TSTP Solution File: SEU164+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 2.93s 1.16s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 12 unt; 0 def)
% Number of atoms : 213 ( 35 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 253 ( 93 ~; 104 |; 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 : 122 ( 1 sgn; 83 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[],[f11]) ).
fof(f13,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f17,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f12]) ).
fof(f22,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,[],[f3]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( subset(sK1(X0,X1),X0)
| in(sK1(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,[sK1])],[f23,f24]) ).
fof(f26,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,[],[f15]) ).
fof(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).
fof(f30,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,[],[f5]) ).
fof(f31,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,[],[f30]) ).
fof(f32,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(sK3(X0,X1),X3) )
| ~ in(sK3(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK3(X0,X1),X4) )
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK3(X0,X1),X4) )
=> ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f31,f34,f33,f32]) ).
fof(f44,plain,
( ? [X0] : union(powerset(X0)) != X0
=> sK9 != union(powerset(sK9)) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
sK9 != union(powerset(sK9)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f17,f44]) ).
fof(f51,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f55,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f61,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK3(X0,X1),sK4(X0,X1))
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK4(X0,X1),X0)
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f63,plain,
! [X3,X0,X1] :
( union(X0) = X1
| ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f68,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f71,plain,
sK9 != union(powerset(sK9)),
inference(cnf_transformation,[],[f45]) ).
fof(f75,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f76,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f51]) ).
cnf(c_56,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_57,plain,
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_61,plain,
( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X2)
| ~ in(X2,X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_62,plain,
( union(X0) = X1
| in(sK3(X0,X1),X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_63,plain,
( union(X0) = X1
| in(sK3(X0,X1),sK4(X0,X1))
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_71,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f68]) ).
cnf(c_74,negated_conjecture,
union(powerset(sK9)) != sK9,
inference(cnf_transformation,[],[f71]) ).
cnf(c_75,plain,
subset(sK9,sK9),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_79,plain,
( ~ subset(sK9,sK9)
| in(sK9,powerset(sK9)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_2106,plain,
( union(powerset(X0)) = X1
| in(sK3(powerset(X0),X1),X1)
| subset(sK4(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_62,c_57]) ).
cnf(c_2149,plain,
( union(powerset(sK9)) = sK9
| in(sK3(powerset(sK9),sK9),sK9)
| subset(sK4(powerset(sK9),sK9),sK9) ),
inference(instantiation,[status(thm)],[c_2106]) ).
cnf(c_2154,plain,
( union(powerset(sK9)) = sK9
| in(sK3(powerset(sK9),sK9),sK4(powerset(sK9),sK9))
| in(sK3(powerset(sK9),sK9),sK9) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2155,plain,
( ~ in(sK3(powerset(sK9),sK9),X0)
| ~ in(sK3(powerset(sK9),sK9),sK9)
| ~ in(X0,powerset(sK9))
| union(powerset(sK9)) = sK9 ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_2156,plain,
( ~ in(sK3(powerset(sK9),sK9),sK9)
| ~ in(sK9,powerset(sK9))
| union(powerset(sK9)) = sK9 ),
inference(instantiation,[status(thm)],[c_2155]) ).
cnf(c_2279,plain,
( ~ in(sK3(powerset(sK9),sK9),sK4(powerset(sK9),sK9))
| ~ subset(sK4(powerset(sK9),sK9),X0)
| in(sK3(powerset(sK9),sK9),X0) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_2284,plain,
( ~ in(sK3(powerset(sK9),sK9),sK4(powerset(sK9),sK9))
| ~ subset(sK4(powerset(sK9),sK9),sK9)
| in(sK3(powerset(sK9),sK9),sK9) ),
inference(instantiation,[status(thm)],[c_2279]) ).
cnf(c_2285,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2284,c_2156,c_2154,c_2149,c_79,c_74,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:59:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.93/1.16 % SZS status Started for theBenchmark.p
% 2.93/1.16 % SZS status Theorem for theBenchmark.p
% 2.93/1.16
% 2.93/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.93/1.16
% 2.93/1.16 ------ iProver source info
% 2.93/1.16
% 2.93/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.93/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.93/1.16 git: non_committed_changes: false
% 2.93/1.16 git: last_make_outside_of_git: false
% 2.93/1.16
% 2.93/1.16 ------ Parsing...
% 2.93/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.93/1.16
% 2.93/1.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 2.93/1.16
% 2.93/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.93/1.16
% 2.93/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.93/1.16 ------ Proving...
% 2.93/1.16 ------ Problem Properties
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16 clauses 25
% 2.93/1.16 conjectures 1
% 2.93/1.16 EPR 4
% 2.93/1.16 Horn 19
% 2.93/1.16 unary 4
% 2.93/1.16 binary 10
% 2.93/1.16 lits 58
% 2.93/1.16 lits eq 14
% 2.93/1.16 fd_pure 0
% 2.93/1.16 fd_pseudo 0
% 2.93/1.16 fd_cond 0
% 2.93/1.16 fd_pseudo_cond 9
% 2.93/1.16 AC symbols 0
% 2.93/1.16
% 2.93/1.16 ------ Schedule dynamic 5 is on
% 2.93/1.16
% 2.93/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16 ------
% 2.93/1.16 Current options:
% 2.93/1.16 ------
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16 ------ Proving...
% 2.93/1.16
% 2.93/1.16
% 2.93/1.16 % SZS status Theorem for theBenchmark.p
% 2.93/1.16
% 2.93/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.93/1.16
% 2.93/1.17
%------------------------------------------------------------------------------