TSTP Solution File: SEU169+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU169+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 17:04:21 EDT 2023
% Result : Theorem 3.62s 1.12s
% Output : CNFRefutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 18 unt; 0 def)
% Number of atoms : 211 ( 29 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 246 ( 88 ~; 89 |; 50 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 2 sgn; 75 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
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] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f33,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f47,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f48,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[],[f47]) ).
fof(f62,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f120,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f129,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f139,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f180,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(f181,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,[],[f180]) ).
fof(f182,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(f183,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])],[f181,f182]) ).
fof(f184,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f190,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,[],[f12]) ).
fof(f191,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,[],[f190]) ).
fof(f192,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,[],[f191]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X0) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X0) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0)
| in(sK4(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,[sK4])],[f192,f193]) ).
fof(f226,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) )
=> ( ? [X2] :
( ~ in(X2,sK17)
& in(X2,sK18) )
& element(sK18,powerset(sK17)) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
( ? [X2] :
( ~ in(X2,sK17)
& in(X2,sK18) )
=> ( ~ in(sK19,sK17)
& in(sK19,sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
( ~ in(sK19,sK17)
& in(sK19,sK18)
& element(sK18,powerset(sK17)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f129,f227,f226]) ).
fof(f266,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f277,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f281,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f293,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f194]) ).
fof(f331,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f347,plain,
element(sK18,powerset(sK17)),
inference(cnf_transformation,[],[f228]) ).
fof(f348,plain,
in(sK19,sK18),
inference(cnf_transformation,[],[f228]) ).
fof(f349,plain,
~ in(sK19,sK17),
inference(cnf_transformation,[],[f228]) ).
fof(f371,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f498,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f277]) ).
fof(f504,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f293]) ).
cnf(c_52,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f266]) ).
cnf(c_66,plain,
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f498]) ).
cnf(c_70,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f281]) ).
cnf(c_80,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f504]) ).
cnf(c_116,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[],[f331]) ).
cnf(c_132,negated_conjecture,
~ in(sK19,sK17),
inference(cnf_transformation,[],[f349]) ).
cnf(c_133,negated_conjecture,
in(sK19,sK18),
inference(cnf_transformation,[],[f348]) ).
cnf(c_134,negated_conjecture,
element(sK18,powerset(sK17)),
inference(cnf_transformation,[],[f347]) ).
cnf(c_156,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f371]) ).
cnf(c_1998,plain,
( powerset(sK17) != X1
| X0 != sK18
| in(X0,X1)
| empty(X1) ),
inference(resolution_lifted,[status(thm)],[c_70,c_134]) ).
cnf(c_1999,plain,
( in(sK18,powerset(sK17))
| empty(powerset(sK17)) ),
inference(unflattening,[status(thm)],[c_1998]) ).
cnf(c_2004,plain,
in(sK18,powerset(sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_1999,c_116]) ).
cnf(c_6126,plain,
subset(sK18,sK17),
inference(superposition,[status(thm)],[c_2004,c_66]) ).
cnf(c_6866,plain,
set_union2(sK18,sK17) = sK17,
inference(superposition,[status(thm)],[c_6126,c_156]) ).
cnf(c_6901,plain,
set_union2(sK17,sK18) = sK17,
inference(demodulation,[status(thm)],[c_6866,c_52]) ).
cnf(c_6915,plain,
( ~ in(X0,sK18)
| in(X0,sK17) ),
inference(superposition,[status(thm)],[c_6901,c_80]) ).
cnf(c_6953,plain,
in(sK19,sK17),
inference(superposition,[status(thm)],[c_133,c_6915]) ).
cnf(c_6957,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6953,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.32 % Computer : n017.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Aug 23 13:56:53 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.62/1.12 % SZS status Started for theBenchmark.p
% 3.62/1.12 % SZS status Theorem for theBenchmark.p
% 3.62/1.12
% 3.62/1.12 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.62/1.12
% 3.62/1.12 ------ iProver source info
% 3.62/1.12
% 3.62/1.12 git: date: 2023-05-31 18:12:56 +0000
% 3.62/1.12 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.62/1.12 git: non_committed_changes: false
% 3.62/1.12 git: last_make_outside_of_git: false
% 3.62/1.12
% 3.62/1.12 ------ Parsing...
% 3.62/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.62/1.12
% 3.62/1.12 ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.62/1.12
% 3.62/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.62/1.12
% 3.62/1.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.62/1.12 ------ Proving...
% 3.62/1.12 ------ Problem Properties
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12 clauses 142
% 3.62/1.12 conjectures 2
% 3.62/1.12 EPR 23
% 3.62/1.12 Horn 111
% 3.62/1.12 unary 31
% 3.62/1.12 binary 63
% 3.62/1.12 lits 308
% 3.62/1.12 lits eq 81
% 3.62/1.12 fd_pure 0
% 3.62/1.12 fd_pseudo 0
% 3.62/1.12 fd_cond 3
% 3.62/1.12 fd_pseudo_cond 35
% 3.62/1.12 AC symbols 0
% 3.62/1.12
% 3.62/1.12 ------ Schedule dynamic 5 is on
% 3.62/1.12
% 3.62/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12 ------
% 3.62/1.12 Current options:
% 3.62/1.12 ------
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12 ------ Proving...
% 3.62/1.12
% 3.62/1.12
% 3.62/1.12 % SZS status Theorem for theBenchmark.p
% 3.62/1.12
% 3.62/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/1.12
% 3.62/1.12
%------------------------------------------------------------------------------