%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM611+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 : Tue Sep 29 12:25:00 PM UTC 2026
% Result : Theorem 4.46s 1.11s
% Output : Refutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 22
% Syntax : Number of formulae : 119 ( 38 unt; 5 def)
% Number of atoms : 379 ( 75 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 446 ( 186 ~; 183 |; 53 &)
% ( 14 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f11,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f26,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( isFinite0(X0)
& aElementOf0(X1,X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f96,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
fof(f99,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f109,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f110,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f118,plain,
xk != sbrdtbr0(xP),
inference(flattening,[],[f110]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f126]) ).
fof(f149,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f150,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f149]) ).
fof(f168,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ isFinite0(X0)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f172]) ).
fof(f193,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f194,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f193]) ).
fof(f252,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f253,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f252]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f253]) ).
fof(f255,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f254]) ).
fof(f270,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f168]) ).
fof(f289,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f194]) ).
fof(f290,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f289]) ).
fof(f291,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f290]) ).
fof(f292,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f291]) ).
fof(f319,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f322,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f357,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f361,plain,
! [X0,X1] :
( szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f376,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f377,plain,
! [X0] :
( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f381,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f411,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f456,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f468,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f469,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
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,
xk != sbrdtbr0(xP),
inference(cnf_transformation,[],[f118]) ).
fof(f544,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f411]) ).
fof(f560,definition,
sF29 = sbrdtbr0(xP),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f561,plain,
sbrdtbr0(xP) = sF29,
inference(reorient_equations,[],[f560]) ).
fof(f562,plain,
xk != sF29,
inference(definition_folding,[],[f522,f561]) ).
fof(f564,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(forward_demodulation,[],[f517,f516]) ).
fof(f582,plain,
sF29 = sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(forward_demodulation,[],[f561,f516]) ).
fof(f583,plain,
aSet0(sdtmndt0(xQ,xp)),
inference(forward_demodulation,[],[f564,f515]) ).
fof(f586,plain,
sF29 = sbrdtbr0(sdtmndt0(xQ,xp)),
inference(forward_demodulation,[],[f582,f515]) ).
fof(f708,definition,
( spl30_14
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl30_14])],[avatar_definition]) ).
fof(f709,plain,
( aSet0(xQ)
| ~ spl30_14 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f741,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f319,f513]) ).
fof(f747,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f741,f357]) ).
fof(f754,plain,
spl30_14,
inference(avatar_split_clause,[],[f747,f708]) ).
fof(f821,definition,
( spl30_18
<=> isFinite0(sdtmndt0(xQ,xp)) ),
introduced(definition,[new_symbols(definition,[spl30_18])],[avatar_definition]) ).
fof(f822,plain,
( ~ isFinite0(sdtmndt0(xQ,xp))
| spl30_18 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f825,definition,
( spl30_19
<=> aElementOf0(sF29,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl30_19])],[avatar_definition]) ).
fof(f826,plain,
( aElementOf0(sF29,szNzAzT0)
| ~ spl30_19 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f827,plain,
( ~ aElementOf0(sF29,szNzAzT0)
| spl30_19 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f842,plain,
( aElementOf0(sF29,szNzAzT0)
| ~ isFinite0(sdtmndt0(xQ,xp))
| ~ aSet0(sdtmndt0(xQ,xp)) ),
inference(superposition,[],[f377,f586]) ).
fof(f844,plain,
( ~ isFinite0(sdtmndt0(xQ,xp))
| ~ aSet0(sdtmndt0(xQ,xp))
| spl30_19 ),
inference(forward_subsumption_resolution,[],[f842,f827]) ).
fof(f845,plain,
( ~ isFinite0(sdtmndt0(xQ,xp))
| spl30_19 ),
inference(forward_subsumption_resolution,[],[f844,f583]) ).
fof(f846,plain,
( ~ spl30_18
| spl30_19 ),
inference(avatar_split_clause,[],[f845,f825,f821]) ).
fof(f1020,plain,
( isFinite0(xP)
| ~ aSet0(xQ)
| ~ isFinite0(xQ) ),
inference(resolution,[],[f322,f520]) ).
fof(f1023,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ spl30_14 ),
inference(forward_subsumption_resolution,[],[f1020,f709]) ).
fof(f1026,plain,
( isFinite0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ isFinite0(xQ)
| ~ spl30_14 ),
inference(forward_demodulation,[],[f1023,f516]) ).
