TSTP Solution File: SET366+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 15:07:42 EDT 2023
% Result : Theorem 2.46s 1.17s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 28 ~; 16 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn; 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f12,conjecture,
! [X0] : member(empty_set,power_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI47) ).
fof(f13,negated_conjecture,
~ ! [X0] : member(empty_set,power_set(X0)),
inference(negated_conjecture,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
? [X0] : ~ member(empty_set,power_set(X0)),
inference(ennf_transformation,[],[f13]) ).
fof(f26,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,[],[f23]) ).
fof(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f48,plain,
( ? [X0] : ~ member(empty_set,power_set(X0))
=> ~ member(empty_set,power_set(sK3)) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
~ member(empty_set,power_set(sK3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f25,f48]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f61,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f76,plain,
~ member(empty_set,power_set(sK3)),
inference(cnf_transformation,[],[f49]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_60,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f61]) ).
cnf(c_75,negated_conjecture,
~ member(empty_set,power_set(sK3)),
inference(cnf_transformation,[],[f76]) ).
cnf(c_962,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_60]) ).
cnf(c_968,plain,
~ subset(empty_set,sK3),
inference(superposition,[status(thm)],[c_52,c_75]) ).
cnf(c_969,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_968,c_962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n025.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 : Sat Aug 26 15:08:53 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
% 2.46/1.17 % SZS status Started for theBenchmark.p
% 2.46/1.17 % SZS status Theorem for theBenchmark.p
% 2.46/1.17
% 2.46/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.46/1.17
% 2.46/1.17 ------ iProver source info
% 2.46/1.17
% 2.46/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.46/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.46/1.17 git: non_committed_changes: false
% 2.46/1.17 git: last_make_outside_of_git: false
% 2.46/1.17
% 2.46/1.17 ------ Parsing...
% 2.46/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.46/1.17
% 2.46/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.46/1.17
% 2.46/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.46/1.17
% 2.46/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.46/1.17 ------ Proving...
% 2.46/1.17 ------ Problem Properties
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 clauses 27
% 2.46/1.17 conjectures 1
% 2.46/1.17 EPR 2
% 2.46/1.17 Horn 22
% 2.46/1.17 unary 5
% 2.46/1.17 binary 15
% 2.46/1.17 lits 56
% 2.46/1.17 lits eq 3
% 2.46/1.17 fd_pure 0
% 2.46/1.17 fd_pseudo 0
% 2.46/1.17 fd_cond 0
% 2.46/1.17 fd_pseudo_cond 2
% 2.46/1.17 AC symbols 0
% 2.46/1.17
% 2.46/1.17 ------ Schedule dynamic 5 is on
% 2.46/1.17
% 2.46/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 ------
% 2.46/1.17 Current options:
% 2.46/1.17 ------
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 ------ Proving...
% 2.46/1.17
% 2.46/1.17
% 2.46/1.17 % SZS status Theorem for theBenchmark.p
% 2.46/1.17
% 2.46/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.46/1.17
% 2.46/1.17
%------------------------------------------------------------------------------