%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU119+2 : 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 : n007.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 12:47:17 PM UTC 2026
% Result : Theorem 2.90s 1.25s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 8 unt; 4 def)
% Number of atoms : 228 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 277 ( 118 ~; 105 |; 46 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 85 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,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(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( ( ~ disjoint(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,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,[],[f4]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK1(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,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f30,plain,
( ( ~ disjoint(sK4,sK5)
& ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5) ) )
| ( in(sK6,sK4)
& in(sK6,sK5)
& disjoint(sK4,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X3,sK6)],[f19]) ).
fof(f32,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5)
| disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
( ~ disjoint(sK4,sK5)
| in(sK6,sK5) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( ~ disjoint(sK4,sK5)
| in(sK6,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f33]) ).
fof(f55,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f37]) ).
fof(f56,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f36]) ).
fof(f57,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f35]) ).
fof(f59,definition,
( spl7_1
<=> disjoint(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f61,plain,
( disjoint(sK4,sK5)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl7_2
<=> ! [X2] :
( ~ in(X2,sK4)
| ~ in(X2,sK5) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f64,plain,
( ! [X2] :
( ~ in(X2,sK5)
| ~ in(X2,sK4) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f48,f63,f59]) ).
fof(f67,definition,
( spl7_3
<=> in(sK6,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f69,plain,
( in(sK6,sK5)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f72,definition,
( spl7_4
<=> in(sK6,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f74,plain,
( in(sK6,sK4)
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f52,f59,f67]) ).
fof(f77,plain,
( spl7_4
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f53,f59,f72]) ).
fof(f93,plain,
! [X0,X1] :
( in(sK0(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f56,f34]) ).
fof(f97,plain,
! [X0,X1] :
( in(sK0(set_intersection2(X0,X1)),X1)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f57,f34]) ).
fof(f134,plain,
( ! [X0] :
( ~ in(sK0(set_intersection2(sK5,X0)),sK4)
| empty_set = set_intersection2(sK5,X0) )
| ~ spl7_2 ),
inference(resolution,[],[f93,f64]) ).
fof(f141,plain,
( empty_set = set_intersection2(sK5,sK4)
| empty_set = set_intersection2(sK5,sK4)
| ~ spl7_2 ),
inference(resolution,[],[f97,f134]) ).
fof(f151,plain,
( empty_set = set_intersection2(sK5,sK4)
| ~ spl7_2 ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f152,plain,
( empty_set = set_intersection2(sK4,sK5)
| ~ spl7_2 ),
inference(forward_demodulation,[],[f151,f32]) ).
fof(f153,plain,
( empty_set != empty_set
| disjoint(sK4,sK5)
| ~ spl7_2 ),
inference(superposition,[],[f42,f152]) ).
fof(f158,plain,
( disjoint(sK4,sK5)
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f153]) ).
fof(f161,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f158,f63,f59]) ).
fof(f162,plain,
( empty_set = set_intersection2(sK4,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f61,f41]) ).
fof(f165,plain,
( ! [X0] :
( ~ in(sK6,X0)
| in(sK6,set_intersection2(sK5,X0)) )
| ~ spl7_3 ),
inference(resolution,[],[f69,f55]) ).
fof(f180,plain,
( in(sK6,set_intersection2(sK5,sK4))
| ~ spl7_3
| ~ spl7_4 ),
inference(resolution,[],[f165,f74]) ).
fof(f181,plain,
( in(sK6,set_intersection2(sK4,sK5))
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f180,f32]) ).
fof(f183,plain,
( in(sK6,empty_set)
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f181,f162]) ).
fof(f184,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f183,f54]) ).
fof(f185,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f184]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f76]) ).
cnf(s5,plain,
( ~ spl7_1
| spl7_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f161]) ).
cnf(s10,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f185]) ).
cnf(s11,plain,
spl7_1,
inference(rat,[],[s1,s8]) ).
cnf(s12,plain,
spl7_4,
inference(rat,[],[s5,s11]) ).
cnf(s13,plain,
spl7_3,
inference(rat,[],[s4,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s10,s12,s11,s13]) ).
fof(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:34:31 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 2.90/1.25 % (2000967)Detected formulas, will run a generic FOF schedule.
% 2.90/1.25 % (2000978)dis-21_1_sil=8000:lcm=predicate:random_seed=2565292833: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)
% 2.90/1.25 % (2000972)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=735324373:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.90/1.25 % (2000978)Instruction limit reached!
% 2.90/1.25 % (2000978)------------------------------
% 2.90/1.25 % (2000978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.25 % (2000978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.25 % (2000978)CaDiCaL version: 2.1.3
% 2.90/1.25 % (2000978)Termination reason: Instruction limit
% 2.90/1.25 % (2000978)Termination phase: Saturation
% 2.90/1.25 % (2000978)Time elapsed: 0.038 s
% 2.90/1.25 % (2000978)Peak memory usage: 88 MB
% 2.90/1.25 % (2000978)Instructions burned: 132 (million)
% 2.90/1.25 % (2000977)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=896888662:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.90/1.25 % (2000976)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3862196447:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.90/1.25 % (2000975)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=867023485:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.90/1.25 % (2000973)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=1238791998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.90/1.25 % (2000974)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=2827872737:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.90/1.25 % (2000977)First to succeed.
% 2.90/1.25 % (2000975)Refutation not found, incomplete strategy
% 2.90/1.25 % (2000975)------------------------------
% 2.90/1.25 % (2000975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.25 % (2000975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.25 % (2000975)CaDiCaL version: 2.1.3
% 2.90/1.25 % (2000975)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.25 % (2000975)Time elapsed: 0.002 s
% 2.90/1.25 % (2000975)Peak memory usage: 88 MB
% 2.90/1.25 % (2000975)Instructions burned: 1 (million)
% 2.90/1.25 % (2000977)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2000967"
% 2.90/1.25 % (2000976)Also succeeded, but the first one will report.
% 2.90/1.25 % (2000982)lrs+10_1_sil=8000:sp=occurrence:random_seed=2237735427:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.90/1.25 % (2000982)Also succeeded, but the first one will report.
% 2.90/1.25 % (2000975)------------------------------
% 2.90/1.25 % (2000975)------------------------------
% 2.90/1.25 % (2000977)Refutation found. Thanks to Tanya!
% 2.90/1.25 % SZS status Theorem for theBenchmark
% 2.90/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.44 % (2000977)------------------------------
% 3.46/1.44 % (2000977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.44 % (2000977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.44 % (2000977)CaDiCaL version: 2.1.3
% 3.46/1.44 % (2000977)Termination reason: Refutation
% 3.46/1.44 % (2000977)Time elapsed: 0.007 s
% 3.46/1.44 % (2000977)Peak memory usage: 90 MB
% 3.46/1.44 % (2000977)Instructions burned: 7 (million)
% 3.46/1.44 % (2000977)------------------------------
% 3.46/1.44 % (2000977)------------------------------
% 3.46/1.44 % (2000967)Success in time 0.404 s
% 3.46/1.44 % Vampire exiting
%------------------------------------------------------------------------------