%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:41:27 PM UTC 2026
% Result : Theorem 2.64s 1.24s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 7 unt; 2 def)
% Number of atoms : 148 ( 17 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 155 ( 60 ~; 67 |; 19 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 48 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f4,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f7,conjecture,
! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0] :
( intersect(X0,X0)
<~> not_equal(X0,empty_set) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f18,plain,
? [X0] :
( ( ~ not_equal(X0,empty_set)
| ~ intersect(X0,X0) )
& ( not_equal(X0,empty_set)
| intersect(X0,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f19,plain,
( ( ~ not_equal(sK2,empty_set)
| ~ intersect(sK2,sK2) )
& ( not_equal(sK2,empty_set)
| intersect(sK2,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| X0 = X1
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
( not_equal(sK2,empty_set)
| intersect(sK2,sK2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
( ~ not_equal(sK2,empty_set)
| ~ intersect(sK2,sK2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f28]) ).
fof(f37,definition,
( spl3_1
<=> intersect(sK2,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f38,plain,
( ~ intersect(sK2,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( intersect(sK2,sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f41,definition,
( spl3_2
<=> not_equal(sK2,empty_set) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f42,plain,
( ~ not_equal(sK2,empty_set)
| spl3_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( not_equal(sK2,empty_set)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f31,f41,f37]) ).
fof(f45,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f32,f41,f37]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(X0,X1)
| intersect(X1,X1) ),
inference(factoring,[],[f22]) ).
fof(f48,plain,
! [X0] :
( member(sK1(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f26,f23]) ).
fof(f56,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0 ),
inference(resolution,[],[f48,f47]) ).
fof(f64,plain,
( empty_set = sK2
| spl3_1 ),
inference(resolution,[],[f56,f38]) ).
fof(f76,plain,
( not_equal(sK2,sK2)
| spl3_1
| ~ spl3_2 ),
inference(superposition,[],[f43,f64]) ).
fof(f77,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f76,f35]) ).
fof(f78,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f79,plain,
( member(sK0(sK2,sK2),sK2)
| ~ spl3_1 ),
inference(resolution,[],[f39,f21]) ).
fof(f82,plain,
( empty_set = sK2
| spl3_2 ),
inference(resolution,[],[f42,f29]) ).
fof(f85,plain,
( ! [X0] : ~ member(X0,sK2)
| spl3_2 ),
inference(superposition,[],[f23,f82]) ).
fof(f89,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f79,f85]) ).
fof(f90,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f89]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s5,plain,
spl3_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:26:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 2.64/1.24 % (2202032)Detected formulas, will run a generic FOF schedule.
% 2.64/1.24 % (2202137)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2949737115:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.24 % (2202137)First to succeed.
% 2.64/1.24 % (2202137)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2202032"
% 2.64/1.24 % (2202138)dis-21_1_sil=8000:lcm=predicate:random_seed=495676821: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)
% 2.64/1.24 % (2202134)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2304564619:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.24 % (2202136)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2357028026:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.24 % (2202132)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=1672194067:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.24 % (2202131)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=2355619182:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.24 % (2202133)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=715294136:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.24 % (2202134)Refutation not found, incomplete strategy
% 2.64/1.24 % (2202134)------------------------------
% 2.64/1.24 % (2202134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (2202134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (2202134)CaDiCaL version: 2.1.3
% 2.64/1.24 % (2202134)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.24 % (2202134)Time elapsed: 0.001 s
% 2.64/1.24 % (2202134)Peak memory usage: 88 MB
% 2.64/1.24 % (2202138)Refutation not found, incomplete strategy
% 2.64/1.24 % (2202138)------------------------------
% 2.64/1.24 % (2202138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (2202138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (2202138)CaDiCaL version: 2.1.3
% 2.64/1.24 % (2202138)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.24 % (2202138)Time elapsed: 0.002 s
% 2.64/1.24 % (2202138)Peak memory usage: 88 MB
% 2.64/1.24 % (2202138)Instructions burned: 1 (million)
% 2.64/1.24 % (2202136)Also succeeded, but the first one will report.
% 2.64/1.24 % (2202137)Refutation found. Thanks to Tanya!
% 2.64/1.24 % SZS status Theorem for theBenchmark
% 2.64/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.24 % (2202137)------------------------------
% 2.64/1.24 % (2202137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (2202137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (2202137)CaDiCaL version: 2.1.3
% 2.64/1.24 % (2202137)Termination reason: Refutation
% 2.64/1.24 % (2202137)Time elapsed: 0.002 s
% 2.64/1.24 % (2202137)Peak memory usage: 90 MB
% 2.64/1.24 % (2202137)Instructions burned: 3 (million)
% 2.64/1.24 % (2202137)------------------------------
% 2.64/1.24 % (2202137)------------------------------
% 2.64/1.24 % (2202032)Success in time 0.294 s
% 2.64/1.24 % Vampire exiting
%------------------------------------------------------------------------------