TSTP Solution File: SEU353+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU353+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 : n002.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 15:30:19 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 51
% Syntax : Number of formulae : 197 ( 49 unt; 0 def)
% Number of atoms : 502 ( 41 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 503 ( 198 ~; 178 |; 82 &)
% ( 17 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 17 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 205 ( 182 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f977,plain,
$false,
inference(avatar_sat_refutation,[],[f283,f289,f323,f328,f329,f330,f331,f515,f613,f688,f697,f761,f774,f975]) ).
fof(f975,plain,
( ~ spl18_1
| spl18_2 ),
inference(avatar_contradiction_clause,[],[f974]) ).
fof(f974,plain,
( $false
| ~ spl18_1
| spl18_2 ),
inference(subsumption_resolution,[],[f973,f146]) ).
fof(f146,plain,
sK2 != apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
( sK2 != apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2)
& element(sK2,the_carrier(sK1))
& one_sorted_str(sK1)
& ~ empty_carrier(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f64,f109,f108]) ).
fof(f108,plain,
( ? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),X1) != X1
& element(X1,the_carrier(sK1)) )
& one_sorted_str(sK1)
& ~ empty_carrier(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X1] :
( apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),X1) != X1
& element(X1,the_carrier(sK1)) )
=> ( sK2 != apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2)
& element(sK2,the_carrier(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1
& element(X1,the_carrier(X0)) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
inference(negated_conjecture,[],[f57]) ).
fof(f57,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(f973,plain,
( sK2 = apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2)
| ~ spl18_1
| spl18_2 ),
inference(forward_demodulation,[],[f972,f341]) ).
fof(f341,plain,
( sK2 = apply(identity_on_carrier(sK1),sK2)
| ~ spl18_1 ),
inference(forward_demodulation,[],[f338,f260]) ).
fof(f260,plain,
identity_on_carrier(sK1) = identity_as_relation_of(the_carrier(sK1)),
inference(resolution,[],[f160,f144]) ).
fof(f144,plain,
one_sorted_str(sK1),
inference(cnf_transformation,[],[f110]) ).
fof(f160,plain,
! [X0] :
( ~ one_sorted_str(X0)
| identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( one_sorted_str(X0)
=> identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(f338,plain,
( sK2 = apply(identity_as_relation_of(the_carrier(sK1)),sK2)
| ~ spl18_1 ),
inference(resolution,[],[f312,f278]) ).
fof(f278,plain,
( in(sK2,the_carrier(sK1))
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f276,plain,
( spl18_1
<=> in(sK2,the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f312,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_as_relation_of(X0),X1) = X1 ),
inference(forward_demodulation,[],[f192,f150]) ).
fof(f150,plain,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f192,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f972,plain,
( apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2) = apply(identity_on_carrier(sK1),sK2)
| spl18_2 ),
inference(subsumption_resolution,[],[f971,f144]) ).
fof(f971,plain,
( apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2) = apply(identity_on_carrier(sK1),sK2)
| ~ one_sorted_str(sK1)
| spl18_2 ),
inference(subsumption_resolution,[],[f959,f281]) ).
fof(f281,plain,
( ~ empty(the_carrier(sK1))
| spl18_2 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f280,plain,
( spl18_2
<=> empty(the_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f959,plain,
( apply_as_element(the_carrier(sK1),the_carrier(sK1),identity_on_carrier(sK1),sK2) = apply(identity_on_carrier(sK1),sK2)
| empty(the_carrier(sK1))
| ~ one_sorted_str(sK1) ),
inference(resolution,[],[f553,f145]) ).
fof(f145,plain,
element(sK2,the_carrier(sK1)),
inference(cnf_transformation,[],[f110]) ).
fof(f553,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X0) = apply(identity_on_carrier(X1),X0)
| empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(subsumption_resolution,[],[f552,f161]) ).
fof(f161,plain,
! [X0] :
( function(identity_on_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0)) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
fof(f552,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X0) = apply(identity_on_carrier(X1),X0)
| ~ function(identity_on_carrier(X1))
| empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(subsumption_resolution,[],[f545,f311]) ).
fof(f311,plain,
! [X0] :
( relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f163,f229]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f163,plain,
! [X0] :
( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f545,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ relation_of2(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X0) = apply(identity_on_carrier(X1),X0)
| ~ function(identity_on_carrier(X1))
| empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(resolution,[],[f233,f162]) ).
