%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET067+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 : 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 12:39:55 PM UTC 2026
% Result : Theorem 4.19s 1.54s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 128 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 129 ( 50 ~; 56 |; 18 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 85 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
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(f44,conjecture,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_contains_other) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f60,plain,
? [X0,X1] : ~ subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f64]) ).
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,
~ subclass(unordered_pair(sK6,sK6),unordered_pair(sK6,sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f104,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f107,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f109,plain,
! [X0,X1] :
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
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(f191,plain,
~ subclass(unordered_pair(sK6,sK6),unordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f109]) ).
fof(f194,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f199,plain,
~ subclass(singleton(sK6),unordered_pair(sK6,sK7)),
inference(superposition,[],[f191,f116]) ).
fof(f215,plain,
! [X2,X0,X1] :
( subclass(X0,X1)
| ~ subclass(X2,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(resolution,[],[f104,f106]) ).
fof(f269,plain,
! [X2,X0,X1] :
( sK0(unordered_pair(X0,X1),X2) = X1
| sK0(unordered_pair(X0,X1),X2) = X0
| subclass(unordered_pair(X0,X1),X2) ),
inference(resolution,[],[f111,f105]) ).
fof(f271,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f111,f116]) ).
fof(f272,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f271]) ).
fof(f303,plain,
! [X0,X1] :
( sK0(singleton(X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(resolution,[],[f272,f105]) ).
fof(f537,plain,
! [X0] :
( ~ subclass(X0,unordered_pair(sK6,sK7))
| ~ member(sK0(singleton(sK6),unordered_pair(sK6,sK7)),X0) ),
inference(resolution,[],[f215,f199]) ).
fof(f545,plain,
~ member(sK0(singleton(sK6),unordered_pair(sK6,sK7)),unordered_pair(sK6,sK7)),
inference(resolution,[],[f537,f192]) ).
fof(f811,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X0))
| subclass(unordered_pair(X1,X0),X2)
| sK0(unordered_pair(X1,X0),X2) = X1
| subclass(unordered_pair(X1,X0),X2) ),
inference(superposition,[],[f105,f269]) ).
fof(f813,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X0))
| subclass(unordered_pair(X1,X0),X2)
| sK0(unordered_pair(X1,X0),X2) = X1 ),
inference(duplicate_literal_removal,[],[f811]) ).
fof(f960,plain,
( ~ member(sK6,unordered_pair(sK6,sK7))
| subclass(singleton(sK6),unordered_pair(sK6,sK7)) ),
inference(superposition,[],[f545,f303]) ).
fof(f963,plain,
~ member(sK6,unordered_pair(sK6,sK7)),
inference(forward_subsumption_resolution,[],[f960,f199]) ).
fof(f969,plain,
~ member(sK6,universal_class),
inference(resolution,[],[f963,f194]) ).
fof(f987,plain,
! [X0] :
( ~ member(sK6,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[],[f969,f104]) ).
fof(f988,plain,
! [X0] : ~ member(sK6,X0),
inference(forward_subsumption_resolution,[],[f987,f107]) ).
fof(f2579,plain,
! [X0,X1] :
( sK0(unordered_pair(X0,sK6),X1) = X0
| subclass(unordered_pair(X0,sK6),X1) ),
inference(resolution,[],[f813,f988]) ).
fof(f2587,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,sK6))
| subclass(unordered_pair(X0,sK6),X1)
| subclass(unordered_pair(X0,sK6),X1) ),
inference(superposition,[],[f105,f2579]) ).
fof(f2589,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,sK6))
| subclass(unordered_pair(X0,sK6),X1) ),
inference(duplicate_literal_removal,[],[f2587]) ).
fof(f2647,plain,
! [X0] :
( member(sK6,singleton(sK6))
| subclass(singleton(sK6),X0) ),
inference(superposition,[],[f2589,f116]) ).
fof(f2648,plain,
! [X0] : subclass(singleton(sK6),X0),
inference(forward_subsumption_resolution,[],[f2647,f988]) ).
fof(f2667,plain,
$false,
inference(resolution,[],[f2648,f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET067+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:28:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 4.19/1.54 % (2563287)Detected formulas, will run a generic FOF schedule.