fof(f1029,plain,
( isFinite0(sdtmndt0(xQ,xp))
| ~ isFinite0(xQ)
| ~ spl30_14 ),
inference(forward_demodulation,[],[f1026,f515]) ).
fof(f1031,plain,
( ~ isFinite0(xQ)
| ~ spl30_14
| spl30_18 ),
inference(forward_subsumption_resolution,[],[f1029,f822]) ).
fof(f1802,plain,
! [X0] :
( szszuzczcdt0(X0) != xK
| xk = X0
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f361,f468]) ).
fof(f1805,plain,
! [X0] :
( szszuzczcdt0(X0) != xK
| xk = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1802,f469]) ).
fof(f1966,plain,
( xK = sbrdtbr0(xQ)
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(resolution,[],[f544,f510]) ).
fof(f1973,plain,
( xK = sbrdtbr0(xQ)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1966,f505]) ).
fof(f1975,plain,
xK = sbrdtbr0(xQ),
inference(forward_subsumption_resolution,[],[f1973,f456]) ).
fof(f1979,plain,
( ~ aElementOf0(xK,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f376,f1975]) ).
fof(f1980,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f1979,f456]) ).
fof(f1981,plain,
( ~ aSet0(xQ)
| ~ spl30_14
| spl30_18 ),
inference(forward_subsumption_resolution,[],[f1980,f1031]) ).
fof(f1982,plain,
( $false
| ~ spl30_14
| spl30_18 ),
inference(forward_subsumption_resolution,[],[f1981,f709]) ).
fof(f1983,plain,
( ~ spl30_14
| spl30_18 ),
inference(avatar_contradiction_clause,[],[f1982]) ).
fof(f1985,definition,
( spl30_73
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[spl30_73])],[avatar_definition]) ).
fof(f1986,plain,
( isFinite0(xQ)
| ~ spl30_73 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f1996,plain,
( isFinite0(xQ)
| ~ spl30_14 ),
inference(forward_subsumption_resolution,[],[f1980,f709]) ).
fof(f2004,plain,
( spl30_73
| ~ spl30_14 ),
inference(avatar_split_clause,[],[f1996,f708,f1985]) ).
fof(f2176,plain,
( ~ isFinite0(xQ)
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp)))
| ~ aSet0(xQ) ),
inference(resolution,[],[f381,f518]) ).
fof(f2179,plain,
( sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp)))
| ~ aSet0(xQ)
| ~ spl30_73 ),
inference(forward_subsumption_resolution,[],[f2176,f1986]) ).
fof(f2187,plain,
( sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp)))
| ~ spl30_14
| ~ spl30_73 ),
inference(forward_subsumption_resolution,[],[f2179,f709]) ).
fof(f2202,plain,
( sbrdtbr0(xQ) = szszuzczcdt0(sF29)
| ~ spl30_14
| ~ spl30_73 ),
inference(forward_demodulation,[],[f2187,f586]) ).
fof(f2204,plain,
( xK = szszuzczcdt0(sF29)
| ~ spl30_14
| ~ spl30_73 ),
inference(forward_demodulation,[],[f2202,f1975]) ).
fof(f10544,plain,
( xK != xK
| xk = sF29
| ~ aElementOf0(sF29,szNzAzT0)
| ~ spl30_14
| ~ spl30_73 ),
inference(superposition,[],[f1805,f2204]) ).
fof(f10545,plain,
( xk = sF29
| ~ aElementOf0(sF29,szNzAzT0)
| ~ spl30_14
| ~ spl30_73 ),
inference(trivial_inequality_removal,[],[f10544]) ).
fof(f10547,plain,
( ~ aElementOf0(sF29,szNzAzT0)
| ~ spl30_14
| ~ spl30_73 ),
inference(forward_subsumption_resolution,[],[f10545,f562]) ).
fof(f10549,plain,
( $false
| ~ spl30_14
| ~ spl30_19
| ~ spl30_73 ),
inference(forward_subsumption_resolution,[],[f10547,f826]) ).
fof(f10550,plain,
( ~ spl30_14
| ~ spl30_19
| ~ spl30_73 ),
inference(avatar_contradiction_clause,[],[f10549]) ).
cnf(s13,plain,
spl30_14,
inference(sat_conversion,[],[f754]) ).
cnf(s17,plain,
( ~ spl30_18
| spl30_19 ),
inference(sat_conversion,[],[f846]) ).
