TSTP Solution File: SEU164+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU164+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 : Thu Aug 31 17:04:17 EDT 2023
% Result : Theorem 24.37s 4.22s
% Output : CNFRefutation 24.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 13 unt; 0 def)
% Number of atoms : 222 ( 34 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 260 ( 96 ~; 108 |; 43 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 131 ( 1 sgn; 90 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f93,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f94,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[],[f93]) ).
fof(f99,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f105,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f144,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f94]) ).
fof(f156,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f157,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f157,f158]) ).
fof(f176,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f177,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f177,f178]) ).
fof(f185,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f186,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f185]) ).
fof(f187,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK12(X0,X1),X3) )
| ~ in(sK12(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK12(X0,X1),X4) )
| in(sK12(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f188,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK12(X0,X1),X4) )
=> ( in(sK13(X0,X1),X0)
& in(sK12(X0,X1),sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f189,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK14(X0,X5),X0)
& in(X5,sK14(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f190,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK12(X0,X1),X3) )
| ~ in(sK12(X0,X1),X1) )
& ( ( in(sK13(X0,X1),X0)
& in(sK12(X0,X1),sK13(X0,X1)) )
| in(sK12(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK14(X0,X5),X0)
& in(X5,sK14(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f186,f189,f188,f187]) ).
fof(f222,plain,
( ? [X0] : union(powerset(X0)) != X0
=> sK21 != union(powerset(sK21)) ),
introduced(choice_axiom,[]) ).
fof(f223,plain,
sK21 != union(powerset(sK21)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f144,f222]) ).
fof(f238,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f159]) ).
fof(f239,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f159]) ).
fof(f262,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f273,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f190]) ).
fof(f274,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK12(X0,X1),sK13(X0,X1))
| in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f275,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK13(X0,X1),X0)
| in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f276,plain,
! [X3,X0,X1] :
( union(X0) = X1
| ~ in(X3,X0)
| ~ in(sK12(X0,X1),X3)
| ~ in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f312,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f99]) ).
fof(f369,plain,
sK21 != union(powerset(sK21)),
inference(cnf_transformation,[],[f223]) ).
fof(f431,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f239]) ).
fof(f432,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f238]) ).
fof(f449,plain,
! [X0,X6,X5] :
( in(X5,union(X0))
| ~ in(X6,X0)
| ~ in(X5,X6) ),
inference(equality_resolution,[],[f273]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f431]) ).
cnf(c_66,plain,
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f432]) ).
cnf(c_89,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f262]) ).
cnf(c_96,plain,
( ~ in(sK12(X0,X1),X1)
| ~ in(sK12(X0,X1),X2)
| ~ in(X2,X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f276]) ).
cnf(c_97,plain,
( union(X0) = X1
| in(sK12(X0,X1),X1)
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f275]) ).
cnf(c_98,plain,
( union(X0) = X1
| in(sK12(X0,X1),sK13(X0,X1))
| in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f274]) ).
cnf(c_99,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| in(X0,union(X2)) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_136,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f312]) ).
cnf(c_191,negated_conjecture,
union(powerset(sK21)) != sK21,
inference(cnf_transformation,[],[f369]) ).
cnf(c_4429,plain,
( ~ subset(X0,sK21)
| in(X0,powerset(sK21)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_6007,plain,
( ~ subset(sK21,sK21)
| in(sK21,powerset(sK21)) ),
inference(instantiation,[status(thm)],[c_4429]) ).
cnf(c_9828,plain,
subset(sK21,sK21),
inference(instantiation,[status(thm)],[c_136]) ).
cnf(c_34121,plain,
( in(sK13(powerset(sK21),sK21),powerset(sK21))
| in(sK12(powerset(sK21),sK21),sK21) ),
inference(resolution,[status(thm)],[c_97,c_191]) ).
cnf(c_41212,plain,
( in(sK12(powerset(sK21),sK21),sK21)
| subset(sK13(powerset(sK21),sK21),sK21) ),
inference(resolution,[status(thm)],[c_34121,c_66]) ).
cnf(c_41213,plain,
( ~ in(X0,sK13(powerset(sK21),sK21))
| in(sK12(powerset(sK21),sK21),sK21)
| in(X0,union(powerset(sK21))) ),
inference(resolution,[status(thm)],[c_34121,c_99]) ).
cnf(c_41292,plain,
( ~ in(X0,sK13(powerset(sK21),sK21))
| in(sK12(powerset(sK21),sK21),sK21)
| in(X0,sK21) ),
inference(resolution,[status(thm)],[c_41212,c_89]) ).
cnf(c_48226,plain,
( union(powerset(sK21)) = sK21
| in(sK12(powerset(sK21),sK21),union(powerset(sK21)))
| in(sK12(powerset(sK21),sK21),sK21) ),
inference(resolution,[status(thm)],[c_98,c_41213]) ).
cnf(c_48227,plain,
( union(powerset(sK21)) = sK21
| in(sK12(powerset(sK21),sK21),sK21) ),
inference(resolution,[status(thm)],[c_98,c_41292]) ).
cnf(c_48260,plain,
in(sK12(powerset(sK21),sK21),sK21),
inference(global_subsumption_just,[status(thm)],[c_48226,c_191,c_48227]) ).
cnf(c_70866,plain,
( ~ in(sK12(powerset(sK21),sK21),sK21)
| ~ in(sK21,powerset(sK21))
| union(powerset(sK21)) = sK21 ),
inference(resolution,[status(thm)],[c_96,c_48260]) ).
cnf(c_70867,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_70866,c_48227,c_9828,c_6007,c_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU164+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 22:36:17 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.37/4.22 % SZS status Started for theBenchmark.p
% 24.37/4.22 % SZS status Theorem for theBenchmark.p
% 24.37/4.22
% 24.37/4.22 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 24.37/4.22
% 24.37/4.22 ------ iProver source info
% 24.37/4.22
% 24.37/4.22 git: date: 2023-05-31 18:12:56 +0000
% 24.37/4.22 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 24.37/4.22 git: non_committed_changes: false
% 24.37/4.22 git: last_make_outside_of_git: false
% 24.37/4.22
% 24.37/4.22 ------ Parsing...
% 24.37/4.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.37/4.22
% 24.37/4.22 ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 24.37/4.22
% 24.37/4.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 24.37/4.22
% 24.37/4.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.37/4.22 ------ Proving...
% 24.37/4.22 ------ Problem Properties
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22 clauses 124
% 24.37/4.22 conjectures 1
% 24.37/4.22 EPR 21
% 24.37/4.22 Horn 95
% 24.37/4.22 unary 25
% 24.37/4.22 binary 55
% 24.37/4.22 lits 274
% 24.37/4.22 lits eq 81
% 24.37/4.22 fd_pure 0
% 24.37/4.22 fd_pseudo 0
% 24.37/4.22 fd_cond 3
% 24.37/4.22 fd_pseudo_cond 35
% 24.37/4.22 AC symbols 0
% 24.37/4.22
% 24.37/4.22 ------ Input Options Time Limit: Unbounded
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22 ------
% 24.37/4.22 Current options:
% 24.37/4.22 ------
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22 ------ Proving...
% 24.37/4.22
% 24.37/4.22
% 24.37/4.22 % SZS status Theorem for theBenchmark.p
% 24.37/4.22
% 24.37/4.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.37/4.22
% 24.37/4.22
%------------------------------------------------------------------------------