%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:39:49 PM UTC 2026
% Result : Theorem 3.78s 1.49s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 8 unt; 3 def)
% Number of atoms : 113 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 45 |; 19 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 41 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f44,conjecture,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
& ! [X3] :
( ~ member(X3,X1)
| member(X3,X0) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f58,plain,
( sK0 != sK1
& ! [X2] :
( ~ member(X2,sK0)
| member(X2,sK1) )
& ! [X3] :
( ~ member(X3,sK1)
| member(X3,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
fof(f61,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f62,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f61]) ).
fof(f65,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f66]) ).
fof(f92,plain,
! [X3] :
( ~ member(X3,sK1)
| member(X3,sK0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f93,plain,
! [X2] :
( member(X2,sK1)
| ~ member(X2,sK0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f94,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f58]) ).
fof(f103,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f108,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f205,definition,
! [X0,X1] :
( sQ7_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ7_eqProxy])],[equality_proxy_definition]) ).
fof(f206,plain,
~ sQ7_eqProxy(sK0,sK1),
inference(equality_proxy_replacement,[],[f94,f205]) ).
fof(f208,plain,
! [X0,X1] :
( sQ7_eqProxy(X0,X1)
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) ),
inference(equality_proxy_replacement,[],[f103,f205]) ).
fof(f242,plain,
( ~ subclass(sK0,sK1)
| ~ subclass(sK1,sK0) ),
inference(resolution,[],[f208,f206]) ).
fof(f245,definition,
( spl8_1
<=> subclass(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f246,plain,
( ~ subclass(sK0,sK1)
| spl8_1 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl8_2
<=> subclass(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f249,plain,
( ~ subclass(sK1,sK0)
| spl8_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ spl8_2
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f242,f245,f248]) ).
fof(f252,plain,
( ~ member(sK2(sK0,sK1),sK1)
| spl8_1 ),
inference(resolution,[],[f246,f109]) ).
fof(f253,plain,
( member(sK2(sK0,sK1),sK0)
| spl8_1 ),
inference(resolution,[],[f246,f108]) ).
fof(f254,plain,
( ~ member(sK2(sK0,sK1),sK0)
| spl8_1 ),
inference(resolution,[],[f252,f93]) ).
fof(f255,plain,
( $false
| spl8_1 ),
inference(resolution,[],[f254,f253]) ).
fof(f256,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f255]) ).
fof(f257,plain,
( ~ member(sK2(sK1,sK0),sK0)
| spl8_2 ),
inference(resolution,[],[f249,f109]) ).
fof(f258,plain,
( member(sK2(sK1,sK0),sK1)
| spl8_2 ),
inference(resolution,[],[f249,f108]) ).
fof(f259,plain,
( member(sK2(sK1,sK0),sK0)
| spl8_2 ),
inference(resolution,[],[f258,f92]) ).
fof(f260,plain,
( $false
| spl8_2 ),
inference(resolution,[],[f259,f257]) ).
fof(f261,plain,
spl8_2,
inference(avatar_contradiction_clause,[],[f260]) ).
cnf(s2,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
spl8_1,
inference(sat_conversion,[],[f256]) ).
cnf(s4,plain,
spl8_2,
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f262,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 00:22:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.78/1.49 % (696019)Detected formulas, will run a generic FOF schedule.
% 3.78/1.49 % (696079)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3779771642:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.78/1.49 % (696072)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=1033614980:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.78/1.49 % (696074)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=2728697934:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.78/1.49 % (696076)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2407408204:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.78/1.49 % (696071)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=1477638736:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.78/1.49 % (696077)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4047454639:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.78/1.49 % (696077)Refutation not found, incomplete strategy
% 3.78/1.49 % (696077)------------------------------
% 3.78/1.49 % (696077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (696076)Refutation not found, incomplete strategy
% 3.78/1.49 % (696076)------------------------------
% 3.78/1.49 % (696076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (696077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (696076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (696077)CaDiCaL version: 2.1.3
% 3.78/1.49 % (696077)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.49 % (696077)Time elapsed: 0.001 s
% 3.78/1.49 % (696076)CaDiCaL version: 2.1.3
% 3.78/1.49 % (696077)Peak memory usage: 87 MB
% 3.78/1.49 % (696076)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.49 % (696076)Time elapsed: 0.001 s
% 3.78/1.49 % (696076)Peak memory usage: 87 MB
% 3.78/1.49 % (696081)dis-21_1_sil=8000:lcm=predicate:random_seed=3071981353: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)
% 3.78/1.49 % (696079)Instruction limit reached!
% 3.78/1.49 % (696079)------------------------------
% 3.78/1.49 % (696079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (696079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (696079)CaDiCaL version: 2.1.3
% 3.78/1.49 % (696079)Termination reason: Instruction limit
% 3.78/1.49 % (696079)Termination phase: Saturation
% 3.78/1.49 % (696079)Time elapsed: 0.058 s
% 3.78/1.49 % (696079)Peak memory usage: 90 MB
% 3.78/1.49 % (696079)Instructions burned: 140 (million)
% 3.78/1.49 % (696081)First to succeed.
% 3.78/1.49 % (696081)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-696019"
% 3.78/1.49 % (696155)lrs+10_1_sil=8000:sp=occurrence:random_seed=22389346:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.78/1.49 % (696155)Refutation not found, incomplete strategy
% 3.78/1.49 % (696155)------------------------------
% 3.78/1.49 % (696155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (696155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (696155)CaDiCaL version: 2.1.3
% 3.78/1.49 % (696155)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.49 % (696155)Time elapsed: 0.001 s
% 3.78/1.49 % (696155)Peak memory usage: 88 MB
% 3.78/1.49 % (696076)------------------------------
% 3.78/1.49 % (696076)------------------------------
% 3.78/1.49 % (696077)------------------------------
% 3.78/1.49 % (696077)------------------------------
% 3.78/1.49 % (696081)Refutation found. Thanks to Tanya!
% 3.78/1.49 % SZS status Theorem for theBenchmark
% 3.78/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.49 % (696081)------------------------------
% 3.78/1.49 % (696081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.49 % (696081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.49 % (696081)CaDiCaL version: 2.1.3
% 3.78/1.49 % (696081)Termination reason: Refutation
% 3.78/1.49 % (696081)Time elapsed: 0.005 s
% 3.78/1.49 % (696081)Peak memory usage: 89 MB
% 3.78/1.49 % (696081)Instructions burned: 6 (million)
% 3.78/1.49 % (696081)------------------------------
% 3.78/1.49 % (696081)------------------------------
% 3.78/1.49 % (696019)Success in time 0.444 s
% 3.78/1.49 % Vampire exiting
%------------------------------------------------------------------------------