%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU139+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:47:22 PM UTC 2026
% Result : Theorem 3.42s 1.14s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 12 unt; 2 def)
% Number of atoms : 82 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 36 ~; 27 |; 14 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 26 ( 1 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f6,conjecture,
! [X0,X1] :
~ ( subset(X0,X1)
& proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
~ ( subset(X0,X1)
& proper_subset(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f4]) ).
fof(f11,plain,
? [X0,X1] :
( subset(X0,X1)
& proper_subset(X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 )
& ( ( subset(X0,X1)
& X0 != X1 )
| ~ proper_subset(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 )
& ( ( subset(X0,X1)
& X0 != X1 )
| ~ proper_subset(X0,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
( subset(sK0,sK1)
& proper_subset(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
fof(f20,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
proper_subset(sK1,sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f38,definition,
( spl2_1
<=> subset(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f39,plain,
( subset(sK1,sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ subset(sK1,sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f42,definition,
( spl2_2
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f44,plain,
( sK0 = sK1
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f51,plain,
( ~ proper_subset(sK1,sK0)
| spl2_1 ),
inference(resolution,[],[f40,f22]) ).
fof(f52,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f51,f26]) ).
fof(f53,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f55,plain,
( sK0 = sK1
| ~ subset(sK0,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f39,f20]) ).
fof(f56,plain,
( sK0 = sK1
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f55,f27]) ).
fof(f57,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f56,f38,f42]) ).
fof(f61,plain,
( proper_subset(sK0,sK0)
| ~ spl2_2 ),
inference(superposition,[],[f26,f44]) ).
fof(f62,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f61,f24]) ).
fof(f63,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f62]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
~ spl2_2,
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
~ spl2_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6]) ).
fof(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU139+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:41:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.42/1.14 % (413730)Detected formulas, will run a generic FOF schedule.
% 3.42/1.14 % (413735)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=2598876795:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.14 % (413738)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1314012847:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.14 % (413740)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=7177508:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.14 % (413736)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=1162494886:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.14 % (413741)dis-21_1_sil=8000:lcm=predicate:random_seed=296949969: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)
% 3.42/1.14 % (413739)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2463382642:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.14 % (413737)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=239007282:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.14 % (413739)Refutation not found, incomplete strategy
% 3.42/1.14 % (413739)------------------------------
% 3.42/1.14 % (413739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.14 % (413739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.14 % (413738)Refutation not found, incomplete strategy
% 3.42/1.14 % (413738)------------------------------
% 3.42/1.14 % (413738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.14 % (413738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.14 % (413739)CaDiCaL version: 2.1.3
% 3.42/1.14 % (413739)Termination reason: Refutation not found, incomplete strategy
% 3.42/1.14 % (413739)Time elapsed: 0.001 s
% 3.42/1.14 % (413738)CaDiCaL version: 2.1.3
% 3.42/1.14 % (413739)Peak memory usage: 87 MB
% 3.42/1.14 % (413738)Termination reason: Refutation not found, incomplete strategy
% 3.42/1.14 % (413738)Time elapsed: 0.001 s
% 3.42/1.14 % (413738)Peak memory usage: 88 MB
% 3.42/1.14 % (413741)Refutation not found, incomplete strategy
% 3.42/1.14 % (413741)------------------------------
% 3.42/1.14 % (413741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.14 % (413741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.14 % (413741)CaDiCaL version: 2.1.3
% 3.42/1.14 % (413741)Termination reason: Refutation not found, incomplete strategy
% 3.42/1.14 % (413741)Time elapsed: 0.001 s
% 3.42/1.14 % (413741)Peak memory usage: 88 MB
% 3.42/1.14 % (413740)First to succeed.
% 3.42/1.14 % (413740)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-413730"
% 3.42/1.14 % (413741)------------------------------
% 3.42/1.14 % (413741)------------------------------
% 3.42/1.14 % (413739)------------------------------
% 3.42/1.14 % (413739)------------------------------
% 3.42/1.14 % (413738)------------------------------
% 3.42/1.14 % (413738)------------------------------
% 3.42/1.14 % (413740)Refutation found. Thanks to Tanya!
% 3.42/1.14 % SZS status Theorem for theBenchmark
% 3.42/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.15 % (413740)------------------------------
% 3.42/1.15 % (413740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.15 % (413740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.15 % (413740)CaDiCaL version: 2.1.3
% 3.42/1.15 % (413740)Termination reason: Refutation
% 3.42/1.15 % (413740)Time elapsed: 0.003 s
% 3.42/1.15 % (413740)Peak memory usage: 89 MB
% 3.42/1.15 % (413740)Instructions burned: 1 (million)
% 3.42/1.15 % (413740)------------------------------
% 3.42/1.15 % (413740)------------------------------
% 3.42/1.15 % (413730)Success in time 0.439 s
% 3.42/1.15 % Vampire exiting
%------------------------------------------------------------------------------