TSTP Solution File: KRS101+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : n006.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 17:30:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 5 unt; 0 def)
% Number of atoms : 286 ( 46 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 375 ( 140 ~; 121 |; 94 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 147 ( 99 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f205,plain,
$false,
inference(resolution,[],[f204,f94]) ).
fof(f94,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f204,plain,
~ cUnsatisfiable(i2003_11_14_17_20_36582),
inference(trivial_inequality_removal,[],[f203]) ).
fof(f203,plain,
( sK5(i2003_11_14_17_20_36582) != sK5(i2003_11_14_17_20_36582)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(superposition,[],[f92,f201]) ).
fof(f201,plain,
sK5(i2003_11_14_17_20_36582) = sK6(i2003_11_14_17_20_36582),
inference(resolution,[],[f200,f94]) ).
fof(f200,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK6(X0) = sK5(X0) ),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK6(X0) = sK5(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f198,f89]) ).
fof(f89,plain,
! [X0] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( ( rs(sK4(X0),sK6(X0))
& sK6(X0) != sK5(X0)
& rs(sK4(X0),sK5(X0))
& rr(X0,sK4(X0))
& sP0(X0)
& ! [X4] :
( ~ rr(X0,X4)
| cd(X4) ) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X5] :
( ! [X6,X7] :
( ~ rs(X5,X7)
| X6 = X7
| ~ rs(X5,X6) )
| ~ rr(X0,X5) )
| ~ sP0(X0)
| ( rr(X0,sK7(X0))
& ~ cd(sK7(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f64,f67,f66,f65]) ).
fof(f65,plain,
! [X0] :
( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
=> ( ? [X3,X2] :
( rs(sK4(X0),X3)
& X2 != X3
& rs(sK4(X0),X2) )
& rr(X0,sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0] :
( ? [X3,X2] :
( rs(sK4(X0),X3)
& X2 != X3
& rs(sK4(X0),X2) )
=> ( rs(sK4(X0),sK6(X0))
& sK6(X0) != sK5(X0)
& rs(sK4(X0),sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ? [X8] :
( rr(X0,X8)
& ~ cd(X8) )
=> ( rr(X0,sK7(X0))
& ~ cd(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ( ( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
& sP0(X0)
& ! [X4] :
( ~ rr(X0,X4)
| cd(X4) ) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X5] :
( ! [X6,X7] :
( ~ rs(X5,X7)
| X6 = X7
| ~ rs(X5,X6) )
| ~ rr(X0,X5) )
| ~ sP0(X0)
| ? [X8] :
( rr(X0,X8)
& ~ cd(X8) ) ) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( ( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
& sP0(X0)
& ! [X7] :
( ~ rr(X0,X7)
| cd(X7) ) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X1] :
( ! [X2,X3] :
( ~ rs(X1,X3)
| X2 = X3
| ~ rs(X1,X2) )
| ~ rr(X0,X1) )
| ~ sP0(X0)
| ? [X7] :
( rr(X0,X7)
& ~ cd(X7) ) ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( ( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
& sP0(X0)
& ! [X7] :
( ~ rr(X0,X7)
| cd(X7) ) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X1] :
( ! [X2,X3] :
( ~ rs(X1,X3)
| X2 = X3
| ~ rs(X1,X2) )
| ~ rr(X0,X1) )
| ~ sP0(X0)
| ? [X7] :
( rr(X0,X7)
& ~ cd(X7) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
& sP0(X0)
& ! [X7] :
( ~ rr(X0,X7)
| cd(X7) ) )
<=> cUnsatisfiable(X0) ),
inference(definition_folding,[],[f52,f53]) ).
