%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM606+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 : n011.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 2.71s 1.28s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 23 unt; 9 def)
% Number of atoms : 213 ( 2 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 235 ( 104 ~; 100 |; 18 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(f98,axiom,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
fof(f100,axiom,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f101,conjecture,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f102,negated_conjecture,
~ aSubsetOf0(xQ,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f101]) ).
fof(f110,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(flattening,[],[f102]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f244,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f245,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f244]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f245]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f246]) ).
fof(f310,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f311,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f312,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f313,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f349,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f450,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f495,plain,
aSet0(xO),
inference(cnf_transformation,[],[f95]) ).
fof(f501,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[],[f98]) ).
fof(f504,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f505,plain,
~ aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f110]) ).
fof(f665,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f311,f450]) ).
fof(f667,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[],[f311,f504]) ).
fof(f670,definition,
( spl30_6
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[spl30_6])],[avatar_definition]) ).
fof(f671,plain,
( ~ aSet0(xO)
| spl30_6 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f673,definition,
( spl30_7
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl30_7])],[avatar_definition]) ).
fof(f675,plain,
( ~ spl30_6
| spl30_7 ),
inference(avatar_split_clause,[],[f667,f673,f670]) ).
fof(f677,definition,
( spl30_8
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl30_8])],[avatar_definition]) ).
fof(f678,plain,
( ~ aSet0(szNzAzT0)
| spl30_8 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f680,definition,
( spl30_9
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl30_9])],[avatar_definition]) ).
fof(f682,plain,
( ~ spl30_8
| spl30_9 ),
inference(avatar_split_clause,[],[f665,f680,f677]) ).
fof(f693,plain,
( $false
| spl30_6 ),
inference(resolution,[],[f671,f495]) ).
fof(f694,plain,
spl30_6,
inference(avatar_contradiction_clause,[],[f693]) ).
fof(f695,plain,
( $false
| spl30_8 ),
inference(resolution,[],[f678,f349]) ).
fof(f696,plain,
spl30_8,
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f895,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f310,f450]) ).
fof(f896,plain,
! [X0] :
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f310,f501]) ).
fof(f897,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO)
| ~ aSet0(xO) ),
inference(resolution,[],[f310,f504]) ).
fof(f900,definition,
( spl30_39
<=> ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO) ) ),
introduced(definition,[new_symbols(definition,[spl30_39])],[avatar_definition]) ).
fof(f901,plain,
( ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xO) )
| ~ spl30_39 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f902,plain,
( ~ spl30_6
| spl30_39 ),
inference(avatar_split_clause,[],[f897,f900,f670]) ).
fof(f904,definition,
( spl30_40
<=> ! [X0] :
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[spl30_40])],[avatar_definition]) ).
fof(f905,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) )
| ~ spl30_40 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f906,plain,
( ~ spl30_9
| spl30_40 ),
inference(avatar_split_clause,[],[f896,f904,f680]) ).
fof(f908,definition,
( spl30_41
<=> ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl30_41])],[avatar_definition]) ).
fof(f909,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
| ~ spl30_41 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f910,plain,
( ~ spl30_8
| spl30_41 ),
inference(avatar_split_clause,[],[f895,f908,f677]) ).
fof(f924,plain,
( ! [X0] :
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,szNzAzT0) )
| ~ spl30_40
| ~ spl30_41 ),
inference(resolution,[],[f909,f905]) ).
fof(f955,plain,
( ~ aSet0(xQ)
| aElementOf0(sK5(szNzAzT0,xQ),xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f312,f505]) ).
fof(f959,definition,
( spl30_46
<=> aElementOf0(sK5(szNzAzT0,xQ),xQ) ),
introduced(definition,[new_symbols(definition,[spl30_46])],[avatar_definition]) ).
fof(f960,plain,
( aElementOf0(sK5(szNzAzT0,xQ),xQ)
| ~ spl30_46 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f961,plain,
( ~ spl30_8
| spl30_46
| ~ spl30_7 ),
inference(avatar_split_clause,[],[f955,f673,f959,f677]) ).
fof(f1004,plain,
( aElementOf0(sK5(szNzAzT0,xQ),xO)
| ~ spl30_39
| ~ spl30_46 ),
inference(resolution,[],[f960,f901]) ).
fof(f1005,plain,
( aElementOf0(sK5(szNzAzT0,xQ),szNzAzT0)
| ~ spl30_39
| ~ spl30_40
| ~ spl30_41
| ~ spl30_46 ),
inference(resolution,[],[f1004,f924]) ).
fof(f1030,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(sK5(szNzAzT0,xQ),szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f313,f505]) ).
fof(f1034,definition,
( spl30_58
<=> aElementOf0(sK5(szNzAzT0,xQ),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl30_58])],[avatar_definition]) ).
fof(f1035,plain,
( ~ aElementOf0(sK5(szNzAzT0,xQ),szNzAzT0)
| spl30_58 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f1036,plain,
( ~ spl30_8
| ~ spl30_58
| ~ spl30_7 ),
inference(avatar_split_clause,[],[f1030,f673,f1034,f677]) ).
