%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU120+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 : n017.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 3.39s 1.26s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 4 unt; 3 def)
% Number of atoms : 192 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 245 ( 107 ~; 85 |; 48 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(f13,axiom,
! [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,conjecture,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,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,[],[f13]) ).
fof(f18,plain,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f21,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,[],[f17]) ).
fof(f22,plain,
? [X0,X1] :
( ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
| ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f28,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,[],[f27]) ).
fof(f29,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))],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ( in(sK4(X0,X1),X0)
& in(sK4(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f21]) ).
fof(f34,plain,
( ( ~ disjoint(sK5,sK6)
& ! [X2] : ~ in(X2,set_intersection2(sK5,sK6)) )
| ( in(sK7,set_intersection2(sK5,sK6))
& disjoint(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X3,sK7)],[f22]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f54,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X2] :
( ~ in(X2,set_intersection2(sK5,sK6))
| disjoint(sK5,sK6) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
( ~ disjoint(sK5,sK6)
| in(sK7,set_intersection2(sK5,sK6)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f41]) ).
fof(f61,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f40]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f39]) ).
fof(f75,definition,
( spl9_1
<=> disjoint(sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f76,plain,
( disjoint(sK5,sK6)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl9_2
<=> ! [X2] : ~ in(X2,set_intersection2(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f79,plain,
( ! [X2] : ~ in(X2,set_intersection2(sK5,sK6))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f55,f78,f75]) ).
fof(f82,definition,
( spl9_3
<=> in(sK7,set_intersection2(sK5,sK6)) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f83,plain,
( in(sK7,set_intersection2(sK5,sK6))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( ~ disjoint(sK5,sK6)
| spl9_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f86,plain,
( spl9_3
| ~ spl9_1 ),
inference(avatar_split_clause,[],[f58,f75,f82]) ).
fof(f90,plain,
( in(sK4(sK5,sK6),sK6)
| spl9_1 ),
inference(resolution,[],[f53,f85]) ).
fof(f94,plain,
( in(sK4(sK5,sK6),sK5)
| spl9_1 ),
inference(resolution,[],[f54,f85]) ).
fof(f112,plain,
( ! [X0] :
( ~ in(X0,sK6)
| ~ in(X0,sK5) )
| ~ spl9_2 ),
inference(resolution,[],[f60,f79]) ).
fof(f118,plain,
( ~ in(sK4(sK5,sK6),sK5)
| spl9_1
| ~ spl9_2 ),
inference(resolution,[],[f112,f90]) ).
fof(f120,plain,
( $false
| spl9_1
| ~ spl9_2 ),
inference(resolution,[],[f118,f94]) ).
fof(f121,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f122,plain,
( ! [X0] :
( ~ in(X0,sK6)
| ~ in(X0,sK5) )
| ~ spl9_1 ),
inference(resolution,[],[f76,f52]) ).
fof(f124,plain,
( in(sK7,sK6)
| ~ spl9_3 ),
inference(resolution,[],[f83,f62]) ).
fof(f125,plain,
( in(sK7,sK5)
| ~ spl9_3 ),
inference(resolution,[],[f83,f61]) ).
fof(f131,plain,
( ~ in(sK7,sK5)
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f122,f124]) ).
fof(f132,plain,
( $false
| ~ spl9_1
| ~ spl9_3 ),
inference(resolution,[],[f131,f125]) ).
fof(f133,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f132]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( ~ spl9_1
| spl9_3 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s6,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
spl9_1,
inference(rat,[],[s1,s4]) ).
cnf(s8,plain,
~ spl9_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f134,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n017.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 03:32:36 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
% 3.39/1.26 % (3183286)Detected formulas, will run a generic FOF schedule.
% 3.39/1.26 % (3183296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2733753313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.26 % (3183292)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=3654228174:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.26 % (3183291)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=152675659:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.26 % (3183295)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=137813818:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.26 % (3183294)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2853111743:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.26 % (3183293)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=4089179253:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.26 % (3183297)dis-21_1_sil=8000:lcm=predicate:random_seed=2205820205: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)
% 3.39/1.26 % (3183297)First to succeed.
% 3.39/1.26 % (3183294)Also succeeded, but the first one will report.
% 3.39/1.26 % (3183296)Also succeeded, but the first one will report.
% 3.39/1.26 % (3183295)Also succeeded, but the first one will report.
% 3.39/1.26 % (3183297)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3183286"
% 3.39/1.26 % (3183297)Refutation found. Thanks to Tanya!
% 3.39/1.26 % SZS status Theorem for theBenchmark
% 3.39/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.26 % (3183297)------------------------------
% 3.39/1.26 % (3183297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.26 % (3183297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.26 % (3183297)CaDiCaL version: 2.1.3
% 3.39/1.26 % (3183297)Termination reason: Refutation
% 3.39/1.26 % (3183297)Time elapsed: 0.004 s
% 3.39/1.26 % (3183297)Peak memory usage: 89 MB
% 3.39/1.26 % (3183297)Instructions burned: 3 (million)
% 3.39/1.26 % (3183297)------------------------------
% 3.39/1.26 % (3183297)------------------------------
% 3.39/1.26 % (3183286)Success in time 0.429 s
% 3.39/1.26 % Vampire exiting
%------------------------------------------------------------------------------