cnf(s58,plain,
( ~ spl30_14
| spl30_18 ),
inference(sat_conversion,[],[f1983]) ).
cnf(s61,plain,
( ~ spl30_14
| spl30_73 ),
inference(sat_conversion,[],[f2004]) ).
cnf(s348,plain,
( ~ spl30_14
| ~ spl30_19
| ~ spl30_73 ),
inference(sat_conversion,[],[f10550]) ).
cnf(s405,plain,
spl30_73,
inference(rat,[],[s61,s13]) ).
cnf(s406,plain,
spl30_18,
inference(rat,[],[s58,s13]) ).
cnf(s410,plain,
~ spl30_19,
inference(rat,[],[s348,s13,s405]) ).
cnf(s411,plain,
$false,
inference(rat,[],[s17,s410,s406]) ).
fof(f10554,plain,
$false,
inference(avatar_sat_refutation,[],[s411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM611+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n010.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 20:45:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.46/1.11 % (1293108)Will run a generic schedule for satisfiability detection.
% 4.46/1.11 % (1293115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2500621580:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.46/1.11 % (1293114)% WARNING: option uhcvi not known.
% 4.46/1.11 % (1293113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3904900945_2999 on theBenchmark for (2999ds/0Mi)
% 4.46/1.11 % (1293114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=976264044:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.46/1.11 % (1293116)dis+10_1_sil=32000:sp=arity:random_seed=2178779918:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.46/1.11 % (1293118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=586691726:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.46/1.11 % (1293117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3143985966:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.46/1.11 % (1293119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2066288383:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.46/1.11 % TRYING [1]
% 4.46/1.11 % TRYING [2]
% 4.46/1.11 % TRYING [3]
% 4.46/1.11 % TRYING [4]
% 4.46/1.11 % (1293116)Instruction limit reached!
% 4.46/1.11 % (1293116)------------------------------
% 4.46/1.11 % (1293116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293116)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293116)Termination reason: Instruction limit
% 4.46/1.11 % (1293116)Termination phase: Saturation
% 4.46/1.11 % (1293116)Time elapsed: 0.067 s
% 4.46/1.11 % (1293116)Peak memory usage: 13 MB
% 4.46/1.11 % (1293116)Instructions burned: 103 (million)
% 4.46/1.11 % (1293117)Instruction limit reached!
% 4.46/1.11 % (1293117)------------------------------
% 4.46/1.11 % (1293117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293117)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293117)Termination reason: Instruction limit
% 4.46/1.11 % (1293117)Termination phase: Saturation
% 4.46/1.11 % (1293117)Time elapsed: 0.075 s
% 4.46/1.11 % (1293117)Peak memory usage: 13 MB
% 4.46/1.11 % (1293117)Instructions burned: 118 (million)
% 4.46/1.11 % (1293118)Instruction limit reached!
% 4.46/1.11 % (1293118)------------------------------
% 4.46/1.11 % (1293118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293118)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293118)Termination reason: Instruction limit
% 4.46/1.11 % (1293118)Termination phase: Saturation
% 4.46/1.11 % (1293118)Time elapsed: 0.080 s
% 4.46/1.11 % (1293118)Peak memory usage: 13 MB
% 4.46/1.11 % (1293118)Instructions burned: 132 (million)
% 4.46/1.11 % (1293127)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=895932178:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 4.46/1.11 % (1293128)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3723618896:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 4.46/1.11 % (1293129)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2084082647:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.46/1.11 % TRYING [1]
% 4.46/1.11 % TRYING [2]
% 4.46/1.11 % (1293119)Instruction limit reached!
% 4.46/1.11 % (1293119)------------------------------
% 4.46/1.11 % (1293119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293119)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293119)Termination reason: Instruction limit
% 4.46/1.11 % (1293119)Termination phase: Saturation
% 4.46/1.11 % (1293119)Time elapsed: 0.114 s
% 4.46/1.11 % (1293119)Peak memory usage: 15 MB
% 4.46/1.11 % (1293119)Instructions burned: 160 (million)
% 4.46/1.11 % TRYING [3]
% 4.46/1.11 % TRYING [5]
% 4.46/1.11 % (1293133)ott-21_1_sil=16000:fs=off:random_seed=3395614211:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.46/1.11 % TRYING [4]
% 4.46/1.11 % (1293128)Instruction limit reached!
