%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM556+3 : 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 : n016.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 02:26:00 PM UTC 2026
% Result : Theorem 8.13s 1.61s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 35 unt; 0 def)
% Number of atoms : 319 ( 66 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 350 ( 134 ~; 127 |; 71 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 71 !; 1 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f18,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aElement0(X0) )
=> ( ~ aElementOf0(X0,X1)
=> sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDiffCons) ).
fof(f21,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
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(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f65,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f70,axiom,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f71,axiom,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2411) ).
fof(f72,conjecture,
( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f73,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f75,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(rectify,[],[f70]) ).
fof(f83,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) )
& aSet0(xQ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f84,plain,
( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& ? [X0] :
( aElementOf0(X0,xP)
& ~ aElementOf0(X0,xS) ) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f116,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f119,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f120,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ) ),
inference(flattening,[],[f119]) ).
fof(f123,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(flattening,[],[f123]) ).
fof(f128,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f129,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f131,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(flattening,[],[f130]) ).
fof(f168,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xQ,xy)) )
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& aSet0(xP)
& ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(nnf_transformation,[],[f75]) ).
fof(f169,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( ( ~ aElementOf0(X1,xP)
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xQ,xy)) )
| ~ aElement0(X1)
| aElementOf0(X1,xP) ) )
& aSet0(xP)
& ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(flattening,[],[f168]) ).
fof(f170,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(nnf_transformation,[],[f71]) ).
fof(f171,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ( xy = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(flattening,[],[f170]) ).
fof(f172,plain,
( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& aElementOf0(sK8,xP)
& ~ aElementOf0(sK8,xS) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f84]) ).
fof(f213,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f241,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f245,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f83]) ).
fof(f247,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f248,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f249,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f250,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f251,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f254,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f169]) ).
fof(f255,plain,
! [X1] :
( ~ aElementOf0(X1,xP)
| xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f169]) ).
fof(f257,plain,
! [X1] :
( xx != X1
| ~ aElement0(X1)
| aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f169]) ).
fof(f259,plain,
aSet0(xP),
inference(cnf_transformation,[],[f169]) ).
fof(f266,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f171]) ).
fof(f269,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f171]) ).
fof(f270,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f171]) ).
fof(f272,plain,
( xk != sbrdtbr0(xP)
| aElementOf0(sK8,xP) ),
inference(cnf_transformation,[],[f172]) ).
fof(f273,plain,
( xk != sbrdtbr0(xP)
| ~ aElementOf0(sK8,xS) ),
inference(cnf_transformation,[],[f172]) ).
fof(f313,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f315,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f317,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f331,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f129]) ).
fof(f332,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f375,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[],[f257]) ).
tcf(c_50,plain,
aSet0(xS),
inference(cnf_transformation,[],[f213]) ).
tcf(c_80,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f241]) ).
tcf(c_82,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_86,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_87,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_88,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[],[f247]) ).
tcf(c_89,plain,
aElement0(xy),
inference(cnf_transformation,[],[f251]) ).
tcf(c_90,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_98,plain,
aSet0(xP),
inference(cnf_transformation,[],[f259]) ).
tcf(c_100,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_102,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 = xx )
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_103,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(cnf_transformation,[],[f254]) ).
tcf(c_104,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f270]) ).
tcf(c_105,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f269]) ).
tcf(c_108,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_110,negated_conjecture,
( ~ aElementOf0(sK8,xS)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_111,negated_conjecture,
( aElementOf0(sK8,xP)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( isFinite0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,X0)
| ( sdtmndt0(sdtpldt0(X0,X1),X1) = X0 )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( isFinite0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_13036,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_80,c_152]) ).
tcf(c_13044,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_13036,c_50]) ).
tcf(c_13054,plain,
aElementOf0(xx,xP),
inference(backward_subsumption_resolution,[status(thm)],[c_100,c_13044]) ).
tcf(c_13904,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ( X0 = xx )
| ~ aElementOf0(X0,xP) ),
inference(superposition,[status(thm)],[c_102,c_108]) ).
tcf(c_14147,plain,
( isFinite0(xP)
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_103,c_154]) ).
tcf(c_14148,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14147,c_13044,c_105]) ).
tcf(c_14186,plain,
( isFinite0(xP)
| ~ aElement0(xy)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_171,c_14148]) ).
tcf(c_14187,plain,
isFinite0(xP),
inference(forward_subsumption_resolution,[status(thm)],[c_14186,c_89,c_87,c_86]) ).
tcf(c_15737,plain,
( ( sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx) = sdtmndt0(xQ,xy) )
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_156,c_104]) ).
