TSTP Solution File: SET800+4 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 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 : n024.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 18:22:18 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 9 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 182 ( 43 ~; 27 |; 82 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 141 ( 102 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f129,plain,
$false,
inference(subsumption_resolution,[],[f126,f89]) ).
fof(f89,plain,
member(sK5,sK4),
inference(unit_resulting_resolution,[],[f64,f77,f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X1,X0)
=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
=> member(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f77,plain,
member(sK5,sK3),
inference(unit_resulting_resolution,[],[f60,f55]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| ( lower_bound(X0,X2,X1)
& member(X0,X1)
& ! [X4] :
( ~ lower_bound(X4,X2,X1)
| apply(X2,X4,X0)
| ~ member(X4,X3) ) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X3,X2,X0,X1] :
( ~ greatest_lower_bound(X3,X2,X0,X1)
| ( lower_bound(X3,X0,X2)
& member(X3,X2)
& ! [X4] :
( ~ lower_bound(X4,X0,X2)
| apply(X0,X4,X3)
| ~ member(X4,X1) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X3,X1,X2] :
( ( member(X3,X2)
& ! [X4] :
( apply(X0,X4,X3)
| ~ lower_bound(X4,X0,X2)
| ~ member(X4,X1) )
& lower_bound(X3,X0,X2) )
| ~ greatest_lower_bound(X3,X2,X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X3,X1,X2] :
( greatest_lower_bound(X3,X2,X0,X1)
=> ( member(X3,X2)
& ! [X4] :
( ( lower_bound(X4,X0,X2)
& member(X4,X1) )
=> apply(X0,X4,X3) )
& lower_bound(X3,X0,X2) ) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f25,plain,
! [X0,X3,X1,X2] :
( greatest_lower_bound(X3,X2,X0,X1)
<=> ( member(X3,X2)
& ! [X4] :
( ( lower_bound(X4,X0,X2)
& member(X4,X1) )
=> apply(X0,X4,X3) )
& lower_bound(X3,X0,X2) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X5,X3,X2,X0] :
( greatest_lower_bound(X0,X2,X5,X3)
<=> ( ! [X7] :
( ( member(X7,X3)
& lower_bound(X7,X5,X2) )
=> apply(X5,X7,X0) )
& lower_bound(X0,X5,X2)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest_lower_bound) ).
fof(f60,plain,
greatest_lower_bound(sK5,sK3,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
( subset(sK3,sK4)
& subset(sK4,sK2)
& greatest_lower_bound(sK6,sK4,sK1,sK2)
& ~ apply(sK1,sK6,sK5)
& greatest_lower_bound(sK5,sK3,sK1,sK2)
& subset(sK3,sK2)
& order(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f45,f48,f47,f46]) ).
fof(f46,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& ? [X4,X5] :
( greatest_lower_bound(X5,X3,X0,X1)
& ~ apply(X0,X5,X4)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X3,X2] :
( subset(X2,X3)
& subset(X3,sK2)
& ? [X5,X4] :
( greatest_lower_bound(X5,X3,sK1,sK2)
& ~ apply(sK1,X5,X4)
& greatest_lower_bound(X4,X2,sK1,sK2) )
& subset(X2,sK2) )
& order(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
( ? [X3,X2] :
( subset(X2,X3)
& subset(X3,sK2)
& ? [X5,X4] :
( greatest_lower_bound(X5,X3,sK1,sK2)
& ~ apply(sK1,X5,X4)
& greatest_lower_bound(X4,X2,sK1,sK2) )
& subset(X2,sK2) )
=> ( subset(sK3,sK4)
& subset(sK4,sK2)
& ? [X5,X4] :
( greatest_lower_bound(X5,sK4,sK1,sK2)
& ~ apply(sK1,X5,X4)
& greatest_lower_bound(X4,sK3,sK1,sK2) )
& subset(sK3,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
( ? [X5,X4] :
( greatest_lower_bound(X5,sK4,sK1,sK2)
& ~ apply(sK1,X5,X4)
& greatest_lower_bound(X4,sK3,sK1,sK2) )
=> ( greatest_lower_bound(sK6,sK4,sK1,sK2)
& ~ apply(sK1,sK6,sK5)
& greatest_lower_bound(sK5,sK3,sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0,X1] :
( ? [X2,X3] :
( subset(X2,X3)
& subset(X3,X1)
& ? [X4,X5] :
( greatest_lower_bound(X5,X3,X0,X1)
& ~ apply(X0,X5,X4)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
? [X1,X0] :
( ? [X3,X2] :
( subset(X3,X2)
