%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:40:09 PM UTC 2026
% Result : Theorem 1.64s 1.13s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 95 ( 27 unt; 22 def)
% Number of atoms : 210 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 206 ( 91 ~; 82 |; 18 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 16 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 43 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
! [X0] :
? [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& X0 = ordered_pair(X1,X2) )
| ( ~ ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
& X1 = X0
& X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).
fof(f45,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& X0 = ordered_pair(X1,X2) )
| ( ~ ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
& X1 = X0
& X2 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0] :
! [X1,X2] :
( ( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != X0 )
& ( ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
| X0 != X1
| X0 != X2 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f47,plain,
! [X1,X2] :
( ( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != sK0 )
& ( ( member(sK1,universal_class)
& member(sK2,universal_class)
& sK0 = ordered_pair(sK1,sK2) )
| sK0 != X1
| sK0 != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2)],[f46]) ).
fof(f50,plain,
! [X2,X1] :
( sK0 = ordered_pair(sK1,sK2)
| sK0 != X1
| sK0 != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f51,plain,
! [X2,X1] :
( member(sK2,universal_class)
| sK0 != X1
| sK0 != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f52,plain,
! [X2,X1] :
( member(sK1,universal_class)
| sK0 != X1
| sK0 != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f53,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != sK0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f57,definition,
~ sP3(sK0),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f58,plain,
! [X2,X1] :
( sP3(ordered_pair(X1,X2))
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(inequality_splitting,[],[f53,f57]) ).
fof(f59,definition,
~ sP4(sK0),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f60,definition,
~ sP5(sK0),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f61,plain,
! [X2,X1] :
( member(sK1,universal_class)
| sP4(X1)
| sP5(X2) ),
inference(inequality_splitting,[],[f52,f60,f59]) ).
fof(f62,definition,
~ sP6(sK0),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f63,definition,
~ sP7(sK0),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f64,plain,
! [X2,X1] :
( member(sK2,universal_class)
| sP6(X1)
| sP7(X2) ),
inference(inequality_splitting,[],[f51,f63,f62]) ).
fof(f65,definition,
~ sP8(sK0),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f66,definition,
~ sP9(sK0),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f67,plain,
! [X2,X1] :
( sK0 = ordered_pair(sK1,sK2)
| sP8(X1)
| sP9(X2) ),
inference(inequality_splitting,[],[f50,f66,f65]) ).
fof(f68,plain,
! [X2] :
( sP5(X2)
| sP10 ),
inference(cnf_transformation,[],[f68_D]) ).
fof(f68_D,definition,
( ! [X2] : sP5(X2)
<=> ~ sP10 ),
introduced(definition,[new_symbols(definition,[sP10])],[general_splitting_component_introduction]) ).
fof(f69,plain,
! [X1] :
( member(sK1,universal_class)
| sP4(X1)
| ~ sP10 ),
inference(general_splitting,[],[f61,f68_D]) ).
fof(f70,plain,
! [X2] :
( sP7(X2)
| sP11 ),
inference(cnf_transformation,[],[f70_D]) ).
fof(f70_D,definition,
( ! [X2] : sP7(X2)
<=> ~ sP11 ),
introduced(definition,[new_symbols(definition,[sP11])],[general_splitting_component_introduction]) ).
fof(f71,plain,
! [X1] :
( member(sK2,universal_class)
| sP6(X1)
| ~ sP11 ),
inference(general_splitting,[],[f64,f70_D]) ).
fof(f72,plain,
! [X2] :
( sP9(X2)
| sP12 ),
inference(cnf_transformation,[],[f72_D]) ).
fof(f72_D,definition,
( ! [X2] : sP9(X2)
<=> ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[general_splitting_component_introduction]) ).
fof(f73,plain,
! [X1] :
( sK0 = ordered_pair(sK1,sK2)
| sP8(X1)
| ~ sP12 ),
inference(general_splitting,[],[f67,f72_D]) ).
fof(f75,definition,
( spl13_1
<=> sP10 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f79,definition,
( spl13_2
<=> ! [X2] : sP5(X2) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] : sP5(X2)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f68,f79,f75]) ).
fof(f83,definition,
( spl13_3
<=> ! [X1] : sP4(X1) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f84,plain,
( ! [X1] : sP4(X1)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl13_4
<=> member(sK1,universal_class) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f88,plain,
( member(sK1,universal_class)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( ~ spl13_1
| spl13_3
| spl13_4 ),
inference(avatar_split_clause,[],[f69,f86,f83,f75]) ).
fof(f91,definition,
( spl13_5
<=> sP11 ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f95,definition,
( spl13_6
<=> ! [X2] : sP7(X2) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f96,plain,
( ! [X2] : sP7(X2)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( spl13_5
| spl13_6 ),
inference(avatar_split_clause,[],[f70,f95,f91]) ).
fof(f99,definition,
( spl13_7
<=> ! [X1] : sP6(X1) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f100,plain,
( ! [X1] : sP6(X1)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl13_8
<=> member(sK2,universal_class) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f104,plain,
( member(sK2,universal_class)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( ~ spl13_5
| spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f71,f102,f99,f91]) ).
fof(f107,definition,
( spl13_9
<=> sP12 ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f111,definition,
( spl13_10
<=> ! [X2] : sP9(X2) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f112,plain,
( ! [X2] : sP9(X2)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( spl13_9
| spl13_10 ),
inference(avatar_split_clause,[],[f72,f111,f107]) ).
