%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:40:04 PM UTC 2026
% Result : Theorem 2.70s 1.35s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 52 ( 31 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 50 ( 17 ~; 15 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 27 ( 23 !; 4 ?)
% 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(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f48,conjecture,
! [X0,X1] :
( ( singleton(member_of(X0)) = X0
& member(X1,X0) )
=> member_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons1_1) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( ( singleton(member_of(X0)) = X0
& member(X1,X0) )
=> member_of(X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f66,plain,
? [X0,X1] :
( member_of(X0) != X1
& singleton(member_of(X0)) = X0
& member(X1,X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f67,plain,
? [X0,X1] :
( member_of(X0) != X1
& singleton(member_of(X0)) = X0
& member(X1,X0) ),
inference(flattening,[],[f66]) ).
fof(f73,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(f74,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,[],[f73]) ).
fof(f110,plain,
( sK7 != member_of(sK6)
& sK6 = singleton(member_of(sK6))
& member(sK7,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f67]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f202,plain,
member(sK7,sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f203,plain,
sK6 = singleton(member_of(sK6)),
inference(cnf_transformation,[],[f110]) ).
fof(f204,plain,
sK7 != member_of(sK6),
inference(cnf_transformation,[],[f110]) ).
fof(f410,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f118,f123]) ).
fof(f411,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f410]) ).
fof(f415,plain,
! [X0] :
( ~ member(X0,sK6)
| member_of(sK6) = X0 ),
inference(superposition,[],[f411,f203]) ).
fof(f436,plain,
sK7 = member_of(sK6),
inference(resolution,[],[f415,f202]) ).
fof(f437,plain,
$false,
inference(forward_subsumption_resolution,[],[f436,f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.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 00:40:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 2.70/1.35 % (2567043)Detected formulas, will run a generic FOF schedule.
% 2.70/1.35 % (2567053)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1635731906:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.35 % (2567053)First to succeed.
% 2.70/1.35 % (2567053)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2567043"
% 2.70/1.35 % (2567054)dis-21_1_sil=8000:lcm=predicate:random_seed=227615669: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)
% 2.70/1.35 % (2567049)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=86170265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.35 % (2567051)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1055633386:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.35 % (2567050)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=604911385:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.35 % (2567048)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=4224897985:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.35 % (2567052)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3389797608:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.35 % (2567051)Refutation not found, incomplete strategy
% 2.70/1.35 % (2567051)------------------------------
% 2.70/1.35 % (2567051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (2567051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.35 % (2567051)CaDiCaL version: 2.1.3
% 2.70/1.35 % (2567051)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.35 % (2567051)Time elapsed: 0.001 s
% 2.70/1.35 % (2567051)Peak memory usage: 88 MB
% 2.70/1.35 % (2567052)Refutation not found, incomplete strategy
% 2.70/1.35 % (2567052)------------------------------
% 2.70/1.35 % (2567052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (2567052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.35 % (2567052)CaDiCaL version: 2.1.3
% 2.70/1.35 % (2567052)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.35 % (2567052)Time elapsed: 0.001 s
% 2.70/1.35 % (2567052)Peak memory usage: 88 MB
% 2.70/1.35 % (2567052)Instructions burned: 1 (million)
% 2.70/1.35 % (2567054)Instruction limit reached!
% 2.70/1.35 % (2567054)------------------------------
% 2.70/1.35 % (2567054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (2567054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.35 % (2567054)CaDiCaL version: 2.1.3
% 2.70/1.35 % (2567054)Termination reason: Instruction limit
% 2.70/1.35 % (2567054)Termination phase: Saturation
% 2.70/1.35 % (2567054)Time elapsed: 0.080 s
% 2.70/1.35 % (2567054)Peak memory usage: 89 MB
% 2.70/1.35 % (2567054)Instructions burned: 130 (million)
% 2.70/1.35 % (2567053)Refutation found. Thanks to Tanya!
% 2.70/1.35 % SZS status Theorem for theBenchmark
% 2.70/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.35 % (2567053)------------------------------
% 2.70/1.35 % (2567053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.35 % (2567053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.36 % (2567053)CaDiCaL version: 2.1.3
% 2.70/1.36 % (2567053)Termination reason: Refutation
% 2.70/1.36 % (2567053)Time elapsed: 0.007 s
% 2.70/1.36 % (2567053)Peak memory usage: 89 MB
% 2.70/1.36 % (2567053)Instructions burned: 14 (million)
% 2.70/1.36 % (2567053)------------------------------
% 2.70/1.36 % (2567053)------------------------------
% 2.70/1.36 % (2567043)Success in time 0.296 s
% 2.70/1.36 % Vampire exiting
%------------------------------------------------------------------------------