%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016+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 : n016.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 12:39:33 PM UTC 2026
% Result : Theorem 4.15s 1.58s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 18 unt; 2 def)
% Number of atoms : 106 ( 43 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 97 ( 40 ~; 37 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 49 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) )
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) )
=> X0 = X2 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) ),
inference(flattening,[],[f60]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f67]) ).
fof(f104,plain,
( sK6 != sK8
& ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9)
& member(sK6,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f61]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f115,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f118,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f192,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
sK6 != sK8,
inference(cnf_transformation,[],[f104]) ).
fof(f197,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f115]) ).
fof(f202,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f116,f117]) ).
fof(f220,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f197,f117]) ).
fof(f431,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f112,f117]) ).
fof(f432,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f431]) ).
fof(f434,plain,
! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| unordered_pair(X0,singleton(X1)) = X2
| singleton(X0) = X2 ),
inference(superposition,[],[f112,f118]) ).
fof(f436,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(superposition,[],[f197,f118]) ).
fof(f438,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[],[f436,f202]) ).
fof(f754,plain,
member(singleton(sK8),ordered_pair(sK6,sK7)),
inference(superposition,[],[f438,f193]) ).
fof(f1426,plain,
( singleton(sK8) = unordered_pair(sK6,singleton(sK7))
| singleton(sK8) = singleton(sK6) ),
inference(resolution,[],[f434,f754]) ).
fof(f1451,definition,
( spl10_80
<=> singleton(sK8) = singleton(sK6) ),
introduced(definition,[new_symbols(definition,[spl10_80])],[avatar_definition]) ).
fof(f1453,plain,
( singleton(sK8) = singleton(sK6)
| ~ spl10_80 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f1455,definition,
( spl10_81
<=> singleton(sK8) = unordered_pair(sK6,singleton(sK7)) ),
introduced(definition,[new_symbols(definition,[spl10_81])],[avatar_definition]) ).
fof(f1457,plain,
( singleton(sK8) = unordered_pair(sK6,singleton(sK7))
| ~ spl10_81 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f1458,plain,
( spl10_80
| spl10_81 ),
inference(avatar_split_clause,[],[f1426,f1455,f1451]) ).
fof(f1798,plain,
( member(sK6,singleton(sK8))
| ~ member(sK6,universal_class)
| ~ spl10_81 ),
inference(superposition,[],[f197,f1457]) ).
fof(f1826,plain,
( member(sK6,singleton(sK8))
| ~ spl10_81 ),
inference(forward_subsumption_resolution,[],[f1798,f192]) ).
fof(f2153,plain,
( sK6 = sK8
| ~ spl10_81 ),
inference(resolution,[],[f1826,f432]) ).
fof(f2154,plain,
( $false
| ~ spl10_81 ),
inference(forward_subsumption_resolution,[],[f2153,f194]) ).
fof(f2155,plain,
~ spl10_81,
inference(avatar_contradiction_clause,[],[f2154]) ).
fof(f2180,plain,
( ! [X0] :
( ~ member(X0,singleton(sK6))
| sK8 = X0 )
| ~ spl10_80 ),
inference(superposition,[],[f432,f1453]) ).
fof(f2667,plain,
( sK6 = sK8
| ~ member(sK6,universal_class)
| ~ spl10_80 ),
inference(resolution,[],[f2180,f220]) ).
fof(f2703,plain,
( ~ member(sK6,universal_class)
| ~ spl10_80 ),
inference(forward_subsumption_resolution,[],[f2667,f194]) ).
fof(f2706,plain,
( $false
| ~ spl10_80 ),
inference(forward_subsumption_resolution,[],[f2703,f192]) ).
fof(f2707,plain,
~ spl10_80,
inference(avatar_contradiction_clause,[],[f2706]) ).
cnf(s65,plain,
( spl10_80
| spl10_81 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s111,plain,
~ spl10_81,
inference(sat_conversion,[],[f2155]) ).
cnf(s163,plain,
~ spl10_80,
inference(sat_conversion,[],[f2707]) ).
cnf(s175,plain,
$false,
inference(rat,[],[s65,s111,s163]) ).
fof(f2713,plain,
$false,
inference(avatar_sat_refutation,[],[s175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 00:11:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 4.15/1.58 % (3139609)Detected formulas, will run a generic FOF schedule.
