%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:41:17 PM UTC 2026
% Result : Theorem 1.78s 1.12s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 13 unt; 9 def)
% Number of atoms : 259 ( 64 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 296 ( 130 ~; 132 |; 22 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X0 = empty_set
& X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X0 = empty_set
& X1 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1] :
( union(X0,X1) = empty_set
<~> ( X0 = empty_set
& X1 = empty_set ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
? [X0,X1] :
( ( empty_set != X0
| empty_set != X1
| union(X0,X1) != empty_set )
& ( ( X0 = empty_set
& X1 = empty_set )
| union(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f13,plain,
? [X0,X1] :
( ( empty_set != X0
| empty_set != X1
| union(X0,X1) != empty_set )
& ( ( X0 = empty_set
& X1 = empty_set )
| union(X0,X1) = empty_set ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( empty_set != sK0
| empty_set != sK1
| empty_set != union(sK0,sK1) )
& ( ( empty_set = sK0
& empty_set = sK1 )
| empty_set = union(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
fof(f15,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,[],[f8]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(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,[sK2]),skolemize(X2,sK2(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( empty_set = sK1
| empty_set = union(sK0,sK1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( empty_set = sK0
| empty_set = union(sK0,sK1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( empty_set != sK0
| empty_set != sK1
| empty_set != union(sK0,sK1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f32,definition,
~ sP3(empty_set),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f33,definition,
~ sP4(empty_set),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f34,definition,
~ sP5(empty_set),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f35,plain,
( sP3(sK0)
| sP4(sK1)
| sP5(union(sK0,sK1)) ),
inference(inequality_splitting,[],[f22,f34,f33,f32]) ).
fof(f39,definition,
( spl6_1
<=> empty_set = union(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f41,plain,
( empty_set = union(sK0,sK1)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl6_2
<=> empty_set = sK1 ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f44,plain,
( empty_set != sK1
| spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( empty_set = sK1
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f20,f43,f39]) ).
fof(f48,definition,
( spl6_3
<=> empty_set = sK0 ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f49,plain,
( empty_set != sK0
| spl6_3 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( empty_set = sK0
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f21,f48,f39]) ).
fof(f53,definition,
( spl6_4
<=> sP5(union(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f55,plain,
( sP5(union(sK0,sK1))
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl6_5
<=> sP4(sK1) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f61,definition,
( spl6_6
<=> sP3(sK0) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f64,plain,
( spl6_4
| spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f35,f61,f57,f53]) ).
fof(f66,plain,
( ~ sP4(sK1)
| ~ spl6_2 ),
inference(superposition,[],[f33,f45]) ).
fof(f68,plain,
( ! [X0] : ~ member(X0,sK1)
| ~ spl6_2 ),
inference(superposition,[],[f31,f45]) ).
fof(f69,plain,
( ~ spl6_5
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f66,f43,f57]) ).
fof(f71,plain,
( sK0 = sK1
| ~ spl6_2
| ~ spl6_3 ),
inference(superposition,[],[f45,f50]) ).
fof(f72,plain,
( ~ sP5(sK0)
| ~ spl6_3 ),
inference(superposition,[],[f34,f50]) ).
fof(f74,plain,
( ~ sP3(sK0)
| ~ spl6_3 ),
inference(superposition,[],[f32,f50]) ).
fof(f75,plain,
( ! [X0] : ~ member(X0,sK0)
| ~ spl6_3 ),
inference(superposition,[],[f31,f50]) ).
fof(f76,plain,
( ~ spl6_6
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f74,f48,f61]) ).
fof(f77,plain,
( ! [X0] :
( sK1 = X0
| member(sK2(X0,sK1),X0) )
| ~ spl6_2 ),
inference(resolution,[],[f68,f25]) ).
fof(f78,plain,
( ! [X0] :
( sK0 = X0
| member(sK2(X0,sK1),X0) )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f77,f71]) ).
fof(f79,plain,
( ! [X0] :
( member(sK2(X0,sK0),X0)
| sK0 = X0 )
| ~ spl6_2
| ~ spl6_3 ),
inference(forward_demodulation,[],[f78,f71]) ).
fof(f83,plain,
( sP5(union(sK0,sK0))
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(superposition,[],[f55,f71]) ).
fof(f87,plain,
( ! [X0,X1] :
( member(sK2(union(X0,X1),sK0),X1)
| union(X0,X1) = sK0
| member(sK2(union(X0,X1),sK0),X0) )
| ~ spl6_2
| ~ spl6_3 ),
inference(resolution,[],[f79,f28]) ).
fof(f95,plain,
( ! [X0] :
( member(sK2(union(X0,sK0),sK0),X0)
| sK0 = union(X0,sK0) )
| ~ spl6_2
| ~ spl6_3 ),
inference(resolution,[],[f87,f75]) ).
fof(f110,plain,
( sK0 = union(sK0,sK0)
| ~ spl6_2
| ~ spl6_3 ),
inference(resolution,[],[f95,f75]) ).
fof(f132,plain,
( sP5(sK0)
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(superposition,[],[f83,f110]) ).
fof(f137,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f132,f72]) ).