fof(f162,plain,
! [X0] :
( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( ~ quasi_total(X2,X0,X1)
| ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| apply_as_element(X0,X1,X2,X3) = apply(X2,X3)
| ~ function(X2)
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( apply_as_element(X0,X1,X2,X3) = apply(X2,X3)
| ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| empty(X0) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( apply_as_element(X0,X1,X2,X3) = apply(X2,X3)
| ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1,X2,X3] :
( ( element(X3,X0)
& relation_of2(X2,X0,X1)
& quasi_total(X2,X0,X1)
& function(X2)
& ~ empty(X0) )
=> apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(f774,plain,
( ~ spl18_15
| spl18_16 ),
inference(avatar_split_clause,[],[f748,f771,f767]) ).
fof(f767,plain,
( spl18_15
<=> empty(identity_on_carrier(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f771,plain,
( spl18_16
<=> empty(the_carrier(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f748,plain,
( empty(the_carrier(sK16))
| ~ empty(identity_on_carrier(sK16)) ),
inference(subsumption_resolution,[],[f747,f307]) ).
fof(f307,plain,
relation_of2(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16)),
inference(superposition,[],[f300,f262]) ).
fof(f262,plain,
identity_on_carrier(sK16) = identity_as_relation_of(the_carrier(sK16)),
inference(resolution,[],[f160,f237]) ).
fof(f237,plain,
one_sorted_str(sK16),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ~ empty_carrier(sK16)
& one_sorted_str(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f42,f139]) ).
fof(f139,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK16)
& one_sorted_str(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f300,plain,
! [X0] : relation_of2(identity_as_relation_of(X0),X0,X0),
inference(resolution,[],[f229,f157]) ).
fof(f157,plain,
! [X0] : relation_of2_as_subset(identity_as_relation_of(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( relation_of2_as_subset(identity_as_relation_of(X0),X0,X0)
& v1_partfun1(identity_as_relation_of(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(f747,plain,
( ~ relation_of2(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16))
| empty(the_carrier(sK16))
| ~ empty(identity_on_carrier(sK16)) ),
inference(subsumption_resolution,[],[f737,f296]) ).
fof(f296,plain,
function(identity_on_carrier(sK16)),
inference(superposition,[],[f243,f262]) ).
fof(f243,plain,
! [X0] : function(identity_as_relation_of(X0)),
inference(superposition,[],[f152,f150]) ).
fof(f152,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( transitive(identity_relation(X0))
& symmetric(identity_relation(X0))
& reflexive(identity_relation(X0))
& function(identity_relation(X0))
& relation(identity_relation(X0)) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( transitive(identity_relation(X0))
& antisymmetric(identity_relation(X0))
& symmetric(identity_relation(X0))
& reflexive(identity_relation(X0))
& function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
fof(f737,plain,
( ~ function(identity_on_carrier(sK16))
| ~ relation_of2(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16))
| empty(the_carrier(sK16))
| ~ empty(identity_on_carrier(sK16)) ),
inference(duplicate_literal_removal,[],[f736]) ).
fof(f736,plain,
( ~ function(identity_on_carrier(sK16))
| ~ relation_of2(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16))
| empty(the_carrier(sK16))
| empty(the_carrier(sK16))
| ~ empty(identity_on_carrier(sK16)) ),
inference(resolution,[],[f459,f295]) ).
fof(f295,plain,
v1_partfun1(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16)),
inference(superposition,[],[f156,f262]) ).
fof(f156,plain,
! [X0] : v1_partfun1(identity_as_relation_of(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f459,plain,
! [X2,X0,X1] :
( ~ v1_partfun1(X0,X1,X2)
| ~ function(X0)
| ~ relation_of2(X0,X1,X2)
| empty(X2)
| empty(X1)
| ~ empty(X0) ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f458,plain,
! [X2,X0,X1] :
( ~ empty(X0)
| ~ function(X0)
| ~ relation_of2(X0,X1,X2)
| empty(X2)
| empty(X1)
| ~ v1_partfun1(X0,X1,X2)
| ~ function(X0)
| ~ relation_of2(X0,X1,X2) ),
inference(resolution,[],[f202,f222]) ).
fof(f222,plain,
! [X2,X0,X1] :
( quasi_total(X2,X0,X1)
| ~ v1_partfun1(X2,X0,X1)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( quasi_total(X2,X0,X1)
& function(X2) )
| ~ v1_partfun1(X2,X0,X1)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( quasi_total(X2,X0,X1)
& function(X2) )
| ~ v1_partfun1(X2,X0,X1)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> ( ( v1_partfun1(X2,X0,X1)
& function(X2) )
=> ( quasi_total(X2,X0,X1)
& function(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ quasi_total(X2,X0,X1)
| ~ empty(X2)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( ( quasi_total(X2,X0,X1)
& v1_partfun1(X2,X0,X1)
& ~ empty(X2)
& function(X2) )
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1) )
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( ( quasi_total(X2,X0,X1)
& v1_partfun1(X2,X0,X1)
& ~ empty(X2)
& function(X2) )
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| ~ relation_of2(X2,X0,X1) )
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ! [X2] :
( relation_of2(X2,X0,X1)
=> ( ( quasi_total(X2,X0,X1)
& function(X2) )
=> ( quasi_total(X2,X0,X1)
& v1_partfun1(X2,X0,X1)
& ~ empty(X2)
& function(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
fof(f761,plain,
( ~ spl18_13
| spl18_14 ),
inference(avatar_split_clause,[],[f746,f758,f754]) ).
