TSTP Solution File: SEU186+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 17:04:30 EDT 2023
% Result : Theorem 3.69s 1.14s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 23 unt; 0 def)
% Number of atoms : 207 ( 66 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 232 ( 95 ~; 85 |; 33 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 168 ( 5 sgn; 111 !; 30 ?)
% 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(f8,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f11,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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(f147,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f148,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
inference(negated_conjecture,[],[f147]) ).
fof(f153,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f180,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f185,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(f276,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f277,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(flattening,[],[f276]) ).
fof(f295,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f180]) ).
fof(f296,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK0(X0)
& in(sK0(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK1(X4),sK2(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK0(X0)
& in(sK0(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f296,f298,f297]) ).
fof(f310,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f311,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f310]) ).
fof(f312,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0] :
( ( empty_set = X0
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f311,f312]) ).
fof(f361,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,[],[f185]) ).
fof(f362,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,[],[f361]) ).
fof(f363,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(f364,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(f365,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK27(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f366,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])],[f362,f365,f364,f363]) ).
fof(f425,plain,
( ? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) )
=> ( empty_set != sK47
& ! [X2,X1] : ~ in(ordered_pair(X1,X2),sK47)
& relation(sK47) ) ),
introduced(choice_axiom,[]) ).
fof(f426,plain,
( empty_set != sK47
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK47)
& relation(sK47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f277,f425]) ).
fof(f436,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f442,plain,
! [X0,X4] :
( ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f458,plain,
! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f513,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f515,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f518,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f672,plain,
relation(sK47),
inference(cnf_transformation,[],[f426]) ).
fof(f673,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK47),
inference(cnf_transformation,[],[f426]) ).
fof(f674,plain,
empty_set != sK47,
inference(cnf_transformation,[],[f426]) ).
fof(f680,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f153]) ).
fof(f697,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f518,f680]) ).
fof(f700,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK1(X4),sK2(X4)),unordered_pair(sK1(X4),sK1(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f442,f697]) ).
fof(f720,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f515,f697]) ).
fof(f722,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,[],[f513,f697]) ).
fof(f774,plain,
! [X2,X1] : ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK47),
inference(definition_unfolding,[],[f673,f697]) ).
fof(f820,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,[],[f722]) ).
cnf(c_52,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f436]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| ~ relation(X1)
| unordered_pair(unordered_pair(sK1(X0),sK2(X0)),unordered_pair(sK1(X0),sK1(X0))) = X0 ),
inference(cnf_transformation,[],[f700]) ).
cnf(c_73,plain,
( X0 = empty_set
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f458]) ).
cnf(c_130,plain,
( ~ relation(X0)
| relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| in(sK25(X0,X1),X1) ),
inference(cnf_transformation,[],[f720]) ).
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,[],[f820]) ).
cnf(c_286,negated_conjecture,
empty_set != sK47,
inference(cnf_transformation,[],[f674]) ).
cnf(c_287,negated_conjecture,
~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK47),
inference(cnf_transformation,[],[f774]) ).
cnf(c_288,negated_conjecture,
relation(sK47),
inference(cnf_transformation,[],[f672]) ).
cnf(c_3092,plain,
( ~ in(X0,X1)
| ~ relation(X1)
| unordered_pair(unordered_pair(sK1(X0),sK1(X0)),unordered_pair(sK1(X0),sK2(X0))) = X0 ),
inference(demodulation,[status(thm)],[c_60,c_52]) ).
cnf(c_3127,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_3219,plain,
( ~ relation(X0)
| relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| in(sK25(X0,X1),X1) ),
inference(demodulation,[status(thm)],[c_130,c_52]) ).
cnf(c_10543,plain,
~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK47),
inference(superposition,[status(thm)],[c_52,c_287]) ).
cnf(c_10547,plain,
~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),sK47),
inference(superposition,[status(thm)],[c_52,c_287]) ).
cnf(c_10989,plain,
( ~ in(X0,relation_rng(sK47))
| ~ relation(sK47) ),
inference(superposition,[status(thm)],[c_3127,c_10543]) ).
