%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:39:47 PM UTC 2026
% Result : Theorem 2.59s 1.33s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 6 unt; 6 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 204 ( 83 ~; 99 |; 11 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( set_equal(X0,X1)
<=> ! [X2] :
( element(X2,X0)
<=> element(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43_1) ).
fof(f2,conjecture,
! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43) ).
fof(f3,negated_conjecture,
~ ! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( set_equal(X0,X1)
<~> set_equal(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ? [X2] :
( ( ~ element(X2,X1)
| ~ element(X2,X0) )
& ( element(X2,X1)
| element(X2,X0) ) ) )
& ( ! [X2] :
( ( element(X2,X0)
| ~ element(X2,X1) )
& ( element(X2,X1)
| ~ element(X2,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ? [X2] :
( ( ~ element(X2,X1)
| ~ element(X2,X0) )
& ( element(X2,X1)
| element(X2,X0) ) ) )
& ( ! [X3] :
( ( element(X3,X0)
| ~ element(X3,X1) )
& ( element(X3,X1)
| ~ element(X3,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( set_equal(X0,X1)
| ( ( ~ element(sK0(X0,X1),X1)
| ~ element(sK0(X0,X1),X0) )
& ( element(sK0(X0,X1),X1)
| element(sK0(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( element(X3,X0)
| ~ element(X3,X1) )
& ( element(X3,X1)
| ~ element(X3,X0) ) )
| ~ set_equal(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( ( ~ set_equal(X1,X0)
| ~ set_equal(X0,X1) )
& ( set_equal(X1,X0)
| set_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f9,plain,
( ( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) )
& ( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f8]) ).
fof(f10,plain,
! [X3,X0,X1] :
( element(X3,X1)
| ~ element(X3,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X3,X0,X1] :
( element(X3,X0)
| ~ element(X3,X1)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( element(sK0(X0,X1),X0)
| element(sK0(X0,X1),X1)
| set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( set_equal(X0,X1)
| ~ element(sK0(X0,X1),X1)
| ~ element(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,definition,
( spl3_1
<=> set_equal(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f20,definition,
( spl3_2
<=> set_equal(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f14,f20,f17]) ).
fof(f23,plain,
( ~ set_equal(sK1,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f24,plain,
( ~ set_equal(sK2,sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f25,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f15,f20,f17]) ).
fof(f28,definition,
( spl3_3
<=> element(sK0(sK1,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f29,plain,
( ~ element(sK0(sK1,sK2),sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,definition,
( spl3_4
<=> element(sK0(sK1,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f32,plain,
( ~ element(sK0(sK1,sK2),sK2)
| spl3_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f36,plain,
( ! [X0] :
( ~ element(sK0(sK1,sK2),X0)
| ~ set_equal(X0,sK1) )
| spl3_3 ),
inference(resolution,[],[f29,f10]) ).
fof(f37,plain,
( element(sK0(sK1,sK2),sK2)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f44,plain,
( ~ set_equal(sK2,sK1)
| spl3_3
| ~ spl3_4 ),
inference(resolution,[],[f36,f37]) ).
fof(f47,plain,
( ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f44,f31,f28,f20]) ).
fof(f51,definition,
( spl3_5
<=> element(sK0(sK2,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f52,plain,
( ~ element(sK0(sK2,sK1),sK2)
| spl3_5 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl3_6
<=> element(sK0(sK2,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f55,plain,
( ~ element(sK0(sK2,sK1),sK1)
| spl3_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f60,plain,
( element(sK0(sK2,sK1),sK1)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f62,plain,
( ! [X0] :
( ~ element(sK0(sK2,sK1),X0)
| ~ set_equal(sK1,X0) )
| spl3_6 ),
inference(resolution,[],[f55,f11]) ).
fof(f64,plain,
( ~ set_equal(sK1,sK2)
| element(sK0(sK2,sK1),sK1)
| set_equal(sK2,sK1)
| spl3_6 ),
inference(resolution,[],[f62,f12]) ).
fof(f67,plain,
( spl3_2
| spl3_6
| ~ spl3_1
| spl3_6 ),
inference(avatar_split_clause,[],[f64,f54,f17,f54,f20]) ).
fof(f68,plain,
( ~ element(sK0(sK1,sK2),sK2)
| ~ element(sK0(sK1,sK2),sK1)
| spl3_1 ),
inference(resolution,[],[f23,f13]) ).
fof(f69,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f68,f17,f31,f28]) ).
fof(f70,plain,
( ! [X0] :
( ~ element(sK0(sK1,sK2),X0)
| ~ set_equal(sK2,X0) )
| spl3_4 ),
inference(resolution,[],[f32,f11]) ).
