%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM605+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 : n005.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 12:15:57 PM UTC 2026
% Result : Theorem 2.66s 1.27s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 20 unt; 2 def)
% Number of atoms : 191 ( 68 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 228 ( 88 ~; 83 |; 43 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
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(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(f78,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(f99,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(f100,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f101,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f109,plain,
slcrc0 = xQ,
inference(flattening,[],[f101]) ).
fof(f111,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f160,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f184,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(f185,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,[],[f184]) ).
fof(f239,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f111]) ).
fof(f240,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f241]) ).
fof(f262,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f160]) ).
fof(f280,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,[],[f185]) ).
fof(f281,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,[],[f280]) ).
fof(f282,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,[],[f281]) ).
fof(f283,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))],[f282]) ).
fof(f304,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f242]) ).
fof(f370,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f402,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f447,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f457,plain,
sz00 != xK,
inference(cnf_transformation,[],[f78]) ).
fof(f494,plain,
aSet0(xO),
inference(cnf_transformation,[],[f95]) ).
fof(f501,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[],[f99]) ).
fof(f502,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f109]) ).
fof(f503,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f304]) ).
fof(f510,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f370]) ).
fof(f524,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f402]) ).
fof(f542,definition,
( spl29_1
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f546,definition,
( spl29_2
<=> sz00 = sbrdtbr0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f548,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f549,plain,
( ~ spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f510,f546,f542]) ).
fof(f555,plain,
spl29_1,
inference(avatar_split_clause,[],[f503,f542]) ).
fof(f556,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xO,xK)),
inference(forward_demodulation,[],[f501,f502]) ).
fof(f793,plain,
( xK = sbrdtbr0(slcrc0)
| ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(resolution,[],[f524,f556]) ).
fof(f798,plain,
( xK = sbrdtbr0(slcrc0)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f793,f494]) ).
fof(f800,plain,
xK = sbrdtbr0(slcrc0),
inference(forward_subsumption_resolution,[],[f798,f447]) ).
fof(f801,plain,
( sz00 = xK
| ~ spl29_2 ),
inference(forward_demodulation,[],[f800,f548]) ).
fof(f802,plain,
( $false
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f801,f457]) ).
fof(f803,plain,
~ spl29_2,
inference(avatar_contradiction_clause,[],[f802]) ).
cnf(s1,plain,
( ~ spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f549]) ).
cnf(s3,plain,
spl29_1,
inference(sat_conversion,[],[f555]) ).
cnf(s20,plain,
~ spl29_2,
inference(sat_conversion,[],[f803]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s20,s3]) ).
fof(f804,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:43:17 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.66/1.27 % (146328)Detected formulas, will run a generic FOF schedule.
% 2.66/1.27 % (146449)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3175870356:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.27 % (146449)Instruction limit reached!
% 2.66/1.27 % (146449)------------------------------
% 2.66/1.27 % (146449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (146449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (146449)CaDiCaL version: 2.1.3
% 2.66/1.27 % (146449)Termination reason: Instruction limit
% 2.66/1.27 % (146449)Termination phase: Saturation
% 2.66/1.27 % (146449)Time elapsed: 0.036 s
% 2.66/1.27 % (146449)Peak memory usage: 89 MB
% 2.66/1.27 % (146449)Instructions burned: 109 (million)
% 2.66/1.27 % (146452)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=398301125:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.27 % (146443)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=2987433568:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.27 % (146446)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=3305416251:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.27 % (146444)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=628707983:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.27 % (146451)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3647556986:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.27 % (146454)dis-21_1_sil=8000:lcm=predicate:random_seed=6090573: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)
% 2.66/1.27 % (146452)First to succeed.
% 2.66/1.27 % (146452)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-146328"
% 2.66/1.27 % (146454)Instruction limit reached!
% 2.66/1.27 % (146454)------------------------------
% 2.66/1.27 % (146454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (146454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (146454)CaDiCaL version: 2.1.3
% 2.66/1.27 % (146454)Termination reason: Instruction limit
% 2.66/1.27 % (146454)Termination phase: Saturation
% 2.66/1.27 % (146454)Time elapsed: 0.063 s
% 2.66/1.27 % (146454)Peak memory usage: 89 MB
% 2.66/1.27 % (146454)Instructions burned: 131 (million)
% 2.66/1.27 % (146451)Instruction limit reached!
% 2.66/1.27 % (146451)------------------------------
% 2.66/1.27 % (146451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (146451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (146451)CaDiCaL version: 2.1.3
% 2.66/1.27 % (146451)Termination reason: Instruction limit
% 2.66/1.27 % (146451)Termination phase: Saturation
% 2.66/1.27 % (146451)Time elapsed: 0.064 s
% 2.66/1.27 % (146451)Peak memory usage: 88 MB
% 2.66/1.27 % (146451)Instructions burned: 119 (million)
% 2.66/1.27 % (146471)lrs+10_1_sil=8000:sp=occurrence:random_seed=1679032740:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.66/1.27 % (146471)Also succeeded, but the first one will report.
% 2.66/1.27 % (146477)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1587950431:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.66/1.27 % (146478)lrs+1011_1_sil=32000:sp=occurrence:random_seed=786547613:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.66/1.27 % (146477)Refutation not found, incomplete strategy
% 2.66/1.27 % (146477)------------------------------
% 2.66/1.27 % (146477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.27 % (146477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.27 % (146477)CaDiCaL version: 2.1.3
% 2.66/1.27 % (146477)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.27 % (146477)Time elapsed: 0.002 s
% 2.66/1.27 % (146477)Peak memory usage: 89 MB
% 2.66/1.27 % (146477)Instructions burned: 1 (million)
% 2.66/1.27 % (146478)Also succeeded, but the first one will report.
% 2.66/1.27 % (146452)Refutation found. Thanks to Tanya!
% 2.66/1.27 % SZS status Theorem for theBenchmark
% 3.55/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.46 % (146452)------------------------------
% 3.55/1.46 % (146452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.46 % (146452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.46 % (146452)CaDiCaL version: 2.1.3
% 3.55/1.46 % (146452)Termination reason: Refutation
% 3.55/1.46 % (146452)Time elapsed: 0.016 s
% 3.55/1.46 % (146452)Peak memory usage: 90 MB
% 3.55/1.46 % (146452)Instructions burned: 20 (million)
% 3.55/1.46 % (146452)------------------------------
% 3.55/1.46 % (146452)------------------------------
% 3.55/1.46 % (146328)Success in time 0.417 s
% 3.55/1.46 % Vampire exiting
%------------------------------------------------------------------------------