%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET347+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:40:48 PM UTC 2026
% Result : Theorem 0.23s 1.60s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 2 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 41 ~; 38 |; 15 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI38) ).
fof(f13,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
~ equal_set(sum(empty_set),empty_set),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f17]) ).
fof(f20,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,[],[f16]) ).
fof(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK1(X0,X1),X1)
& member(X0,sK1(X0,X1)) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f34]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
~ equal_set(sum(empty_set),empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f74,plain,
! [X0,X1] :
( equal_set(X0,X1)
| member(sK0(X0,X1),X0)
| ~ subset(X1,X0) ),
inference(resolution,[],[f40,f42]) ).
fof(f104,plain,
( member(sK0(sum(empty_set),empty_set),sum(empty_set))
| ~ subset(empty_set,sum(empty_set)) ),
inference(resolution,[],[f74,f66]) ).
fof(f106,definition,
( spl3_1
<=> subset(empty_set,sum(empty_set)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f108,plain,
( ~ subset(empty_set,sum(empty_set))
| spl3_1 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl3_2
<=> member(sK0(sum(empty_set),empty_set),sum(empty_set)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f112,plain,
( member(sK0(sum(empty_set),empty_set),sum(empty_set))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f104,f110,f106]) ).
fof(f114,plain,
( member(sK0(empty_set,sum(empty_set)),empty_set)
| spl3_1 ),
inference(resolution,[],[f108,f40]) ).
fof(f115,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f114,f51]) ).
fof(f116,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f161,plain,
( member(sK1(sK0(sum(empty_set),empty_set),empty_set),empty_set)
| ~ spl3_2 ),
inference(resolution,[],[f112,f61]) ).
fof(f162,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f161,f51]) ).
fof(f163,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f162]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f116]) ).
cnf(s5,plain,
~ spl3_2,
inference(sat_conversion,[],[f163]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s5,s2]) ).
fof(f164,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET347+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 % Computer : n007.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 28 01:30:41 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 0.23/1.60 % (1945796)Detected formulas, will run a generic FOF schedule.
% 0.23/1.60 % (1945806)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2084606071:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 0.23/1.60 % (1945806)Refutation not found, incomplete strategy
% 0.23/1.60 % (1945806)------------------------------
% 0.23/1.60 % (1945806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.60 % (1945806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.60 % (1945806)CaDiCaL version: 2.1.3
% 0.23/1.60 % (1945806)Termination reason: Refutation not found, incomplete strategy
% 0.23/1.60 % (1945806)Time elapsed: 0.0000 s
% 0.23/1.60 % (1945806)Peak memory usage: 87 MB
% 0.23/1.60 % (1945803)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=3041498918:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 0.23/1.60 % (1945804)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=2144525850:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 0.23/1.60 % (1945805)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=2680861036:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 0.23/1.60 % (1945810)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3802428497:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 0.23/1.60 % (1945810)First to succeed.
% 0.23/1.60 % (1945810)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1945796"
% 0.23/1.60 % (1945811)dis-21_1_sil=8000:lcm=predicate:random_seed=288585134:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 0.23/1.60 % (1945811)Also succeeded, but the first one will report.
% 0.23/1.60 % (1945808)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2992080457:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 0.23/1.60 % (1945808)Also succeeded, but the first one will report.
% 0.23/1.60 % (1945806)------------------------------
% 0.23/1.60 % (1945806)------------------------------
% 0.23/1.60 % (1945824)lrs+10_1_sil=8000:sp=occurrence:random_seed=1176090779:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 0.23/1.60 % (1945824)Also succeeded, but the first one will report.
% 0.23/1.60 % (1945825)lrs+10_1_sil=32000:urr=on:br=off:random_seed=839683858:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 0.23/1.60 % (1945810)Refutation found. Thanks to Tanya!
% 0.23/1.60 % SZS status Theorem for theBenchmark
% 0.23/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.61 % (1945810)------------------------------
% 0.23/1.61 % (1945810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.61 % (1945810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.61 % (1945810)CaDiCaL version: 2.1.3
% 0.23/1.61 % (1945810)Termination reason: Refutation
% 0.23/1.61 % (1945810)Time elapsed: 0.006 s
% 0.23/1.61 % (1945810)Peak memory usage: 89 MB
% 0.23/1.61 % (1945810)Instructions burned: 5 (million)
% 0.23/1.61 % (1945810)------------------------------
% 0.23/1.61 % (1945810)------------------------------
% 0.23/1.61 % (1945796)Success in time 0.621 s
% 0.23/1.61 % Vampire exiting
%------------------------------------------------------------------------------