%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU245+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 : n016.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 12:47:59 PM UTC 2026
% Result : Theorem 3.58s 1.50s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 6 unt; 0 def)
% Number of atoms : 158 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 198 ( 79 ~; 77 |; 34 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<~> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f31,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| in(X0,relation_restriction(X2,X1)) )
& relation(X2) ),
inference(nnf_transformation,[],[f29]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ( ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| in(X0,relation_restriction(X2,X1)) )
& relation(X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ( ~ in(sK0,sK2)
| ~ in(sK0,cartesian_product2(sK1,sK1))
| ~ in(sK0,relation_restriction(sK2,sK1)) )
& ( ( in(sK0,sK2)
& in(sK0,cartesian_product2(sK1,sK1)) )
| in(sK0,relation_restriction(sK2,sK1)) )
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f40]) ).
fof(f44,plain,
relation(sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f45,plain,
( in(sK0,cartesian_product2(sK1,sK1))
| in(sK0,relation_restriction(sK2,sK1)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f46,plain,
( in(sK0,relation_restriction(sK2,sK1))
| in(sK0,sK2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f47,plain,
( ~ in(sK0,cartesian_product2(sK1,sK1))
| ~ in(sK0,sK2)
| ~ in(sK0,relation_restriction(sK2,sK1)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f55,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f55]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f54]) ).
fof(f65,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f53]) ).
fof(f86,plain,
! [X2,X0,X1] :
( in(X2,cartesian_product2(X1,X1))
| ~ in(X2,relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(superposition,[],[f65,f49]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ in(X2,relation_restriction(X0,X1))
| in(X2,X0)
| ~ relation(X0) ),
inference(superposition,[],[f64,f49]) ).
fof(f98,plain,
! [X2,X0,X1] :
( in(X2,relation_restriction(X0,X1))
| ~ in(X2,X0)
| ~ in(X2,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(superposition,[],[f63,f49]) ).
fof(f102,plain,
( in(sK0,sK2)
| ~ relation(sK2)
| in(sK0,sK2) ),
inference(resolution,[],[f87,f46]) ).
fof(f103,plain,
( in(sK0,sK2)
| ~ relation(sK2) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f104,plain,
in(sK0,sK2),
inference(forward_subsumption_resolution,[],[f103,f44]) ).
fof(f164,plain,
! [X0] :
( ~ in(sK0,relation_restriction(X0,sK1))
| ~ relation(X0)
| ~ in(sK0,sK2)
| ~ in(sK0,relation_restriction(sK2,sK1)) ),
inference(resolution,[],[f86,f47]) ).
fof(f166,plain,
! [X0] :
( ~ in(sK0,relation_restriction(sK2,sK1))
| ~ relation(X0)
| ~ in(sK0,relation_restriction(X0,sK1)) ),
inference(forward_subsumption_resolution,[],[f164,f104]) ).
fof(f170,plain,
( ~ in(sK0,relation_restriction(sK2,sK1))
| ~ relation(sK2) ),
inference(factoring,[],[f166]) ).
fof(f171,plain,
~ in(sK0,relation_restriction(sK2,sK1)),
inference(forward_subsumption_resolution,[],[f170,f44]) ).
fof(f234,plain,
( ~ in(sK0,sK2)
| ~ in(sK0,cartesian_product2(sK1,sK1))
| ~ relation(sK2) ),
inference(resolution,[],[f98,f171]) ).
fof(f241,plain,
( ~ in(sK0,cartesian_product2(sK1,sK1))
| ~ relation(sK2) ),
inference(forward_subsumption_resolution,[],[f234,f104]) ).
fof(f243,plain,
~ in(sK0,cartesian_product2(sK1,sK1)),
inference(forward_subsumption_resolution,[],[f241,f44]) ).
fof(f245,plain,
in(sK0,relation_restriction(sK2,sK1)),
inference(resolution,[],[f243,f45]) ).
fof(f247,plain,
$false,
inference(forward_subsumption_resolution,[],[f245,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n016.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 04:23:18 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
% 3.58/1.50 % (3254778)Detected formulas, will run a generic FOF schedule.
% 3.58/1.50 % (3254783)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=3475324810:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.50 % (3254784)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=3772602252:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.50 % (3254787)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2207201324:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.50 % (3254788)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1340938916:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.50 % (3254786)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1579241927:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.50 % (3254785)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=2498283575:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.50 % (3254786)Refutation not found, incomplete strategy
% 3.58/1.50 % (3254786)------------------------------
% 3.58/1.50 % (3254786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.50 % (3254786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.50 % (3254786)CaDiCaL version: 2.1.3
% 3.58/1.50 % (3254786)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.50 % (3254786)Time elapsed: 0.002 s
% 3.58/1.50 % (3254786)Peak memory usage: 88 MB
% 3.58/1.50 % (3254787)First to succeed.
% 3.58/1.50 % (3254788)Also succeeded, but the first one will report.
% 3.58/1.50 % (3254787)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3254778"
% 3.58/1.50 % (3254789)dis-21_1_sil=8000:lcm=predicate:random_seed=2102022841: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)
% 3.58/1.50 % (3254789)Instruction limit reached!
% 3.58/1.50 % (3254789)------------------------------
% 3.58/1.50 % (3254789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.50 % (3254789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.50 % (3254789)CaDiCaL version: 2.1.3
% 3.58/1.50 % (3254789)Termination reason: Instruction limit
% 3.58/1.50 % (3254789)Termination phase: Saturation
% 3.58/1.50 % (3254789)Time elapsed: 0.072 s
% 3.58/1.50 % (3254789)Peak memory usage: 89 MB
% 3.58/1.50 % (3254789)Instructions burned: 130 (million)
% 3.58/1.50 % (3254786)------------------------------
% 3.58/1.50 % (3254786)------------------------------
% 3.58/1.50 % (3254797)lrs+10_1_sil=8000:sp=occurrence:random_seed=2768770170:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.58/1.50 % (3254787)Refutation found. Thanks to Tanya!
% 3.58/1.50 % SZS status Theorem for theBenchmark
% 3.58/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.50 % (3254787)------------------------------
% 3.71/1.50 % (3254787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.50 % (3254787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.50 % (3254787)CaDiCaL version: 2.1.3
% 3.71/1.50 % (3254787)Termination reason: Refutation
% 3.71/1.50 % (3254787)Time elapsed: 0.007 s
% 3.71/1.50 % (3254787)Peak memory usage: 88 MB
% 3.71/1.50 % (3254787)Instructions burned: 8 (million)
% 3.71/1.50 % (3254787)------------------------------
% 3.71/1.50 % (3254787)------------------------------
% 3.71/1.50 % (3254778)Success in time 0.428 s
% 3.71/1.50 % Vampire exiting
%------------------------------------------------------------------------------