%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET194+3 : 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 : n020.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 12:40:28 PM UTC 2026
% Result : Theorem 2.52s 1.33s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 24 ~; 20 |; 10 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_union) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] : subset(X0,union(X0,X1)),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1] : ~ subset(X0,union(X0,X1)),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,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,[],[f8]) ).
fof(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f18,plain,
~ subset(sK2,union(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f9]) ).
fof(f21,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
~ subset(sK2,union(sK2,sK3)),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
member(sK0(sK2,union(sK2,sK3)),sK2),
inference(resolution,[],[f23,f31]) ).
fof(f41,plain,
~ member(sK0(sK2,union(sK2,sK3)),union(sK2,sK3)),
inference(resolution,[],[f24,f31]) ).
fof(f42,plain,
~ member(sK0(sK2,union(sK2,sK3)),sK2),
inference(resolution,[],[f41,f21]) ).
fof(f47,plain,
$false,
inference(resolution,[],[f42,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET194+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 01:04:35 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.52/1.33 % (3938660)Detected formulas, will run a generic FOF schedule.
% 2.52/1.33 % (3938671)dis-21_1_sil=8000:lcm=predicate:random_seed=491123894: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)
% 2.52/1.33 % (3938671)First to succeed.
% 2.52/1.33 % (3938671)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3938660"
% 2.52/1.33 % (3938667)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=3615279439:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.52/1.33 % (3938668)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1273619072:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.52/1.33 % (3938666)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=138570133:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.52/1.33 % (3938665)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=1258384373:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.52/1.33 % (3938668)Refutation not found, incomplete strategy
% 2.52/1.33 % (3938668)------------------------------
% 2.52/1.33 % (3938668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3938668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3938668)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3938668)Termination reason: Refutation not found, incomplete strategy
% 2.52/1.33 % (3938668)Time elapsed: 0.001 s
% 2.52/1.33 % (3938668)Peak memory usage: 88 MB
% 2.52/1.33 % (3938669)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2800649128:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.52/1.33 % (3938670)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2614153782:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.52/1.33 % (3938669)Also succeeded, but the first one will report.
% 2.52/1.33 % (3938670)Also succeeded, but the first one will report.
% 2.52/1.33 % (3938671)Refutation found. Thanks to Tanya!
% 2.52/1.33 % SZS status Theorem for theBenchmark
% 2.52/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.33 % (3938671)------------------------------
% 2.52/1.33 % (3938671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.33 % (3938671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.33 % (3938671)CaDiCaL version: 2.1.3
% 2.52/1.33 % (3938671)Termination reason: Refutation
% 2.52/1.33 % (3938671)Time elapsed: 0.001 s
% 2.52/1.33 % (3938671)Peak memory usage: 88 MB
% 2.52/1.33 % (3938671)Instructions burned: 1 (million)
% 2.52/1.33 % (3938671)------------------------------
% 2.52/1.33 % (3938671)------------------------------
% 2.52/1.33 % (3938660)Success in time 0.271 s
% 2.52/1.33 % Vampire exiting
%------------------------------------------------------------------------------