fof(f53,plain,
! [X0] :
( sP0(X0)
<=> ! [X4] :
( cc(X4)
| ! [X6,X5] :
( ~ rs(X4,X6)
| ~ rs(X4,X5)
| X5 = X6 )
| ~ rr(X0,X4) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f52,plain,
! [X0] :
( ( ? [X1] :
( ? [X2,X3] :
( rs(X1,X3)
& X2 != X3
& rs(X1,X2) )
& rr(X0,X1) )
& ! [X4] :
( cc(X4)
| ! [X6,X5] :
( ~ rs(X4,X6)
| ~ rs(X4,X5)
| X5 = X6 )
| ~ rr(X0,X4) )
& ! [X7] :
( ~ rr(X0,X7)
| cd(X7) ) )
<=> cUnsatisfiable(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X4] :
( cc(X4)
| ! [X6,X5] :
( ~ rs(X4,X6)
| ~ rs(X4,X5)
| X5 = X6 )
| ~ rr(X0,X4) )
& ! [X7] :
( ~ rr(X0,X7)
| cd(X7) )
& ? [X1] :
( ? [X2,X3] :
( X2 != X3
& rs(X1,X2)
& rs(X1,X3) )
& rr(X0,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ! [X4] :
( rr(X0,X4)
=> ( cc(X4)
| ~ ? [X5,X6] :
( X5 != X6
& rs(X4,X6)
& rs(X4,X5) ) ) )
& ! [X7] :
( rr(X0,X7)
=> cd(X7) )
& ? [X1] :
( ~ ! [X2,X3] :
( ( rs(X1,X2)
& rs(X1,X3) )
=> X2 = X3 )
& rr(X0,X1) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3] :
( ( ? [X4] :
( rr(X3,X4)
& ~ ! [X5,X6] :
( ( rs(X4,X5)
& rs(X4,X6) )
=> X5 = X6 ) )
& ! [X4] :
( rr(X3,X4)
=> ( cc(X4)
| ~ ? [X5,X6] :
( X5 != X6
& rs(X4,X6)
& rs(X4,X5) ) ) )
& ! [X4] :
( rr(X3,X4)
=> cd(X4) ) )
<=> cUnsatisfiable(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f198,plain,
! [X0] :
( ~ sP0(X0)
| ~ cUnsatisfiable(X0)
| sK6(X0) = sK5(X0) ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ~ sP0(X0)
| ~ cUnsatisfiable(X0)
| sK6(X0) = sK5(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f196,f128]) ).
fof(f128,plain,
! [X0] :
( ~ cc(sK4(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f127,f104]) ).
fof(f104,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0] :
( cc(X0)
=> ~ cd(X0) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] :
( cc(X3)
=> ~ cd(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f127,plain,
! [X1] :
( cd(sK4(X1))
| ~ cUnsatisfiable(X1) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f126,plain,
! [X1] :
( ~ cUnsatisfiable(X1)
| cd(sK4(X1))
| ~ cUnsatisfiable(X1) ),
inference(resolution,[],[f88,f90]) ).
fof(f90,plain,
! [X0] :
( rr(X0,sK4(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f88,plain,
! [X0,X4] :
( ~ rr(X0,X4)
| cd(X4)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f196,plain,
! [X0] :
( cc(sK4(X0))
| ~ sP0(X0)
| sK6(X0) = sK5(X0)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literal_removal,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK6(X0) = sK5(X0)
| cc(sK4(X0))
| ~ sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f190,f130]) ).
fof(f130,plain,
! [X1] :
( sP8(sK4(X1))
| ~ sP0(X1)
| ~ cUnsatisfiable(X1) ),
inference(resolution,[],[f118,f90]) ).
fof(f118,plain,
! [X0,X4] :
( ~ rr(X0,X4)
| sP8(X4)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f118_D]) ).
fof(f118_D,plain,
! [X4] :
( ! [X0] :
( ~ rr(X0,X4)
| ~ sP0(X0) )
<=> ~ sP8(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
fof(f190,plain,
! [X1] :
( ~ sP8(sK4(X1))
| sK6(X1) = sK5(X1)
| ~ cUnsatisfiable(X1)
| cc(sK4(X1)) ),
inference(duplicate_literal_removal,[],[f188]) ).
