TSTP Solution File: SEU188+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU188+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 : n019.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 18:27:14 EDT 2022
% Result : Theorem 1.25s 0.52s
% Output : Refutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 81 ( 12 unt; 0 def)
% Number of atoms : 234 ( 55 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 252 ( 99 ~; 103 |; 27 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 78 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f244,plain,
$false,
inference(avatar_sat_refutation,[],[f154,f182,f188,f193,f243]) ).
fof(f243,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f241,f202]) ).
fof(f202,plain,
( empty(sF14)
| ~ spl16_4 ),
inference(subsumption_resolution,[],[f199,f163]) ).
fof(f163,plain,
( empty(sK4)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f162,plain,
( spl16_4
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f199,plain,
( empty(sF14)
| ~ empty(sK4) ),
inference(superposition,[],[f111,f143]) ).
fof(f143,plain,
relation_rng(sK4) = sF14,
introduced(function_definition,[]) ).
fof(f111,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ~ empty(X0)
| ( empty(relation_rng(X0))
& relation(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_rng(X0))
& relation(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f241,plain,
~ empty(sF14),
inference(resolution,[],[f239,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X1,X0] :
( ~ empty(X0)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
~ ( in(X1,X0)
& empty(X0) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X1,X0] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f239,plain,
in(sK13(sK4),sF14),
inference(subsumption_resolution,[],[f238,f107]) ).
fof(f107,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( empty_set != sK4
& ( empty_set = relation_rng(sK4)
| empty_set = relation_dom(sK4) )
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f52,f70]) ).
fof(f70,plain,
( ? [X0] :
( empty_set != X0
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) )
=> ( empty_set != sK4
& ( empty_set = relation_rng(sK4)
| empty_set = relation_dom(sK4) )
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0] :
( empty_set != X0
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
? [X0] :
( empty_set != X0
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> empty_set = X0 ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f238,plain,
( empty_set = sK4
| in(sK13(sK4),sF14) ),
inference(subsumption_resolution,[],[f237,f105]) ).
fof(f105,plain,
relation(sK4),
inference(cnf_transformation,[],[f71]) ).
fof(f237,plain,
( in(sK13(sK4),sF14)
| ~ relation(sK4)
| empty_set = sK4 ),
inference(superposition,[],[f233,f143]) ).
fof(f233,plain,
! [X1] :
( in(sK13(X1),relation_rng(X1))
| empty_set = X1
| ~ relation(X1) ),
inference(duplicate_literal_removal,[],[f228]) ).
fof(f228,plain,
! [X1] :
( ~ relation(X1)
| in(sK13(X1),relation_rng(X1))
| empty_set = X1
| ~ relation(X1) ),
inference(resolution,[],[f138,f139]) ).
fof(f139,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f130]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f115,f126]) ).
fof(f126,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK6(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f75,f78,f77,f76]) ).
fof(f76,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK6(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(X6,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK7(X0,X1)),X0)
=> in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f138,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0)
| empty_set = X0
| ~ relation(X0) ),
inference(definition_unfolding,[],[f121,f126]) ).
fof(f121,plain,
! [X0] :
( ~ relation(X0)
| empty_set = X0
| in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ~ relation(X0)
| empty_set = X0
| in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f41,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( relation(X0)
=> ( ! [X2,X1] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f193,plain,
( ~ spl16_1
| spl16_5 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f192,plain,
( $false
| ~ spl16_1
| spl16_5 ),
inference(subsumption_resolution,[],[f191,f125]) ).
fof(f125,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f191,plain,
( ~ empty(empty_set)
| ~ spl16_1
| spl16_5 ),
inference(forward_demodulation,[],[f185,f149]) ).
fof(f149,plain,
( empty_set = sF15
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f147,plain,
( spl16_1
<=> empty_set = sF15 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f185,plain,
( ~ empty(sF15)
| spl16_5 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f184,plain,
( spl16_5
<=> empty(sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f188,plain,
( ~ spl16_5
| spl16_4 ),
inference(avatar_split_clause,[],[f174,f162,f184]) ).
fof(f174,plain,
( empty(sK4)
| ~ empty(sF15) ),
inference(subsumption_resolution,[],[f173,f105]) ).
fof(f173,plain,
( ~ empty(sF15)
| ~ relation(sK4)
| empty(sK4) ),
inference(superposition,[],[f89,f144]) ).
fof(f144,plain,
sF15 = relation_dom(sK4),
introduced(function_definition,[]) ).
fof(f89,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f182,plain,
( spl16_4
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f179,f151,f162]) ).
fof(f151,plain,
( spl16_2
<=> empty_set = sF14 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f179,plain,
( empty(sK4)
| ~ spl16_2 ),
inference(subsumption_resolution,[],[f178,f105]) ).
fof(f178,plain,
( ~ relation(sK4)
| empty(sK4)
| ~ spl16_2 ),
inference(subsumption_resolution,[],[f177,f125]) ).
fof(f177,plain,
( ~ empty(empty_set)
| ~ relation(sK4)
| empty(sK4)
| ~ spl16_2 ),
inference(superposition,[],[f104,f155]) ).
fof(f155,plain,
( empty_set = relation_rng(sK4)
| ~ spl16_2 ),
inference(forward_demodulation,[],[f143,f153]) ).
fof(f153,plain,
( empty_set = sF14
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f104,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f154,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f145,f151,f147]) ).
fof(f145,plain,
( empty_set = sF14
| empty_set = sF15 ),
inference(definition_folding,[],[f106,f144,f143]) ).
fof(f106,plain,
( empty_set = relation_rng(sK4)
| empty_set = relation_dom(sK4) ),
inference(cnf_transformation,[],[f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n019.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 14:51:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.50 % (24816)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (24827)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)
% 0.19/0.50 % (24800)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 % (24800)First to succeed.
% 0.19/0.51 % (24808)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)
% 0.19/0.51 % (24806)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)
% 1.25/0.52 % (24801)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)
% 1.25/0.52 % (24816)Instruction limit reached!
% 1.25/0.52 % (24816)------------------------------
% 1.25/0.52 % (24816)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52 % (24816)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52 % (24816)Termination reason: Unknown
% 1.25/0.52 % (24816)Termination phase: Saturation
% 1.25/0.52
% 1.25/0.52 % (24816)Memory used [KB]: 5884
% 1.25/0.52 % (24816)Time elapsed: 0.004 s
% 1.25/0.52 % (24816)Instructions burned: 3 (million)
% 1.25/0.52 % (24816)------------------------------
% 1.25/0.52 % (24816)------------------------------
% 1.25/0.52 % (24800)Refutation found. Thanks to Tanya!
% 1.25/0.52 % SZS status Theorem for theBenchmark
% 1.25/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.25/0.52 % (24800)------------------------------
% 1.25/0.52 % (24800)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52 % (24800)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52 % (24800)Termination reason: Refutation
% 1.25/0.52
% 1.25/0.52 % (24800)Memory used [KB]: 6012
% 1.25/0.52 % (24800)Time elapsed: 0.097 s
% 1.25/0.52 % (24800)Instructions burned: 5 (million)
% 1.25/0.52 % (24800)------------------------------
% 1.25/0.52 % (24800)------------------------------
% 1.25/0.52 % (24796)Success in time 0.163 s
%------------------------------------------------------------------------------