% 4.46/1.11 % (1293128)------------------------------
% 4.46/1.11 % (1293128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293128)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293128)Termination reason: Instruction limit
% 4.46/1.11 % (1293128)Termination phase: Saturation
% 4.46/1.11 % (1293128)Time elapsed: 0.087 s
% 4.46/1.11 % (1293128)Peak memory usage: 13 MB
% 4.46/1.11 % (1293128)Instructions burned: 132 (million)
% 4.46/1.11 % (1293135)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1734370475:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 4.46/1.11 % TRYING [5]
% 4.46/1.11 % (1293133)Instruction limit reached!
% 4.46/1.11 % (1293133)------------------------------
% 4.46/1.11 % (1293133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293133)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293133)Termination reason: Instruction limit
% 4.46/1.11 % (1293133)Termination phase: Saturation
% 4.46/1.11 % (1293133)Time elapsed: 0.104 s
% 4.46/1.11 % (1293133)Peak memory usage: 13 MB
% 4.46/1.11 % (1293133)Instructions burned: 181 (million)
% 4.46/1.11 % (1293137)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4157957627:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 4.46/1.11 % TRYING [1]
% 4.46/1.11 % TRYING [2]
% 4.46/1.11 % TRYING [6]
% 4.46/1.11 % TRYING [3]
% 4.46/1.11 % (1293127)Instruction limit reached!
% 4.46/1.11 % (1293127)------------------------------
% 4.46/1.11 % (1293127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293127)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293127)Termination reason: Instruction limit
% 4.46/1.11 % (1293127)Termination phase: Finite model building constraint generation
% 4.46/1.11 % (1293127)Time elapsed: 0.284 s
% 4.46/1.11 % (1293127)Peak memory usage: 34 MB
% 4.46/1.11 % (1293127)Instructions burned: 714 (million)
% 4.46/1.11 % (1293139)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4289180514:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 4.46/1.11 % TRYING [4]
% 4.46/1.11 % (1293129)Instruction limit reached!
% 4.46/1.11 % (1293129)------------------------------
% 4.46/1.11 % (1293129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293129)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293129)Termination reason: Instruction limit
% 4.46/1.11 % (1293129)Termination phase: Saturation
% 4.46/1.11 % (1293129)Time elapsed: 0.379 s
% 4.46/1.11 % (1293129)Peak memory usage: 18 MB
% 4.46/1.11 % (1293129)Instructions burned: 685 (million)
% 4.46/1.11 % (1293141)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=388134639:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 4.46/1.11 % (1293135)Instruction limit reached!
% 4.46/1.11 % (1293135)------------------------------
% 4.46/1.11 % (1293135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293135)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293135)Termination reason: Instruction limit
% 4.46/1.11 % (1293135)Termination phase: Saturation
% 4.46/1.11 % (1293135)Time elapsed: 0.331 s
% 4.46/1.11 % (1293135)Peak memory usage: 15 MB
% 4.46/1.11 % (1293135)Instructions burned: 477 (million)
% 4.46/1.11 % (1293143)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2908243044:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 4.46/1.11 % (1293137)Instruction limit reached!
% 4.46/1.11 % (1293137)------------------------------
% 4.46/1.11 % (1293137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293137)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293137)Termination reason: Instruction limit
% 4.46/1.11 % (1293137)Termination phase: Finite model building SAT solving
% 4.46/1.11 % (1293137)Time elapsed: 0.366 s
% 4.46/1.11 % (1293137)Peak memory usage: 22 MB
% 4.46/1.11 % (1293137)Instructions burned: 866 (million)
% 4.46/1.11 % (1293139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1293108-1293139"...
% 4.46/1.11 % (1293139)...printing done.
% 4.46/1.11 % (1293139)Refutation found. Thanks to Tanya!
% 4.46/1.11 % SZS status Theorem for theBenchmark
% 4.46/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 4.46/1.11 % (1293139)------------------------------
% 4.46/1.11 % (1293139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.11 % (1293139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.11 % (1293139)CaDiCaL version: 2.1.3
% 4.46/1.11 % (1293139)Termination reason: Refutation
% 4.46/1.11 % (1293139)Time elapsed: 0.247 s
% 4.46/1.11 % (1293139)Peak memory usage: 17 MB
% 4.46/1.11 % (1293139)Instructions burned: 379 (million)
% 4.46/1.11 % (1293108)Success in time 0.687 s
% 4.46/1.11 % Vampire exiting
%------------------------------------------------------------------------------