TSTP Solution File: SYN549+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYN549+1 : TPTP v8.1.0. Released v2.2.0.
% 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 : n001.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 19:27:42 EDT 2022
% Result : Theorem 0.22s 0.54s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 5 unt; 0 def)
% Number of atoms : 297 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 364 ( 134 ~; 146 |; 68 &)
% ( 4 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 145 ( 103 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f217,plain,
$false,
inference(resolution,[],[f216,f40]) ).
fof(f40,plain,
! [X0] : reachable(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : reachable(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
fof(f216,plain,
! [X0] : ~ reachable(initial_world,X0),
inference(resolution,[],[f215,f37]) ).
fof(f37,plain,
! [X0] :
( sP1(sK6(X0))
| ~ reachable(initial_world,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ~ reachable(initial_world,X0)
| ( reachable(X0,sK6(X0))
& sP1(sK6(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f12,f24]) ).
fof(f24,plain,
! [X0] :
( ? [X1] :
( reachable(X0,X1)
& sP1(X1) )
=> ( reachable(X0,sK6(X0))
& sP1(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
! [X0] :
( ~ reachable(initial_world,X0)
| ? [X1] :
( reachable(X0,X1)
& sP1(X1) ) ),
inference(definition_folding,[],[f9,f11,f10]) ).
fof(f10,plain,
! [X1] :
( sP0(X1)
<=> ( ? [X5] :
( p(X5)
& reachable(X1,X5) )
| ? [X4] :
( q(X4)
& reachable(X1,X4) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f11,plain,
! [X1] :
( ( ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) )
<~> sP0(X1) )
| ~ sP1(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f9,plain,
! [X0] :
( ~ reachable(initial_world,X0)
| ? [X1] :
( reachable(X0,X1)
& ( ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) )
<~> ( ? [X5] :
( p(X5)
& reachable(X1,X5) )
| ? [X4] :
( q(X4)
& reachable(X1,X4) ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
~ ? [X0] :
( ! [X1] :
( reachable(X0,X1)
=> ( ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) )
<=> ( ? [X5] :
( p(X5)
& reachable(X1,X5) )
| ? [X4] :
( q(X4)
& reachable(X1,X4) ) ) ) )
& reachable(initial_world,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( reachable(X0,X1)
=> ( ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) )
<=> ( ? [X4] :
( q(X4)
& reachable(X1,X4) )
| ? [X4] :
( p(X4)
& reachable(X1,X4) ) ) ) )
& reachable(initial_world,X0) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
? [X0] :
( ! [X1] :
( reachable(X0,X1)
=> ( ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) )
<=> ( ? [X4] :
( q(X4)
& reachable(X1,X4) )
| ? [X4] :
( p(X4)
& reachable(X1,X4) ) ) ) )
& reachable(initial_world,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f215,plain,
! [X0] : ~ sP1(X0),
inference(subsumption_resolution,[],[f214,f161]) ).
fof(f161,plain,
! [X0] :
( ~ sP1(X0)
| sP0(X0) ),
inference(subsumption_resolution,[],[f160,f65]) ).
fof(f65,plain,
! [X0] :
( q(sK3(X0))
| sP0(X0)
| ~ sP1(X0) ),
inference(subsumption_resolution,[],[f27,f48]) ).
fof(f48,plain,
! [X0] :
( ~ p(sK2(X0))
| ~ sP1(X0)
| sP0(X0) ),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ~ sP1(X0)
| ~ p(sK2(X0))
| sP0(X0)
| sP0(X0) ),
inference(resolution,[],[f28,f36]) ).
fof(f36,plain,
! [X0,X1] :
( ~ reachable(X0,X1)
| ~ p(X1)
| sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X1] :
( ~ p(X1)
| ~ reachable(X0,X1) )
& ! [X2] :
( ~ q(X2)
| ~ reachable(X0,X2) ) ) )
& ( ( p(sK4(X0))
& reachable(X0,sK4(X0)) )
| ( q(sK5(X0))
& reachable(X0,sK5(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f20,f22,f21]) ).