fof(f1061,plain,
( $false
| ~ spl30_39
| ~ spl30_40
| ~ spl30_41
| ~ spl30_46
| spl30_58 ),
inference(resolution,[],[f1035,f1005]) ).
fof(f1062,plain,
( ~ spl30_39
| ~ spl30_40
| ~ spl30_41
| ~ spl30_46
| spl30_58 ),
inference(avatar_contradiction_clause,[],[f1061]) ).
cnf(s5,plain,
( ~ spl30_6
| spl30_7 ),
inference(sat_conversion,[],[f675]) ).
cnf(s6,plain,
( ~ spl30_8
| spl30_9 ),
inference(sat_conversion,[],[f682]) ).
cnf(s10,plain,
spl30_6,
inference(sat_conversion,[],[f694]) ).
cnf(s11,plain,
spl30_8,
inference(sat_conversion,[],[f696]) ).
cnf(s34,plain,
( ~ spl30_6
| spl30_39 ),
inference(sat_conversion,[],[f902]) ).
cnf(s35,plain,
( ~ spl30_9
| spl30_40 ),
inference(sat_conversion,[],[f906]) ).
cnf(s36,plain,
( ~ spl30_8
| spl30_41 ),
inference(sat_conversion,[],[f910]) ).
cnf(s41,plain,
( ~ spl30_7
| ~ spl30_8
| spl30_46 ),
inference(sat_conversion,[],[f961]) ).
cnf(s56,plain,
( ~ spl30_7
| ~ spl30_8
| ~ spl30_58 ),
inference(sat_conversion,[],[f1036]) ).
cnf(s63,plain,
( ~ spl30_39
| ~ spl30_40
| ~ spl30_41
| ~ spl30_46
| spl30_58 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s84,plain,
spl30_41,
inference(rat,[],[s36,s11]) ).
cnf(s87,plain,
spl30_39,
inference(rat,[],[s34,s10]) ).
cnf(s94,plain,
spl30_9,
inference(rat,[],[s6,s11]) ).
cnf(s95,plain,
spl30_40,
inference(rat,[],[s35,s94]) ).
cnf(s97,plain,
spl30_7,
inference(rat,[],[s5,s10]) ).
cnf(s98,plain,
~ spl30_58,
inference(rat,[],[s56,s11,s97]) ).
cnf(s99,plain,
spl30_46,
inference(rat,[],[s41,s11,s97]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s63,s95,s87,s84,s98,s99]) ).
fof(f1063,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM606+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:43:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.71/1.28 % (2741413)Detected formulas, will run a generic FOF schedule.
% 2.71/1.28 % (2741419)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=745699075:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.28 % (2741421)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2030177303:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.28 % (2741422)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=216199281:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.28 % (2741420)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=2112248617:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.28 % (2741418)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=2609115784:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.28 % (2741424)dis-21_1_sil=8000:lcm=predicate:random_seed=1659993394: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)
% 2.71/1.28 % (2741423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2064114811:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.28 % (2741424)First to succeed.
% 2.71/1.28 % (2741424)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2741413"
% 2.71/1.28 % (2741422)Also succeeded, but the first one will report.
% 2.71/1.28 % (2741423)Also succeeded, but the first one will report.
% 2.71/1.28 % (2741421)Instruction limit reached!
% 2.71/1.28 % (2741421)------------------------------
% 2.71/1.28 % (2741421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.28 % (2741421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.28 % (2741421)CaDiCaL version: 2.1.3
% 2.71/1.28 % (2741421)Termination reason: Instruction limit
% 2.71/1.28 % (2741421)Termination phase: Saturation
% 2.71/1.28 % (2741421)Time elapsed: 0.063 s
% 2.71/1.28 % (2741421)Peak memory usage: 89 MB
% 2.71/1.28 % (2741421)Instructions burned: 111 (million)
% 2.71/1.28 % (2741432)lrs+10_1_sil=8000:sp=occurrence:random_seed=1912197626:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.28 % (2741424)Refutation found. Thanks to Tanya!
% 2.71/1.28 % SZS status Theorem for theBenchmark
% 2.71/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.37 % (2741424)------------------------------
% 3.43/1.37 % (2741424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.37 % (2741424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.37 % (2741424)CaDiCaL version: 2.1.3
% 3.43/1.37 % (2741424)Termination reason: Refutation
% 3.43/1.37 % (2741424)Time elapsed: 0.014 s
% 3.43/1.37 % (2741424)Peak memory usage: 90 MB
% 3.43/1.37 % (2741424)Instructions burned: 18 (million)
% 3.43/1.37 % (2741424)------------------------------
% 3.43/1.37 % (2741424)------------------------------
% 3.43/1.37 % (2741413)Success in time 0.421 s
% 3.43/1.37 % Vampire exiting
%------------------------------------------------------------------------------