TSTP Solution File: SEU204+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU204+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 : n021.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 18:27:22 EDT 2022
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 214 ( 24 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 256 ( 92 ~; 90 |; 48 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 159 ( 126 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f216,plain,
$false,
inference(subsumption_resolution,[],[f211,f145]) ).
fof(f145,plain,
~ subset(relation_image(sK7,sK8),relation_rng(sK7)),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ~ subset(relation_image(sK7,sK8),relation_rng(sK7))
& relation(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f62,f98]) ).
fof(f98,plain,
( ? [X0,X1] :
( ~ subset(relation_image(X0,X1),relation_rng(X0))
& relation(X0) )
=> ( ~ subset(relation_image(sK7,sK8),relation_rng(sK7))
& relation(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
? [X0,X1] :
( ~ subset(relation_image(X0,X1),relation_rng(X0))
& relation(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
~ ! [X0,X1] :
( relation(X0)
=> subset(relation_image(X0,X1),relation_rng(X0)) ),
inference(rectify,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X1,X0] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X1,X0] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f211,plain,
subset(relation_image(sK7,sK8),relation_rng(sK7)),
inference(resolution,[],[f209,f135]) ).
fof(f135,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f91,f92]) ).
fof(f92,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
=> ( in(sK6(X0,X1),X0)
& ~ in(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f90]) ).
fof(f90,plain,
! [X1,X0] :
( ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) )
& ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f209,plain,
in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_rng(sK7)),
inference(subsumption_resolution,[],[f205,f144]) ).
fof(f144,plain,
relation(sK7),
inference(cnf_transformation,[],[f99]) ).
fof(f205,plain,
( ~ relation(sK7)
| in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_rng(sK7)) ),
inference(resolution,[],[f197,f178]) ).
fof(f178,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f171,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,[],[f158,f116]) ).
fof(f116,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(rectify,[],[f50]) ).
fof(f50,plain,
! [X1,X0] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK10(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK11(X0,X1)),X0)
| ~ in(sK11(X0,X1),X1) )
& ( in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0)
| in(sK11(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f103,f106,f105,f104]) ).
fof(f104,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK10(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f105,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,sK11(X0,X1)),X0)
| ~ in(sK11(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK11(X0,X1)),X0)
| in(sK11(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK11(X0,X1)),X0)
=> in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f103,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,[],[f102]) ).
fof(f102,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,[],[f6]) ).
fof(f6,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(f197,plain,
in(unordered_pair(unordered_pair(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))),sK6(relation_image(sK7,sK8),relation_rng(sK7))),singleton(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))))),sK7),
inference(subsumption_resolution,[],[f192,f144]) ).
fof(f192,plain,
( in(unordered_pair(unordered_pair(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))),sK6(relation_image(sK7,sK8),relation_rng(sK7))),singleton(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))))),sK7)
| ~ relation(sK7) ),
inference(resolution,[],[f191,f175]) ).
fof(f175,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2 ),
inference(definition_unfolding,[],[f122,f116]) ).
fof(f122,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| in(ordered_pair(sK2(X0,X1,X6),X6),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) ) )
& ( in(sK0(X0,X1,X2),X2)
| ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) ) ) ) )
& ( ! [X6] :
( ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) )
& ( in(X6,X2)
| ! [X8] :
( ~ in(ordered_pair(X8,X6),X0)
| ~ in(X8,X1) ) ) )
| relation_image(X0,X1) != X2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f77,f80,f79,f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) ) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) ) )
& ( in(sK0(X0,X1,X2),X2)
| ? [X5] :
( in(ordered_pair(X5,sK0(X0,X1,X2)),X0)
& in(X5,X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(ordered_pair(X5,sK0(X0,X1,X2)),X0)
& in(X5,X1) )
=> ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X6] :
( ? [X7] :
( in(ordered_pair(X7,X6),X0)
& in(X7,X1) )
=> ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) ) ) ) )
& ( ! [X6] :
( ( ? [X7] :
( in(ordered_pair(X7,X6),X0)
& in(X7,X1) )
| ~ in(X6,X2) )
& ( in(X6,X2)
| ! [X8] :
( ~ in(ordered_pair(X8,X6),X0)
| ~ in(X8,X1) ) ) )
| relation_image(X0,X1) != X2 ) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) )
& ( ! [X3] :
( ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) ) )
| relation_image(X0,X1) != X2 ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
<=> in(X3,X2) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
<=> in(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f191,plain,
in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_image(sK7,sK8)),
inference(resolution,[],[f145,f136]) ).
fof(f136,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU204+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30 % Computer : n021.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 30 14:46:41 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.46 % (24266)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.46 % (24276)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.15/0.46 % (24260)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)
% 0.15/0.47 % (24282)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.15/0.47 % (24268)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)
% 0.15/0.47 % (24268)Instruction limit reached!
% 0.15/0.47 % (24268)------------------------------
% 0.15/0.47 % (24268)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47 % (24266)First to succeed.
% 0.15/0.47 % (24274)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)
% 0.15/0.48 % (24266)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (24266)------------------------------
% 0.15/0.48 % (24266)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48 % (24266)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48 % (24266)Termination reason: Refutation
% 0.15/0.48
% 0.15/0.48 % (24266)Memory used [KB]: 1535
% 0.15/0.48 % (24266)Time elapsed: 0.116 s
% 0.15/0.48 % (24266)Instructions burned: 4 (million)
% 0.15/0.48 % (24266)------------------------------
% 0.15/0.48 % (24266)------------------------------
% 0.15/0.48 % (24253)Success in time 0.174 s
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