%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:41:59 PM UTC 2026
% Result : Theorem 2.23s 1.30s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 11 unt; 5 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 226 ( 86 ~; 87 |; 36 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( member(X1,X0)
=> subset(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV10) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> equal_set(X0,intersection(X0,power_set(X0))) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f24,plain,
? [X0] :
( ~ equal_set(X0,intersection(X0,power_set(X0)))
& member(X0,on) ),
inference(ennf_transformation,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
( ~ equal_set(sK1,intersection(sK1,power_set(sK1)))
& member(sK1,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f24]) ).
fof(f39,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f43]) ).
fof(f45,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ( ~ subset(sK3(X0),X0)
& member(sK3(X0),X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f47]) ).
fof(f67,plain,
member(sK1,on),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
~ equal_set(sK1,intersection(sK1,power_set(sK1))),
inference(cnf_transformation,[],[f38]) ).
fof(f70,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f76,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f77,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f78,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ member(X2,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f48]) ).
fof(f126,plain,
( ~ subset(sK1,intersection(sK1,power_set(sK1)))
| ~ subset(intersection(sK1,power_set(sK1)),sK1) ),
inference(resolution,[],[f77,f68]) ).
fof(f128,definition,
( spl14_1
<=> subset(intersection(sK1,power_set(sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f129,plain,
( ~ subset(intersection(sK1,power_set(sK1)),sK1)
| spl14_1 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,definition,
( spl14_2
<=> subset(sK1,intersection(sK1,power_set(sK1))) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f132,plain,
( ~ subset(sK1,intersection(sK1,power_set(sK1)))
| spl14_2 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f126,f131,f128]) ).
fof(f134,plain,
( ~ member(sK2(intersection(sK1,power_set(sK1)),sK1),sK1)
| spl14_1 ),
inference(resolution,[],[f129,f76]) ).
fof(f135,plain,
( member(sK2(intersection(sK1,power_set(sK1)),sK1),intersection(sK1,power_set(sK1)))
| spl14_1 ),
inference(resolution,[],[f129,f75]) ).
fof(f137,plain,
( member(sK2(intersection(sK1,power_set(sK1)),sK1),sK1)
| spl14_1 ),
inference(resolution,[],[f135,f72]) ).
fof(f139,plain,
( $false
| spl14_1 ),
inference(resolution,[],[f137,f134]) ).
fof(f140,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f141,plain,
( ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),intersection(sK1,power_set(sK1)))
| spl14_2 ),
inference(resolution,[],[f132,f76]) ).
fof(f142,plain,
( member(sK2(sK1,intersection(sK1,power_set(sK1))),sK1)
| spl14_2 ),
inference(resolution,[],[f132,f75]) ).
fof(f145,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(X1,on)
| ~ member(X0,X1) ),
inference(resolution,[],[f78,f70]) ).
fof(f160,plain,
( ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),sK1)
| ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),power_set(sK1))
| spl14_2 ),
inference(resolution,[],[f73,f141]) ).
fof(f162,definition,
( spl14_5
<=> member(sK2(sK1,intersection(sK1,power_set(sK1))),power_set(sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f163,plain,
( ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),power_set(sK1))
| spl14_5 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,definition,
( spl14_6
<=> member(sK2(sK1,intersection(sK1,power_set(sK1))),sK1) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f166,plain,
( ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),sK1)
| spl14_6 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f167,plain,
( ~ spl14_5
| ~ spl14_6
| spl14_2 ),
inference(avatar_split_clause,[],[f160,f131,f165,f162]) ).
fof(f290,plain,
( ~ member(sK1,on)
| ~ member(sK2(sK1,intersection(sK1,power_set(sK1))),sK1)
| spl14_5 ),
inference(resolution,[],[f145,f163]) ).
fof(f296,definition,
( spl14_12
<=> member(sK1,on) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
fof(f297,plain,
( ~ member(sK1,on)
| spl14_12 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( ~ spl14_6
| ~ spl14_12
| spl14_5 ),
inference(avatar_split_clause,[],[f290,f162,f296,f165]) ).
fof(f358,plain,
( $false
| spl14_12 ),
inference(resolution,[],[f297,f67]) ).
fof(f360,plain,
spl14_12,
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f361,plain,
( $false
| spl14_2
| spl14_6 ),
inference(resolution,[],[f166,f142]) ).
fof(f364,plain,
( spl14_2
| spl14_6 ),
inference(avatar_contradiction_clause,[],[f361]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f133]) ).
cnf(s2,plain,
spl14_1,
inference(sat_conversion,[],[f140]) ).
