%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET102+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 : n002.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 3.53s 1.38s
% Output : Refutation 3.53s
% 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(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0,X1] : ~ member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f47,plain,
~ member(unordered_pair(sK0,singleton(sK1)),ordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f46]) ).
fof(f48,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(f49,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,[],[f48]) ).
fof(f52,plain,
~ member(unordered_pair(sK0,singleton(sK1)),ordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f47]) ).
fof(f53,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X2 ),
inference(cnf_transformation,[],[f49]) ).
fof(f63,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f53,f54,f54]) ).
fof(f64,plain,
~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1)))),
inference(definition_unfolding,[],[f52,f54,f63]) ).
fof(f69,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f58]) ).
fof(f71,plain,
~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class),
inference(resolution,[],[f69,f64]) ).
fof(f73,plain,
$false,
inference(forward_subsumption_resolution,[],[f71,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET102+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 : n002.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 00:45:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 3.53/1.38 % (4053376)Detected formulas, will run a generic FOF schedule.
% 3.53/1.38 % (4053383)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=239088079:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.38 % (4053381)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=3494201443:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.38 % (4053384)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2783542195:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.38 % (4053382)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=2628963954:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.38 % (4053387)dis-21_1_sil=8000:lcm=predicate:random_seed=2816666767: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)
% 3.53/1.38 % (4053385)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2282283849:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.38 % (4053386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2204822671:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.38 % (4053384)Also succeeded, but the first one will report.
% 3.53/1.38 % (4053385)First to succeed.
% 3.53/1.38 % (4053385)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4053376"
% 3.53/1.38 % (4053387)Also succeeded, but the first one will report.
% 3.53/1.38 % (4053386)Also succeeded, but the first one will report.
% 3.53/1.38 % (4053385)Refutation found. Thanks to Tanya!
% 3.53/1.38 % SZS status Theorem for theBenchmark
% 3.53/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.38 % (4053385)------------------------------
% 3.53/1.38 % (4053385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.38 % (4053385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.38 % (4053385)CaDiCaL version: 2.1.3
% 3.53/1.38 % (4053385)Termination reason: Refutation
% 3.53/1.38 % (4053385)Time elapsed: 0.002 s
% 3.53/1.38 % (4053385)Peak memory usage: 88 MB
% 3.53/1.38 % (4053385)Instructions burned: 1 (million)
% 3.53/1.38 % (4053385)------------------------------
% 3.53/1.38 % (4053385)------------------------------
% 3.53/1.38 % (4053376)Success in time 0.435 s
% 3.53/1.38 % Vampire exiting
%------------------------------------------------------------------------------