%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU120+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 2.78s 1.36s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 6 unt; 5 def)
% Number of atoms : 114 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 129 ( 63 ~; 44 |; 17 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f13,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)],[f12]) ).
fof(f14,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,[],[f13]) ).
fof(f16,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,[],[f14]) ).
fof(f19,plain,
( ( ~ disjoint(sK0,sK1)
& ! [X2] : ~ in(X2,set_intersection2(sK0,sK1)) )
| ( in(sK2,set_intersection2(sK0,sK1))
& disjoint(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[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(sK3(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X2] :
( ~ in(X2,set_intersection2(sK0,sK1))
| disjoint(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
( ~ disjoint(sK0,sK1)
| in(sK2,set_intersection2(sK0,sK1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X0] :
( in(sK3(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,definition,
~ sP4(empty_set),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f37,plain,
! [X2,X0] :
( ~ in(X2,X0)
| sP4(X0) ),
inference(inequality_splitting,[],[f30,f36]) ).
fof(f38,definition,
~ sP5(empty_set),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f39,plain,
! [X0,X1] :
( sP5(set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(inequality_splitting,[],[f35,f38]) ).
fof(f41,definition,
( spl6_1
<=> disjoint(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f42,plain,
( ~ disjoint(sK0,sK1)
| spl6_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( disjoint(sK0,sK1)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl6_2
<=> ! [X2] : ~ in(X2,set_intersection2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f46,plain,
( ! [X2] : ~ in(X2,set_intersection2(sK0,sK1))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f24,f45,f41]) ).
fof(f49,definition,
( spl6_3
<=> in(sK2,set_intersection2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f51,plain,
( in(sK2,set_intersection2(sK0,sK1))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,plain,
( spl6_3
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f27,f41,f49]) ).
fof(f54,plain,
( empty_set = set_intersection2(sK0,sK1)
| ~ spl6_2 ),
inference(resolution,[],[f46,f31]) ).
fof(f57,plain,
( sP5(empty_set)
| disjoint(sK0,sK1)
| ~ spl6_2 ),
inference(superposition,[],[f39,f54]) ).
fof(f58,plain,
( disjoint(sK0,sK1)
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f57,f38]) ).
fof(f59,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f58,f42]) ).
fof(f60,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f67,plain,
( in(sK2,empty_set)
| ~ disjoint(sK0,sK1)
| ~ spl6_3 ),
inference(superposition,[],[f51,f34]) ).
fof(f68,plain,
( in(sK2,empty_set)
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f67,f43]) ).
fof(f70,plain,
( sP4(empty_set)
| ~ spl6_1
| ~ spl6_3 ),
inference(resolution,[],[f68,f37]) ).
fof(f71,plain,
( $false
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f70,f36]) ).
fof(f72,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s6,plain,
( ~ spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f72]) ).
cnf(s7,plain,
spl6_1,
inference(rat,[],[s1,s4]) ).
cnf(s8,plain,
~ spl6_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f73,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU120+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:37:25 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.78/1.36 % (1844750)Detected formulas, will run a generic FOF schedule.
% 2.78/1.36 % (1844758)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3558767845:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.36 % (1844758)First to succeed.
% 2.78/1.36 % (1844758)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1844750"
% 2.78/1.36 % (1844759)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1010345748:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.36 % (1844761)dis-21_1_sil=8000:lcm=predicate:random_seed=3926905353: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)
% 2.78/1.36 % (1844755)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=1931419210:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.36 % (1844756)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=3847656260:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.36 % (1844757)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=1891914642:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.36 % (1844760)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=605214597:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.36 % (1844761)Refutation not found, incomplete strategy
% 2.78/1.36 % (1844761)------------------------------
% 2.78/1.36 % (1844761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.36 % (1844761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.36 % (1844761)CaDiCaL version: 2.1.3
% 2.78/1.36 % (1844761)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.36 % (1844761)Time elapsed: 0.002 s
% 2.78/1.36 % (1844761)Peak memory usage: 88 MB
% 2.78/1.36 % (1844761)Instructions burned: 1 (million)
% 2.78/1.36 % (1844759)Also succeeded, but the first one will report.
% 2.78/1.36 % (1844760)Also succeeded, but the first one will report.
% 2.78/1.36 % (1844758)Refutation found. Thanks to Tanya!
% 2.78/1.36 % SZS status Theorem for theBenchmark
% 2.78/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.37 % (1844758)------------------------------
% 2.78/1.37 % (1844758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (1844758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (1844758)CaDiCaL version: 2.1.3
% 2.78/1.37 % (1844758)Termination reason: Refutation
% 2.78/1.37 % (1844758)Time elapsed: 0.002 s
% 2.78/1.37 % (1844758)Peak memory usage: 89 MB
% 2.78/1.37 % (1844758)Instructions burned: 2 (million)
% 2.78/1.37 % (1844758)------------------------------
% 2.78/1.37 % (1844758)------------------------------
% 2.78/1.37 % (1844750)Success in time 0.313 s
% 2.78/1.37 % Vampire exiting
%------------------------------------------------------------------------------