% 4.19/1.54 % (2563296)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=90389237:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.19/1.54 % (2563296)Instruction limit reached!
% 4.19/1.54 % (2563296)------------------------------
% 4.19/1.54 % (2563296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.54 % (2563296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.54 % (2563296)CaDiCaL version: 2.1.3
% 4.19/1.54 % (2563296)Termination reason: Instruction limit
% 4.19/1.54 % (2563296)Termination phase: Saturation
% 4.19/1.54 % (2563296)Time elapsed: 0.027 s
% 4.19/1.54 % (2563296)Peak memory usage: 88 MB
% 4.19/1.54 % (2563296)Instructions burned: 121 (million)
% 4.19/1.54 % (2563292)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=3879805072:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.19/1.54 % (2563293)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=4105301670:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.19/1.54 % (2563294)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=1454704865:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.19/1.54 % (2563298)dis-21_1_sil=8000:lcm=predicate:random_seed=3687503183: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)
% 4.19/1.54 % (2563295)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=868197432:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.19/1.54 % (2563297)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2775160696:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.19/1.54 % (2563295)Refutation not found, incomplete strategy
% 4.19/1.54 % (2563295)------------------------------
% 4.19/1.54 % (2563295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.54 % (2563295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.54 % (2563295)CaDiCaL version: 2.1.3
% 4.19/1.54 % (2563295)Termination reason: Refutation not found, incomplete strategy
% 4.19/1.54 % (2563295)Time elapsed: 0.002 s
% 4.19/1.54 % (2563295)Peak memory usage: 88 MB
% 4.19/1.54 % (2563297)First to succeed.
% 4.19/1.54 % (2563298)Instruction limit reached!
% 4.19/1.54 % (2563298)------------------------------
% 4.19/1.54 % (2563298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.54 % (2563298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.54 % (2563298)CaDiCaL version: 2.1.3
% 4.19/1.54 % (2563298)Termination reason: Instruction limit
% 4.19/1.54 % (2563298)Termination phase: Saturation
% 4.19/1.54 % (2563298)Time elapsed: 0.079 s
% 4.19/1.54 % (2563298)Peak memory usage: 89 MB
% 4.19/1.54 % (2563298)Instructions burned: 131 (million)
% 4.19/1.54 % (2563297)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2563287"
% 4.19/1.54 % (2563300)lrs+10_1_sil=8000:sp=occurrence:random_seed=36904833:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.19/1.54 % (2563300)Also succeeded, but the first one will report.
% 4.19/1.54 % (2563295)------------------------------
% 4.19/1.54 % (2563295)------------------------------
% 4.19/1.54 % (2563307)lrs+10_1_sil=32000:urr=on:br=off:random_seed=664387975:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.19/1.54 % (2563297)Refutation found. Thanks to Tanya!
% 4.19/1.54 % SZS status Theorem for theBenchmark
% 4.19/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.54 % (2563297)------------------------------
% 4.19/1.54 % (2563297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.54 % (2563297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.54 % (2563297)CaDiCaL version: 2.1.3
% 4.19/1.54 % (2563297)Termination reason: Refutation
% 4.19/1.54 % (2563297)Time elapsed: 0.079 s
% 4.19/1.54 % (2563297)Peak memory usage: 90 MB
% 4.19/1.54 % (2563297)Instructions burned: 101 (million)
% 4.19/1.54 % (2563297)------------------------------
% 4.19/1.54 % (2563297)------------------------------
% 4.19/1.54 % (2563287)Success in time 0.509 s
% 4.19/1.54 % Vampire exiting
%------------------------------------------------------------------------------