TSTP Solution File: SEU045+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU045+1 : 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_uns --cores 0 -t %d %s
% Computer : n027.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 18:26:26 EDT 2022
% Result : Theorem 1.71s 0.58s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 250 ( 36 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 309 ( 105 ~; 98 |; 78 &)
% ( 11 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 112 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f231,plain,
$false,
inference(unit_resulting_resolution,[],[f172,f170,f224,f159]) ).
fof(f159,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X0))
| apply(X0,X5) = apply(X1,X5) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( in(sK10(X0,X1),relation_dom(X0))
& apply(X0,sK10(X0,X1)) != apply(X1,sK10(X0,X1)) )
| ( ( ~ in(sK11(X0,X1,X2),relation_dom(X1))
| ~ in(apply(X1,sK11(X0,X1,X2)),X2)
| ~ in(sK11(X0,X1,X2),relation_dom(X0)) )
& ( ( in(sK11(X0,X1,X2),relation_dom(X1))
& in(apply(X1,sK11(X0,X1,X2)),X2) )
| in(sK11(X0,X1,X2),relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( ~ in(X5,relation_dom(X0))
| apply(X0,X5) = apply(X1,X5) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(X6,relation_dom(X1))
| ~ in(apply(X1,X6),X2) )
& ( ( in(X6,relation_dom(X1))
& in(apply(X1,X6),X2) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f107,f109,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,relation_dom(X0))
& apply(X1,X3) != apply(X0,X3) )
=> ( in(sK10(X0,X1),relation_dom(X0))
& apply(X0,sK10(X0,X1)) != apply(X1,sK10(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,relation_dom(X1))
| ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) )
| in(X4,relation_dom(X0)) ) )
=> ( ( ~ in(sK11(X0,X1,X2),relation_dom(X1))
| ~ in(apply(X1,sK11(X0,X1,X2)),X2)
| ~ in(sK11(X0,X1,X2),relation_dom(X0)) )
& ( ( in(sK11(X0,X1,X2),relation_dom(X1))
& in(apply(X1,sK11(X0,X1,X2)),X2) )
| in(sK11(X0,X1,X2),relation_dom(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( in(X3,relation_dom(X0))
& apply(X1,X3) != apply(X0,X3) )
| ? [X4] :
( ( ~ in(X4,relation_dom(X1))
| ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X0)) )
& ( ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) )
| in(X4,relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( ~ in(X5,relation_dom(X0))
| apply(X0,X5) = apply(X1,X5) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(X6,relation_dom(X1))
| ~ in(apply(X1,X6),X2) )
& ( ( in(X6,relation_dom(X1))
& in(apply(X1,X6),X2) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( in(X3,relation_dom(X1))
& apply(X2,X3) != apply(X1,X3) )
| ? [X4] :
( ( ~ in(X4,relation_dom(X2))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ in(apply(X2,X4),X0) )
& ( ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( in(X3,relation_dom(X1))
& apply(X2,X3) != apply(X1,X3) )
| ? [X4] :
( ( ~ in(X4,relation_dom(X2))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ in(apply(X2,X4),X0) )
& ( ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X1,X2,X0] :
( sP0(X1,X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f224,plain,
! [X0] : sP0(relation_rng_restriction(X0,sK14),sK14,X0),
inference(resolution,[],[f216,f183]) ).
fof(f183,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X2,X1),X1,X2)
| sP0(relation_rng_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f155]) ).
fof(f155,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| relation_rng_restriction(X2,X1) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( ( sP0(X0,X1,X2)
| relation_rng_restriction(X2,X1) != X0 )
& ( relation_rng_restriction(X2,X1) = X0
| ~ sP0(X0,X1,X2) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f103]) ).
fof(f103,plain,
! [X1,X2,X0] :
( ( ( sP0(X1,X2,X0)
| relation_rng_restriction(X0,X2) != X1 )
& ( relation_rng_restriction(X0,X2) = X1
| ~ sP0(X1,X2,X0) ) )
| ~ sP1(X1,X2,X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
<=> relation_rng_restriction(X0,X2) = X1 )
| ~ sP1(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f216,plain,
! [X8,X9] : sP1(relation_rng_restriction(X8,sK14),sK14,X9),
inference(subsumption_resolution,[],[f211,f171]) ).
fof(f171,plain,
relation(sK14),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( function(sK14)
& in(sK16,relation_dom(relation_rng_restriction(sK15,sK14)))
& relation(sK14)
& apply(relation_rng_restriction(sK15,sK14),sK16) != apply(sK14,sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f115,f116]) ).