fof(f21,plain,
! [X0] :
( ? [X3] :
( p(X3)
& reachable(X0,X3) )
=> ( p(sK4(X0))
& reachable(X0,sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0] :
( ? [X4] :
( q(X4)
& reachable(X0,X4) )
=> ( q(sK5(X0))
& reachable(X0,sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X1] :
( ~ p(X1)
| ~ reachable(X0,X1) )
& ! [X2] :
( ~ q(X2)
| ~ reachable(X0,X2) ) ) )
& ( ? [X3] :
( p(X3)
& reachable(X0,X3) )
| ? [X4] :
( q(X4)
& reachable(X0,X4) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1] :
( ( sP0(X1)
| ( ! [X5] :
( ~ p(X5)
| ~ reachable(X1,X5) )
& ! [X4] :
( ~ q(X4)
| ~ reachable(X1,X4) ) ) )
& ( ? [X5] :
( p(X5)
& reachable(X1,X5) )
| ? [X4] :
( q(X4)
& reachable(X1,X4) )
| ~ sP0(X1) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X1] :
( ( sP0(X1)
| ( ! [X5] :
( ~ p(X5)
| ~ reachable(X1,X5) )
& ! [X4] :
( ~ q(X4)
| ~ reachable(X1,X4) ) ) )
& ( ? [X5] :
( p(X5)
& reachable(X1,X5) )
| ? [X4] :
( q(X4)
& reachable(X1,X4) )
| ~ sP0(X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0] :
( reachable(X0,sK2(X0))
| ~ sP1(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] :
( ( ( ~ sP0(X0)
| ! [X1] :
( ~ reachable(X0,X1)
| ( ! [X2] :
( ~ q(X2)
| ~ reachable(X1,X2) )
& ~ p(X1) ) ) )
& ( sP0(X0)
| ( reachable(X0,sK2(X0))
& ( ( q(sK3(X0))
& reachable(sK2(X0),sK3(X0)) )
| p(sK2(X0)) ) ) ) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f14,f16,f15]) ).
fof(f15,plain,
! [X0] :
( ? [X3] :
( reachable(X0,X3)
& ( ? [X4] :
( q(X4)
& reachable(X3,X4) )
| p(X3) ) )
=> ( reachable(X0,sK2(X0))
& ( ? [X4] :
( q(X4)
& reachable(sK2(X0),X4) )
| p(sK2(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
( ? [X4] :
( q(X4)
& reachable(sK2(X0),X4) )
=> ( q(sK3(X0))
& reachable(sK2(X0),sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ( ( ~ sP0(X0)
| ! [X1] :
( ~ reachable(X0,X1)
| ( ! [X2] :
( ~ q(X2)
| ~ reachable(X1,X2) )
& ~ p(X1) ) ) )
& ( sP0(X0)
| ? [X3] :
( reachable(X0,X3)
& ( ? [X4] :
( q(X4)
& reachable(X3,X4) )
| p(X3) ) ) ) )
| ~ sP1(X0) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1] :
( ( ( ~ sP0(X1)
| ! [X2] :
( ~ reachable(X1,X2)
| ( ! [X3] :
( ~ q(X3)
| ~ reachable(X2,X3) )
& ~ p(X2) ) ) )
& ( sP0(X1)
| ? [X2] :
( reachable(X1,X2)
& ( ? [X3] :
( q(X3)
& reachable(X2,X3) )
| p(X2) ) ) ) )
| ~ sP1(X1) ),
inference(nnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0] :
( p(sK2(X0))
| sP0(X0)
| q(sK3(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f160,plain,
! [X0] :
( sP0(X0)
| ~ sP1(X0)
| ~ q(sK3(X0)) ),
inference(duplicate_literal_removal,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ~ q(sK3(X0))
| sP0(X0)
| sP0(X0)
| ~ sP1(X0)
| ~ sP1(X0) ),
inference(resolution,[],[f150,f92]) ).
fof(f92,plain,
! [X6,X7] :
( ~ reachable(sK2(X6),X7)
| sP0(X6)
| ~ q(X7)
| ~ sP1(X6) ),
inference(duplicate_literal_removal,[],[f87]) ).
fof(f87,plain,
! [X6,X7] :
( sP0(X6)
| ~ reachable(sK2(X6),X7)
| ~ q(X7)
| ~ sP1(X6)
| sP0(X6) ),
inference(resolution,[],[f64,f28]) ).
fof(f64,plain,
! [X8,X6,X7] :
( ~ reachable(X8,X6)
| ~ reachable(X6,X7)
| ~ q(X7)
| sP0(X8) ),
inference(resolution,[],[f39,f35]) ).
fof(f35,plain,
! [X2,X0] :
( ~ reachable(X0,X2)
| ~ q(X2)
| sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X2,X0,X1] :
( reachable(X2,X1)
| ~ reachable(X0,X1)
| ~ reachable(X2,X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ reachable(X2,X0)
| reachable(X2,X1)
| ~ reachable(X0,X1) ),
inference(flattening,[],[f7]) ).
fof(f7,plain,
! [X2,X1,X0] :
( reachable(X2,X1)
| ~ reachable(X0,X1)
| ~ reachable(X2,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,plain,
! [X2,X1,X0] :
( ( reachable(X0,X1)
& reachable(X2,X0) )
=> reachable(X2,X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( ( reachable(X0,X1)
& reachable(X1,X2) )
=> reachable(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_reachable) ).
fof(f150,plain,
! [X0] :
( reachable(sK2(X0),sK3(X0))
| ~ sP1(X0)
| sP0(X0) ),
inference(subsumption_resolution,[],[f26,f48]) ).