fof(f138,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f137]) ).
fof(f139,plain,
( sK0 = union(sK0,sK1)
| ~ spl6_1
| ~ spl6_3 ),
inference(forward_demodulation,[],[f41,f50]) ).
fof(f141,plain,
( sP5(sK0)
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(superposition,[],[f55,f139]) ).
fof(f146,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f141,f72]) ).
fof(f147,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f158,plain,
( sK1 != union(sK0,sK1)
| ~ spl6_1
| spl6_2 ),
inference(forward_demodulation,[],[f44,f41]) ).
fof(f163,plain,
( ! [X0] : ~ member(X0,union(sK0,sK1))
| ~ spl6_1 ),
inference(superposition,[],[f31,f41]) ).
fof(f165,plain,
( ! [X0] : ~ member(X0,sK1)
| ~ spl6_1 ),
inference(resolution,[],[f163,f29]) ).
fof(f166,plain,
( ! [X0] : ~ member(X0,sK0)
| ~ spl6_1 ),
inference(resolution,[],[f163,f30]) ).
fof(f167,plain,
( ! [X0] :
( member(sK2(X0,sK1),X0)
| sK1 = X0 )
| ~ spl6_1 ),
inference(resolution,[],[f165,f25]) ).
fof(f171,plain,
( sK1 = union(sK0,sK1)
| ~ spl6_1 ),
inference(resolution,[],[f167,f163]) ).
fof(f172,plain,
( empty_set = sK1
| ~ spl6_1 ),
inference(resolution,[],[f167,f31]) ).
fof(f173,plain,
( sK0 = sK1
| ~ spl6_1 ),
inference(resolution,[],[f167,f166]) ).
fof(f176,plain,
( empty_set = sK0
| ~ spl6_1 ),
inference(forward_demodulation,[],[f172,f173]) ).
fof(f177,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f171,f158]) ).
fof(f178,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f180,plain,
( $false
| ~ spl6_1
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f176,f49]) ).
fof(f181,plain,
( ~ spl6_1
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( spl6_4
| spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
( ~ spl6_2
| ~ spl6_5 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( ~ spl6_3
| ~ spl6_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f138]) ).
cnf(s7,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f147]) ).
cnf(s9,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s10,plain,
( ~ spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f181]) ).
cnf(s11,plain,
spl6_1,
inference(rat,[],[s3,s4,s6,s5,s1,s2]) ).
cnf(s12,plain,
spl6_3,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl6_2,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
~ spl6_4,
inference(rat,[],[s7,s12,s11]) ).
cnf(s15,plain,
~ spl6_6,
inference(rat,[],[s5,s12]) ).
cnf(s16,plain,
~ spl6_5,
inference(rat,[],[s4,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s3,s15,s16,s14]) ).
fof(f184,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.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 02:23:18 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 1.78/1.12 % (4154629)Detected formulas, will run a generic FOF schedule.
% 1.78/1.12 % (4154637)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3404903675:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.78/1.12 % (4154637)First to succeed.
% 1.78/1.12 % (4154637)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4154629"
% 1.78/1.12 % (4154638)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2457878769:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.78/1.12 % (4154636)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=1646720157:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.78/1.12 % (4154635)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=3657337557:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.78/1.12 % (4154640)dis-21_1_sil=8000:lcm=predicate:random_seed=2200049998: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)
% 1.78/1.12 % (4154634)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=2962717736:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.78/1.12 % (4154638)Also succeeded, but the first one will report.
% 1.78/1.12 % (4154639)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1697344787:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.78/1.12 % (4154639)Also succeeded, but the first one will report.
% 1.78/1.12 % (4154640)Instruction limit reached!
% 1.78/1.12 % (4154640)------------------------------
% 1.78/1.12 % (4154640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.78/1.12 % (4154640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/1.12 % (4154640)CaDiCaL version: 2.1.3
% 1.78/1.12 % (4154640)Termination reason: Instruction limit
% 1.78/1.12 % (4154640)Termination phase: Saturation
% 1.78/1.12 % (4154640)Time elapsed: 0.068 s
% 1.78/1.12 % (4154640)Peak memory usage: 89 MB
% 1.78/1.12 % (4154640)Instructions burned: 131 (million)
% 1.78/1.12 % (4154637)Refutation found. Thanks to Tanya!
% 1.78/1.12 % SZS status Theorem for theBenchmark
% 1.78/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.31 % (4154637)------------------------------
% 2.63/1.31 % (4154637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.31 % (4154637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.31 % (4154637)CaDiCaL version: 2.1.3
% 2.63/1.31 % (4154637)Termination reason: Refutation
% 2.63/1.31 % (4154637)Time elapsed: 0.004 s
% 2.63/1.31 % (4154637)Peak memory usage: 90 MB
% 2.63/1.31 % (4154637)Instructions burned: 6 (million)
% 2.63/1.31 % (4154637)------------------------------
% 2.63/1.31 % (4154637)------------------------------
% 2.63/1.31 % (4154629)Success in time 0.286 s
% 2.63/1.31 % Vampire exiting
%------------------------------------------------------------------------------