TSTP Solution File: SEU187+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Fri May 3 03:04:54 EDT 2024
% Result : Theorem 0.46s 1.14s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 195 ( 50 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 230 ( 94 ~; 90 |; 28 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 144 ( 5 sgn 99 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f11,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f25,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f64,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f151,conjecture,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f152,negated_conjecture,
~ ( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
inference(negated_conjecture,[],[f151]) ).
fof(f156,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f286,plain,
( empty_set != relation_rng(empty_set)
| empty_set != relation_dom(empty_set) ),
inference(ennf_transformation,[],[f152]) ).
fof(f318,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f319,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f318]) ).
fof(f320,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ( empty_set = X0
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f319,f320]) ).
fof(f352,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f187]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f352]) ).
fof(f354,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK18(X0,X1),X4),X0)
| in(sK18(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK18(X0,X1),X4),X0)
=> in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK20(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f357,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f353,f356,f355,f354]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f188]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f369]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
=> in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f373,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK27(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1) )
& ( in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f370,f373,f372,f371]) ).
fof(f444,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f465,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f321]) ).
fof(f466,plain,
! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f504,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f521,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f526,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f564,plain,
relation(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f684,plain,
( empty_set != relation_rng(empty_set)
| empty_set != relation_dom(empty_set) ),
inference(cnf_transformation,[],[f286]) ).
fof(f689,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f156]) ).
fof(f706,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f526,f689]) ).
fof(f727,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f504,f706]) ).
fof(f731,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f521,f706]) ).
fof(f801,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f465]) ).
fof(f821,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f727]) ).
fof(f829,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f731]) ).
cnf(c_52,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f444]) ).
cnf(c_73,plain,
( X0 = empty_set
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f466]) ).
cnf(c_74,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f801]) ).
cnf(c_115,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK20(X1,X0)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f821]) ).
cnf(c_132,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1) ),
inference(cnf_transformation,[],[f829]) ).
cnf(c_170,plain,
relation(empty_set),
inference(cnf_transformation,[],[f564]) ).
cnf(c_290,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(cnf_transformation,[],[f684]) ).
cnf(c_3032,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK20(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_115,c_52]) ).
cnf(c_3173,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK27(X1,X0)),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_132,c_52]) ).
cnf(c_10528,plain,
( ~ in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_3032,c_74]) ).
cnf(c_10543,plain,
( ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_3173,c_74]) ).
cnf(c_10655,plain,
~ in(X0,relation_dom(empty_set)),
inference(global_subsumption_just,[status(thm)],[c_10528,c_170,c_10528]) ).
cnf(c_10658,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_10655]) ).
cnf(c_10680,plain,
~ in(X0,relation_rng(empty_set)),
inference(global_subsumption_just,[status(thm)],[c_10543,c_170,c_10543]) ).
cnf(c_10683,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_10680]) ).
cnf(c_10689,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10683,c_10658,c_290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 17:37:27 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.46/1.14 % SZS status Started for theBenchmark.p
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.14
% 0.46/1.14 ------ iProver source info
% 0.46/1.14
% 0.46/1.14 git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.14 git: non_committed_changes: false
% 0.46/1.14
% 0.46/1.14 ------ Parsing...
% 0.46/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... sup_sim: 21 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
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.14 ------ Proving...
% 0.46/1.14 ------ Problem Properties
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 clauses 230
% 0.46/1.14 conjectures 1
% 0.46/1.14 EPR 33
% 0.46/1.14 Horn 179
% 0.46/1.14 unary 39
% 0.46/1.14 binary 85
% 0.46/1.14 lits 576
% 0.46/1.14 lits eq 128
% 0.46/1.14 fd_pure 0
% 0.46/1.14 fd_pseudo 0
% 0.46/1.14 fd_cond 11
% 0.46/1.14 fd_pseudo_cond 50
% 0.46/1.14 AC symbols 0
% 0.46/1.14
% 0.46/1.14 ------ Input Options Time Limit: Unbounded
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------
% 0.46/1.14 Current options:
% 0.46/1.14 ------
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------ Proving...
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.14
% 0.46/1.15
%------------------------------------------------------------------------------