%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:40:50 PM UTC 2026
% Result : Theorem 4.41s 1.74s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 11 unt; 1 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 33 ~; 26 |; 15 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 38 !; 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(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI43) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1] :
( ~ subset(X1,sum(X0))
& member(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
( ~ subset(sK1,sum(sK0))
& member(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f18,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,[],[f15]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK3(X0,X1),X1)
& member(X0,sK3(X0,X1)) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f22]) ).
fof(f24,plain,
member(sK1,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
~ subset(sK1,sum(sK0)),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
member(sK2(sK1,sum(sK0)),sK1),
inference(resolution,[],[f29,f25]) ).
fof(f38,plain,
~ member(sK2(sK1,sum(sK0)),sum(sK0)),
inference(resolution,[],[f30,f25]) ).
fof(f43,plain,
! [X0] :
( ~ member(sK2(sK1,sum(sK0)),X0)
| ~ member(X0,sK0) ),
inference(resolution,[],[f33,f38]) ).
fof(f44,plain,
~ member(sK1,sK0),
inference(resolution,[],[f43,f36]) ).
fof(f52,definition,
( spl4_2
<=> member(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f53,plain,
( ~ member(sK1,sK0)
| spl4_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f44,f52]) ).
fof(f56,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f53,f24]) ).
fof(f57,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f56]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f58,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 28 01:32:56 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.47 Running first-order theorem proving
% 0.23/0.47 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
% 4.41/1.74 % (350008)Detected formulas, will run a generic FOF schedule.
% 4.41/1.74 % (350021)dis-21_1_sil=8000:lcm=predicate:random_seed=3776019068: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)
% 4.41/1.74 % (350021)First to succeed.
% 4.41/1.74 % (350021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-350008"
% 4.41/1.74 % (350019)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4279188834:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.41/1.74 % (350017)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=1456611419:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.41/1.74 % (350018)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4094489921:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.41/1.74 % (350015)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=666747118:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.41/1.74 % (350020)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=387133833:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.41/1.74 % (350016)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=4006979207:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.41/1.74 % (350018)Refutation not found, incomplete strategy
% 4.41/1.74 % (350018)------------------------------
% 4.41/1.74 % (350018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.74 % (350018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.74 % (350019)Also succeeded, but the first one will report.
% 4.41/1.74 % (350018)CaDiCaL version: 2.1.3
% 4.41/1.74 % (350018)Termination reason: Refutation not found, incomplete strategy
% 4.41/1.74 % (350018)Time elapsed: 0.002 s
% 4.41/1.74 % (350018)Peak memory usage: 88 MB
% 4.41/1.74 % (350020)Also succeeded, but the first one will report.
% 4.41/1.74 % (350021)Refutation found. Thanks to Tanya!
% 4.41/1.74 % SZS status Theorem for theBenchmark
% 4.41/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.41/1.74 % (350021)------------------------------
% 4.41/1.74 % (350021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.74 % (350021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.74 % (350021)CaDiCaL version: 2.1.3
% 4.41/1.74 % (350021)Termination reason: Refutation
% 4.41/1.74 % (350021)Time elapsed: 0.003 s
% 4.41/1.74 % (350021)Peak memory usage: 89 MB
% 4.41/1.74 % (350021)Instructions burned: 1 (million)
% 4.41/1.74 % (350021)------------------------------
% 4.41/1.74 % (350021)------------------------------
% 4.41/1.74 % (350008)Success in time 0.506 s
% 4.41/1.74 % Vampire exiting
%------------------------------------------------------------------------------