fof(f26,plain,
! [X0] :
( p(sK2(X0))
| sP0(X0)
| ~ sP1(X0)
| reachable(sK2(X0),sK3(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f214,plain,
! [X0] :
( ~ sP0(X0)
| ~ sP1(X0) ),
inference(duplicate_literal_removal,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(resolution,[],[f207,f58]) ).
fof(f58,plain,
! [X0] :
( q(sK5(X0))
| ~ sP1(X0)
| ~ sP0(X0) ),
inference(subsumption_resolution,[],[f55,f34]) ).
fof(f34,plain,
! [X0] :
( q(sK5(X0))
| p(sK4(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f55,plain,
! [X0] :
( ~ sP0(X0)
| ~ sP1(X0)
| q(sK5(X0))
| ~ p(sK4(X0)) ),
inference(resolution,[],[f32,f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ reachable(X0,X1)
| ~ p(X1)
| ~ sP1(X0) ),
inference(subsumption_resolution,[],[f29,f36]) ).
fof(f29,plain,
! [X0,X1] :
( ~ sP0(X0)
| ~ p(X1)
| ~ sP1(X0)
| ~ reachable(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0] :
( reachable(X0,sK4(X0))
| q(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f207,plain,
! [X2] :
( ~ q(sK5(X2))
| ~ sP1(X2) ),
inference(subsumption_resolution,[],[f205,f189]) ).
fof(f189,plain,
! [X8] :
( p(sK4(X8))
| ~ sP1(X8) ),
inference(subsumption_resolution,[],[f188,f161]) ).
fof(f188,plain,
! [X8] :
( ~ sP0(X8)
| ~ sP1(X8)
| p(sK4(X8)) ),
inference(subsumption_resolution,[],[f182,f34]) ).
fof(f182,plain,
! [X8] :
( ~ sP1(X8)
| ~ q(sK5(X8))
| ~ sP0(X8)
| p(sK4(X8)) ),
inference(resolution,[],[f165,f33]) ).
fof(f33,plain,
! [X0] :
( reachable(X0,sK5(X0))
| ~ sP0(X0)
| p(sK4(X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f165,plain,
! [X0,X1] :
( ~ reachable(X1,X0)
| ~ q(X0)
| ~ sP1(X1) ),
inference(resolution,[],[f164,f40]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ reachable(X1,X2)
| ~ q(X2)
| ~ sP1(X0)
| ~ reachable(X0,X1) ),
inference(subsumption_resolution,[],[f30,f64]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ sP1(X0)
| ~ reachable(X1,X2)
| ~ q(X2)
| ~ sP0(X0)
| ~ reachable(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f205,plain,
! [X2] :
( ~ p(sK4(X2))
| ~ q(sK5(X2))
| ~ sP1(X2) ),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f193,plain,
! [X2] :
( ~ q(sK5(X2))
| ~ sP1(X2)
| ~ p(sK4(X2))
| ~ sP1(X2) ),
inference(resolution,[],[f187,f49]) ).
fof(f187,plain,
! [X7] :
( reachable(X7,sK4(X7))
| ~ sP1(X7)
| ~ q(sK5(X7)) ),
inference(subsumption_resolution,[],[f181,f161]) ).
fof(f181,plain,
! [X7] :
( ~ q(sK5(X7))
| reachable(X7,sK4(X7))
| ~ sP1(X7)
| ~ sP0(X7) ),
inference(resolution,[],[f165,f31]) ).
fof(f31,plain,
! [X0] :
( reachable(X0,sK5(X0))
| reachable(X0,sK4(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN549+1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 22:28:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.51 % (10497)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.22/0.51 % (10510)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.52 % (10526)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.22/0.52 % (10497)First to succeed.
% 0.22/0.52 % (10521)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)
% 0.22/0.52 % (10505)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.22/0.53 % (10502)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)
% 0.22/0.53 % (10504)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)
% 0.22/0.54 % (10517)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)
% 0.22/0.54 % (10498)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.22/0.54 % (10501)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)
% 0.22/0.54 % (10500)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)
% 0.22/0.54 % (10499)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.54 % (10499)Refutation not found, incomplete strategy% (10499)------------------------------
% 0.22/0.54 % (10499)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54 % (10497)Refutation found. Thanks to Tanya!
% 0.22/0.54 % SZS status Theorem for theBenchmark
% 0.22/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.54 % (10497)------------------------------
% 0.22/0.54 % (10497)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.54 % (10497)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.54 % (10497)Termination reason: Refutation
% 0.22/0.54
% 0.22/0.54 % (10497)Memory used [KB]: 6012
% 0.22/0.54 % (10497)Time elapsed: 0.103 s
% 0.22/0.54 % (10497)Instructions burned: 8 (million)
% 0.22/0.54 % (10497)------------------------------
% 0.22/0.54 % (10497)------------------------------
% 0.22/0.54 % (10496)Success in time 0.181 s
%------------------------------------------------------------------------------