TSTP Solution File: SEU204+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 17:04:40 EDT 2023
% Result : Theorem 3.92s 1.19s
% Output : CNFRefutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 231 ( 26 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 282 ( 106 ~; 105 |; 48 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 170 ( 0 sgn; 117 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[],[f32]) ).
fof(f45,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK0(X0,X1,X2)),X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK0(X0,X1,X2)),X0) )
=> ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
=> ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ( in(sK2(X0,X1,X6),X1)
& in(ordered_pair(sK2(X0,X1,X6),X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f63,f66,f65,f64]) ).
fof(f68,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f69,f70]) ).
fof(f72,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,[],[f47]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,sK4(X0,X1)),X0)
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK4(X0,X1)),X0)
=> in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK6(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK4(X0,X1)),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK5(X0,X1),sK4(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK6(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f73,f76,f75,f74]) ).
fof(f92,plain,
( ? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_image(sK15,sK14),relation_rng(sK15))
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ~ subset(relation_image(sK15,sK14),relation_rng(sK15))
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f52,f92]) ).
fof(f98,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f105,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f106,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f108,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f111,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f134,plain,
relation(sK15),
inference(cnf_transformation,[],[f93]) ).
fof(f135,plain,
~ subset(relation_image(sK15,sK14),relation_rng(sK15)),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f98,f111]) ).
fof(f151,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f108,f111]) ).
fof(f156,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f157,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f151]) ).
cnf(c_57,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK2(X1,X2,X0),X0),singleton(sK2(X1,X2,X0))),X1) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_58,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_59,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_63,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_87,negated_conjecture,
~ subset(relation_image(sK15,sK14),relation_rng(sK15)),
inference(cnf_transformation,[],[f135]) ).
cnf(c_88,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f134]) ).
cnf(c_150,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
cnf(c_160,plain,
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
cnf(c_161,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_160]) ).
cnf(c_698,plain,
( relation_image(sK15,sK14) != X0
| relation_rng(sK15) != X1
| in(sK3(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_161,c_87]) ).
cnf(c_699,plain,
in(sK3(relation_image(sK15,sK14),relation_rng(sK15)),relation_image(sK15,sK14)),
inference(unflattening,[status(thm)],[c_698]) ).
cnf(c_703,plain,
( relation_image(sK15,sK14) != X0
| relation_rng(sK15) != X1
| ~ in(sK3(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_150,c_87]) ).
cnf(c_704,plain,
~ in(sK3(relation_image(sK15,sK14),relation_rng(sK15)),relation_rng(sK15)),
inference(unflattening,[status(thm)],[c_703]) ).
cnf(c_3964,plain,
( ~ in(sK3(relation_image(sK15,sK14),relation_rng(sK15)),relation_image(sK15,sK14))
| ~ relation(sK15)
| in(unordered_pair(unordered_pair(sK2(sK15,sK14,sK3(relation_image(sK15,sK14),relation_rng(sK15))),sK3(relation_image(sK15,sK14),relation_rng(sK15))),singleton(sK2(sK15,sK14,sK3(relation_image(sK15,sK14),relation_rng(sK15))))),sK15) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_4806,plain,
( ~ in(unordered_pair(unordered_pair(sK2(sK15,sK14,sK3(relation_image(sK15,sK14),relation_rng(sK15))),sK3(relation_image(sK15,sK14),relation_rng(sK15))),singleton(sK2(sK15,sK14,sK3(relation_image(sK15,sK14),relation_rng(sK15))))),sK15)
| ~ relation(sK15)
| in(sK3(relation_image(sK15,sK14),relation_rng(sK15)),relation_rng(sK15)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_4807,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4806,c_3964,c_704,c_699,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n022.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 : Wed Aug 23 13:49:11 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
% 3.92/1.19 % SZS status Started for theBenchmark.p
% 3.92/1.19 % SZS status Theorem for theBenchmark.p
% 3.92/1.19
% 3.92/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.92/1.19
% 3.92/1.19 ------ iProver source info
% 3.92/1.19
% 3.92/1.19 git: date: 2023-05-31 18:12:56 +0000
% 3.92/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.92/1.19 git: non_committed_changes: false
% 3.92/1.19 git: last_make_outside_of_git: false
% 3.92/1.19
% 3.92/1.19 ------ Parsing...
% 3.92/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.92/1.19
% 3.92/1.19 ------ Preprocessing... sup_sim: 0 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
% 3.92/1.19
% 3.92/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.92/1.19
% 3.92/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.92/1.19 ------ Proving...
% 3.92/1.19 ------ Problem Properties
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19 clauses 47
% 3.92/1.19 conjectures 2
% 3.92/1.19 EPR 20
% 3.92/1.19 Horn 41
% 3.92/1.19 unary 18
% 3.92/1.19 binary 13
% 3.92/1.19 lits 99
% 3.92/1.19 lits eq 8
% 3.92/1.19 fd_pure 0
% 3.92/1.19 fd_pseudo 0
% 3.92/1.19 fd_cond 1
% 3.92/1.19 fd_pseudo_cond 6
% 3.92/1.19 AC symbols 0
% 3.92/1.19
% 3.92/1.19 ------ Input Options Time Limit: Unbounded
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19 ------
% 3.92/1.19 Current options:
% 3.92/1.19 ------
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19 ------ Proving...
% 3.92/1.19
% 3.92/1.19
% 3.92/1.19 % SZS status Theorem for theBenchmark.p
% 3.92/1.19
% 3.92/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.19
% 3.92/1.20
%------------------------------------------------------------------------------