TSTP Solution File: SET800+4 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n020.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 18:25:41 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 202 ( 52 ~; 34 |; 88 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 146 ( 104 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f390,plain,
$false,
inference(subsumption_resolution,[],[f388,f191]) ).
fof(f191,plain,
member(sK5,sK4),
inference(resolution,[],[f181,f110]) ).
fof(f110,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( subset(sK4,sK1)
& subset(sK3,sK4)
& subset(sK3,sK1)
& greatest_lower_bound(sK5,sK3,sK2,sK1)
& ~ apply(sK2,sK6,sK5)
& greatest_lower_bound(sK6,sK4,sK2,sK1)
& order(sK2,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f66,f69,f68,f67]) ).
fof(f67,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( subset(X3,X0)
& subset(X2,X3)
& subset(X2,X0)
& ? [X4,X5] :
( greatest_lower_bound(X4,X2,X1,X0)
& ~ apply(X1,X5,X4)
& greatest_lower_bound(X5,X3,X1,X0) ) )
& order(X1,X0) )
=> ( ? [X3,X2] :
( subset(X3,sK1)
& subset(X2,X3)
& subset(X2,sK1)
& ? [X5,X4] :
( greatest_lower_bound(X4,X2,sK2,sK1)
& ~ apply(sK2,X5,X4)
& greatest_lower_bound(X5,X3,sK2,sK1) ) )
& order(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X3,X2] :
( subset(X3,sK1)
& subset(X2,X3)
& subset(X2,sK1)
& ? [X5,X4] :
( greatest_lower_bound(X4,X2,sK2,sK1)
& ~ apply(sK2,X5,X4)
& greatest_lower_bound(X5,X3,sK2,sK1) ) )
=> ( subset(sK4,sK1)
& subset(sK3,sK4)
& subset(sK3,sK1)
& ? [X5,X4] :
( greatest_lower_bound(X4,sK3,sK2,sK1)
& ~ apply(sK2,X5,X4)
& greatest_lower_bound(X5,sK4,sK2,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ? [X5,X4] :
( greatest_lower_bound(X4,sK3,sK2,sK1)
& ~ apply(sK2,X5,X4)
& greatest_lower_bound(X5,sK4,sK2,sK1) )
=> ( greatest_lower_bound(sK5,sK3,sK2,sK1)
& ~ apply(sK2,sK6,sK5)
& greatest_lower_bound(sK6,sK4,sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
? [X0,X1] :
( ? [X2,X3] :
( subset(X3,X0)
& subset(X2,X3)
& subset(X2,X0)
& ? [X4,X5] :
( greatest_lower_bound(X4,X2,X1,X0)
& ~ apply(X1,X5,X4)
& greatest_lower_bound(X5,X3,X1,X0) ) )
& order(X1,X0) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
? [X0,X1] :
( ? [X3,X2] :
( subset(X2,X0)
& subset(X3,X2)
& subset(X3,X0)
& ? [X4,X5] :
( greatest_lower_bound(X4,X3,X1,X0)
& ~ apply(X1,X5,X4)
& greatest_lower_bound(X5,X2,X1,X0) ) )
& order(X1,X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
? [X0,X1] :
( ? [X3,X2] :
( ? [X5,X4] :
( ~ apply(X1,X5,X4)
& greatest_lower_bound(X4,X3,X1,X0)
& greatest_lower_bound(X5,X2,X1,X0) )
& subset(X2,X0)
& subset(X3,X0)
& subset(X3,X2) )
& order(X1,X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
~ ! [X0,X1] :
( order(X1,X0)
=> ! [X3,X2] :
( ( subset(X2,X0)
& subset(X3,X0)
& subset(X3,X2) )
=> ! [X5,X4] :
( ( greatest_lower_bound(X4,X3,X1,X0)
& greatest_lower_bound(X5,X2,X1,X0) )
=> apply(X1,X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X3,X5] :
( order(X5,X3)
=> ! [X9,X8] :
( ( subset(X9,X3)
& subset(X8,X9)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( 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(X9,X3)
& subset(X8,X9)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV12) ).
fof(f181,plain,
! [X27] :
( ~ subset(sK3,X27)
| member(sK5,X27) ),
inference(resolution,[],[f121,f139]) ).
fof(f139,plain,
member(sK5,sK3),
inference(resolution,[],[f118,f108]) ).
