%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET811+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 : n016.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 3.12s 1.35s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 10 unt; 2 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 208 ( 76 ~; 78 |; 38 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 86 !; 7 ?)
% 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(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(f15,axiom,
! [X0,X1] :
( apply(member_predicate,X0,X1)
<=> member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( member(X3,initial_segment(X0,X1,X2))
<=> ( member(X3,X2)
& apply(X1,X3,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_segment) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> ! [X1] :
( member(X1,X0)
=> equal_set(X1,initial_segment(X1,member_predicate,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV5) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ! [X1] :
( member(X1,X0)
=> equal_set(X1,initial_segment(X1,member_predicate,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,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f25]) ).
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(f36,plain,
? [X0] :
( ? [X1] :
( ~ equal_set(X1,initial_segment(X1,member_predicate,X0))
& member(X1,X0) )
& member(X0,on) ),
inference(ennf_transformation,[],[f21]) ).
fof(f39,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,[],[f24]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f40]) ).
fof(f58,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(f59,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,[],[f58]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ( ~ subset(sK4(X0),X0)
& member(sK4(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,[sK4]),skolemize(X1,sK4(X0))],[f60]) ).
fof(f70,plain,
! [X0,X1] :
( ( apply(member_predicate,X0,X1)
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ( member(X3,initial_segment(X0,X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X3,X0) )
& ( ( member(X3,X2)
& apply(X1,X3,X0) )
| ~ member(X3,initial_segment(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( member(X3,initial_segment(X0,X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X3,X0) )
& ( ( member(X3,X2)
& apply(X1,X3,X0) )
| ~ member(X3,initial_segment(X0,X1,X2)) ) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
( ~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14))
& member(sK15,sK14)
& member(sK14,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f36]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f109,plain,
! [X2,X0] :
( ~ member(X0,on)
| ~ member(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f124,plain,
! [X0,X1] :
( ~ apply(member_predicate,X0,X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f125,plain,
! [X0,X1] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,initial_segment(X0,X1,X2))
| apply(X1,X3,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X3,initial_segment(X0,X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f145,plain,
member(sK14,on),
inference(cnf_transformation,[],[f81]) ).
fof(f146,plain,
member(sK15,sK14),
inference(cnf_transformation,[],[f81]) ).
fof(f147,plain,
~ equal_set(sK15,initial_segment(sK15,member_predicate,sK14)),
inference(cnf_transformation,[],[f81]) ).
fof(f157,plain,
( ~ subset(sK15,initial_segment(sK15,member_predicate,sK14))
| ~ subset(initial_segment(sK15,member_predicate,sK14),sK15) ),
inference(resolution,[],[f85,f147]) ).
fof(f159,definition,
( spl16_1
<=> subset(initial_segment(sK15,member_predicate,sK14),sK15) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f161,plain,
( ~ subset(initial_segment(sK15,member_predicate,sK14),sK15)
| spl16_1 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f163,definition,
( spl16_2
<=> subset(sK15,initial_segment(sK15,member_predicate,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f165,plain,
( ~ subset(sK15,initial_segment(sK15,member_predicate,sK14))
| spl16_2 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f157,f163,f159]) ).
fof(f167,plain,
( member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),initial_segment(sK15,member_predicate,sK14))
| spl16_1 ),
inference(resolution,[],[f161,f83]) ).
fof(f169,plain,
! [X0] :
( ~ member(X0,sK14)
| subset(X0,sK14) ),
inference(resolution,[],[f109,f145]) ).
fof(f180,plain,
subset(sK15,sK14),
inference(resolution,[],[f169,f146]) ).
fof(f182,plain,
! [X0] :
( ~ member(X0,sK15)
| member(X0,sK14) ),
inference(resolution,[],[f180,f82]) ).
fof(f188,plain,
( apply(member_predicate,sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15)
| spl16_1 ),
inference(resolution,[],[f140,f167]) ).
fof(f194,plain,
( member(sK1(initial_segment(sK15,member_predicate,sK14),sK15),sK15)
| spl16_1 ),
inference(resolution,[],[f188,f124]) ).
fof(f198,plain,
( subset(initial_segment(sK15,member_predicate,sK14),sK15)
| spl16_1 ),
inference(resolution,[],[f194,f84]) ).
fof(f200,plain,
( $false
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f198,f161]) ).
fof(f201,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f209,plain,
( member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| spl16_2 ),
inference(resolution,[],[f165,f83]) ).
fof(f213,plain,
( member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK14)
| spl16_2 ),
inference(resolution,[],[f209,f182]) ).
fof(f245,plain,
! [X2,X0,X1] :
( member(X0,initial_segment(X2,member_predicate,X1))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(resolution,[],[f142,f125]) ).
