%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:42:26 PM UTC 2026
% Result : Theorem 2.71s 1.34s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 16 unt; 5 def)
% Number of atoms : 174 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 85 ~; 74 |; 22 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 94 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f13,conjecture,
! [X0,X1,X2] :
~ ( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
? [X0,X1,X2] :
( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
( empty_set != sK9
& ( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) )
& ~ subset(sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f18]) ).
fof(f36,plain,
! [X0] :
( empty_set = X0
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f57,plain,
~ subset(sK10,sK11),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
empty_set != sK9,
inference(cnf_transformation,[],[f32]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f53,f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f52,f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f51,f48]) ).
fof(f74,definition,
! [X0,X1] :
( sQ12_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ12_eqProxy])],[equality_proxy_definition]) ).
fof(f76,plain,
! [X0] :
( sQ12_eqProxy(empty_set,X0)
| in(sK0(X0),X0) ),
inference(equality_proxy_replacement,[],[f36,f74]) ).
fof(f82,plain,
~ sQ12_eqProxy(empty_set,sK9),
inference(equality_proxy_replacement,[],[f59,f74]) ).
fof(f86,definition,
( spl13_1
<=> subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f87,plain,
( subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,definition,
( spl13_2
<=> subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f90,plain,
( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f58,f89,f86]) ).
fof(f95,plain,
in(sK0(sK9),sK9),
inference(resolution,[],[f76,f82]) ).
fof(f96,plain,
in(sK6(sK10,sK11),sK10),
inference(resolution,[],[f46,f57]) ).
fof(f99,plain,
~ in(sK6(sK10,sK11),sK11),
inference(resolution,[],[f47,f57]) ).
fof(f100,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK11,sK9))
| ~ in(X0,cartesian_product2(sK10,sK9)) )
| ~ spl13_2 ),
inference(resolution,[],[f45,f90]) ).
fof(f119,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK10,sK9))
| in(X0,sK11) )
| ~ spl13_2 ),
inference(resolution,[],[f66,f100]) ).
fof(f123,plain,
( ! [X0,X1] :
( ~ in(X0,sK10)
| ~ in(X1,sK9)
| in(X0,sK11) )
| ~ spl13_2 ),
inference(resolution,[],[f65,f119]) ).
fof(f128,definition,
( spl13_3
<=> ! [X1] : ~ in(X1,sK9) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f129,plain,
( ! [X1] : ~ in(X1,sK9)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,definition,
( spl13_4
<=> ! [X0] :
( ~ in(X0,sK10)
| in(X0,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f132,plain,
( ! [X0] :
( in(X0,sK11)
| ~ in(X0,sK10) )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( spl13_3
| spl13_4
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f123,f89,f131,f128]) ).
fof(f134,plain,
( $false
| ~ spl13_3 ),
inference(resolution,[],[f129,f95]) ).
fof(f137,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f142,plain,
( ~ in(sK6(sK10,sK11),sK10)
| ~ spl13_4 ),
inference(resolution,[],[f132,f99]) ).
fof(f150,plain,
( $false
| ~ spl13_4 ),
inference(resolution,[],[f142,f96]) ).
fof(f151,plain,
~ spl13_4,
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f152,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK9,sK11))
| ~ in(X0,cartesian_product2(sK9,sK10)) )
| ~ spl13_1 ),
inference(resolution,[],[f87,f45]) ).
fof(f156,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
| in(X1,sK11) )
| ~ spl13_1 ),
inference(resolution,[],[f152,f67]) ).
fof(f163,plain,
( ! [X0,X1] :
( in(X0,sK11)
| ~ in(X1,sK9)
| ~ in(X0,sK10) )
| ~ spl13_1 ),
inference(resolution,[],[f156,f65]) ).
fof(f164,plain,
( spl13_3
| spl13_4
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f163,f86,f131,f128]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( ~ spl13_2
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s3,plain,
~ spl13_3,
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
~ spl13_4,
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( ~ spl13_1
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f164]) ).
cnf(s7,plain,
~ spl13_1,
inference(rat,[],[s6,s5,s3]) ).
cnf(s8,plain,
~ spl13_2,
inference(rat,[],[s2,s5,s3]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
fof(f165,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 03:16:30 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.40 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
% 2.71/1.34 % (2631425)Detected formulas, will run a generic FOF schedule.
% 2.71/1.34 % (2631436)dis-21_1_sil=8000:lcm=predicate:random_seed=1056375171: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)
% 2.71/1.34 % (2631436)First to succeed.
% 2.71/1.34 % (2631436)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2631425"
% 2.71/1.34 % (2631432)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=1534598120:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.34 % (2631434)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=391518781:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.34 % (2631431)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=3637840256:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.34 % (2631430)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=3196084468:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.34 % (2631433)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=215920247:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.34 % (2631435)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3127428075:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.34 % (2631433)Also succeeded, but the first one will report.
% 2.71/1.34 % (2631434)Also succeeded, but the first one will report.
% 2.71/1.34 % (2631435)Also succeeded, but the first one will report.
% 2.71/1.34 % (2631436)Refutation found. Thanks to Tanya!
% 2.71/1.34 % SZS status Theorem for theBenchmark
% 2.71/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.34 % (2631436)------------------------------
% 2.71/1.34 % (2631436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.34 % (2631436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.34 % (2631436)CaDiCaL version: 2.1.3
% 2.71/1.34 % (2631436)Termination reason: Refutation
% 2.71/1.34 % (2631436)Time elapsed: 0.003 s
% 2.71/1.34 % (2631436)Peak memory usage: 89 MB
% 2.71/1.34 % (2631436)Instructions burned: 5 (million)
% 2.71/1.34 % (2631436)------------------------------
% 2.71/1.34 % (2631436)------------------------------
% 2.71/1.34 % (2631425)Success in time 0.299 s
% 2.71/1.34 % Vampire exiting
%------------------------------------------------------------------------------