& subset(X2,X0)
& ? [X5,X4] :
( greatest_lower_bound(X4,X2,X1,X0)
& ~ apply(X1,X4,X5)
& greatest_lower_bound(X5,X3,X1,X0) )
& subset(X3,X0) )
& order(X1,X0) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
? [X0,X1] :
( ? [X3,X2] :
( ? [X4,X5] :
( ~ apply(X1,X4,X5)
& greatest_lower_bound(X4,X2,X1,X0)
& greatest_lower_bound(X5,X3,X1,X0) )
& subset(X2,X0)
& subset(X3,X0)
& subset(X3,X2) )
& order(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
~ ! [X0,X1] :
( order(X1,X0)
=> ! [X3,X2] :
( ( subset(X2,X0)
& subset(X3,X0)
& subset(X3,X2) )
=> ! [X4,X5] :
( ( greatest_lower_bound(X4,X2,X1,X0)
& greatest_lower_bound(X5,X3,X1,X0) )
=> apply(X1,X4,X5) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X3,X5] :
( order(X5,X3)
=> ! [X9,X8] :
( ( subset(X8,X3)
& subset(X8,X9)
& subset(X9,X3) )
=> ! [X11,X10] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X3,X5] :
( order(X5,X3)
=> ! [X9,X8] :
( ( subset(X8,X3)
& subset(X8,X9)
& subset(X9,X3) )
=> ! [X11,X10] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).
fof(f64,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
fof(f126,plain,
~ member(sK5,sK4),
inference(unit_resulting_resolution,[],[f61,f83,f51]) ).
fof(f51,plain,
! [X2,X0,X1,X4] :
( apply(X2,X1,X4)
| ~ member(X4,X0)
| ~ lower_bound(X1,X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( lower_bound(X1,X2,X0)
| ( member(sK0(X0,X1,X2),X0)
& ~ apply(X2,X1,sK0(X0,X1,X2)) ) )
& ( ! [X4] :
( ~ member(X4,X0)
| apply(X2,X1,X4) )
| ~ lower_bound(X1,X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f41,f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X0)
& ~ apply(X2,X1,X3) )
=> ( member(sK0(X0,X1,X2),X0)
& ~ apply(X2,X1,sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( lower_bound(X1,X2,X0)
| ? [X3] :
( member(X3,X0)
& ~ apply(X2,X1,X3) ) )
& ( ! [X4] :
( ~ member(X4,X0)
| apply(X2,X1,X4) )
| ~ lower_bound(X1,X2,X0) ) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X1,X0,X2] :
( ( lower_bound(X0,X2,X1)
| ? [X3] :
( member(X3,X1)
& ~ apply(X2,X0,X3) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| apply(X2,X0,X3) )
| ~ lower_bound(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( lower_bound(X0,X2,X1)
<=> ! [X3] :
( ~ member(X3,X1)
| apply(X2,X0,X3) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X2,X0,X1] :
( lower_bound(X0,X2,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X2,X0,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X7,X3,X5] :
( lower_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X7,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).
fof(f83,plain,
lower_bound(sK6,sK1,sK4),
inference(unit_resulting_resolution,[],[f62,f56]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f62,plain,
greatest_lower_bound(sK6,sK4,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f61,plain,
~ apply(sK1,sK6,sK5),
inference(cnf_transformation,[],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:23:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (2485)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50 % (2492)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50 % (2492)First to succeed.
% 0.19/0.51 % (2496)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)
% 0.19/0.51 % (2492)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (2492)------------------------------
% 0.19/0.51 % (2492)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (2492)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (2492)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (2492)Memory used [KB]: 6012
% 0.19/0.51 % (2492)Time elapsed: 0.102 s
% 0.19/0.51 % (2492)Instructions burned: 3 (million)
% 0.19/0.51 % (2492)------------------------------
% 0.19/0.51 % (2492)------------------------------
% 0.19/0.51 % (2484)Success in time 0.165 s
%------------------------------------------------------------------------------