TSTP Solution File: SET814+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 15:09:59 EDT 2023
% Result : Theorem 8.08s 1.69s
% Output : CNFRefutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 5 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 218 ( 82 ~; 74 |; 46 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn; 62 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
fof(f21,conjecture,
! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV14) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> subset(sum(X0),X0) ),
inference(negated_conjecture,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f32,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( member(X1,X0)
=> subset(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f43,plain,
! [X0] :
( member(X0,on)
<=> ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f53,plain,
? [X0] :
( ~ subset(sum(X0),X0)
& member(X0,on) ),
inference(ennf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f57,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f57,f58]) ).
fof(f70,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f71,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f71,f72]) ).
fof(f78,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f79,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( member(X0,on)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) )
=> ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ( member(X0,on)
| ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) )
| ~ strict_well_order(member_predicate,X0)
| ~ set(X0) )
& ( ( ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) )
& strict_well_order(member_predicate,X0)
& set(X0) )
| ~ member(X0,on) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f80,f81]) ).
fof(f108,plain,
( ? [X0] :
( ~ subset(sum(X0),X0)
& member(X0,on) )
=> ( ~ subset(sum(sK14),sK14)
& member(sK14,on) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ~ subset(sum(sK14),sK14)
& member(sK14,on) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f53,f108]) ).
fof(f110,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f111,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f112,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f130,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f131,plain,
! [X0,X1] :
( member(X0,sK2(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f138,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ member(X2,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[],[f82]) ).
fof(f173,plain,
member(sK14,on),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
~ subset(sum(sK14),sK14),
inference(cnf_transformation,[],[f109]) ).
cnf(c_49,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_50,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_70,plain,
( ~ member(X0,sum(X1))
| member(X0,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_71,plain,
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_77,plain,
( ~ member(X0,X1)
| ~ member(X1,on)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_112,negated_conjecture,
~ subset(sum(sK14),sK14),
inference(cnf_transformation,[],[f174]) ).
cnf(c_113,negated_conjecture,
member(sK14,on),
inference(cnf_transformation,[],[f173]) ).
cnf(c_3410,plain,
( ~ member(sK1(sum(sK14),sK14),sK14)
| subset(sum(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_3411,plain,
( member(sK1(sum(sK14),sK14),sum(sK14))
| subset(sum(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_3431,plain,
( ~ member(X0,sK14)
| ~ member(sK14,on)
| subset(X0,sK14) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_3461,plain,
( ~ member(sK1(sum(sK14),sK14),X0)
| ~ subset(X0,sK14)
| member(sK1(sum(sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_3948,plain,
( ~ member(sK2(X0,sK14),sK14)
| ~ member(sK14,on)
| subset(sK2(X0,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_3431]) ).
cnf(c_4881,plain,
( ~ member(sK1(sum(sK14),sK14),sK2(sK1(sum(sK14),sK14),X0))
| ~ subset(sK2(sK1(sum(sK14),sK14),X0),sK14)
| member(sK1(sum(sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_3461]) ).
cnf(c_5529,plain,
( ~ member(X0,sum(sK14))
| member(sK2(X0,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_10434,plain,
( ~ member(sK1(sum(sK14),sK14),sum(sK14))
| member(sK2(sK1(sum(sK14),sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_5529]) ).
cnf(c_11218,plain,
( ~ member(sK1(sum(sK14),sK14),sum(X0))
| member(sK1(sum(sK14),sK14),sK2(sK1(sum(sK14),sK14),X0)) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_14327,plain,
( ~ member(sK2(sK1(sum(sK14),sK14),sK14),sK14)
| ~ member(sK14,on)
| subset(sK2(sK1(sum(sK14),sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_3948]) ).
cnf(c_17355,plain,
( ~ member(sK1(sum(sK14),sK14),sK2(sK1(sum(sK14),sK14),sK14))
| ~ subset(sK2(sK1(sum(sK14),sK14),sK14),sK14)
| member(sK1(sum(sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_4881]) ).
cnf(c_19838,plain,
( ~ member(sK1(sum(sK14),sK14),sum(sK14))
| member(sK1(sum(sK14),sK14),sK2(sK1(sum(sK14),sK14),sK14)) ),
inference(instantiation,[status(thm)],[c_11218]) ).
cnf(c_19839,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19838,c_17355,c_14327,c_10434,c_3410,c_3411,c_112,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n019.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 : Sat Aug 26 12:39:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.08/1.69 % SZS status Started for theBenchmark.p
% 8.08/1.69 % SZS status Theorem for theBenchmark.p
% 8.08/1.69
% 8.08/1.69 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 8.08/1.69
% 8.08/1.69 ------ iProver source info
% 8.08/1.69
% 8.08/1.69 git: date: 2023-05-31 18:12:56 +0000
% 8.08/1.69 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 8.08/1.69 git: non_committed_changes: false
% 8.08/1.69 git: last_make_outside_of_git: false
% 8.08/1.69
% 8.08/1.69 ------ Parsing...
% 8.08/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.08/1.69
% 8.08/1.69 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 8.08/1.69
% 8.08/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 8.08/1.69
% 8.08/1.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.08/1.69 ------ Proving...
% 8.08/1.69 ------ Problem Properties
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69 clauses 65
% 8.08/1.69 conjectures 2
% 8.08/1.69 EPR 16
% 8.08/1.69 Horn 46
% 8.08/1.69 unary 6
% 8.08/1.69 binary 32
% 8.08/1.69 lits 161
% 8.08/1.69 lits eq 5
% 8.08/1.69 fd_pure 0
% 8.08/1.69 fd_pseudo 0
% 8.08/1.69 fd_cond 0
% 8.08/1.69 fd_pseudo_cond 3
% 8.08/1.69 AC symbols 0
% 8.08/1.69
% 8.08/1.69 ------ Input Options Time Limit: Unbounded
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69 ------
% 8.08/1.69 Current options:
% 8.08/1.69 ------
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69 ------ Proving...
% 8.08/1.69
% 8.08/1.69
% 8.08/1.69 % SZS status Theorem for theBenchmark.p
% 8.08/1.69
% 8.08/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.08/1.69
% 8.08/1.69
%------------------------------------------------------------------------------