true = or(not(eq(xS,slcrc0)),not(true)),
inference(cp,[status(thm)],[t398,t3526]) ).
cnf(t33453,plain,
true = or(not(eq(xS,slcrc0)),false),
inference(step,[status(thm)],[t3528,t2513]) ).
cnf(t11,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t264,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t33454,plain,
true = not(eq(xS,slcrc0)),
inference(step,[status(thm)],[t33453,t264]) ).
cnf(t3560,plain,
not(eq(xS,slcrc0)) = true,
inference(orient,[status(thm)],[t33454]) ).
cnf(t3561,plain,
false = ifeq(true,true,eq(xS,slcrc0),false),
inference(cp,[status(thm)],[t2280,t3560]) ).
cnf(t33455,plain,
false = eq(xS,slcrc0),
inference(step,[status(thm)],[t3561,t256]) ).
cnf(t3562,plain,
eq(xS,slcrc0) = false,
inference(orient,[status(thm)],[t33455]) ).
cnf(t33456,plain,
or(false,aElementOf0(szmzazxdt0(xS),xS)) = true,
inference(step,[status(thm)],[t385,t3562]) ).
cnf(t33457,plain,
aElementOf0(szmzazxdt0(xS),xS) = true,
inference(step,[status(thm)],[t33456,t265]) ).
cnf(t3578,plain,
aElementOf0(szmzazxdt0(xS),xS) = true,
inference(rw,[status(thm)],[t33457]) ).
cnf(t3680,plain,
aElementOf0(szmzazxdt0(xS),xS) = true,
inference(orient,[status(thm)],[t3578]) ).
cnf(t32675,plain,
true = ifeq(true,true,aElementOf0(szmzazxdt0(xS),szNzAzT0),true),
inference(cp,[status(thm)],[t32673,t3680]) ).
cnf(t35691,plain,
true = aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(step,[status(thm)],[t32675,t256]) ).
cnf(t32859,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0) = true,
inference(orient,[status(thm)],[t35691]) ).
cnf(t32867,plain,
true = ifeq(true,true,aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),true),
inference(cp,[status(thm)],[t296,t32859]) ).
cnf(t35694,plain,
true = aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(step,[status(thm)],[t32867,t256]) ).
fof(f55,hypothesis,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2035) ).
fof(f55_nnf,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c111,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(t151,plain,
or(eq(xS,slcrc0),aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) = true,
inference(equality_encoding,[status(esa)],[c111]) ).
cnf(t388,plain,
or(eq(xS,slcrc0),aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) = true,
inference(orient,[status(thm)],[t151]) ).
cnf(t33460,plain,
or(false,aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) = true,
inference(step,[status(thm)],[t388,t3562]) ).
cnf(t33461,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) = true,
inference(step,[status(thm)],[t33460,t265]) ).
cnf(t3580,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) = true,
inference(rw,[status(thm)],[t33461]) ).
cnf(t4837,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) = true,
inference(orient,[status(thm)],[t3580]) ).
cnf(t4839,plain,
true = or(not(aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)),not(true)),
inference(cp,[status(thm)],[t394,t4837]) ).
cnf(t33617,plain,
true = or(not(aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)),false),
inference(step,[status(thm)],[t4839,t2513]) ).
cnf(t33618,plain,
true = not(aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)),
inference(step,[status(thm)],[t33617,t264]) ).
cnf(t5633,plain,
not(aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)) = true,
inference(orient,[status(thm)],[t33618]) ).
cnf(t5634,plain,
false = ifeq(true,true,aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),false),
inference(cp,[status(thm)],[t2280,t5633]) ).
cnf(t33619,plain,
false = aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(step,[status(thm)],[t5634,t256]) ).
cnf(t5635,plain,
aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0) = false,
inference(orient,[status(thm)],[t33619]) ).
cnf(t35695,plain,
true = false,
inference(step,[status(thm)],[t35694,t5635]) ).
cnf(t33004,plain,
false = true,
inference(orient,[status(thm)],[t35695]) ).
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]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c9,c10,c36,c56,c60,c63,c112]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t33004]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM545+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 04:35:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 92.19/12.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.19/12.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------