cnf(c_10990,plain,
~ in(X0,relation_rng(sK47)),
inference(forward_subsumption_resolution,[status(thm)],[c_10989,c_288]) ).
cnf(c_11130,plain,
relation_rng(sK47) = empty_set,
inference(superposition,[status(thm)],[c_73,c_10990]) ).
cnf(c_11330,plain,
( ~ relation(sK47)
| relation_rng(sK47) = X0
| in(sK25(sK47,X0),X0) ),
inference(superposition,[status(thm)],[c_3219,c_10543]) ).
cnf(c_11331,plain,
( ~ relation(sK47)
| X0 = empty_set
| in(sK25(sK47,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_11330,c_11130]) ).
cnf(c_11332,plain,
( X0 = empty_set
| in(sK25(sK47,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11331,c_288]) ).
cnf(c_11490,plain,
( ~ relation(X0)
| unordered_pair(unordered_pair(sK1(sK25(sK47,X0)),sK1(sK25(sK47,X0))),unordered_pair(sK1(sK25(sK47,X0)),sK2(sK25(sK47,X0)))) = sK25(sK47,X0)
| X0 = empty_set ),
inference(superposition,[status(thm)],[c_11332,c_3092]) ).
cnf(c_11570,plain,
( unordered_pair(unordered_pair(sK1(sK25(sK47,sK47)),sK1(sK25(sK47,sK47))),unordered_pair(sK1(sK25(sK47,sK47)),sK2(sK25(sK47,sK47)))) = sK25(sK47,sK47)
| empty_set = sK47 ),
inference(superposition,[status(thm)],[c_288,c_11490]) ).
cnf(c_11572,plain,
unordered_pair(unordered_pair(sK1(sK25(sK47,sK47)),sK1(sK25(sK47,sK47))),unordered_pair(sK1(sK25(sK47,sK47)),sK2(sK25(sK47,sK47)))) = sK25(sK47,sK47),
inference(forward_subsumption_resolution,[status(thm)],[c_11570,c_286]) ).
cnf(c_11602,plain,
~ in(sK25(sK47,sK47),sK47),
inference(superposition,[status(thm)],[c_11572,c_10547]) ).
cnf(c_11907,plain,
empty_set = sK47,
inference(superposition,[status(thm)],[c_11332,c_11602]) ).
cnf(c_11908,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11907,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n010.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 : Wed Aug 23 20:16:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.69/1.14 % SZS status Started for theBenchmark.p
% 3.69/1.14 % SZS status Theorem for theBenchmark.p
% 3.69/1.14
% 3.69/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.69/1.14
% 3.69/1.14 ------ iProver source info
% 3.69/1.14
% 3.69/1.14 git: date: 2023-05-31 18:12:56 +0000
% 3.69/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.69/1.14 git: non_committed_changes: false
% 3.69/1.14 git: last_make_outside_of_git: false
% 3.69/1.14
% 3.69/1.14 ------ Parsing...
% 3.69/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.69/1.14
% 3.69/1.14 ------ Preprocessing... sup_sim: 20 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
% 3.69/1.14
% 3.69/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.69/1.14
% 3.69/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.14 ------ Proving...
% 3.69/1.14 ------ Problem Properties
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14 clauses 229
% 3.69/1.14 conjectures 3
% 3.69/1.14 EPR 35
% 3.69/1.14 Horn 179
% 3.69/1.14 unary 42
% 3.69/1.14 binary 84
% 3.69/1.14 lits 568
% 3.69/1.14 lits eq 126
% 3.69/1.14 fd_pure 0
% 3.69/1.14 fd_pseudo 0
% 3.69/1.14 fd_cond 10
% 3.69/1.14 fd_pseudo_cond 50
% 3.69/1.14 AC symbols 0
% 3.69/1.14
% 3.69/1.14 ------ Schedule dynamic 5 is on
% 3.69/1.14
% 3.69/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14 ------
% 3.69/1.14 Current options:
% 3.69/1.14 ------
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14 ------ Proving...
% 3.69/1.14
% 3.69/1.14
% 3.69/1.14 % SZS status Theorem for theBenchmark.p
% 3.69/1.14
% 3.69/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.14
% 3.69/1.14
%------------------------------------------------------------------------------