TSTP Solution File: SEU114+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 17:03:46 EDT 2023
% Result : Theorem 8.10s 1.66s
% Output : CNFRefutation 8.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 12 unt; 0 def)
% Number of atoms : 246 ( 27 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 291 ( 115 ~; 114 |; 45 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 114 ( 1 sgn; 80 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f10,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f26,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f27,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f28,axiom,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f29,conjecture,
! [X0] :
( finite(X0)
=> powerset(X0) = finite_subsets(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( finite(X0)
=> powerset(X0) = finite_subsets(X0) ),
inference(negated_conjecture,[],[f29]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f60,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
? [X0] :
( powerset(X0) != finite_subsets(X0)
& finite(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f71,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f71]) ).
fof(f73,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,[],[f54]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f74,f75]) ).
fof(f77,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f55]) ).
fof(f78,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) )
=> ( ( ~ finite(sK1(X0,X1))
| ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ( finite(sK1(X0,X1))
& subset(sK1(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ( ( ~ finite(sK1(X0,X1))
| ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ( finite(sK1(X0,X1))
& subset(sK1(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f79,f80]) ).
fof(f102,plain,
( ? [X0] :
( powerset(X0) != finite_subsets(X0)
& finite(X0) )
=> ( powerset(sK12) != finite_subsets(sK12)
& finite(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( powerset(sK12) != finite_subsets(sK12)
& finite(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f62,f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f114,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f117,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f158,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f159,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f160,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f161,plain,
finite(sK12),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
powerset(sK12) != finite_subsets(sK12),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
! [X3,X0] :
( in(X3,finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f120]) ).
cnf(c_56,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_59,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_60,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ finite(X0)
| in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_68,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f124]) ).
cnf(c_102,plain,
( ~ subset(X0,X1)
| ~ finite(X1)
| finite(X0) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_103,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_104,plain,
subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[],[f160]) ).
cnf(c_105,negated_conjecture,
powerset(sK12) != finite_subsets(sK12),
inference(cnf_transformation,[],[f162]) ).
cnf(c_106,negated_conjecture,
finite(sK12),
inference(cnf_transformation,[],[f161]) ).
cnf(c_109,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_329,plain,
( ~ subset(X0,X1)
| ~ finite(X0)
| in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_68]) ).
cnf(c_2571,plain,
( ~ subset(powerset(sK12),finite_subsets(sK12))
| ~ subset(finite_subsets(sK12),powerset(sK12))
| powerset(sK12) = finite_subsets(sK12) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2597,plain,
subset(finite_subsets(sK12),powerset(sK12)),
inference(instantiation,[status(thm)],[c_104]) ).
cnf(c_2633,plain,
( ~ in(sK0(X0,finite_subsets(sK12)),finite_subsets(sK12))
| subset(X0,finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_2634,plain,
( in(sK0(X0,finite_subsets(sK12)),X0)
| subset(X0,finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_2777,plain,
( ~ subset(sK0(X0,finite_subsets(sK12)),sK12)
| ~ finite(sK0(X0,finite_subsets(sK12)))
| in(sK0(X0,finite_subsets(sK12)),finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_329]) ).
cnf(c_2787,plain,
( in(sK0(powerset(sK12),finite_subsets(sK12)),powerset(sK12))
| subset(powerset(sK12),finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_2634]) ).
cnf(c_3073,plain,
( ~ subset(X0,sK12)
| ~ finite(sK12)
| finite(X0) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_7247,plain,
( ~ in(sK0(powerset(sK12),X0),powerset(sK12))
| element(sK0(powerset(sK12),X0),powerset(sK12)) ),
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_7989,plain,
( ~ subset(sK0(X0,finite_subsets(sK12)),sK12)
| ~ finite(sK12)
| finite(sK0(X0,finite_subsets(sK12))) ),
inference(instantiation,[status(thm)],[c_3073]) ).
cnf(c_15326,plain,
( ~ element(sK0(X0,finite_subsets(sK12)),powerset(sK12))
| subset(sK0(X0,finite_subsets(sK12)),sK12) ),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_17706,plain,
( ~ subset(sK0(powerset(sK12),finite_subsets(sK12)),sK12)
| ~ finite(sK0(powerset(sK12),finite_subsets(sK12)))
| in(sK0(powerset(sK12),finite_subsets(sK12)),finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_2777]) ).
cnf(c_17751,plain,
( ~ in(sK0(powerset(sK12),finite_subsets(sK12)),finite_subsets(sK12))
| subset(powerset(sK12),finite_subsets(sK12)) ),
inference(instantiation,[status(thm)],[c_2633]) ).
cnf(c_21233,plain,
( ~ element(sK0(powerset(sK12),finite_subsets(sK12)),powerset(sK12))
| subset(sK0(powerset(sK12),finite_subsets(sK12)),sK12) ),
inference(instantiation,[status(thm)],[c_15326]) ).
cnf(c_31861,plain,
( ~ in(sK0(powerset(sK12),finite_subsets(sK12)),powerset(sK12))
| element(sK0(powerset(sK12),finite_subsets(sK12)),powerset(sK12)) ),
inference(instantiation,[status(thm)],[c_7247]) ).
cnf(c_36367,plain,
( ~ subset(sK0(powerset(sK12),finite_subsets(sK12)),sK12)
| ~ finite(sK12)
| finite(sK0(powerset(sK12),finite_subsets(sK12))) ),
inference(instantiation,[status(thm)],[c_7989]) ).
cnf(c_36370,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_36367,c_31861,c_21233,c_17751,c_17706,c_2787,c_2597,c_2571,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 22:07:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.10/1.66 % SZS status Started for theBenchmark.p
% 8.10/1.66 % SZS status Theorem for theBenchmark.p
% 8.10/1.66
% 8.10/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 8.10/1.66
% 8.10/1.66 ------ iProver source info
% 8.10/1.66
% 8.10/1.66 git: date: 2023-05-31 18:12:56 +0000
% 8.10/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 8.10/1.66 git: non_committed_changes: false
% 8.10/1.66 git: last_make_outside_of_git: false
% 8.10/1.66
% 8.10/1.66 ------ Parsing...
% 8.10/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.10/1.66
% 8.10/1.66 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 8.10/1.66
% 8.10/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.10/1.66
% 8.10/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.10/1.66 ------ Proving...
% 8.10/1.66 ------ Problem Properties
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66 clauses 52
% 8.10/1.66 conjectures 2
% 8.10/1.66 EPR 21
% 8.10/1.66 Horn 43
% 8.10/1.66 unary 21
% 8.10/1.66 binary 20
% 8.10/1.66 lits 98
% 8.10/1.66 lits eq 7
% 8.10/1.66 fd_pure 0
% 8.10/1.66 fd_pseudo 0
% 8.10/1.66 fd_cond 1
% 8.10/1.66 fd_pseudo_cond 5
% 8.10/1.66 AC symbols 0
% 8.10/1.66
% 8.10/1.66 ------ Input Options Time Limit: Unbounded
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66 ------
% 8.10/1.66 Current options:
% 8.10/1.66 ------
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66 ------ Proving...
% 8.10/1.66
% 8.10/1.66
% 8.10/1.66 % SZS status Theorem for theBenchmark.p
% 8.10/1.66
% 8.10/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.10/1.66
% 8.10/1.67
%------------------------------------------------------------------------------