%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET082+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 : n026.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 12:40:00 PM UTC 2026
% Result : Theorem 3.67s 1.41s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 97 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 98 ( 35 ~; 35 |; 21 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 51 !; 5 ?)
% 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(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(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f44,conjecture,
! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
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(f57,plain,
! [X0] :
( ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) )
| null_class = X0 ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
? [X0] :
( singleton(X0) != null_class
& ~ member(X0,universal_class) ),
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(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(f101,plain,
! [X0] :
( ( member(sK4(X0),universal_class)
& member(sK4(X0),X0)
& disjoint(sK4(X0),X0) )
| null_class = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f103,plain,
( null_class != singleton(sK6)
& ~ member(sK6,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f60]) ).
fof(f104,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f107,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f186,plain,
! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f101]) ).
fof(f187,plain,
! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f101]) ).
fof(f191,plain,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
null_class != singleton(sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f223,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f104,f107]) ).
fof(f233,plain,
! [X0] : ~ member(sK6,X0),
inference(resolution,[],[f223,f191]) ).
fof(f394,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f111,f116]) ).
fof(f395,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f539,plain,
! [X0] :
( sK4(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f395,f186]) ).
fof(f1283,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f187,f539]) ).
fof(f1288,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f1283]) ).
fof(f1314,plain,
null_class = singleton(sK6),
inference(resolution,[],[f1288,f233]) ).
fof(f1315,plain,
$false,
inference(forward_subsumption_resolution,[],[f1314,f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 00:37:11 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.67/1.41 % (3366918)Detected formulas, will run a generic FOF schedule.
% 3.67/1.41 % (3366923)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=684686760:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.41 % (3366925)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=1356651311:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.41 % (3366927)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1686086848:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.41 % (3366929)dis-21_1_sil=8000:lcm=predicate:random_seed=1860093911: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)
% 3.67/1.41 % (3366926)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=571903543:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.41 % (3366924)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=1785402778:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.41 % (3366928)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1706006984:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.41 % (3366927)Refutation not found, incomplete strategy
% 3.67/1.41 % (3366927)------------------------------
% 3.67/1.41 % (3366927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.41 % (3366927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.41 % (3366926)Refutation not found, incomplete strategy
% 3.67/1.41 % (3366926)------------------------------
% 3.67/1.41 % (3366926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.41 % (3366927)CaDiCaL version: 2.1.3
% 3.67/1.41 % (3366926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.41 % (3366927)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.41 % (3366927)Time elapsed: 0.001 s
% 3.67/1.41 % (3366927)Peak memory usage: 87 MB
% 3.67/1.41 % (3366926)CaDiCaL version: 2.1.3
% 3.67/1.41 % (3366926)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.41 % (3366926)Time elapsed: 0.001 s
% 3.67/1.41 % (3366926)Peak memory usage: 87 MB
% 3.67/1.41 % (3366928)First to succeed.
% 3.67/1.41 % (3366928)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3366918"
% 3.67/1.41 % (3366929)Instruction limit reached!
% 3.67/1.41 % (3366929)------------------------------
% 3.67/1.41 % (3366929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.41 % (3366929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.41 % (3366929)CaDiCaL version: 2.1.3
% 3.67/1.41 % (3366929)Termination reason: Instruction limit
% 3.67/1.41 % (3366929)Termination phase: Saturation
% 3.67/1.41 % (3366929)Time elapsed: 0.077 s
% 3.67/1.41 % (3366929)Peak memory usage: 89 MB
% 3.67/1.41 % (3366929)Instructions burned: 129 (million)
% 3.67/1.41 % (3366937)lrs+10_1_sil=8000:sp=occurrence:random_seed=2990149978:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.67/1.41 % (3366927)------------------------------
% 3.67/1.41 % (3366927)------------------------------
% 3.67/1.41 % (3366926)------------------------------
% 3.67/1.41 % (3366926)------------------------------
% 3.67/1.41 % (3366928)Refutation found. Thanks to Tanya!
% 3.67/1.41 % SZS status Theorem for theBenchmark
% 3.67/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.41 % (3366928)------------------------------
% 3.67/1.41 % (3366928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.41 % (3366928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.41 % (3366928)CaDiCaL version: 2.1.3
% 3.67/1.41 % (3366928)Termination reason: Refutation
% 3.67/1.41 % (3366928)Time elapsed: 0.035 s
% 3.67/1.41 % (3366928)Peak memory usage: 89 MB
% 3.67/1.41 % (3366928)Instructions burned: 43 (million)
% 3.67/1.41 % (3366928)------------------------------
% 3.67/1.41 % (3366928)------------------------------
% 3.67/1.41 % (3366918)Success in time 0.443 s
% 3.67/1.41 % Vampire exiting
%------------------------------------------------------------------------------