%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Tue Sep 29 12:15:43 PM UTC 2026
% Result : Theorem 8.31s 2.44s
% Output : Refutation 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 2 def)
% Number of atoms : 160 ( 30 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 204 ( 76 ~; 68 |; 50 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 60 ( 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f66,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(f68,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
fof(f71,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f73,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(flattening,[],[f72]) ).
fof(f124,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f124]) ).
fof(f148,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f149,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f150,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f125,f149,f148]) ).
fof(f173,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f149]) ).
fof(f174,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f173]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f148]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| X2 = X3
| ~ aElementOf0(X3,X0) )
& ( ( aElement0(X3)
& aElementOf0(X3,X1)
& X2 != X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK10(X0,X1,X2))
| ~ aElementOf0(sK10(X0,X1,X2),X1)
| sK10(X0,X1,X2) = X2
| ~ aElementOf0(sK10(X0,X1,X2),X0) )
& ( ( aElement0(sK10(X0,X1,X2))
& aElementOf0(sK10(X0,X1,X2),X1)
& sK10(X0,X1,X2) != X2 )
| aElementOf0(sK10(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f177]) ).
fof(f190,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f192,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f193,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f196,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f73]) ).
fof(f254,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
fof(f257,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f265,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f290,plain,
! [X0,X1] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f254]) ).
fof(f356,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,sdtmndt0(X1,X2))
| aElementOf0(X0,X1)
| ~ sP3(X2,X1) ),
inference(resolution,[],[f257,f290]) ).
fof(f925,plain,
( aElementOf0(xx,xQ)
| ~ sP3(xy,xQ) ),
inference(resolution,[],[f356,f196]) ).
fof(f935,plain,
~ sP3(xy,xQ),
inference(forward_subsumption_resolution,[],[f925,f193]) ).
fof(f937,plain,
( ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(resolution,[],[f935,f265]) ).
fof(f938,plain,
~ aElement0(xy),
inference(forward_subsumption_resolution,[],[f937,f190]) ).
fof(f939,plain,
$false,
inference(forward_subsumption_resolution,[],[f938,f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 20:28:01 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.31/2.44 % (1138673)Detected formulas, will run a generic FOF schedule.
% 8.31/2.44 % (1138681)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=2126779859:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.31/2.44 % (1138680)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=1061039946:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.31/2.44 % (1138682)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2757648209:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.31/2.44 % (1138684)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=713272119:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.31/2.44 % (1138679)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=2809067338:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.31/2.44 % (1138683)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2407141879:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.31/2.44 % (1138683)First to succeed.
% 8.31/2.44 % (1138683)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1138673"
% 8.31/2.44 % (1138685)dis-21_1_sil=8000:lcm=predicate:random_seed=1471083269: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)
% 8.31/2.44 % (1138682)Also succeeded, but the first one will report.
% 8.31/2.44 % (1138684)Instruction limit reached!
% 8.31/2.44 % (1138684)------------------------------
% 8.31/2.44 % (1138684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.44 % (1138684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.44 % (1138684)CaDiCaL version: 2.1.3
% 8.31/2.44 % (1138684)Termination reason: Instruction limit
% 8.31/2.44 % (1138684)Termination phase: Saturation
% 8.31/2.44 % (1138684)Time elapsed: 0.153 s
% 8.31/2.44 % (1138684)Peak memory usage: 90 MB
% 8.31/2.44 % (1138684)Instructions burned: 139 (million)
% 8.31/2.44 % (1138685)Instruction limit reached!
% 8.31/2.44 % (1138685)------------------------------
% 8.31/2.44 % (1138685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.44 % (1138685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.44 % (1138685)CaDiCaL version: 2.1.3
% 8.31/2.44 % (1138685)Termination reason: Instruction limit
% 8.31/2.44 % (1138685)Termination phase: Saturation
% 8.31/2.44 % (1138685)Time elapsed: 0.096 s
% 8.31/2.44 % (1138685)Peak memory usage: 88 MB
% 8.31/2.44 % (1138685)Instructions burned: 129 (million)
% 8.31/2.44 % (1138694)lrs+10_1_sil=8000:sp=occurrence:random_seed=3765904518:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 8.31/2.44 % (1138695)lrs+10_1_sil=32000:urr=on:br=off:random_seed=575030922:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 8.31/2.44 % (1138695)Also succeeded, but the first one will report.
% 8.31/2.44 % (1138694)Also succeeded, but the first one will report.
% 8.31/2.44 % (1138681)Also succeeded, but the first one will report.
% 8.31/2.44 % (1138698)lrs+1011_1_sil=32000:sp=occurrence:random_seed=122431940:i=325:sd=1:ss=axioms:sgt=32_2992 on theBenchmark for (2992ds/325Mi)
% 8.31/2.44 % (1138683)Refutation found. Thanks to Tanya!
% 8.31/2.44 % SZS status Theorem for theBenchmark
% 8.31/2.44 % SZS output start Proof for theBenchmark
% See solution above
% 8.31/2.44 % (1138683)------------------------------
% 8.31/2.44 % (1138683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.31/2.44 % (1138683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.31/2.44 % (1138683)CaDiCaL version: 2.1.3
% 8.31/2.44 % (1138683)Termination reason: Refutation
% 8.31/2.44 % (1138683)Time elapsed: 0.031 s
% 8.31/2.44 % (1138683)Peak memory usage: 88 MB
% 8.31/2.44 % (1138683)Instructions burned: 28 (million)
% 8.31/2.44 % (1138683)------------------------------
% 8.31/2.44 % (1138683)------------------------------
% 8.31/2.44 % (1138673)Success in time 1.115 s
% 8.31/2.44 % Vampire exiting
%------------------------------------------------------------------------------