%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET009+3 : 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 : n018.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 12:39:29 PM UTC 2026
% Result : Theorem 2.65s 1.27s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 13 unt; 2 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 40 ~; 32 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
? [X0,X1,X2] :
( ~ subset(difference(X2,X1),difference(X2,X0))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f8]) ).
fof(f10,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,[],[f6]) ).
fof(f11,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,[],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
( ~ subset(difference(sK3,sK2),difference(sK3,sK1))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ subset(difference(sK3,sK2),difference(sK3,sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK2)),
inference(resolution,[],[f18,f22]) ).
fof(f24,plain,
member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3),
inference(resolution,[],[f23,f15]) ).
fof(f25,plain,
~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK2),
inference(resolution,[],[f23,f14]) ).
fof(f26,plain,
~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),difference(sK3,sK1)),
inference(resolution,[],[f19,f22]) ).
fof(f27,plain,
! [X0] :
( member(X0,sK2)
| ~ member(X0,sK1) ),
inference(resolution,[],[f17,f21]) ).
fof(f33,plain,
~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1),
inference(resolution,[],[f25,f27]) ).
fof(f34,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3)
| member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1) ),
inference(resolution,[],[f26,f16]) ).
fof(f36,definition,
( spl4_1
<=> member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f37,plain,
( member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,definition,
( spl4_2
<=> member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f40,plain,
( ~ member(sK0(difference(sK3,sK2),difference(sK3,sK1)),sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f34,f39,f36]) ).
fof(f42,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f40,f24]) ).
fof(f43,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f42]) ).
fof(f44,plain,
( $false
| ~ spl4_1 ),
inference(resolution,[],[f33,f37]) ).
fof(f45,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f44]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:05:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.65/1.27 % (2869510)Detected formulas, will run a generic FOF schedule.
% 2.65/1.27 % (2869539)dis-21_1_sil=8000:lcm=predicate:random_seed=1722297499: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)
% 2.65/1.27 % (2869539)First to succeed.
% 2.65/1.27 % (2869539)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2869510"
% 2.65/1.27 % (2869534)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=1051184430:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.27 % (2869535)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=4013035763:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.27 % (2869538)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3241693428:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.27 % (2869537)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2832255655:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.27 % (2869536)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2819243459:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.27 % (2869533)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=3073513732:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.27 % (2869536)Refutation not found, incomplete strategy
% 2.65/1.27 % (2869536)------------------------------
% 2.65/1.27 % (2869536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (2869536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (2869536)CaDiCaL version: 2.1.3
% 2.65/1.27 % (2869536)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.27 % (2869536)Time elapsed: 0.001 s
% 2.65/1.27 % (2869536)Peak memory usage: 87 MB
% 2.65/1.27 % (2869538)Also succeeded, but the first one will report.
% 2.65/1.27 % (2869537)Also succeeded, but the first one will report.
% 2.65/1.27 % (2869539)Refutation found. Thanks to Tanya!
% 2.65/1.27 % SZS status Theorem for theBenchmark
% 2.65/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.27 % (2869539)------------------------------
% 2.65/1.27 % (2869539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (2869539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (2869539)CaDiCaL version: 2.1.3
% 2.65/1.27 % (2869539)Termination reason: Refutation
% 2.65/1.27 % (2869539)Time elapsed: 0.002 s
% 2.65/1.27 % (2869539)Peak memory usage: 89 MB
% 2.65/1.27 % (2869539)Instructions burned: 1 (million)
% 2.65/1.27 % (2869539)------------------------------
% 2.65/1.27 % (2869539)------------------------------
% 2.65/1.27 % (2869510)Success in time 0.304 s
% 2.65/1.27 % Vampire exiting
%------------------------------------------------------------------------------