fof(f332,plain,
! [X2,X0,X1] :
( subset(X0,initial_segment(X1,member_predicate,X2))
| ~ member(sK1(X0,initial_segment(X1,member_predicate,X2)),X1)
| ~ member(sK1(X0,initial_segment(X1,member_predicate,X2)),X2) ),
inference(resolution,[],[f245,f84]) ).
fof(f1009,plain,
( ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK15)
| ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK14)
| spl16_2 ),
inference(resolution,[],[f332,f165]) ).
fof(f1010,plain,
( ~ member(sK1(sK15,initial_segment(sK15,member_predicate,sK14)),sK14)
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f1009,f209]) ).
fof(f1011,plain,
( $false
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f1010,f213]) ).
fof(f1012,plain,
spl16_2,
inference(avatar_contradiction_clause,[],[f1011]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s3,plain,
spl16_1,
inference(sat_conversion,[],[f201]) ).
cnf(s27,plain,
spl16_2,
inference(sat_conversion,[],[f1012]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s27,s3]) ).
fof(f1013,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:56:36 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.12/1.35 % (3216425)Detected formulas, will run a generic FOF schedule.
% 3.12/1.35 % (3216433)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=11649143:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.35 % (3216433)Refutation not found, incomplete strategy
% 3.12/1.35 % (3216433)------------------------------
% 3.12/1.35 % (3216433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.35 % (3216433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.35 % (3216433)CaDiCaL version: 2.1.3
% 3.12/1.35 % (3216433)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.35 % (3216433)Time elapsed: 0.001 s
% 3.12/1.35 % (3216433)Peak memory usage: 88 MB
% 3.12/1.35 % (3216433)Instructions burned: 1 (million)
% 3.12/1.35 % (3216430)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=2459680227:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.35 % (3216432)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=2549410210:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.35 % (3216431)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=1778606247:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.35 % (3216436)dis-21_1_sil=8000:lcm=predicate:random_seed=1568232780: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)
% 3.12/1.35 % (3216435)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2245917029:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.35 % (3216434)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3380365138:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.35 % (3216435)First to succeed.
% 3.12/1.35 % (3216435)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3216425"
% 3.12/1.35 % (3216436)Also succeeded, but the first one will report.
% 3.12/1.35 % (3216434)Instruction limit reached!
% 3.12/1.35 % (3216434)------------------------------
% 3.12/1.35 % (3216434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.35 % (3216434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.35 % (3216434)CaDiCaL version: 2.1.3
% 3.12/1.35 % (3216434)Termination reason: Instruction limit
% 3.12/1.35 % (3216434)Termination phase: Saturation
% 3.12/1.35 % (3216434)Time elapsed: 0.057 s
% 3.12/1.35 % (3216434)Peak memory usage: 88 MB
% 3.12/1.35 % (3216434)Instructions burned: 120 (million)
% 3.12/1.35 % (3216433)------------------------------
% 3.12/1.35 % (3216433)------------------------------
% 3.12/1.35 % (3216444)lrs+10_1_sil=8000:sp=occurrence:random_seed=1381765123:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.35 % (3216445)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1615275592:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.12/1.35 % (3216445)Instruction limit reached!
% 3.12/1.35 % (3216445)------------------------------
% 3.12/1.35 % (3216445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.35 % (3216445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.35 % (3216445)CaDiCaL version: 2.1.3
% 3.12/1.35 % (3216445)Termination reason: Instruction limit
% 3.12/1.35 % (3216445)Termination phase: Saturation
% 3.12/1.35 % (3216445)Time elapsed: 0.043 s
% 3.12/1.35 % (3216445)Peak memory usage: 91 MB
% 3.12/1.35 % (3216445)Instructions burned: 159 (million)
% 3.12/1.35 % (3216435)Refutation found. Thanks to Tanya!
% 3.12/1.35 % SZS status Theorem for theBenchmark
% 3.12/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.55 % (3216435)------------------------------
% 4.01/1.55 % (3216435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.55 % (3216435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.55 % (3216435)CaDiCaL version: 2.1.3
% 4.01/1.55 % (3216435)Termination reason: Refutation
% 4.01/1.55 % (3216435)Time elapsed: 0.044 s
% 4.01/1.55 % (3216435)Peak memory usage: 90 MB
% 4.01/1.55 % (3216435)Instructions burned: 60 (million)
% 4.01/1.55 % (3216435)------------------------------
% 4.01/1.55 % (3216435)------------------------------
% 4.01/1.55 % (3216425)Success in time 0.478 s
% 4.01/1.55 % Vampire exiting
%------------------------------------------------------------------------------