cnf(s4,plain,
( spl14_2
| ~ spl14_5
| ~ spl14_6 ),
inference(sat_conversion,[],[f167]) ).
cnf(s10,plain,
( spl14_5
| ~ spl14_6
| ~ spl14_12 ),
inference(sat_conversion,[],[f298]) ).
cnf(s22,plain,
spl14_12,
inference(sat_conversion,[],[f360]) ).
cnf(s23,plain,
( spl14_2
| spl14_6 ),
inference(sat_conversion,[],[f364]) ).
cnf(s25,plain,
( spl14_5
| ~ spl14_6 ),
inference(rat,[],[s10,s22]) ).
cnf(s26,plain,
~ spl14_2,
inference(rat,[],[s1,s2]) ).
cnf(s27,plain,
spl14_6,
inference(rat,[],[s23,s26]) ).
cnf(s29,plain,
~ spl14_5,
inference(rat,[],[s4,s27,s26]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s25,s27,s29]) ).
fof(f366,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:51:37 UTC 2026
% 0.03/0.38 % CPUTime :
% 0.03/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.42 Running first-order theorem proving
% 0.03/0.42 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
% 2.23/1.30 % (1392302)Detected formulas, will run a generic FOF schedule.
% 2.23/1.30 % (1392311)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2481742590:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.23/1.30 % (1392307)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=1009972564:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.23/1.30 % (1392309)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=498903779:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.23/1.30 % (1392308)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=610720532:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.23/1.30 % (1392310)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3401894691:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.23/1.30 % (1392310)Refutation not found, incomplete strategy
% 2.23/1.30 % (1392310)------------------------------
% 2.23/1.30 % (1392310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.30 % (1392310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.30 % (1392310)CaDiCaL version: 2.1.3
% 2.23/1.30 % (1392310)Termination reason: Refutation not found, incomplete strategy
% 2.23/1.30 % (1392310)Time elapsed: 0.002 s
% 2.23/1.30 % (1392310)Peak memory usage: 88 MB
% 2.23/1.30 % (1392313)dis-21_1_sil=8000:lcm=predicate:random_seed=2695567366: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)
% 2.23/1.30 % (1392312)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=875816919:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.23/1.30 % (1392311)Instruction limit reached!
% 2.23/1.30 % (1392311)------------------------------
% 2.23/1.30 % (1392311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.30 % (1392311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.30 % (1392311)CaDiCaL version: 2.1.3
% 2.23/1.30 % (1392311)Termination reason: Instruction limit
% 2.23/1.30 % (1392311)Termination phase: Saturation
% 2.23/1.30 % (1392311)Time elapsed: 0.042 s
% 2.23/1.30 % (1392311)Peak memory usage: 89 MB
% 2.23/1.30 % (1392311)Instructions burned: 123 (million)
% 2.23/1.30 % (1392313)First to succeed.
% 2.23/1.30 % (1392313)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1392302"
% 2.23/1.30 % (1392312)Also succeeded, but the first one will report.
% 2.23/1.30 % (1392321)lrs+10_1_sil=8000:sp=occurrence:random_seed=121145035:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.23/1.30 % (1392310)------------------------------
% 2.23/1.30 % (1392310)------------------------------
% 2.23/1.30 % (1392321)Instruction limit reached!
% 2.23/1.30 % (1392321)------------------------------
% 2.23/1.30 % (1392321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.30 % (1392321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.30 % (1392321)CaDiCaL version: 2.1.3
% 2.23/1.30 % (1392321)Termination reason: Instruction limit
% 2.23/1.30 % (1392321)Termination phase: Saturation
% 2.23/1.30 % (1392321)Time elapsed: 0.093 s
% 2.23/1.30 % (1392321)Peak memory usage: 92 MB
% 2.23/1.30 % (1392321)Instructions burned: 288 (million)
% 2.23/1.30 % (1392313)Refutation found. Thanks to Tanya!
% 2.23/1.30 % SZS status Theorem for theBenchmark
% 2.23/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (1392313)------------------------------
% 0.16/1.50 % (1392313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1392313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1392313)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1392313)Termination reason: Refutation
% 0.16/1.50 % (1392313)Time elapsed: 0.007 s
% 0.16/1.50 % (1392313)Peak memory usage: 89 MB
% 0.16/1.50 % (1392313)Instructions burned: 8 (million)
% 0.16/1.50 % (1392313)------------------------------
% 0.16/1.50 % (1392313)------------------------------
% 0.16/1.50 % (1392302)Success in time 0.439 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------