fof(f116,plain,
( ? [X0,X1,X2] :
( function(X0)
& in(X2,relation_dom(relation_rng_restriction(X1,X0)))
& relation(X0)
& apply(relation_rng_restriction(X1,X0),X2) != apply(X0,X2) )
=> ( function(sK14)
& in(sK16,relation_dom(relation_rng_restriction(sK15,sK14)))
& relation(sK14)
& apply(relation_rng_restriction(sK15,sK14),sK16) != apply(sK14,sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
? [X0,X1,X2] :
( function(X0)
& in(X2,relation_dom(relation_rng_restriction(X1,X0)))
& relation(X0)
& apply(relation_rng_restriction(X1,X0),X2) != apply(X0,X2) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X0,X2,X1] :
( function(X0)
& in(X1,relation_dom(relation_rng_restriction(X2,X0)))
& relation(X0)
& apply(relation_rng_restriction(X2,X0),X1) != apply(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X1,X2,X0] :
( apply(relation_rng_restriction(X2,X0),X1) != apply(X0,X1)
& in(X1,relation_dom(relation_rng_restriction(X2,X0)))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
~ ! [X1,X2,X0] :
( ( function(X0)
& relation(X0) )
=> ( in(X1,relation_dom(relation_rng_restriction(X2,X0)))
=> apply(relation_rng_restriction(X2,X0),X1) = apply(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X2,X1,X0] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X2,X1,X0] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
fof(f211,plain,
! [X8,X9] :
( ~ relation(sK14)
| sP1(relation_rng_restriction(X8,sK14),sK14,X9) ),
inference(resolution,[],[f200,f173]) ).
fof(f173,plain,
function(sK14),
inference(cnf_transformation,[],[f117]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sP1(relation_rng_restriction(X0,X1),sK14,X2) ),
inference(subsumption_resolution,[],[f194,f146]) ).
fof(f146,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X1,X0] :
( ~ function(X0)
| ~ relation(X0)
| ( relation(relation_rng_restriction(X1,X0))
& function(relation_rng_restriction(X1,X0)) ) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X1,X0))
& function(relation_rng_restriction(X1,X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( relation(relation_rng_restriction(X1,X0))
& function(relation_rng_restriction(X1,X0)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X1,X0] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ function(X1)
| sP1(relation_rng_restriction(X0,X1),sK14,X2)
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(resolution,[],[f186,f145]) ).
fof(f145,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f186,plain,
! [X2,X1] :
( ~ function(X1)
| ~ relation(X1)
| sP1(X1,sK14,X2) ),
inference(subsumption_resolution,[],[f185,f171]) ).
fof(f185,plain,
! [X2,X1] :
( sP1(X1,sK14,X2)
| ~ relation(X1)
| ~ relation(sK14)
| ~ function(X1) ),
inference(resolution,[],[f173,f166]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X1)
| sP1(X1,X2,X0)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ function(X1)
| ! [X2] :
( ~ relation(X2)
| sP1(X1,X2,X0)
| ~ function(X2) )
| ~ relation(X1) ),
inference(definition_folding,[],[f64,f78,f77]) ).
fof(f64,plain,
! [X0,X1] :
( ~ function(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) ) ) )
<=> relation_rng_restriction(X0,X2) = X1 )
| ~ function(X2) )
| ~ relation(X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X1,X0] :
( ! [X2] :
( ( ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) ) ) )
<=> relation_rng_restriction(X0,X2) = X1 )
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(X4,relation_dom(X2))
& in(apply(X2,X4),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) ) )
<=> relation_rng_restriction(X0,X2) = X1 ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f170,plain,
apply(relation_rng_restriction(sK15,sK14),sK16) != apply(sK14,sK16),
inference(cnf_transformation,[],[f117]) ).
fof(f172,plain,
in(sK16,relation_dom(relation_rng_restriction(sK15,sK14))),
inference(cnf_transformation,[],[f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU045+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.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 14:54:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.43/0.56 % (13947)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.43/0.56 % (13928)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)
% 1.43/0.56 % (13939)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.43/0.57 % (13934)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.43/0.57 % (13931)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)
% 1.43/0.57 % (13947)First to succeed.
% 1.71/0.58 % (13939)Instruction limit reached!
% 1.71/0.58 % (13939)------------------------------
% 1.71/0.58 % (13939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.58 % (13939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.58 % (13939)Termination reason: Unknown
% 1.71/0.58 % (13938)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)
% 1.71/0.58 % (13939)Termination phase: Saturation
% 1.71/0.58
% 1.71/0.58 % (13939)Memory used [KB]: 6012
% 1.71/0.58 % (13939)Time elapsed: 0.088 s
% 1.71/0.58 % (13939)Instructions burned: 7 (million)
% 1.71/0.58 % (13939)------------------------------
% 1.71/0.58 % (13939)------------------------------
% 1.71/0.58 % (13947)Refutation found. Thanks to Tanya!
% 1.71/0.58 % SZS status Theorem for theBenchmark
% 1.71/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.71/0.58 % (13947)------------------------------
% 1.71/0.58 % (13947)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.58 % (13947)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.58 % (13947)Termination reason: Refutation
% 1.71/0.58
% 1.71/0.58 % (13947)Memory used [KB]: 1663
% 1.71/0.58 % (13947)Time elapsed: 0.091 s
% 1.71/0.58 % (13947)Instructions burned: 6 (million)
% 1.71/0.58 % (13947)------------------------------
% 1.71/0.58 % (13947)------------------------------
% 1.71/0.58 % (13923)Success in time 0.228 s
%------------------------------------------------------------------------------