TSTP Solution File: SET908+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 15:10:35 EDT 2023
% Result : Theorem 0.53s 1.17s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 163 ( 57 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 199 ( 76 ~; 76 |; 38 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 3 sgn; 70 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f12,conjecture,
! [X0,X1] : empty_set != set_union2(singleton(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : empty_set != set_union2(singleton(X0),X1),
inference(negated_conjecture,[],[f12]) ).
fof(f18,plain,
? [X0,X1] : empty_set = set_union2(singleton(X0),X1),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f20,f21]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0] :
( ( empty_set = X0
| in(sK1(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f29,f30]) ).
fof(f36,plain,
( ? [X0,X1] : empty_set = set_union2(singleton(X0),X1)
=> empty_set = set_union2(singleton(sK5),sK6) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
empty_set = set_union2(singleton(sK5),sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f18,f36]) ).
fof(f39,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
empty_set = set_union2(singleton(sK5),sK6),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f41]) ).
fof(f60,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f59]) ).
fof(f62,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f44]) ).
fof(f63,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f48]) ).
cnf(c_50,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f39]) ).
cnf(c_53,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f60]) ).
cnf(c_56,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f62]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_69,negated_conjecture,
set_union2(singleton(sK5),sK6) = empty_set,
inference(cnf_transformation,[],[f58]) ).
cnf(c_171,plain,
set_union2(sK6,singleton(sK5)) = empty_set,
inference(demodulation,[status(thm)],[c_69,c_50]) ).
cnf(c_519,plain,
( ~ in(X0,singleton(sK5))
| in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_171,c_60]) ).
cnf(c_522,plain,
~ in(X0,singleton(sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_519,c_56]) ).
cnf(c_527,plain,
$false,
inference(superposition,[status(thm)],[c_53,c_522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 14:05:12 EDT 2023
% 0.14/0.34 % 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
% 0.53/1.17 % SZS status Started for theBenchmark.p
% 0.53/1.17 % SZS status Theorem for theBenchmark.p
% 0.53/1.17
% 0.53/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.53/1.17
% 0.53/1.17 ------ iProver source info
% 0.53/1.17
% 0.53/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.53/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.53/1.17 git: non_committed_changes: false
% 0.53/1.17 git: last_make_outside_of_git: false
% 0.53/1.17
% 0.53/1.17 ------ Parsing...
% 0.53/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.53/1.17
% 0.53/1.17 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.53/1.17
% 0.53/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.53/1.17
% 0.53/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.53/1.17 ------ Proving...
% 0.53/1.17 ------ Problem Properties
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17 clauses 21
% 0.53/1.17 conjectures 0
% 0.53/1.17 EPR 5
% 0.53/1.17 Horn 17
% 0.53/1.17 unary 8
% 0.53/1.17 binary 7
% 0.53/1.17 lits 41
% 0.53/1.17 lits eq 12
% 0.53/1.17 fd_pure 0
% 0.53/1.17 fd_pseudo 0
% 0.53/1.17 fd_cond 1
% 0.53/1.17 fd_pseudo_cond 5
% 0.53/1.17 AC symbols 0
% 0.53/1.17
% 0.53/1.17 ------ Schedule dynamic 5 is on
% 0.53/1.17
% 0.53/1.17 ------ no conjectures: strip conj schedule
% 0.53/1.17
% 0.53/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17 ------
% 0.53/1.17 Current options:
% 0.53/1.17 ------
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17 ------ Proving...
% 0.53/1.17
% 0.53/1.17
% 0.53/1.17 % SZS status Theorem for theBenchmark.p
% 0.53/1.17
% 0.53/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.53/1.17
% 0.53/1.17
%------------------------------------------------------------------------------