TSTP Solution File: SEU187+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU187+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:27:14 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 8 unt; 0 def)
% Number of atoms : 226 ( 38 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 257 ( 91 ~; 113 |; 30 &)
% ( 11 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 137 ( 108 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f195,plain,
$false,
inference(subsumption_resolution,[],[f194,f110]) ).
fof(f110,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f194,plain,
~ empty(empty_set),
inference(resolution,[],[f191,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
! [X1,X0] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f191,plain,
in(sK3(empty_set,relation_dom(empty_set)),empty_set),
inference(subsumption_resolution,[],[f189,f110]) ).
fof(f189,plain,
( ~ empty(empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(resolution,[],[f178,f94]) ).
fof(f178,plain,
( in(unordered_pair(unordered_pair(sK3(empty_set,relation_dom(empty_set)),sK7(empty_set,sK3(empty_set,relation_dom(empty_set)))),singleton(sK3(empty_set,relation_dom(empty_set)))),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(subsumption_resolution,[],[f174,f111]) ).
fof(f111,plain,
relation(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f174,plain,
( ~ relation(empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),empty_set)
| in(unordered_pair(unordered_pair(sK3(empty_set,relation_dom(empty_set)),sK7(empty_set,sK3(empty_set,relation_dom(empty_set)))),singleton(sK3(empty_set,relation_dom(empty_set)))),empty_set) ),
inference(resolution,[],[f172,f131]) ).
fof(f131,plain,
! [X2,X0] :
( ~ in(X2,relation_dom(X0))
| ~ relation(X0)
| in(unordered_pair(unordered_pair(X2,sK7(X0,X2)),singleton(X2)),X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X2,sK7(X0,X2)),singleton(X2)),X0)
| ~ in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f108,f84]) ).
fof(f84,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(ordered_pair(X2,sK7(X0,X2)),X0)
| ~ in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,sK7(X0,X2)),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(sK8(X0,X1),X6),X0)
| ~ in(sK8(X0,X1),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0)
| in(sK8(X0,X1),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f75,f78,f77,f76]) ).
fof(f76,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X2,X4),X0)
=> in(ordered_pair(X2,sK7(X0,X2)),X0) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(sK8(X0,X1),X6),X0)
| ~ in(sK8(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(sK8(X0,X1),X7),X0)
| in(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(sK8(X0,X1),X7),X0)
=> in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| in(X5,X1) ) ) ) ) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 )
& ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) )
<=> relation_dom(X0) = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) )
<=> relation_dom(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f172,plain,
( in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set))
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(subsumption_resolution,[],[f171,f110]) ).
fof(f171,plain,
( ~ empty(empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set))
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(resolution,[],[f168,f94]) ).
fof(f168,plain,
( in(sK3(empty_set,relation_rng(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set)) ),
inference(subsumption_resolution,[],[f166,f110]) ).
fof(f166,plain,
( in(sK3(empty_set,relation_rng(empty_set)),empty_set)
| ~ empty(empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set)) ),
inference(resolution,[],[f160,f94]) ).
fof(f160,plain,
( in(unordered_pair(unordered_pair(sK0(empty_set,sK3(empty_set,relation_rng(empty_set))),sK3(empty_set,relation_rng(empty_set))),singleton(sK0(empty_set,sK3(empty_set,relation_rng(empty_set))))),empty_set)
| in(sK3(empty_set,relation_rng(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set))
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(subsumption_resolution,[],[f156,f111]) ).
fof(f156,plain,
( in(unordered_pair(unordered_pair(sK0(empty_set,sK3(empty_set,relation_rng(empty_set))),sK3(empty_set,relation_rng(empty_set))),singleton(sK0(empty_set,sK3(empty_set,relation_rng(empty_set))))),empty_set)
| in(sK3(empty_set,relation_rng(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set))
| in(sK3(empty_set,relation_dom(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(resolution,[],[f154,f129]) ).
fof(f129,plain,
! [X2,X0] :
( ~ in(X2,relation_rng(X0))
| ~ relation(X0)
| in(unordered_pair(unordered_pair(sK0(X0,X2),X2),singleton(sK0(X0,X2))),X0) ),
inference(equality_resolution,[],[f120]) ).
fof(f120,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK0(X0,X2),X2),singleton(sK0(X0,X2))),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f88,f84]) ).
fof(f88,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK0(X0,X2),X2),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK0(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK1(X0,X1)),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f56,f59,f58,f57]) ).
fof(f57,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK0(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(X6,sK1(X0,X1)),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK1(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK1(X0,X1)),X0)
=> in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f154,plain,
( in(sK3(empty_set,relation_rng(empty_set)),relation_rng(empty_set))
| in(sK3(empty_set,relation_rng(empty_set)),empty_set)
| in(sK3(empty_set,relation_dom(empty_set)),relation_dom(empty_set))
| in(sK3(empty_set,relation_dom(empty_set)),empty_set) ),
inference(resolution,[],[f147,f139]) ).
fof(f139,plain,
! [X0,X1] :
( sQ12_eqProxy(X0,X1)
| in(sK3(X0,X1),X0)
| in(sK3(X0,X1),X1) ),
inference(equality_proxy_replacement,[],[f97,f132]) ).
fof(f132,plain,
! [X0,X1] :
( sQ12_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> in(X2,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f147,plain,
( ~ sQ12_eqProxy(empty_set,relation_dom(empty_set))
| in(sK3(empty_set,relation_rng(empty_set)),relation_rng(empty_set))
| in(sK3(empty_set,relation_rng(empty_set)),empty_set) ),
inference(resolution,[],[f142,f139]) ).
fof(f142,plain,
( ~ sQ12_eqProxy(empty_set,relation_rng(empty_set))
| ~ sQ12_eqProxy(empty_set,relation_dom(empty_set)) ),
inference(equality_proxy_replacement,[],[f118,f132,f132]) ).
fof(f118,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ( empty_set = relation_dom(empty_set)
& empty_set = relation_rng(empty_set) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
( empty_set = relation_dom(empty_set)
& empty_set = relation_rng(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 15:00:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.46 % (32530)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.47 % (32546)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.47 % (32538)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.47 % (32530)First to succeed.
% 0.20/0.47 % (32542)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.48 % (32530)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (32530)------------------------------
% 0.20/0.48 % (32530)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48 % (32530)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48 % (32530)Termination reason: Refutation
% 0.20/0.48
% 0.20/0.48 % (32530)Memory used [KB]: 1535
% 0.20/0.48 % (32530)Time elapsed: 0.094 s
% 0.20/0.48 % (32530)Instructions burned: 3 (million)
% 0.20/0.48 % (32530)------------------------------
% 0.20/0.48 % (32530)------------------------------
% 0.20/0.48 % (32517)Success in time 0.133 s
%------------------------------------------------------------------------------