%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:15:44 PM UTC 2026
% Result : Theorem 2.77s 1.34s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 158 ( 40 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 203 ( 83 ~; 78 |; 35 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 46 ( 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f70,axiom,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f71,axiom,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2411) ).
fof(f72,axiom,
( aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).
fof(f73,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f74,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f75,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(flattening,[],[f74]) ).
fof(f100,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(f101,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,[],[f100]) ).
fof(f150,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,[],[f101]) ).
fof(f151,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,[],[f150]) ).
fof(f152,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,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK7(X0,X1,X2),X0)
| sbrdtbr0(sK7(X0,X1,X2)) != X1
| ~ aElementOf0(sK7(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK7(X0,X1,X2),X0)
& sbrdtbr0(sK7(X0,X1,X2)) = X1 )
| aElementOf0(sK7(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,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f152]) ).
fof(f169,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f172,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f184,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[],[f70]) ).
fof(f185,plain,
xk = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),
inference(cnf_transformation,[],[f71]) ).
fof(f187,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f72]) ).
fof(f188,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[],[f72]) ).
fof(f189,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f75]) ).
fof(f216,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f282,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f216]) ).
fof(f283,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f282]) ).
fof(f302,plain,
aElementOf0(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),szNzAzT0),
inference(forward_demodulation,[],[f169,f185]) ).
fof(f406,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f283,f187]) ).
fof(f407,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_demodulation,[],[f406,f185]) ).
fof(f416,plain,
! [X0] :
( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(X0,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_demodulation,[],[f407,f184]) ).
fof(f424,plain,
! [X0] :
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),X0)
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(X0,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))))
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_demodulation,[],[f416,f184]) ).
fof(f431,plain,
! [X0] :
( ~ aElementOf0(szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))),szNzAzT0)
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),X0)
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(X0,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))))
| ~ aSet0(X0) ),
inference(forward_demodulation,[],[f424,f185]) ).
fof(f437,plain,
! [X0] :
( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(X0,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f431,f302]) ).
fof(f495,plain,
aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xS),
inference(superposition,[],[f188,f184]) ).
fof(f496,plain,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk)),
inference(superposition,[],[f189,f184]) ).
fof(f497,plain,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))))),
inference(forward_demodulation,[],[f496,f185]) ).
fof(f1795,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f437,f497]) ).
fof(f1820,plain,
~ aSet0(xS),
inference(forward_subsumption_resolution,[],[f1795,f495]) ).
fof(f1830,plain,
$false,
inference(forward_subsumption_resolution,[],[f1820,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.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 : Sun Sep 27 20:29:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.77/1.34 % (2373658)Detected formulas, will run a generic FOF schedule.
% 2.77/1.34 % (2373666)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=840339501:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.34 % (2373666)First to succeed.
% 2.77/1.34 % (2373666)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2373658"
% 2.77/1.34 % (2373669)dis-21_1_sil=8000:lcm=predicate:random_seed=1395618861:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.77/1.34 % (2373663)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3607743474:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.34 % (2373667)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=267545738:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.34 % (2373665)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3637213028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.34 % (2373664)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3832831565:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.34 % (2373668)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4106588545:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.34 % (2373668)Also succeeded, but the first one will report.
% 2.77/1.34 % (2373667)Also succeeded, but the first one will report.
% 2.77/1.34 % (2373669)Instruction limit reached!
% 2.77/1.34 % (2373669)------------------------------
% 2.77/1.34 % (2373669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (2373669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (2373669)CaDiCaL version: 2.1.3
% 2.77/1.34 % (2373669)Termination reason: Instruction limit
% 2.77/1.34 % (2373669)Termination phase: Saturation
% 2.77/1.34 % (2373669)Time elapsed: 0.061 s
% 2.77/1.34 % (2373669)Peak memory usage: 88 MB
% 2.77/1.34 % (2373669)Instructions burned: 130 (million)
% 2.77/1.34 % (2373666)Refutation found. Thanks to Tanya!
% 2.77/1.34 % SZS status Theorem for theBenchmark
% 2.77/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.34 % (2373666)------------------------------
% 2.77/1.34 % (2373666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (2373666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (2373666)CaDiCaL version: 2.1.3
% 2.77/1.34 % (2373666)Termination reason: Refutation
% 2.77/1.34 % (2373666)Time elapsed: 0.019 s
% 2.77/1.34 % (2373666)Peak memory usage: 89 MB
% 2.77/1.34 % (2373666)Instructions burned: 47 (million)
% 2.77/1.34 % (2373666)------------------------------
% 2.77/1.34 % (2373666)------------------------------
% 2.77/1.34 % (2373658)Success in time 0.309 s
% 2.77/1.34 % Vampire exiting
%------------------------------------------------------------------------------