fof(f72,plain,
( ~ set_equal(sK2,sK1)
| element(sK0(sK1,sK2),sK2)
| set_equal(sK1,sK2)
| spl3_4 ),
inference(resolution,[],[f70,f12]) ).
fof(f75,plain,
( spl3_1
| spl3_4
| ~ spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f72,f31,f20,f31,f17]) ).
fof(f76,plain,
( ~ element(sK0(sK2,sK1),sK1)
| ~ element(sK0(sK2,sK1),sK2)
| spl3_2 ),
inference(resolution,[],[f24,f13]) ).
fof(f77,plain,
( ~ spl3_5
| ~ spl3_6
| spl3_2 ),
inference(avatar_split_clause,[],[f76,f20,f54,f51]) ).
fof(f80,plain,
( ! [X0] :
( ~ element(sK0(sK2,sK1),X0)
| ~ set_equal(X0,sK2) )
| spl3_5 ),
inference(resolution,[],[f52,f10]) ).
fof(f90,plain,
( ~ set_equal(sK1,sK2)
| spl3_5
| ~ spl3_6 ),
inference(resolution,[],[f80,f60]) ).
fof(f93,plain,
( ~ spl3_1
| spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f90,f54,f51,f17]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s5,plain,
( ~ spl3_2
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s9,plain,
( spl3_6
| spl3_2
| ~ spl3_1
| spl3_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s10,plain,
( ~ spl3_1
| spl3_2
| spl3_6 ),
inference(rat,[],[s9]) ).
cnf(s11,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f69]) ).
cnf(s12,plain,
( spl3_4
| ~ spl3_2
| spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f75]) ).
cnf(s13,plain,
( spl3_1
| ~ spl3_2
| spl3_4 ),
inference(rat,[],[s12]) ).
cnf(s14,plain,
( spl3_2
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s16,plain,
( ~ spl3_1
| spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f93]) ).
cnf(s17,plain,
( spl3_1
| ~ spl3_2 ),
inference(rat,[],[s5,s11,s13]) ).
cnf(s18,plain,
spl3_1,
inference(rat,[],[s17,s1]) ).
cnf(s19,plain,
~ spl3_2,
inference(rat,[],[s2,s18]) ).
cnf(s20,plain,
spl3_6,
inference(rat,[],[s10,s18,s19]) ).
cnf(s21,plain,
~ spl3_5,
inference(rat,[],[s14,s19,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s16,s18,s20,s21]) ).
fof(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:25:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.59/1.33 % (3362411)Detected formulas, will run a generic FOF schedule.
% 2.59/1.33 % (3362422)dis-21_1_sil=8000:lcm=predicate:random_seed=952656155: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)
% 2.59/1.33 % (3362422)First to succeed.
% 2.59/1.33 % (3362422)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3362411"
% 2.59/1.33 % (3362421)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1611950496:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.33 % (3362420)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4249794709:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.33 % (3362419)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4230250537:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.33 % (3362418)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=1951663468:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.33 % (3362417)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=975008969:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.33 % (3362416)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=3637397025:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.33 % (3362420)Refutation not found, incomplete strategy
% 2.59/1.33 % (3362420)------------------------------
% 2.59/1.33 % (3362420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.33 % (3362420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.33 % (3362420)CaDiCaL version: 2.1.3
% 2.59/1.33 % (3362420)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.33 % (3362420)Time elapsed: 0.001 s
% 2.59/1.33 % (3362420)Peak memory usage: 87 MB
% 2.59/1.33 % (3362419)Refutation not found, incomplete strategy
% 2.59/1.33 % (3362419)------------------------------
% 2.59/1.33 % (3362419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.33 % (3362419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.33 % (3362419)CaDiCaL version: 2.1.3
% 2.59/1.33 % (3362419)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.33 % (3362419)Time elapsed: 0.001 s
% 2.59/1.33 % (3362419)Peak memory usage: 87 MB
% 2.59/1.33 % (3362421)Also succeeded, but the first one will report.
% 2.59/1.33 % (3362422)Refutation found. Thanks to Tanya!
% 2.59/1.33 % SZS status Theorem for theBenchmark
% 2.59/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.34 % (3362422)------------------------------
% 2.59/1.34 % (3362422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.34 % (3362422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.34 % (3362422)CaDiCaL version: 2.1.3
% 2.59/1.34 % (3362422)Termination reason: Refutation
% 2.59/1.34 % (3362422)Time elapsed: 0.002 s
% 2.59/1.34 % (3362422)Peak memory usage: 89 MB
% 2.59/1.34 % (3362422)Instructions burned: 2 (million)
% 2.59/1.34 % (3362422)------------------------------
% 2.59/1.34 % (3362422)------------------------------
% 2.59/1.34 % (3362411)Success in time 0.277 s
% 2.59/1.34 % Vampire exiting
%------------------------------------------------------------------------------