%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM612+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 02:26:14 PM UTC 2026
% Result : Theorem 3.28s 2.19s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 93 ( 38 unt; 3 def)
% Number of atoms : 325 ( 61 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 357 ( 144 ~; 142 |; 53 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 87 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f11,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(f96,axiom,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f99,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
fof(f109,conjecture,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f110,negated_conjecture,
~ ( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f124,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f125,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f126,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ) ),
inference(flattening,[],[f125]) ).
fof(f167,plain,
! [X0] :
( ~ aSet0(X0)
| ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f171,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f172,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(flattening,[],[f171]) ).
fof(f192,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f193,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f192]) ).
fof(f241,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f252,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f253,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f252]) ).
fof(f254,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f253]) ).
fof(f255,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f254]) ).
fof(f270,plain,
! [X0] :
( ~ aSet0(X0)
| ( ( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) )
& ( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ) ) ),
inference(nnf_transformation,[],[f167]) ).
fof(f289,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f193]) ).
fof(f290,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(flattening,[],[f289]) ).
fof(f291,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(rectify,[],[f290]) ).
fof(f292,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ! [X2] :
( ( slbdtsldtrb0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) ) )
& ( sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK14(X0,X1,X2),X2)
| ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK14(X0,X1,X2),X2)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = slbdtsldtrb0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f291]) ).
fof(f319,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f322,plain,
! [X0,X1] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| isFinite0(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f357,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f376,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f377,plain,
! [X0] :
( ~ aSet0(X0)
| ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f381,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f172]) ).
fof(f411,plain,
! [X2,X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X1 ),
inference(cnf_transformation,[],[f292]) ).
fof(f456,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f505,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f510,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f99]) ).
fof(f513,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f515,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f516,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f517,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f518,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f520,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f522,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(cnf_transformation,[],[f241]) ).
fof(f544,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1 ),
inference(equality_resolution,[],[f411]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( isFinite0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f357]) ).
tcf(c_114,plain,
! [X0: $i] :
( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_115,plain,
! [X0: $i] :
( isFinite0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f376]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f381]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sbrdtbr0(X0) = X2 )
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
inference(cnf_transformation,[],[f544]) ).
tcf(c_194,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f456]) ).
tcf(c_242,plain,
aSet0(xO),
inference(cnf_transformation,[],[f505]) ).
tcf(c_248,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f510]) ).
tcf(c_251,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f513]) ).
tcf(c_253,plain,
szmzizndt0(xQ) = xp,
inference(cnf_transformation,[],[f515]) ).
tcf(c_254,plain,
aSet0(xP),
inference(cnf_transformation,[],[f517]) ).
tcf(c_255,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(cnf_transformation,[],[f516]) ).
tcf(c_256,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_258,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_260,negated_conjecture,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ( szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ) ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_1772,plain,
sdtmndt0(xQ,xp) = xP,
inference(light_normalisation,[status(thm)],[c_255,c_253]) ).
tcf(c_15267,definition,
iPr_def_10 = sbrdtbr0(xP),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_15268,definition,
iPr_def_11 = szszuzczcdt0(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_15269,definition,
iPr_def_12 = sbrdtbr0(xQ),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_15270,negated_conjecture,
( ~ aElementOf0(iPr_def_10,szNzAzT0)
| ( iPr_def_11 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_260,c_15269,c_15267,c_15268]) ).
tcf(c_18571,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(superposition,[status(thm)],[c_251,c_58]) ).
tcf(c_18575,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[status(thm)],[c_18571,c_94]) ).
tcf(c_18687,plain,
( aElementOf0(iPr_def_10,szNzAzT0)
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_15267,c_114]) ).
tcf(c_18698,plain,
( aElementOf0(iPr_def_10,szNzAzT0)
| ~ isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18687,c_254]) ).
tcf(c_18729,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(iPr_def_12,szNzAzT0) ),
inference(superposition,[status(thm)],[c_15269,c_115]) ).
tcf(c_18730,plain,
( isFinite0(xQ)
| ~ aElementOf0(iPr_def_12,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18729,c_18575]) ).
tcf(c_19204,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_258,c_60]) ).
tcf(c_19207,plain,
( isFinite0(xP)
| ~ isFinite0(xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19204,c_18575]) ).
tcf(c_23220,plain,
( ( sbrdtbr0(xQ) = xK )
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[c_248,c_155]) ).
tcf(c_23222,plain,
( ( xK = iPr_def_12 )
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_23220,c_15269]) ).
tcf(c_23223,plain,
xK = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_23222,c_242,c_194]) ).
tcf(c_23284,plain,
aElementOf0(iPr_def_12,szNzAzT0),
inference(demodulation,[status(thm)],[c_194,c_23223]) ).
tcf(c_23285,plain,
isFinite0(xQ),
inference(backward_subsumption_resolution,[status(thm)],[c_18730,c_23284]) ).
tcf(c_23290,plain,
isFinite0(xP),
inference(backward_subsumption_resolution,[status(thm)],[c_19207,c_23285]) ).
tcf(c_23321,plain,
aElementOf0(iPr_def_10,szNzAzT0),
inference(backward_subsumption_resolution,[status(thm)],[c_18698,c_23290]) ).
tcf(c_23328,plain,
iPr_def_11 != iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_15270,c_23321]) ).
tcf(c_24150,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_256,c_119]) ).
tcf(c_24161,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(light_normalisation,[status(thm)],[c_24150,c_1772,c_15267,c_15268,c_15269]) ).
tcf(c_24162,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_24161,c_23328,c_23285,c_18575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM612+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.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
% 0.11/0.38 % DateTime : Thu Sep 24 04:57:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.28/2.19 % SZS status Started for theBenchmark.p
% 3.28/2.19 % SZS status Theorem for theBenchmark.p
% 3.28/2.19
% 3.28/2.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.28/2.19
% 3.28/2.19 % ------ iProver source info
% 3.28/2.19
% 3.28/2.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.28/2.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.28/2.19 % git: non_committed_changes: false
% 3.28/2.19
% 3.28/2.19 % ------ Parsing...
% 3.28/2.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.28/2.19
% 3.28/2.19 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.28/2.19
% 3.28/2.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.28/2.19
% 3.28/2.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.28/2.19 % ------ Proving...
% 3.28/2.19 % ------ Problem Properties
% 3.28/2.19
% 3.28/2.19 %
% 3.28/2.19 % clauses 210
% 3.28/2.19 % conjectures 1
% 3.28/2.19 % EPR 53
% 3.28/2.19 % Horn 171
% 3.28/2.19 % unary 51
% 3.28/2.19 % binary 33
% 3.28/2.19 % lits 666
% 3.28/2.19 % lits eq 110
% 3.28/2.19 % fd_pure 0
% 3.28/2.19 % fd_pseudo 0
% 3.28/2.19 % fd_cond 10
% 3.28/2.19 % fd_pseudo_cond 25
% 3.28/2.19 % AC symbols 0
% 3.28/2.19
% 3.28/2.19 % ------ Schedule dynamic 5 is on
% 3.28/2.19
% 3.28/2.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.28/2.19
% 3.28/2.19
% 3.28/2.19 % ------
% 3.28/2.19 % Current options:
% 3.28/2.19 % ------
% 3.28/2.19
% 3.28/2.19
% 3.28/2.19 %
% 3.28/2.19
% 3.28/2.19 % ------ Proving...
% 3.28/2.19 %
% 3.28/2.19
% 3.28/2.19 % SZS status Theorem for theBenchmark.p
% 3.28/2.19
% 3.28/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.28/2.19
% 3.28/2.19
%------------------------------------------------------------------------------