% 4.15/1.58 % (3139615)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=228306708:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.15/1.58 % (3139619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4186814252:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.15/1.58 % (3139620)dis-21_1_sil=8000:lcm=predicate:random_seed=2707042757: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)
% 4.15/1.58 % (3139618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1884444913:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.15/1.58 % (3139616)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=3989868670:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.15/1.58 % (3139617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=467522984:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.15/1.58 % (3139614)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=3263802858:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.15/1.58 % (3139618)Refutation not found, incomplete strategy
% 4.15/1.58 % (3139618)------------------------------
% 4.15/1.58 % (3139618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139618)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139618)Termination reason: Refutation not found, incomplete strategy
% 4.15/1.58 % (3139618)Time elapsed: 0.002 s
% 4.15/1.58 % (3139618)Peak memory usage: 87 MB
% 4.15/1.58 % (3139618)Instructions burned: 1 (million)
% 4.15/1.58 % (3139617)Refutation not found, incomplete strategy
% 4.15/1.58 % (3139617)------------------------------
% 4.15/1.58 % (3139617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139617)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139617)Termination reason: Refutation not found, incomplete strategy
% 4.15/1.58 % (3139617)Time elapsed: 0.002 s
% 4.15/1.58 % (3139617)Peak memory usage: 88 MB
% 4.15/1.58 % (3139617)Instructions burned: 1 (million)
% 4.15/1.58 % (3139619)First to succeed.
% 4.15/1.58 % (3139619)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3139609"
% 4.15/1.58 % (3139620)Instruction limit reached!
% 4.15/1.58 % (3139620)------------------------------
% 4.15/1.58 % (3139620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139620)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139620)Termination reason: Instruction limit
% 4.15/1.58 % (3139620)Termination phase: Saturation
% 4.15/1.58 % (3139620)Time elapsed: 0.078 s
% 4.15/1.58 % (3139620)Peak memory usage: 89 MB
% 4.15/1.58 % (3139620)Instructions burned: 130 (million)
% 4.15/1.58 % (3139617)------------------------------
% 4.15/1.58 % (3139617)------------------------------
% 4.15/1.58 % (3139618)------------------------------
% 4.15/1.58 % (3139618)------------------------------
% 4.15/1.58 % (3139628)lrs+10_1_sil=8000:sp=occurrence:random_seed=1976952041:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.15/1.58 % (3139628)Refutation not found, incomplete strategy
% 4.15/1.58 % (3139628)------------------------------
% 4.15/1.58 % (3139628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139628)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139628)Termination reason: Refutation not found, incomplete strategy
% 4.15/1.58 % (3139628)Time elapsed: 0.002 s
% 4.15/1.58 % (3139628)Peak memory usage: 88 MB
% 4.15/1.58 % (3139628)Instructions burned: 1 (million)
% 4.15/1.58 % (3139615)Refutation not found, incomplete strategy
% 4.15/1.58 % (3139615)------------------------------
% 4.15/1.58 % (3139615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139615)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139615)Termination reason: Refutation not found, incomplete strategy
% 4.15/1.58 % (3139615)Time elapsed: 0.339 s
% 4.15/1.58 % (3139615)Peak memory usage: 128 MB
% 4.15/1.58 % (3139615)Instructions burned: 899 (million)
% 4.15/1.58 % (3139619)Refutation found. Thanks to Tanya!
% 4.15/1.58 % SZS status Theorem for theBenchmark
% 4.15/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 4.15/1.58 % (3139619)------------------------------
% 4.15/1.58 % (3139619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.15/1.58 % (3139619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.15/1.58 % (3139619)CaDiCaL version: 2.1.3
% 4.15/1.58 % (3139619)Termination reason: Refutation
% 4.15/1.58 % (3139619)Time elapsed: 0.068 s
% 4.15/1.58 % (3139619)Peak memory usage: 91 MB
% 4.15/1.58 % (3139619)Instructions burned: 89 (million)
% 4.15/1.58 % (3139619)------------------------------
% 4.15/1.58 % (3139619)------------------------------
% 4.15/1.58 % (3139609)Success in time 0.503 s
% 4.15/1.58 % Vampire exiting
%------------------------------------------------------------------------------