TSTP Solution File: SET062+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET062+3 : 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 15:06:02 EDT 2023
% Result : Theorem 0.74s 1.14s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 22 ~; 12 |; 8 &)
% ( 2 <=>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn; 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,conjecture,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_empty_set_subset) ).
fof(f6,negated_conjecture,
~ ! [X0] : subset(empty_set,X0),
inference(negated_conjecture,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
? [X0] : ~ subset(empty_set,X0),
inference(ennf_transformation,[],[f6]) ).
fof(f9,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,[],[f7]) ).
fof(f10,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,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f12,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])],[f10,f11]) ).
fof(f13,plain,
( ? [X0] : ~ subset(empty_set,X0)
=> ~ subset(empty_set,sK1) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
~ subset(empty_set,sK1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f8,f13]) ).
fof(f15,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
~ subset(empty_set,sK1),
inference(cnf_transformation,[],[f14]) ).
cnf(c_49,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f15]) ).
cnf(c_51,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_54,negated_conjecture,
~ subset(empty_set,sK1),
inference(cnf_transformation,[],[f20]) ).
cnf(c_97,plain,
member(sK0(empty_set,sK1),empty_set),
inference(resolution,[status(thm)],[c_51,c_54]) ).
cnf(c_100,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_97,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET062+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 12:25:53 EDT 2023
% 0.16/0.34 % 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
% 0.74/1.14 % SZS status Started for theBenchmark.p
% 0.74/1.14 % SZS status Theorem for theBenchmark.p
% 0.74/1.14
% 0.74/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.74/1.14
% 0.74/1.14 ------ iProver source info
% 0.74/1.14
% 0.74/1.14 git: date: 2023-05-31 18:12:56 +0000
% 0.74/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.74/1.14 git: non_committed_changes: false
% 0.74/1.14 git: last_make_outside_of_git: false
% 0.74/1.14
% 0.74/1.14 ------ Parsing...
% 0.74/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.74/1.14
% 0.74/1.14 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s
% 0.74/1.14
% 0.74/1.14 % SZS status Theorem for theBenchmark.p
% 0.74/1.14
% 0.74/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.74/1.14
% 0.74/1.14
%------------------------------------------------------------------------------