%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET079+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 : n012.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 12:39:59 PM UTC 2026
% Result : Theorem 1.97s 0.87s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 45 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 14 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 21 !; 1 ?)
% 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(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f44,conjecture,
! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0] :
( singleton(X0) = null_class
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f66,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(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(flattening,[],[f66]) ).
fof(f103,plain,
( null_class = singleton(sK6)
& member(sK6,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f60]) ).
fof(f114,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f135,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f191,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
null_class = singleton(sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f195,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f212,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f195,f116]) ).
fof(f214,plain,
( member(sK6,null_class)
| ~ member(sK6,universal_class) ),
inference(superposition,[],[f212,f192]) ).
fof(f215,plain,
~ member(sK6,universal_class),
inference(forward_subsumption_resolution,[],[f214,f135]) ).
fof(f216,plain,
$false,
inference(forward_subsumption_resolution,[],[f215,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET079+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 00:32:49 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 1.97/0.87 % (2906545)Detected formulas, will run a generic FOF schedule.
% 1.97/0.87 % (2906555)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=825486394:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.97/0.87 % (2906553)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=588852869:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.97/0.87 % (2906554)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2767848471:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.97/0.87 % (2906552)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=1965257125:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.97/0.87 % (2906550)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=2678055677:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.97/0.87 % (2906551)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=1219432127:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.97/0.87 % (2906554)Refutation not found, incomplete strategy
% 1.97/0.87 % (2906554)------------------------------
% 1.97/0.87 % (2906554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.97/0.87 % (2906554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.87 % (2906553)Refutation not found, incomplete strategy
% 1.97/0.87 % (2906553)------------------------------
% 1.97/0.87 % (2906553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.97/0.87 % (2906554)CaDiCaL version: 2.1.3
% 1.97/0.87 % (2906554)Termination reason: Refutation not found, incomplete strategy
% 1.97/0.87 % (2906554)Time elapsed: 0.001 s
% 1.97/0.87 % (2906553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.87 % (2906554)Peak memory usage: 88 MB
% 1.97/0.87 % (2906553)CaDiCaL version: 2.1.3
% 1.97/0.87 % (2906553)Termination reason: Refutation not found, incomplete strategy
% 1.97/0.87 % (2906553)Time elapsed: 0.0000 s
% 1.97/0.87 % (2906553)Peak memory usage: 88 MB
% 1.97/0.87 % (2906555)First to succeed.
% 1.97/0.87 % (2906555)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2906545"
% 1.97/0.87 % (2906556)dis-21_1_sil=8000:lcm=predicate:random_seed=3035538449: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)
% 1.97/0.87 % (2906556)Instruction limit reached!
% 1.97/0.87 % (2906556)------------------------------
% 1.97/0.87 % (2906556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.97/0.87 % (2906556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.87 % (2906556)CaDiCaL version: 2.1.3
% 1.97/0.87 % (2906556)Termination reason: Instruction limit
% 1.97/0.87 % (2906556)Termination phase: Saturation
% 1.97/0.87 % (2906556)Time elapsed: 0.039 s
% 1.97/0.87 % (2906556)Peak memory usage: 89 MB
% 1.97/0.87 % (2906556)Instructions burned: 133 (million)
% 1.97/0.87 % (2906554)------------------------------
% 1.97/0.87 % (2906554)------------------------------
% 1.97/0.87 % (2906553)------------------------------
% 1.97/0.87 % (2906553)------------------------------
% 1.97/0.87 % (2906555)Refutation found. Thanks to Tanya!
% 1.97/0.87 % SZS status Theorem for theBenchmark
% 1.97/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 1.97/0.87 % (2906555)------------------------------
% 1.97/0.87 % (2906555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.97/0.87 % (2906555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.87 % (2906555)CaDiCaL version: 2.1.3
% 1.97/0.87 % (2906555)Termination reason: Refutation
% 1.97/0.87 % (2906555)Time elapsed: 0.003 s
% 1.97/0.87 % (2906555)Peak memory usage: 88 MB
% 1.97/0.87 % (2906555)Instructions burned: 6 (million)
% 1.97/0.87 % (2906555)------------------------------
% 1.97/0.87 % (2906555)------------------------------
% 1.97/0.87 % (2906545)Success in time 0.253 s
% 1.97/0.87 % Vampire exiting
%------------------------------------------------------------------------------