%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 209.56s 29.48s
% Output : CNFRefutation 209.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 37 unt; 0 def)
% Number of atoms : 301 ( 63 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 322 ( 124 ~; 122 |; 59 &)
% ( 4 <=>; 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 : 71 ( 0 sgn 70 !; 1 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(f21,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(f22,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(f62,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(f69,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2338) ).
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/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(f71,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f80,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(f82,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(flattening,[],[f101]) ).
fof(f107,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f108,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f110,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ) ),
inference(flattening,[],[f109]) ).
fof(f134,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f135,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ),
inference(flattening,[],[f134]) ).
fof(f165,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(f166,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& ? [X0] :
( aElementOf0(X0,xP)
& ~ aElementOf0(X0,xS) ) ) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f220,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,[],[f80]) ).
fof(f221,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,[],[f220]) ).
fof(f222,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( xk != sbrdtbr0(xP)
| ( ~ aSubsetOf0(xP,xS)
& aElementOf0(sK19,xP)
& ~ aElementOf0(sK19,xS) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f166]) ).
fof(f223,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f263,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aElement0(X0)
| aElementOf0(X0,X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f266,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtpldt0(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f267,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f292,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ),
inference(cnf_transformation,[],[f135]) ).
fof(f335,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f363,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f367,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f165]) ).
fof(f369,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f370,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f371,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f372,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f67]) ).
fof(f373,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f375,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f69]) ).
fof(f376,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f221]) ).
fof(f377,plain,
! [X1] :
( ~ aElementOf0(X1,xP)
| xx = X1
| aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f379,plain,
! [X1] :
( xx != X1
| ~ aElement0(X1)
| aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f221]) ).
fof(f381,plain,
aSet0(xP),
inference(cnf_transformation,[],[f221]) ).
fof(f383,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f221]) ).
fof(f386,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f221]) ).
fof(f389,plain,
( xk != sbrdtbr0(xP)
| aElementOf0(sK19,xP) ),
inference(cnf_transformation,[],[f222]) ).
fof(f390,plain,
( xk != sbrdtbr0(xP)
| ~ aElementOf0(sK19,xS) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[],[f379]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ( sdtmndt0(sdtpldt0(X1,X0),X0) = X1 )
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) )
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_159,plain,
aSet0(xS),
inference(cnf_transformation,[],[f335]) ).
tcf(c_189,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f363]) ).
tcf(c_191,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_195,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_196,plain,
isFinite0(xQ),
inference(cnf_transformation,[],[f370]) ).
tcf(c_197,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[],[f369]) ).
tcf(c_198,plain,
aElement0(xy),
inference(cnf_transformation,[],[f373]) ).
tcf(c_199,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_201,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_202,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f386]) ).
tcf(c_205,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_207,plain,
aSet0(xP),
inference(cnf_transformation,[],[f381]) ).
tcf(c_209,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_211,plain,
! [X0: $i] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
| ( X0 = xx )
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[],[f377]) ).
tcf(c_212,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(cnf_transformation,[],[f376]) ).
tcf(c_213,negated_conjecture,
( ~ aElementOf0(sK19,xS)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_214,negated_conjecture,
( aElementOf0(sK19,xP)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_36192,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_189,c_49]) ).
tcf(c_36196,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_36192,c_159]) ).
tcf(c_36199,plain,
aElementOf0(xx,xP),
inference(backward_subsumption_resolution,[status(thm)],[c_209,c_36196]) ).
tcf(c_36284,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ( X0 = xx )
| ~ aElementOf0(X0,xP) ),
inference(superposition,[status(thm)],[c_211,c_205]) ).
tcf(c_36452,plain,
( isFinite0(xP)
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_212,c_92]) ).
tcf(c_36453,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36452,c_36196,c_202]) ).
tcf(c_36455,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(superposition,[status(thm)],[c_93,c_36453]) ).
tcf(c_36456,plain,
isFinite0(xP),
inference(forward_subsumption_resolution,[status(thm)],[c_36455,c_196,c_195,c_198]) ).
tcf(c_37631,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ( sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),X0),X0) = sdtmndt0(xQ,xy) )
| ~ aElement0(X0)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[c_89,c_205]) ).
tcf(c_37671,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ( sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),X0),X0) = sdtmndt0(xQ,xy) )
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37631,c_202]) ).
tcf(c_38183,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xQ) )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm)],[c_199,c_118]) ).
tcf(c_38186,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xP) )
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm)],[c_36199,c_118]) ).
