%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU165+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 : n003.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 12:47:31 PM UTC 2026
% Result : Theorem 2.71s 1.36s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 7 unt; 3 def)
% Number of atoms : 122 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 50 ~; 53 |; 14 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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(f11,conjecture,
! [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',t106_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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(f15,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X0,X2)
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X0,X2)
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) )
& ( ( in(sK2,sK4)
& in(sK3,sK5) )
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f19]) ).
fof(f21,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,[],[f13]) ).
fof(f22,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,[],[f21]) ).
fof(f28,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
( in(sK3,sK5)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( in(sK2,sK4)
| in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f31,f28]) ).
fof(f37,plain,
( in(sK2,sK4)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f30,f28]) ).
fof(f38,plain,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f39,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,[],[f34,f28]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f33,f28]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f32,f28]) ).
fof(f47,definition,
( spl7_1
<=> in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f48,plain,
( in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,definition,
( spl7_2
<=> in(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f52,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f38,f50,f47]) ).
fof(f54,definition,
( spl7_3
<=> in(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f56,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f37,f54,f47]) ).
fof(f57,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| spl7_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f60,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f36,f54,f50,f47]) ).
fof(f62,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK5)
| spl7_1 ),
inference(resolution,[],[f39,f57]) ).
fof(f67,plain,
( ~ spl7_2
| ~ spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f62,f47,f54,f50]) ).
fof(f68,plain,
( in(sK3,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f48,f41]) ).
fof(f69,plain,
( in(sK2,sK4)
| ~ spl7_1 ),
inference(resolution,[],[f48,f40]) ).
fof(f72,plain,
( spl7_2
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f68,f47,f50]) ).
fof(f73,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f69,f47,f54]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f72]) ).
cnf(s6,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s7,plain,
spl7_1,
inference(rat,[],[s4,s1,s2]) ).
cnf(s8,plain,
spl7_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl7_2,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s8,s9,s7]) ).
fof(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:51:57 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.71/1.36 % (1166766)Detected formulas, will run a generic FOF schedule.
% 2.71/1.36 % (1166777)dis-21_1_sil=8000:lcm=predicate:random_seed=35698461: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)
% 2.71/1.36 % (1166777)First to succeed.
% 2.71/1.36 % (1166777)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1166766"
% 2.71/1.36 % (1166773)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=2036060890:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.36 % (1166771)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=1688704086:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.36 % (1166774)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3850437238:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.36 % (1166775)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2032847364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.36 % (1166772)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=1572621917:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.36 % (1166776)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1542982712:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.36 % (1166774)Also succeeded, but the first one will report.
% 2.71/1.36 % (1166775)Also succeeded, but the first one will report.
% 2.71/1.36 % (1166776)Also succeeded, but the first one will report.
% 2.71/1.36 % (1166777)Refutation found. Thanks to Tanya!
% 2.71/1.36 % SZS status Theorem for theBenchmark
% 2.71/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.36 % (1166777)------------------------------
% 2.71/1.36 % (1166777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.36 % (1166777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.36 % (1166777)CaDiCaL version: 2.1.3
% 2.71/1.36 % (1166777)Termination reason: Refutation
% 2.71/1.36 % (1166777)Time elapsed: 0.002 s
% 2.71/1.36 % (1166777)Peak memory usage: 89 MB
% 2.71/1.36 % (1166777)Instructions burned: 2 (million)
% 2.71/1.36 % (1166777)------------------------------
% 2.71/1.36 % (1166777)------------------------------
% 2.71/1.36 % (1166766)Success in time 0.3 s
% 2.71/1.36 % Vampire exiting
%------------------------------------------------------------------------------