tcf(c_15810,plain,
( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(light_normalisation,[status(thm)],[c_15737,c_103]) ).
tcf(c_15811,plain,
sdtmndt0(xQ,xy) = sdtmndt0(xP,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_15810,c_13044,c_105]) ).
tcf(c_17445,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_90,c_170]) ).
tcf(c_17448,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xP) )
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_13054,c_170]) ).
tcf(c_17485,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP) )
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(light_normalisation,[status(thm)],[c_17448,c_15811]) ).
tcf(c_17486,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(forward_subsumption_resolution,[status(thm)],[c_17485,c_14187,c_98]) ).
tcf(c_17487,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(light_normalisation,[status(thm)],[c_17445,c_88]) ).
tcf(c_17488,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(forward_subsumption_resolution,[status(thm)],[c_17487,c_87,c_86]) ).
tcf(c_18511,plain,
sbrdtbr0(xP) = xk,
inference(demodulation,[status(thm)],[c_17486,c_17488]) ).
tcf(c_18513,plain,
( ~ aElementOf0(sK8,xS)
| ( xk != xk ) ),
inference(demodulation,[status(thm)],[c_110,c_18511]) ).
tcf(c_18514,plain,
( aElementOf0(sK8,xP)
| ( xk != xk ) ),
inference(demodulation,[status(thm)],[c_111,c_18511]) ).
tcf(c_18515,plain,
aElementOf0(sK8,xP),
inference(equality_resolution_simp,[status(thm)],[c_18514]) ).
tcf(c_18516,plain,
~ aElementOf0(sK8,xS),
inference(equality_resolution_simp,[status(thm)],[c_18513]) ).
tcf(c_18668,plain,
( aElementOf0(sK8,xQ)
| ( xx = sK8 ) ),
inference(superposition,[status(thm)],[c_18515,c_13904]) ).
tcf(c_18698,plain,
( aElementOf0(sK8,xS)
| ( xx = sK8 ) ),
inference(superposition,[status(thm)],[c_18668,c_82]) ).
tcf(c_18702,plain,
xx = sK8,
inference(forward_subsumption_resolution,[status(thm)],[c_18698,c_18516]) ).
tcf(c_18704,plain,
~ aElementOf0(xx,xS),
inference(demodulation,[status(thm)],[c_18516,c_18702]) ).
tcf(c_18706,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18704,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:41:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.13/1.61 % SZS status Started for theBenchmark.p
% 8.13/1.61 % SZS status Theorem for theBenchmark.p
% 8.13/1.61
% 8.13/1.61 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.13/1.61
% 8.13/1.61 % ------ iProver source info
% 8.13/1.61
% 8.13/1.61 % git: date: 2026-07-19 20:42:38 +0200
% 8.13/1.61 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.13/1.61 % git: non_committed_changes: false
% 8.13/1.61
% 8.13/1.61 % ------ Parsing...
% 8.13/1.61 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.13/1.61
% 8.13/1.61 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.13/1.61
% 8.13/1.61 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.13/1.61
% 8.13/1.61 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.13/1.61 % ------ Proving...
% 8.13/1.61 % ------ Problem Properties
% 8.13/1.61
% 8.13/1.61 %
% 8.13/1.61 % clauses 149
% 8.13/1.61 % conjectures 3
% 8.13/1.61 % EPR 44
% 8.13/1.61 % Horn 123
% 8.13/1.61 % unary 32
% 8.13/1.61 % binary 32
% 8.13/1.61 % lits 429
% 8.13/1.61 % lits eq 59
% 8.13/1.61 % fd_pure 0
% 8.13/1.61 % fd_pseudo 0
% 8.13/1.61 % fd_cond 6
% 8.13/1.61 % fd_pseudo_cond 14
% 8.13/1.61 % AC symbols 0
% 8.13/1.61
% 8.13/1.61 % ------ Schedule dynamic 5 is on
% 8.13/1.61
% 8.13/1.61 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.13/1.61
% 8.13/1.61
% 8.13/1.61 % ------
% 8.13/1.61 % Current options:
% 8.13/1.61 % ------
% 8.13/1.61
% 8.13/1.61
% 8.13/1.61 %
% 8.13/1.61
% 8.13/1.61 % ------ Proving...
% 8.13/1.61 %
% 8.13/1.61
% 8.13/1.61 % SZS status Theorem for theBenchmark.p
% 8.13/1.61
% 8.13/1.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.13/1.61
% 8.13/1.61
%------------------------------------------------------------------------------