%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET101+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 : n013.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 12:40:07 PM UTC 2026
% Result : Theorem 3.66s 1.50s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 40 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 30 !; 2 ?)
% 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] : member(singleton(X0),ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
? [X0,X1] : ~ member(singleton(X0),ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f57,plain,
~ member(singleton(sK0),ordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
fof(f71,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(f72,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,[],[f71]) ).
fof(f92,plain,
~ member(singleton(sK0),ordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f57]) ).
fof(f107,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f108,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f123,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f151,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f165,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f107,f108,f108]) ).
fof(f167,plain,
~ member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1)))),
inference(definition_unfolding,[],[f92,f108,f165]) ).
fof(f193,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f123]) ).
fof(f213,plain,
~ member(unordered_pair(sK0,sK0),universal_class),
inference(resolution,[],[f193,f167]) ).
fof(f216,plain,
$false,
inference(resolution,[],[f213,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 00:41:07 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.66/1.50 % (705597)Detected formulas, will run a generic FOF schedule.
% 3.66/1.50 % (705605)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3857861059:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.50 % (705605)Refutation not found, incomplete strategy
% 3.66/1.50 % (705605)------------------------------
% 3.66/1.50 % (705605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.50 % (705605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.50 % (705605)CaDiCaL version: 2.1.3
% 3.66/1.50 % (705605)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.50 % (705605)Time elapsed: 0.001 s
% 3.66/1.50 % (705605)Peak memory usage: 87 MB
% 3.66/1.50 % (705603)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=1484002348:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.50 % (705606)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2246367847:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.50 % (705602)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=77053667:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.50 % (705608)dis-21_1_sil=8000:lcm=predicate:random_seed=961249925: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)
% 3.66/1.50 % (705604)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=1979915338:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.50 % (705607)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1455232382:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.50 % (705606)Refutation not found, incomplete strategy
% 3.66/1.50 % (705606)------------------------------
% 3.66/1.50 % (705606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.50 % (705606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.50 % (705606)CaDiCaL version: 2.1.3
% 3.66/1.50 % (705606)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.50 % (705606)Time elapsed: 0.001 s
% 3.66/1.50 % (705606)Peak memory usage: 87 MB
% 3.66/1.50 % (705608)First to succeed.
% 3.66/1.50 % (705608)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-705597"
% 3.66/1.50 % (705607)Also succeeded, but the first one will report.
% 3.66/1.50 % (705605)------------------------------
% 3.66/1.50 % (705605)------------------------------
% 3.66/1.50 % (705616)lrs+10_1_sil=8000:sp=occurrence:random_seed=3599271322:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.50 % (705616)Also succeeded, but the first one will report.
% 3.66/1.50 % (705606)------------------------------
% 3.66/1.50 % (705606)------------------------------
% 3.66/1.50 % (705608)Refutation found. Thanks to Tanya!
% 3.66/1.50 % SZS status Theorem for theBenchmark
% 3.66/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.50 % (705608)------------------------------
% 3.79/1.50 % (705608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.50 % (705608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.50 % (705608)CaDiCaL version: 2.1.3
% 3.79/1.50 % (705608)Termination reason: Refutation
% 3.79/1.50 % (705608)Time elapsed: 0.004 s
% 3.79/1.50 % (705608)Peak memory usage: 88 MB
% 3.79/1.50 % (705608)Instructions burned: 4 (million)
% 3.79/1.50 % (705608)------------------------------
% 3.79/1.50 % (705608)------------------------------
% 3.79/1.50 % (705597)Success in time 0.443 s
% 3.79/1.50 % Vampire exiting
%------------------------------------------------------------------------------