TSTP Solution File: SEU147+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 17:04:04 EDT 2023
% Result : Theorem 3.98s 1.17s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 208 ( 104 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 245 ( 94 ~; 108 |; 35 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 103 ( 1 sgn; 63 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f24,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f44,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f45,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[],[f44]) ).
fof(f50,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f57,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f65,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f66,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f76,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f45]) ).
fof(f100,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f57]) ).
fof(f106,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f121,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f122,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f122,f123]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f127,f128]) ).
fof(f181,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f182,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f188,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0
| in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f129]) ).
fof(f190,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK3(X0,X1,X2) != X1
| ~ in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f129]) ).
fof(f215,plain,
empty(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f239,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f76]) ).
fof(f245,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f255,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f100]) ).
fof(f264,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f265,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f295,plain,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f239,f264]) ).
fof(f307,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f182]) ).
fof(f308,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f181]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f307]) ).
cnf(c_66,plain,
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f308]) ).
cnf(c_67,plain,
( sK3(X0,X1,X2) != X1
| ~ in(sK3(X0,X1,X2),X2)
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_69,plain,
( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| unordered_pair(X0,X1) = X2
| in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_97,plain,
empty(empty_set),
inference(cnf_transformation,[],[f215]) ).
cnf(c_121,negated_conjecture,
unordered_pair(empty_set,empty_set) != powerset(empty_set),
inference(cnf_transformation,[],[f295]) ).
cnf(c_127,plain,
subset(empty_set,X0),
inference(cnf_transformation,[],[f245]) ).
cnf(c_137,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(cnf_transformation,[],[f255]) ).
cnf(c_145,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f265]) ).
cnf(c_152,plain,
subset(empty_set,empty_set),
inference(instantiation,[status(thm)],[c_127]) ).
cnf(c_161,plain,
( ~ empty(empty_set)
| empty_set = empty_set ),
inference(instantiation,[status(thm)],[c_145]) ).
cnf(c_2268,plain,
( X0 != X1
| X2 != X3
| ~ subset(X1,X3)
| subset(X0,X2) ),
theory(equality) ).
cnf(c_4647,plain,
( sK3(X0,X1,powerset(X2)) != X1
| ~ in(sK3(X0,X1,powerset(X2)),powerset(X2))
| unordered_pair(X0,X1) = powerset(X2) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_4648,plain,
( ~ subset(sK3(X0,X1,powerset(X2)),X2)
| in(sK3(X0,X1,powerset(X2)),powerset(X2)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_4649,plain,
( sK3(empty_set,empty_set,powerset(empty_set)) != empty_set
| ~ in(sK3(empty_set,empty_set,powerset(empty_set)),powerset(empty_set))
| unordered_pair(empty_set,empty_set) = powerset(empty_set) ),
inference(instantiation,[status(thm)],[c_4647]) ).
cnf(c_4650,plain,
( ~ subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set)
| in(sK3(empty_set,empty_set,powerset(empty_set)),powerset(empty_set)) ),
inference(instantiation,[status(thm)],[c_4648]) ).
cnf(c_9338,plain,
( sK3(X0,X1,powerset(X2)) != X3
| X2 != X4
| ~ subset(X3,X4)
| subset(sK3(X0,X1,powerset(X2)),X2) ),
inference(instantiation,[status(thm)],[c_2268]) ).
cnf(c_9339,plain,
( sK3(empty_set,empty_set,powerset(empty_set)) != empty_set
| empty_set != empty_set
| ~ subset(empty_set,empty_set)
| subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[c_9338]) ).
cnf(c_11954,plain,
( sK3(X0,X1,powerset(X2)) = X0
| sK3(X0,X1,powerset(X2)) = X1
| unordered_pair(X0,X1) = powerset(X2)
| subset(sK3(X0,X1,powerset(X2)),X2) ),
inference(superposition,[status(thm)],[c_69,c_66]) ).
cnf(c_12023,plain,
( sK3(empty_set,empty_set,powerset(empty_set)) = empty_set
| unordered_pair(empty_set,empty_set) = powerset(empty_set)
| subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[c_11954]) ).
cnf(c_12856,plain,
( ~ subset(sK3(X0,empty_set,powerset(X1)),empty_set)
| sK3(X0,empty_set,powerset(X1)) = empty_set ),
inference(instantiation,[status(thm)],[c_137]) ).
cnf(c_12857,plain,
( ~ subset(sK3(empty_set,empty_set,powerset(empty_set)),empty_set)
| sK3(empty_set,empty_set,powerset(empty_set)) = empty_set ),
inference(instantiation,[status(thm)],[c_12856]) ).
cnf(c_14055,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12857,c_12023,c_9339,c_4650,c_4649,c_121,c_161,c_152,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 20:19:24 EDT 2023
% 0.22/0.36 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.98/1.17 % SZS status Started for theBenchmark.p
% 3.98/1.17 % SZS status Theorem for theBenchmark.p
% 3.98/1.17
% 3.98/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.98/1.17
% 3.98/1.17 ------ iProver source info
% 3.98/1.17
% 3.98/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.98/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.98/1.17 git: non_committed_changes: false
% 3.98/1.17 git: last_make_outside_of_git: false
% 3.98/1.17
% 3.98/1.17 ------ Parsing...
% 3.98/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.98/1.17
% 3.98/1.17 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.98/1.17
% 3.98/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.98/1.17
% 3.98/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.98/1.17 ------ Proving...
% 3.98/1.17 ------ Problem Properties
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 clauses 92
% 3.98/1.17 conjectures 1
% 3.98/1.17 EPR 21
% 3.98/1.17 Horn 71
% 3.98/1.17 unary 23
% 3.98/1.17 binary 36
% 3.98/1.17 lits 198
% 3.98/1.17 lits eq 55
% 3.98/1.17 fd_pure 0
% 3.98/1.17 fd_pseudo 0
% 3.98/1.17 fd_cond 3
% 3.98/1.17 fd_pseudo_cond 22
% 3.98/1.17 AC symbols 0
% 3.98/1.17
% 3.98/1.17 ------ Schedule dynamic 5 is on
% 3.98/1.17
% 3.98/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 ------
% 3.98/1.17 Current options:
% 3.98/1.17 ------
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 ------ Proving...
% 3.98/1.17
% 3.98/1.17
% 3.98/1.17 % SZS status Theorem for theBenchmark.p
% 3.98/1.17
% 3.98/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.98/1.17
% 3.98/1.17
%------------------------------------------------------------------------------