fof(f115,definition,
( spl13_11
<=> ! [X1] : sP8(X1) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f116,plain,
( ! [X1] : sP8(X1)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl13_12
<=> sK0 = ordered_pair(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f120,plain,
( sK0 = ordered_pair(sK1,sK2)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl13_9
| spl13_11
| spl13_12 ),
inference(avatar_split_clause,[],[f73,f118,f115,f107]) ).
fof(f122,plain,
( $false
| ~ spl13_2 ),
inference(resolution,[],[f80,f60]) ).
fof(f123,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f124,plain,
( $false
| ~ spl13_6 ),
inference(resolution,[],[f96,f63]) ).
fof(f125,plain,
~ spl13_6,
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f126,plain,
( $false
| ~ spl13_7 ),
inference(resolution,[],[f100,f62]) ).
fof(f127,plain,
~ spl13_7,
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f128,plain,
( $false
| ~ spl13_10 ),
inference(resolution,[],[f112,f66]) ).
fof(f129,plain,
~ spl13_10,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f130,plain,
( $false
| ~ spl13_11 ),
inference(resolution,[],[f116,f65]) ).
fof(f131,plain,
~ spl13_11,
inference(avatar_contradiction_clause,[],[f130]) ).
fof(f132,plain,
( ~ sP3(ordered_pair(sK1,sK2))
| ~ spl13_12 ),
inference(superposition,[],[f57,f120]) ).
fof(f139,plain,
( ~ member(sK2,universal_class)
| ~ member(sK1,universal_class)
| ~ spl13_12 ),
inference(resolution,[],[f132,f58]) ).
fof(f140,plain,
( ~ member(sK1,universal_class)
| ~ spl13_8
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f139,f104]) ).
fof(f141,plain,
( $false
| ~ spl13_4
| ~ spl13_8
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f140,f88]) ).
fof(f142,plain,
( ~ spl13_4
| ~ spl13_8
| ~ spl13_12 ),
inference(avatar_contradiction_clause,[],[f141]) ).
fof(f143,plain,
( $false
| ~ spl13_3 ),
inference(resolution,[],[f84,f59]) ).
fof(f144,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
( ~ spl13_1
| spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f89]) ).
cnf(s3,plain,
( spl13_5
| spl13_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s4,plain,
( ~ spl13_5
| spl13_7
| spl13_8 ),
inference(sat_conversion,[],[f105]) ).
cnf(s5,plain,
( spl13_9
| spl13_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s6,plain,
( ~ spl13_9
| spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s7,plain,
~ spl13_2,
inference(sat_conversion,[],[f123]) ).
cnf(s8,plain,
~ spl13_6,
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
~ spl13_7,
inference(sat_conversion,[],[f127]) ).
cnf(s10,plain,
~ spl13_10,
inference(sat_conversion,[],[f129]) ).
cnf(s11,plain,
~ spl13_11,
inference(sat_conversion,[],[f131]) ).
cnf(s12,plain,
( ~ spl13_4
| ~ spl13_8
| ~ spl13_12 ),
inference(sat_conversion,[],[f142]) ).
cnf(s13,plain,
~ spl13_3,
inference(sat_conversion,[],[f144]) ).
cnf(s14,plain,
( ~ spl13_9
| spl13_12 ),
inference(rat,[],[s6,s11]) ).
cnf(s15,plain,
spl13_9,
inference(rat,[],[s5,s10]) ).
cnf(s16,plain,
spl13_12,
inference(rat,[],[s14,s15]) ).
cnf(s17,plain,
( ~ spl13_5
| spl13_8 ),
inference(rat,[],[s4,s9]) ).
cnf(s18,plain,
spl13_5,
inference(rat,[],[s3,s8]) ).
cnf(s19,plain,
spl13_8,
inference(rat,[],[s17,s18]) ).
cnf(s20,plain,
~ spl13_4,
inference(rat,[],[s12,s16,s19]) ).
cnf(s21,plain,
~ spl13_1,
inference(rat,[],[s2,s20,s13]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s7,s21]) ).
fof(f145,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.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 00:44:49 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
% 1.64/1.13 % (3558836)Detected formulas, will run a generic FOF schedule.
% 1.64/1.13 % (3558844)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4212112911:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.64/1.13 % (3558844)First to succeed.
% 1.64/1.13 % (3558844)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3558836"
% 1.64/1.13 % (3558845)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2172556024:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.64/1.13 % (3558842)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=2818749047:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.64/1.13 % (3558847)dis-21_1_sil=8000:lcm=predicate:random_seed=1992501744: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)
% 1.64/1.13 % (3558841)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=1342601736:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.64/1.13 % (3558843)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=2558152892:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.64/1.13 % (3558846)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2814850199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.64/1.13 % (3558845)Also succeeded, but the first one will report.
% 1.64/1.13 % (3558847)Also succeeded, but the first one will report.
% 1.64/1.13 % (3558846)Also succeeded, but the first one will report.
% 1.64/1.13 % (3558844)Refutation found. Thanks to Tanya!
% 1.64/1.13 % SZS status Theorem for theBenchmark
% 1.64/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.32 % (3558844)------------------------------
% 2.53/1.32 % (3558844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (3558844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (3558844)CaDiCaL version: 2.1.3
% 2.53/1.32 % (3558844)Termination reason: Refutation
% 2.53/1.32 % (3558844)Time elapsed: 0.002 s
% 2.53/1.32 % (3558844)Peak memory usage: 89 MB
% 2.53/1.32 % (3558844)Instructions burned: 3 (million)
% 2.53/1.32 % (3558844)------------------------------
% 2.53/1.32 % (3558844)------------------------------
% 2.53/1.32 % (3558836)Success in time 0.268 s
% 2.53/1.32 % Vampire exiting
%------------------------------------------------------------------------------