%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET020+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 : n017.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 12:39:36 PM UTC 2026
% Result : Theorem 2.61s 1.33s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 11 unt; 4 def)
% Number of atoms : 96 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 43 ~; 33 |; 19 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( member(X0,universal_class)
& member(X1,universal_class) )
=> ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_second) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ( member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) )
=> ( first(X2) = X0
& second(X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) )
=> ( first(X2) = X0
& second(X2) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ( first(X2) != X0
| second(X2) != X1 )
& member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ( first(X2) != X0
| second(X2) != X1 )
& member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,plain,
! [X0,X1] :
( ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ( sK0 != first(sK2)
| sK1 != second(sK2) )
& member(sK0,universal_class)
& member(sK1,universal_class)
& sK2 = ordered_pair(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f47]) ).
fof(f54,plain,
sK2 = ordered_pair(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f55,plain,
member(sK1,universal_class),
inference(cnf_transformation,[],[f51]) ).
fof(f56,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f51]) ).
fof(f57,plain,
( sK0 != first(sK2)
| sK1 != second(sK2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f62,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f50]) ).
fof(f63,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f50]) ).
fof(f64,definition,
~ sP3(sK0),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f65,definition,
~ sP4(sK1),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f66,plain,
( sP3(first(sK2))
| sP4(second(sK2)) ),
inference(inequality_splitting,[],[f57,f65,f64]) ).
fof(f67,plain,
( sP3(first(ordered_pair(sK0,sK1)))
| sP4(second(sK2)) ),
inference(forward_demodulation,[],[f66,f54]) ).
fof(f68,plain,
( sP4(second(ordered_pair(sK0,sK1)))
| sP3(first(ordered_pair(sK0,sK1))) ),
inference(forward_demodulation,[],[f67,f54]) ).
fof(f70,definition,
( spl5_1
<=> sP3(first(ordered_pair(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f72,plain,
( sP3(first(ordered_pair(sK0,sK1)))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl5_2
<=> sP4(second(ordered_pair(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f76,plain,
( sP4(second(ordered_pair(sK0,sK1)))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f68,f74,f70]) ).
fof(f78,plain,
( sP4(sK1)
| ~ member(sK0,universal_class)
| ~ member(sK1,universal_class)
| ~ spl5_2 ),
inference(superposition,[],[f76,f62]) ).
fof(f79,plain,
( ~ member(sK0,universal_class)
| ~ member(sK1,universal_class)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f78,f65]) ).
fof(f80,plain,
( ~ member(sK1,universal_class)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f79,f56]) ).
fof(f81,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f80,f55]) ).
fof(f82,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f83,plain,
( sP3(sK0)
| ~ member(sK0,universal_class)
| ~ member(sK1,universal_class)
| ~ spl5_1 ),
inference(superposition,[],[f72,f63]) ).
fof(f84,plain,
( ~ member(sK0,universal_class)
| ~ member(sK1,universal_class)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f83,f64]) ).
fof(f85,plain,
( ~ member(sK1,universal_class)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f84,f56]) ).
fof(f86,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f85,f55]) ).
fof(f87,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f86]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f88,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:05:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.61/1.33 % (3098381)Detected formulas, will run a generic FOF schedule.
% 2.61/1.33 % (3098389)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1093902276:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.33 % (3098389)First to succeed.
% 2.61/1.33 % (3098389)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3098381"
% 2.61/1.33 % (3098386)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=1696168292:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.33 % (3098387)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=209595477:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.33 % (3098388)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=2320187741:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.33 % (3098392)dis-21_1_sil=8000:lcm=predicate:random_seed=971098620: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)
% 2.61/1.33 % (3098391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=454158446:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.33 % (3098390)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=668773687:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.33 % (3098390)Also succeeded, but the first one will report.
% 2.61/1.33 % (3098391)Also succeeded, but the first one will report.
% 2.61/1.33 % (3098392)Instruction limit reached!
% 2.61/1.33 % (3098392)------------------------------
% 2.61/1.33 % (3098392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.33 % (3098392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.33 % (3098392)CaDiCaL version: 2.1.3
% 2.61/1.33 % (3098392)Termination reason: Instruction limit
% 2.61/1.33 % (3098392)Termination phase: Saturation
% 2.61/1.33 % (3098392)Time elapsed: 0.085 s
% 2.61/1.33 % (3098392)Peak memory usage: 89 MB
% 2.61/1.33 % (3098392)Instructions burned: 130 (million)
% 2.61/1.33 % (3098389)Refutation found. Thanks to Tanya!
% 2.61/1.33 % SZS status Theorem for theBenchmark
% 2.61/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.33 % (3098389)------------------------------
% 2.61/1.33 % (3098389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.33 % (3098389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.33 % (3098389)CaDiCaL version: 2.1.3
% 2.61/1.33 % (3098389)Termination reason: Refutation
% 2.61/1.33 % (3098389)Time elapsed: 0.002 s
% 2.61/1.33 % (3098389)Peak memory usage: 89 MB
% 2.61/1.33 % (3098389)Instructions burned: 2 (million)
% 2.61/1.33 % (3098389)------------------------------
% 2.61/1.33 % (3098389)------------------------------
% 2.61/1.33 % (3098381)Success in time 0.285 s
% 2.61/1.33 % Vampire exiting
%------------------------------------------------------------------------------