TSTP Solution File: SEU263+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 17:05:18 EDT 2023
% Result : Theorem 3.55s 1.10s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 16 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 75 ~; 61 |; 16 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 160 ( 9 sgn; 88 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f9,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f14,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f22,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f14]) ).
fof(f23,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(relation_rng(X3),X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(relation_rng(X3),X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) )
& ( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f41,plain,
( ? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(relation_rng(X3),X1)
& relation_of2_as_subset(X3,X2,X0) )
=> ( ~ relation_of2_as_subset(sK6,sK5,sK4)
& subset(relation_rng(sK6),sK4)
& relation_of2_as_subset(sK6,sK5,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
( ~ relation_of2_as_subset(sK6,sK5,sK4)
& subset(relation_rng(sK6),sK4)
& relation_of2_as_subset(sK6,sK5,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f29,f41]) ).
fof(f44,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f52,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f55,plain,
! [X2,X0,X1] :
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f57,plain,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_49,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_50,plain,
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_52,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_56,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_58,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f53]) ).
cnf(c_59,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cartesian_product2(X2,X0),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_61,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(relation_dom(X0),X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_62,negated_conjecture,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f59]) ).
cnf(c_63,negated_conjecture,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f58]) ).
cnf(c_64,negated_conjecture,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f57]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_66,plain,
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_69,plain,
subset(sK6,sK6),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_88,plain,
( relation_of2_as_subset(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_56,c_50]) ).
cnf(c_89,plain,
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_88]) ).
cnf(c_98,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
cnf(c_100,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
cnf(c_101,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_100]) ).
cnf(c_106,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(relation_dom(X0),X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_239,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[status(thm)],[c_101,c_98]) ).
cnf(c_337,plain,
~ subset(sK6,cartesian_product2(sK5,sK4)),
inference(resolution,[status(thm)],[c_89,c_62]) ).
cnf(c_341,plain,
relation(sK6),
inference(resolution,[status(thm)],[c_239,c_64]) ).
cnf(c_349,plain,
subset(relation_dom(sK6),sK5),
inference(resolution,[status(thm)],[c_106,c_64]) ).
cnf(c_433,plain,
~ subset(sK6,cartesian_product2(sK5,sK4)),
inference(subtyping,[status(esa)],[c_337]) ).
cnf(c_443,plain,
( ~ relation(X0_13)
| subset(X0_13,cartesian_product2(relation_dom(X0_13),relation_rng(X0_13))) ),
inference(subtyping,[status(esa)],[c_66]) ).
cnf(c_444,plain,
( ~ subset(X0_13,X1_13)
| ~ subset(X1_13,X2_13)
| subset(X0_13,X2_13) ),
inference(subtyping,[status(esa)],[c_65]) ).
cnf(c_446,plain,
( ~ subset(X0_13,X1_13)
| ~ subset(X2_13,X3_13)
| subset(cartesian_product2(X2_13,X0_13),cartesian_product2(X3_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_59]) ).
cnf(c_476,plain,
( ~ subset(X0_13,cartesian_product2(sK5,sK4))
| ~ subset(sK6,X0_13) ),
inference(resolution,[status(thm)],[c_444,c_433]) ).
cnf(c_494,plain,
( ~ subset(X0_13,cartesian_product2(sK5,sK4))
| ~ subset(X1_13,X0_13)
| ~ subset(sK6,X1_13) ),
inference(resolution,[status(thm)],[c_476,c_444]) ).
cnf(c_630,plain,
( ~ subset(X0_13,sK4)
| ~ subset(X1_13,sK5)
| subset(cartesian_product2(X1_13,X0_13),cartesian_product2(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_446]) ).
cnf(c_1079,plain,
( ~ subset(relation_dom(sK6),sK5)
| ~ subset(X0_13,sK4)
| subset(cartesian_product2(relation_dom(sK6),X0_13),cartesian_product2(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_630]) ).
cnf(c_3886,plain,
( ~ subset(relation_rng(sK6),sK4)
| ~ subset(relation_dom(sK6),sK5)
| subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_1079]) ).
cnf(c_5493,plain,
( ~ subset(cartesian_product2(relation_dom(X0_13),relation_rng(X0_13)),cartesian_product2(sK5,sK4))
| ~ subset(sK6,X0_13)
| ~ relation(X0_13) ),
inference(resolution,[status(thm)],[c_494,c_443]) ).
cnf(c_5494,plain,
( ~ subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4))
| ~ subset(sK6,sK6)
| ~ relation(sK6) ),
inference(instantiation,[status(thm)],[c_5493]) ).
cnf(c_5495,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5494,c_3886,c_349,c_341,c_63,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n009.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 18:28:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.55/1.10 % SZS status Started for theBenchmark.p
% 3.55/1.10 % SZS status Theorem for theBenchmark.p
% 3.55/1.10
% 3.55/1.10 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.55/1.10
% 3.55/1.10 ------ iProver source info
% 3.55/1.10
% 3.55/1.10 git: date: 2023-05-31 18:12:56 +0000
% 3.55/1.10 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.55/1.10 git: non_committed_changes: false
% 3.55/1.10 git: last_make_outside_of_git: false
% 3.55/1.10
% 3.55/1.10 ------ Parsing...
% 3.55/1.10 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.55/1.10
% 3.55/1.10 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 3.55/1.10
% 3.55/1.10 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.55/1.10 ------ Proving...
% 3.55/1.10 ------ Problem Properties
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10 clauses 23
% 3.55/1.10 conjectures 1
% 3.55/1.10 EPR 3
% 3.55/1.10 Horn 23
% 3.55/1.10 unary 17
% 3.55/1.10 binary 4
% 3.55/1.10 lits 31
% 3.55/1.10 lits eq 0
% 3.55/1.10 fd_pure 0
% 3.55/1.10 fd_pseudo 0
% 3.55/1.10 fd_cond 0
% 3.55/1.10 fd_pseudo_cond 0
% 3.55/1.10 AC symbols 0
% 3.55/1.10
% 3.55/1.10 ------ Input Options Time Limit: Unbounded
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10 ------
% 3.55/1.10 Current options:
% 3.55/1.10 ------
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10 ------ Proving...
% 3.55/1.10
% 3.55/1.10
% 3.55/1.10 % SZS status Theorem for theBenchmark.p
% 3.55/1.10
% 3.55/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.10
% 3.55/1.10
%------------------------------------------------------------------------------