TSTP Solution File: SEU171+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU171+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 : n012.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 18:27:05 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 198 ( 29 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 247 ( 93 ~; 60 |; 66 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 87 ( 68 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f114,plain,
$false,
inference(subsumption_resolution,[],[f112,f103]) ).
fof(f103,plain,
in(sK3,sK1),
inference(unit_resulting_resolution,[],[f95,f78,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( ( ( empty(X0)
| ~ element(X0,X1) )
& ( element(X0,X1)
| ~ empty(X0) ) )
| ~ empty(X1) )
& ( ( ( element(X0,X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ element(X0,X1) ) )
| empty(X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( ( empty(X0)
<=> element(X0,X1) )
| ~ empty(X1) )
& ( ( element(X0,X1)
<=> in(X0,X1) )
| empty(X1) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X1,X0] :
( ( empty(X1)
=> ( empty(X0)
<=> element(X0,X1) ) )
& ( ~ empty(X1)
=> ( element(X0,X1)
<=> in(X0,X1) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f78,plain,
element(sK3,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
( ~ in(sK3,subset_complement(sK1,sK2))
& element(sK3,sK1)
& ~ in(sK3,sK2)
& element(sK2,powerset(sK1))
& empty_set != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f32,f50,f49,f48]) ).
fof(f48,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(X0,X1))
& element(X2,X0)
& ~ in(X2,X1) )
& element(X1,powerset(X0)) )
& empty_set != X0 )
=> ( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(sK1,X1))
& element(X2,sK1)
& ~ in(X2,X1) )
& element(X1,powerset(sK1)) )
& empty_set != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(sK1,X1))
& element(X2,sK1)
& ~ in(X2,X1) )
& element(X1,powerset(sK1)) )
=> ( ? [X2] :
( ~ in(X2,subset_complement(sK1,sK2))
& element(X2,sK1)
& ~ in(X2,sK2) )
& element(sK2,powerset(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
( ? [X2] :
( ~ in(X2,subset_complement(sK1,sK2))
& element(X2,sK1)
& ~ in(X2,sK2) )
=> ( ~ in(sK3,subset_complement(sK1,sK2))
& element(sK3,sK1)
& ~ in(sK3,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(X0,X1))
& element(X2,X0)
& ~ in(X2,X1) )
& element(X1,powerset(X0)) )
& empty_set != X0 ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,subset_complement(X0,X1))
& ~ in(X2,X1)
& element(X2,X0) )
& element(X1,powerset(X0)) )
& empty_set != X0 ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f95,plain,
~ empty(sK1),
inference(unit_resulting_resolution,[],[f86,f75,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| ~ empty(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
~ ( X0 != X1
& empty(X1)
& empty(X0) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X1,X0] :
~ ( X0 != X1
& empty(X0)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f75,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f112,plain,
~ in(sK3,sK1),
inference(unit_resulting_resolution,[],[f77,f110,f93]) ).
fof(f93,plain,
! [X3,X0,X1] :
( in(X3,set_difference(X0,X1))
| ~ in(X3,X0)
| in(X3,X1) ),
inference(equality_resolution,[],[f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) ) )
| set_difference(X0,X1) != X2 )
& ( set_difference(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1) )
& ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f45,f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( in(X4,X2)
| ( in(X4,X0)
& ~ in(X4,X1) ) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1) )
& ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) ) )
| set_difference(X0,X1) != X2 )
& ( set_difference(X0,X1) = X2
| ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( in(X4,X2)
| ( in(X4,X0)
& ~ in(X4,X1) ) ) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) )
| set_difference(X0,X2) != X1 )
& ( set_difference(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& ~ in(X3,X2) ) ) ) ) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( ( in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) )
| set_difference(X0,X2) != X1 )
& ( set_difference(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& ~ in(X3,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X2,X1] :
( ! [X3] :
( ( in(X3,X0)
& ~ in(X3,X2) )
<=> in(X3,X1) )
<=> set_difference(X0,X2) = X1 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X2,X1] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( ( ~ in(X3,X1)
& in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f110,plain,
~ in(sK3,set_difference(sK1,sK2)),
inference(backward_demodulation,[],[f79,f104]) ).
fof(f104,plain,
set_difference(sK1,sK2) = subset_complement(sK1,sK2),
inference(unit_resulting_resolution,[],[f76,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
( ~ element(X0,powerset(X1))
| subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( element(X0,powerset(X1))
=> subset_complement(X1,X0) = set_difference(X1,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f76,plain,
element(sK2,powerset(sK1)),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
~ in(sK3,subset_complement(sK1,sK2)),
inference(cnf_transformation,[],[f51]) ).
fof(f77,plain,
~ in(sK3,sK2),
inference(cnf_transformation,[],[f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU171+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:44:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.52 % (22864)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)
% 0.20/0.52 % (22856)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (22863)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (22858)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (22854)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (22854)First to succeed.
% 0.20/0.52 % (22877)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)
% 0.20/0.53 % (22857)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.53 % (22854)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (22854)------------------------------
% 0.20/0.53 % (22854)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (22854)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (22854)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (22854)Memory used [KB]: 6012
% 0.20/0.53 % (22854)Time elapsed: 0.128 s
% 0.20/0.53 % (22854)Instructions burned: 3 (million)
% 0.20/0.53 % (22854)------------------------------
% 0.20/0.53 % (22854)------------------------------
% 0.20/0.53 % (22848)Success in time 0.175 s
%------------------------------------------------------------------------------