fof(f108,plain,
greatest_lower_bound(sK5,sK3,sK2,sK1),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X1,X3,X0,X2)
| member(X1,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( apply(X0,X4,X1)
| ~ member(X4,X2)
| ~ lower_bound(X4,X0,X3) )
& lower_bound(X1,X0,X3)
& member(X1,X3) )
| ~ greatest_lower_bound(X1,X3,X0,X2) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X3,X0,X1,X2] :
( ( lower_bound(X1,X0,X3)
& ! [X4] :
( apply(X0,X4,X1)
| ~ member(X4,X2)
| ~ lower_bound(X4,X0,X3) )
& member(X1,X3) )
| ~ greatest_lower_bound(X1,X3,X0,X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X3,X0,X1,X2] :
( greatest_lower_bound(X1,X3,X0,X2)
=> ( lower_bound(X1,X0,X3)
& ! [X4] :
( ( member(X4,X2)
& lower_bound(X4,X0,X3) )
=> apply(X0,X4,X1) )
& member(X1,X3) ) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f38,plain,
! [X3,X0,X1,X2] :
( ( lower_bound(X1,X0,X3)
& ! [X4] :
( ( member(X4,X2)
& lower_bound(X4,X0,X3) )
=> apply(X0,X4,X1) )
& member(X1,X3) )
<=> greatest_lower_bound(X1,X3,X0,X2) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X5,X0,X3,X2] :
( ( member(X0,X2)
& ! [X7] :
( ( lower_bound(X7,X5,X2)
& member(X7,X3) )
=> apply(X5,X7,X0) )
& lower_bound(X0,X5,X2) )
<=> greatest_lower_bound(X0,X2,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest_lower_bound) ).
fof(f121,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f79,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f388,plain,
~ member(sK5,sK4),
inference(resolution,[],[f371,f107]) ).
fof(f107,plain,
~ apply(sK2,sK6,sK5),
inference(cnf_transformation,[],[f70]) ).
fof(f371,plain,
! [X0] :
( apply(sK2,sK6,X0)
| ~ member(X0,sK4) ),
inference(resolution,[],[f132,f170]) ).
fof(f170,plain,
lower_bound(sK6,sK2,sK4),
inference(resolution,[],[f119,f106]) ).
fof(f106,plain,
greatest_lower_bound(sK6,sK4,sK2,sK1),
inference(cnf_transformation,[],[f70]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X1,X3,X0,X2)
| lower_bound(X1,X0,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ lower_bound(X2,X1,X0)
| ~ member(X3,X0)
| apply(X1,X2,X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ member(X3,X0)
| apply(X1,X2,X3) )
| ~ lower_bound(X2,X1,X0) )
& ( lower_bound(X2,X1,X0)
| ( member(sK9(X0,X1,X2),X0)
& ~ apply(X1,X2,sK9(X0,X1,X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f88,f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& ~ apply(X1,X2,X4) )
=> ( member(sK9(X0,X1,X2),X0)
& ~ apply(X1,X2,sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ member(X3,X0)
| apply(X1,X2,X3) )
| ~ lower_bound(X2,X1,X0) )
& ( lower_bound(X2,X1,X0)
| ? [X4] :
( member(X4,X0)
& ~ apply(X1,X2,X4) ) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ member(X3,X0)
| apply(X1,X2,X3) )
| ~ lower_bound(X2,X1,X0) )
& ( lower_bound(X2,X1,X0)
| ? [X3] :
( member(X3,X0)
& ~ apply(X1,X2,X3) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ member(X3,X0)
| apply(X1,X2,X3) )
<=> lower_bound(X2,X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X2,X0] :
( lower_bound(X2,X1,X0)
<=> ! [X3] :
( member(X3,X0)
=> apply(X1,X2,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X5,X7] :
( lower_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X7,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:22:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48 % (20097)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.48 % (20106)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.49 % (20106)First to succeed.
% 0.20/0.49 % (20122)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.51 % (20114)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51 % (20106)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (20106)------------------------------
% 0.20/0.51 % (20106)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (20106)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (20106)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (20106)Memory used [KB]: 5628
% 0.20/0.51 % (20106)Time elapsed: 0.099 s
% 0.20/0.51 % (20106)Instructions burned: 12 (million)
% 0.20/0.51 % (20106)------------------------------
% 0.20/0.51 % (20106)------------------------------
% 0.20/0.51 % (20092)Success in time 0.149 s
%------------------------------------------------------------------------------