fof(f754,plain,
( spl18_13
<=> empty(identity_on_carrier(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f758,plain,
( spl18_14
<=> empty(the_carrier(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f746,plain,
( empty(the_carrier(sK14))
| ~ empty(identity_on_carrier(sK14)) ),
inference(subsumption_resolution,[],[f745,f306]) ).
fof(f306,plain,
relation_of2(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14)),
inference(superposition,[],[f300,f261]) ).
fof(f261,plain,
identity_on_carrier(sK14) = identity_as_relation_of(the_carrier(sK14)),
inference(resolution,[],[f160,f235]) ).
fof(f235,plain,
one_sorted_str(sK14),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
one_sorted_str(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f24,f135]) ).
fof(f135,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK14) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f745,plain,
( ~ relation_of2(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14))
| empty(the_carrier(sK14))
| ~ empty(identity_on_carrier(sK14)) ),
inference(subsumption_resolution,[],[f738,f293]) ).
fof(f293,plain,
function(identity_on_carrier(sK14)),
inference(superposition,[],[f243,f261]) ).
fof(f738,plain,
( ~ function(identity_on_carrier(sK14))
| ~ relation_of2(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14))
| empty(the_carrier(sK14))
| ~ empty(identity_on_carrier(sK14)) ),
inference(duplicate_literal_removal,[],[f735]) ).
fof(f735,plain,
( ~ function(identity_on_carrier(sK14))
| ~ relation_of2(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14))
| empty(the_carrier(sK14))
| empty(the_carrier(sK14))
| ~ empty(identity_on_carrier(sK14)) ),
inference(resolution,[],[f459,f292]) ).
fof(f292,plain,
v1_partfun1(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14)),
inference(superposition,[],[f156,f261]) ).
fof(f697,plain,
( spl18_11
| ~ spl18_12 ),
inference(avatar_split_clause,[],[f604,f694,f691]) ).
fof(f691,plain,
( spl18_11
<=> ! [X0] : ~ in(X0,identity_on_carrier(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f694,plain,
( spl18_12
<=> empty(cartesian_product2(the_carrier(sK16),the_carrier(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f604,plain,
! [X0] :
( ~ empty(cartesian_product2(the_carrier(sK16),the_carrier(sK16)))
| ~ in(X0,identity_on_carrier(sK16)) ),
inference(resolution,[],[f384,f294]) ).
fof(f294,plain,
relation_of2_as_subset(identity_on_carrier(sK16),the_carrier(sK16),the_carrier(sK16)),
inference(superposition,[],[f157,f262]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ),
inference(resolution,[],[f217,f231]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f217,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f688,plain,
( spl18_9
| ~ spl18_10 ),
inference(avatar_split_clause,[],[f603,f685,f682]) ).
fof(f682,plain,
( spl18_9
<=> ! [X0] : ~ in(X0,identity_on_carrier(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
fof(f685,plain,
( spl18_10
<=> empty(cartesian_product2(the_carrier(sK14),the_carrier(sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
fof(f603,plain,
! [X0] :
( ~ empty(cartesian_product2(the_carrier(sK14),the_carrier(sK14)))
| ~ in(X0,identity_on_carrier(sK14)) ),
inference(resolution,[],[f384,f291]) ).
fof(f291,plain,
relation_of2_as_subset(identity_on_carrier(sK14),the_carrier(sK14),the_carrier(sK14)),
inference(superposition,[],[f157,f261]) ).
fof(f613,plain,
( spl18_7
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f602,f610,f607]) ).
fof(f607,plain,
( spl18_7
<=> ! [X0] : ~ in(X0,identity_on_carrier(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f610,plain,
( spl18_8
<=> empty(cartesian_product2(the_carrier(sK1),the_carrier(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
fof(f602,plain,
! [X0] :
( ~ empty(cartesian_product2(the_carrier(sK1),the_carrier(sK1)))
| ~ in(X0,identity_on_carrier(sK1)) ),
inference(resolution,[],[f384,f272]) ).
