TSTP Solution File: SEU215+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 : Tue Apr 30 15:24:09 EDT 2024
% Result : Theorem 70.76s 13.14s
% Output : Refutation 70.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 18 unt; 0 def)
% Number of atoms : 256 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 299 ( 105 ~; 98 |; 65 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 113 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f927964,plain,
$false,
inference(subsumption_resolution,[],[f927960,f927943]) ).
fof(f927943,plain,
empty_set = apply(sK6,apply(sK5,sK4)),
inference(unit_resulting_resolution,[],[f310,f927933,f161]) ).
fof(f161,plain,
! [X2,X1] :
( ~ sP1(empty_set,X1,X2)
| in(X1,relation_dom(X2))
| empty_set = apply(X2,X1) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X2,X0,X1] :
( apply(X2,X1) = X0
| empty_set != X0
| in(X1,relation_dom(X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( ( apply(X2,X1) = X0
| empty_set != X0 )
& ( empty_set = X0
| apply(X2,X1) != X0 ) )
| in(X1,relation_dom(X2))
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X2,X1,X0] :
( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0))
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X2,X1,X0] :
( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0))
| ~ sP1(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f927933,plain,
~ in(apply(sK5,sK4),relation_dom(sK6)),
inference(unit_resulting_resolution,[],[f108,f927929,f147]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ in(apply(X2,X1),relation_dom(X0))
| sP2(X0,X1,X2)
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ in(apply(X2,X1),relation_dom(X0))
| ~ in(X1,relation_dom(X2)) )
& ( ( in(apply(X2,X1),relation_dom(X0))
& in(X1,relation_dom(X2)) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f90]) ).
fof(f90,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f927929,plain,
~ sP2(sK6,sK4,sK5),
inference(unit_resulting_resolution,[],[f449502,f927598,f144]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| ~ sP2(X2,X1,X0)
| in(X1,relation_dom(relation_composition(X0,X2))) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ( in(X1,relation_dom(relation_composition(X0,X2)))
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| ~ in(X1,relation_dom(relation_composition(X0,X2))) ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ sP3(X2,X0,X1) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> sP2(X1,X0,X2) )
| ~ sP3(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f927598,plain,
~ in(sK4,relation_dom(relation_composition(sK5,sK6))),
inference(unit_resulting_resolution,[],[f106,f107,f104,f105,f109,f142]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f109,plain,
apply(relation_composition(sK5,sK6),sK4) != apply(sK6,apply(sK5,sK4)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( apply(relation_composition(sK5,sK6),sK4) != apply(sK6,apply(sK5,sK4))
& in(sK4,relation_dom(sK5))
& function(sK6)
& relation(sK6)
& function(sK5)
& relation(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f45,f79,f78]) ).
fof(f78,plain,
( ? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) )
=> ( ? [X2] :
( apply(relation_composition(sK5,X2),sK4) != apply(X2,apply(sK5,sK4))
& in(sK4,relation_dom(sK5))
& function(X2)
& relation(X2) )
& function(sK5)
& relation(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
( ? [X2] :
( apply(relation_composition(sK5,X2),sK4) != apply(X2,apply(sK5,sK4))
& in(sK4,relation_dom(sK5))
& function(X2)
& relation(X2) )
=> ( apply(relation_composition(sK5,sK6),sK4) != apply(sK6,apply(sK5,sK4))
& in(sK4,relation_dom(sK5))
& function(sK6)
& relation(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f105,plain,
function(sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f104,plain,
relation(sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f107,plain,
function(sK6),
inference(cnf_transformation,[],[f80]) ).
fof(f106,plain,
relation(sK6),
inference(cnf_transformation,[],[f80]) ).
fof(f449502,plain,
! [X0] : sP3(sK5,X0,sK6),
inference(unit_resulting_resolution,[],[f106,f107,f105,f104,f148]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ function(X2)
| sP3(X2,X0,X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( sP3(X2,X0,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f67,f76,f75]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f108,plain,
in(sK4,relation_dom(sK5)),
inference(cnf_transformation,[],[f80]) ).
fof(f310,plain,
! [X0,X1] : sP1(X0,X1,sK6),
inference(unit_resulting_resolution,[],[f107,f106,f127]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1,X2] :
( sP1(X2,X1,X0)
& sP0(X0,X2,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f53,f73,f72]) ).
fof(f72,plain,
! [X0,X2,X1] :
( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f53,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f927960,plain,
empty_set != apply(sK6,apply(sK5,sK4)),
inference(superposition,[],[f109,f927931]) ).
fof(f927931,plain,
empty_set = apply(relation_composition(sK5,sK6),sK4),
inference(unit_resulting_resolution,[],[f439082,f927598,f161]) ).
fof(f439082,plain,
! [X0,X1] : sP1(X0,X1,relation_composition(sK5,sK6)),
inference(unit_resulting_resolution,[],[f48665,f438168,f127]) ).
fof(f438168,plain,
function(relation_composition(sK5,sK6)),
inference(unit_resulting_resolution,[],[f104,f105,f106,f107,f141]) ).
fof(f141,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f48665,plain,
relation(relation_composition(sK5,sK6)),
inference(unit_resulting_resolution,[],[f104,f106,f149]) ).
fof(f149,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_composition(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:33:55 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % (17214)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (17217)WARNING: value z3 for option sas not known
% 0.11/0.34 % (17217)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (17220)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.36 % (17215)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.36 % (17221)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.37 TRYING [1]
% 0.16/0.37 % (17218)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.37 % (17219)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.37 TRYING [1]
% 0.16/0.37 TRYING [2]
% 0.16/0.38 % (17216)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 TRYING [3]
% 0.16/0.38 TRYING [2]
% 0.16/0.40 TRYING [4]
% 0.16/0.41 TRYING [3]
% 0.16/0.47 TRYING [5]
% 0.16/0.49 TRYING [4]
% 1.35/0.64 TRYING [6]
% 1.51/0.70 TRYING [5]
% 2.99/0.98 TRYING [7]
% 5.39/1.46 TRYING [1]
% 5.39/1.46 TRYING [2]
% 5.39/1.47 TRYING [3]
% 5.60/1.49 TRYING [4]
% 5.85/1.57 TRYING [5]
% 6.56/1.71 TRYING [8]
% 6.56/1.76 TRYING [6]
% 6.56/1.77 TRYING [6]
% 8.80/2.22 TRYING [7]
% 12.86/2.99 TRYING [9]
% 14.12/3.22 TRYING [8]
% 23.10/5.07 TRYING [9]
% 24.50/5.35 TRYING [10]
% 27.09/5.84 TRYING [7]
% 41.86/8.26 TRYING [10]
% 49.73/9.58 TRYING [11]
% 70.76/13.12 % (17221)First to succeed.
% 70.76/13.14 % (17221)Refutation found. Thanks to Tanya!
% 70.76/13.14 % SZS status Theorem for theBenchmark
% 70.76/13.14 % SZS output start Proof for theBenchmark
% See solution above
% 70.76/13.14 % (17221)------------------------------
% 70.76/13.14 % (17221)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 70.76/13.14 % (17221)Termination reason: Refutation
% 70.76/13.14
% 70.76/13.14 % (17221)Memory used [KB]: 138523
% 70.76/13.14 % (17221)Time elapsed: 12.761 s
% 70.76/13.14 % (17221)Instructions burned: 26801 (million)
% 70.76/13.14 % (17221)------------------------------
% 70.76/13.14 % (17221)------------------------------
% 70.76/13.14 % (17214)Success in time 12.717 s
%------------------------------------------------------------------------------