tcf(c_38203,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xP),
inference(forward_subsumption_resolution,[status(thm)],[c_38186,c_36456,c_207]) ).
tcf(c_38204,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk )
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(demodulation,[status(thm)],[c_38183,c_197]) ).
tcf(c_38205,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(forward_subsumption_resolution,[status(thm)],[c_38204,c_196,c_195]) ).
tcf(c_51337,plain,
( ( sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx) = sdtmndt0(xQ,xy) )
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_37671,c_201]) ).
tcf(c_51339,plain,
( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
| ~ aElement0(xx) ),
inference(demodulation,[status(thm)],[c_51337,c_212]) ).
tcf(c_51340,plain,
sdtmndt0(xQ,xy) = sdtmndt0(xP,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_51339,c_36196]) ).
tcf(c_51351,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(demodulation,[status(thm)],[c_38203,c_51340]) ).
tcf(c_51352,plain,
sbrdtbr0(xP) = xk,
inference(demodulation,[status(thm)],[c_51351,c_38205]) ).
tcf(c_51400,plain,
( ~ aElementOf0(sK19,xS)
| ( xk != xk ) ),
inference(demodulation,[status(thm)],[c_213,c_51352]) ).
tcf(c_51401,plain,
( aElementOf0(sK19,xP)
| ( xk != xk ) ),
inference(demodulation,[status(thm)],[c_214,c_51352]) ).
tcf(c_51418,plain,
aElementOf0(sK19,xP),
inference(equality_resolution_simp,[status(thm)],[c_51401]) ).
tcf(c_51419,plain,
~ aElementOf0(sK19,xS),
inference(equality_resolution_simp,[status(thm)],[c_51400]) ).
tcf(c_51577,plain,
( aElementOf0(sK19,xQ)
| ( xx = sK19 ) ),
inference(superposition,[status(thm)],[c_51418,c_36284]) ).
tcf(c_51627,plain,
( aElementOf0(sK19,xS)
| ( xx = sK19 ) ),
inference(superposition,[status(thm)],[c_51577,c_191]) ).
tcf(c_51628,plain,
xx = sK19,
inference(forward_subsumption_resolution,[status(thm)],[c_51627,c_51419]) ).
tcf(c_51630,plain,
~ aElementOf0(xx,xS),
inference(demodulation,[status(thm)],[c_51419,c_51628]) ).
tcf(c_51632,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_51630,c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:35:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 209.56/29.48 % SZS status Started for theBenchmark.p
% 209.56/29.48 % SZS status Theorem for theBenchmark.p
% 209.56/29.48
% 209.56/29.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 209.56/29.48
% 209.56/29.48 % ------ iProver source info
% 209.56/29.48
% 209.56/29.48 % git: date: 2026-07-19 20:42:38 +0200
% 209.56/29.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 209.56/29.48 % git: non_committed_changes: false
% 209.56/29.48
% 209.56/29.48 % ------ Parsing...
% 209.56/29.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 209.56/29.48
% 209.56/29.48 % ------ 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 %
% 209.56/29.48
% 209.56/29.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 209.56/29.48
% 209.56/29.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 209.56/29.48 % ------ Proving...
% 209.56/29.48 % ------ Problem Properties
% 209.56/29.48
% 209.56/29.48 %
% 209.56/29.48 % clauses 158
% 209.56/29.48 % conjectures 4
% 209.56/29.48 % EPR 44
% 209.56/29.48 % Horn 123
% 209.56/29.48 % unary 32
% 209.56/29.48 % binary 32
% 209.56/29.48 % lits 475
% 209.56/29.48 % lits eq 74
% 209.56/29.48 % fd_pure 0
% 209.56/29.48 % fd_pseudo 0
% 209.56/29.48 % fd_cond 11
% 209.56/29.48 % fd_pseudo_cond 18
% 209.56/29.48 % AC symbols 0
% 209.56/29.48
% 209.56/29.48 % ------ Input Options Time Limit: Unbounded
% 209.56/29.48
% 209.56/29.48
% 209.56/29.48 % ------
% 209.56/29.48 % Current options:
% 209.56/29.48 % ------
% 209.56/29.48
% 209.56/29.48
% 209.56/29.48 %
% 209.56/29.48
% 209.56/29.48 % ------ Proving...
% 209.56/29.48 %
% 209.56/29.48
% 209.56/29.48 % SZS status Theorem for theBenchmark.p
% 209.56/29.48
% 209.56/29.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 209.56/29.48
% 209.56/29.48
%------------------------------------------------------------------------------