TSTP Solution File: SET867+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 15:10:24 EDT 2023
% Result : Theorem 1.83s 1.17s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 105 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 124 ( 47 ~; 43 |; 27 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 64 ( 2 sgn; 44 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,conjecture,
empty_set = union(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(f8,negated_conjecture,
empty_set != union(empty_set),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
empty_set != union(empty_set),
inference(flattening,[],[f8]) ).
fof(f11,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ( empty_set = X0
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
fof(f15,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,[],[f3]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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(sK1(X0,X1),X3) )
| ~ in(sK1(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK1(X0,X1),X4) )
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK1(X0,X1),X4) )
=> ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK1(X0,X1),X3) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f16,f19,f18,f17]) ).
fof(f26,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] :
( empty_set = X0
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X1,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
empty_set != union(empty_set),
inference(cnf_transformation,[],[f9]) ).
fof(f38,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f26]) ).
fof(f40,plain,
! [X0,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f29]) ).
cnf(c_50,plain,
( X0 = empty_set
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_51,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f38]) ).
cnf(c_56,plain,
( ~ in(X0,union(X1))
| in(sK3(X1,X0),X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_61,negated_conjecture,
union(empty_set) != empty_set,
inference(cnf_transformation,[],[f37]) ).
cnf(c_370,plain,
~ in(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_56,c_51]) ).
cnf(c_436,plain,
union(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_50,c_370]) ).
cnf(c_440,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_436,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:53:17 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.83/1.17 % SZS status Started for theBenchmark.p
% 1.83/1.17 % SZS status Theorem for theBenchmark.p
% 1.83/1.17
% 1.83/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.83/1.17
% 1.83/1.17 ------ iProver source info
% 1.83/1.17
% 1.83/1.17 git: date: 2023-05-31 18:12:56 +0000
% 1.83/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.83/1.17 git: non_committed_changes: false
% 1.83/1.17 git: last_make_outside_of_git: false
% 1.83/1.17
% 1.83/1.17 ------ Parsing...
% 1.83/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.83/1.17
% 1.83/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 1.83/1.17
% 1.83/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.83/1.17
% 1.83/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.83/1.17 ------ Proving...
% 1.83/1.17 ------ Problem Properties
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17 clauses 13
% 1.83/1.17 conjectures 1
% 1.83/1.17 EPR 5
% 1.83/1.17 Horn 10
% 1.83/1.17 unary 5
% 1.83/1.17 binary 4
% 1.83/1.17 lits 26
% 1.83/1.17 lits eq 5
% 1.83/1.17 fd_pure 0
% 1.83/1.17 fd_pseudo 0
% 1.83/1.17 fd_cond 1
% 1.83/1.17 fd_pseudo_cond 3
% 1.83/1.17 AC symbols 0
% 1.83/1.17
% 1.83/1.17 ------ Schedule dynamic 5 is on
% 1.83/1.17
% 1.83/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17 ------
% 1.83/1.17 Current options:
% 1.83/1.17 ------
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17 ------ Proving...
% 1.83/1.17
% 1.83/1.17
% 1.83/1.17 % SZS status Theorem for theBenchmark.p
% 1.83/1.17
% 1.83/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.83/1.17
% 1.83/1.17
%------------------------------------------------------------------------------