fof(f272,plain,
relation_of2_as_subset(identity_on_carrier(sK1),the_carrier(sK1),the_carrier(sK1)),
inference(superposition,[],[f157,f260]) ).
fof(f515,plain,
( spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f443,f512,f508]) ).
fof(f508,plain,
( spl18_5
<=> empty(sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
fof(f512,plain,
( spl18_6
<=> in(empty_set,sK3(powerset(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f443,plain,
( in(empty_set,sK3(powerset(empty_set)))
| empty(sK3(powerset(empty_set))) ),
inference(superposition,[],[f267,f428]) ).
fof(f428,plain,
empty_set = sK5(sK3(powerset(empty_set))),
inference(resolution,[],[f421,f147]) ).
fof(f147,plain,
empty(empty_set),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f421,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK5(sK3(powerset(X0))) ),
inference(resolution,[],[f415,f164]) ).
fof(f164,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f415,plain,
! [X0] :
( empty(sK5(sK3(powerset(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f406,f267]) ).
fof(f406,plain,
! [X0,X1] :
( ~ in(X1,sK5(sK3(powerset(X0))))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f403,f148]) ).
fof(f148,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f403,plain,
! [X0,X1] :
( empty(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK5(sK3(powerset(X0)))) ),
inference(resolution,[],[f400,f231]) ).
fof(f400,plain,
! [X0] :
( element(sK5(sK3(X0)),X0)
| empty(X0) ),
inference(subsumption_resolution,[],[f399,f159]) ).
fof(f159,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f65,f111]) ).
fof(f111,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f399,plain,
! [X0] :
( element(sK5(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) ),
inference(resolution,[],[f390,f267]) ).
fof(f390,plain,
! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty(X1) ),
inference(resolution,[],[f228,f158]) ).
fof(f158,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f267,plain,
! [X0] :
( in(sK5(X0),X0)
| empty(X0) ),
inference(resolution,[],[f193,f170]) ).
fof(f170,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f26,f115]) ).
fof(f115,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f193,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f331,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f324,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f322,f147]) ).
fof(f322,plain,
( ! [X0] : ~ empty(X0)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f321,plain,
( spl18_4
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f330,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f325,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f322,f172]) ).
fof(f172,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f39,f117]) ).
fof(f117,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f329,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f326,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f322,f236]) ).
fof(f236,plain,
empty(sK15),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
empty(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f36,f137]) ).
fof(f137,plain,
( ? [X0] : empty(X0)
=> empty(sK15) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f328,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f327,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f322,f242]) ).
fof(f242,plain,
empty(sK17),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( empty(sK17)
& one_to_one(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f34,f141]) ).
fof(f141,plain,
( ? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( empty(sK17)
& one_to_one(sK17)
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(f323,plain,
( spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f314,f321,f318]) ).
fof(f318,plain,
( spl18_3
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f314,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,empty_set) ),
inference(resolution,[],[f231,f252]) ).
fof(f252,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f171,f245]) ).
fof(f245,plain,
! [X0] : empty_set = sK6(X0),
inference(resolution,[],[f164,f172]) ).
fof(f171,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f118]) ).
fof(f289,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f288,plain,
( $false
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f287,f143]) ).
fof(f143,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f110]) ).
fof(f287,plain,
( empty_carrier(sK1)
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f284,f144]) ).
fof(f284,plain,
( ~ one_sorted_str(sK1)
| empty_carrier(sK1)
| ~ spl18_2 ),
inference(resolution,[],[f282,f165]) ).
fof(f165,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f282,plain,
( empty(the_carrier(sK1))
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f265,f280,f276]) ).
fof(f265,plain,
( empty(the_carrier(sK1))
| in(sK2,the_carrier(sK1)) ),
inference(resolution,[],[f193,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 21:20:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (17083)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (17087)WARNING: value z3 for option sas not known
% 0.15/0.38 % (17088)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (17085)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (17086)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (17089)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)
% 0.15/0.38 % (17090)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)
% 0.15/0.38 % (17087)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)
% 0.15/0.38 % (17091)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.41 % (17087)First to succeed.
% 0.21/0.42 % (17087)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42 % (17087)------------------------------
% 0.21/0.42 % (17087)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.42 % (17087)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (17087)Memory used [KB]: 1248
% 0.21/0.42 % (17087)Time elapsed: 0.035 s
% 0.21/0.42 % (17087)Instructions burned: 51 (million)
% 0.21/0.42 % (17087)------------------------------
% 0.21/0.42 % (17087)------------------------------
% 0.21/0.42 % (17083)Success in time 0.053 s
%------------------------------------------------------------------------------