fof(f188,plain,
! [X1] :
( ~ sP8(sK4(X1))
| ~ cUnsatisfiable(X1)
| ~ cUnsatisfiable(X1)
| sK6(X1) = sK5(X1)
| cc(sK4(X1)) ),
inference(resolution,[],[f143,f93]) ).
fof(f93,plain,
! [X0] :
( rs(sK4(X0),sK6(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f143,plain,
! [X4,X5] :
( ~ rs(sK4(X4),X5)
| sK5(X4) = X5
| cc(sK4(X4))
| ~ cUnsatisfiable(X4)
| ~ sP8(sK4(X4)) ),
inference(resolution,[],[f119,f91]) ).
fof(f91,plain,
! [X0] :
( rs(sK4(X0),sK5(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f119,plain,
! [X6,X4,X5] :
( ~ rs(X4,X6)
| cc(X4)
| ~ sP8(X4)
| X5 = X6
| ~ rs(X4,X5) ),
inference(general_splitting,[],[f80,f118_D]) ).
fof(f80,plain,
! [X0,X6,X4,X5] :
( cc(X4)
| ~ rs(X4,X5)
| ~ rs(X4,X6)
| X5 = X6
| ~ rr(X0,X4)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( sP0(X0)
| ( ~ cc(sK1(X0))
& rs(sK1(X0),sK2(X0))
& rs(sK1(X0),sK3(X0))
& sK3(X0) != sK2(X0)
& rr(X0,sK1(X0)) ) )
& ( ! [X4] :
( cc(X4)
| ! [X5,X6] :
( ~ rs(X4,X5)
| ~ rs(X4,X6)
| X5 = X6 )
| ~ rr(X0,X4) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f58,f60,f59]) ).
fof(f59,plain,
! [X0] :
( ? [X1] :
( ~ cc(X1)
& ? [X2,X3] :
( rs(X1,X2)
& rs(X1,X3)
& X2 != X3 )
& rr(X0,X1) )
=> ( ~ cc(sK1(X0))
& ? [X3,X2] :
( rs(sK1(X0),X2)
& rs(sK1(X0),X3)
& X2 != X3 )
& rr(X0,sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ? [X3,X2] :
( rs(sK1(X0),X2)
& rs(sK1(X0),X3)
& X2 != X3 )
=> ( rs(sK1(X0),sK2(X0))
& rs(sK1(X0),sK3(X0))
& sK3(X0) != sK2(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ~ cc(X1)
& ? [X2,X3] :
( rs(X1,X2)
& rs(X1,X3)
& X2 != X3 )
& rr(X0,X1) ) )
& ( ! [X4] :
( cc(X4)
| ! [X5,X6] :
( ~ rs(X4,X5)
| ~ rs(X4,X6)
| X5 = X6 )
| ~ rr(X0,X4) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( sP0(X0)
| ? [X4] :
( ~ cc(X4)
& ? [X6,X5] :
( rs(X4,X6)
& rs(X4,X5)
& X5 != X6 )
& rr(X0,X4) ) )
& ( ! [X4] :
( cc(X4)
| ! [X6,X5] :
( ~ rs(X4,X6)
| ~ rs(X4,X5)
| X5 = X6 )
| ~ rr(X0,X4) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X0] :
( sK6(X0) != sK5(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS101+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n006.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 00:32:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52 % (22122)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53 % (22106)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (22106)First to succeed.
% 0.19/0.53 % (22106)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (22106)------------------------------
% 0.19/0.53 % (22106)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (22106)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (22106)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (22106)Memory used [KB]: 5500
% 0.19/0.53 % (22106)Time elapsed: 0.145 s
% 0.19/0.53 % (22106)Instructions burned: 5 (million)
% 0.19/0.53 % (22106)------------------------------
% 0.19/0.53 % (22106)------------------------------
% 0.19/0.53 % (22095)Success in time 0.184 s
%------------------------------------------------------------------------------