TSTP Solution File: SEU204+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU204+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 17.70s 3.19s
% Output : CNFRefutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 141 ( 5 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 155 ( 58 ~; 52 |; 32 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn; 75 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,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(f124,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f125,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f126,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[],[f125]) ).
fof(f133,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f181,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f224,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f293,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f124]) ).
fof(f294,plain,
? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f126]) ).
fof(f300,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f133]) ).
fof(f301,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f300]) ).
fof(f436,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,[],[f224]) ).
fof(f437,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,[],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK29(X0,X1),X1)
& in(sK29(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f439,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK29(X0,X1),X1)
& in(sK29(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f437,f438]) ).
fof(f513,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f293]) ).
fof(f514,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f513]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK57(X0,X1,X2),X1)
& in(ordered_pair(sK57(X0,X1,X2),X0),X2)
& in(sK57(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f516,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ( in(sK57(X0,X1,X2),X1)
& in(ordered_pair(sK57(X0,X1,X2),X0),X2)
& in(sK57(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f514,f515]) ).
fof(f517,plain,
( ? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_image(sK59,sK58),relation_rng(sK59))
& relation(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f518,plain,
( ~ subset(relation_image(sK59,sK58),relation_rng(sK59))
& relation(sK59) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f294,f517]) ).
fof(f633,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK29(X0,X1),X0) ),
inference(cnf_transformation,[],[f439]) ).
fof(f634,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK29(X0,X1),X1) ),
inference(cnf_transformation,[],[f439]) ).
fof(f663,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f777,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK57(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f516]) ).
fof(f780,plain,
relation(sK59),
inference(cnf_transformation,[],[f518]) ).
fof(f781,plain,
~ subset(relation_image(sK59,sK58),relation_rng(sK59)),
inference(cnf_transformation,[],[f518]) ).
fof(f789,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f301]) ).
fof(f857,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f181]) ).
fof(f886,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f663,f857]) ).
fof(f975,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK57(X0,X1,X2),X0),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f777,f886]) ).
fof(f979,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f789,f886]) ).
cnf(c_134,plain,
( ~ in(sK29(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f634]) ).
cnf(c_135,plain,
( in(sK29(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f633]) ).
cnf(c_279,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK57(X0,X2,X1),X0),unordered_pair(sK57(X0,X2,X1),sK57(X0,X2,X1))),X1) ),
inference(cnf_transformation,[],[f975]) ).
cnf(c_281,negated_conjecture,
~ subset(relation_image(sK59,sK58),relation_rng(sK59)),
inference(cnf_transformation,[],[f781]) ).
cnf(c_282,negated_conjecture,
relation(sK59),
inference(cnf_transformation,[],[f780]) ).
cnf(c_289,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f979]) ).
cnf(c_1103,plain,
( in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_image(sK59,sK58))
| subset(relation_image(sK59,sK58),relation_rng(sK59)) ),
inference(instantiation,[status(thm)],[c_135]) ).
cnf(c_1182,plain,
( ~ in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_rng(sK59))
| subset(relation_image(sK59,sK58),relation_rng(sK59)) ),
inference(instantiation,[status(thm)],[c_134]) ).
cnf(c_2695,plain,
( ~ in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_image(sK59,sK58))
| ~ relation(sK59)
| in(unordered_pair(unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK29(relation_image(sK59,sK58),relation_rng(sK59))),unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59))),sK59) ),
inference(instantiation,[status(thm)],[c_279]) ).
cnf(c_11927,plain,
( ~ in(unordered_pair(unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK29(relation_image(sK59,sK58),relation_rng(sK59))),unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59))),sK59)
| ~ relation(sK59)
| in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_rng(sK59)) ),
inference(instantiation,[status(thm)],[c_289]) ).
cnf(c_11928,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11927,c_2695,c_1182,c_1103,c_281,c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n002.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 16:39:16 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.70/3.19 % SZS status Started for theBenchmark.p
% 17.70/3.19 % SZS status Theorem for theBenchmark.p
% 17.70/3.19
% 17.70/3.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.70/3.19
% 17.70/3.19 ------ iProver source info
% 17.70/3.19
% 17.70/3.19 git: date: 2023-05-31 18:12:56 +0000
% 17.70/3.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.70/3.19 git: non_committed_changes: false
% 17.70/3.19 git: last_make_outside_of_git: false
% 17.70/3.19
% 17.70/3.19 ------ Parsing...
% 17.70/3.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.70/3.19
% 17.70/3.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 17.70/3.19
% 17.70/3.19 ------ Preprocessing...
% 17.70/3.19
% 17.70/3.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.70/3.19 ------ Proving...
% 17.70/3.19 ------ Problem Properties
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19 clauses 313
% 17.70/3.19 conjectures 22
% 17.70/3.19 EPR 32
% 17.70/3.19 Horn 252
% 17.70/3.19 unary 53
% 17.70/3.19 binary 102
% 17.70/3.19 lits 829
% 17.70/3.19 lits eq 161
% 17.70/3.19 fd_pure 0
% 17.70/3.19 fd_pseudo 0
% 17.70/3.19 fd_cond 13
% 17.70/3.19 fd_pseudo_cond 65
% 17.70/3.19 AC symbols 0
% 17.70/3.19
% 17.70/3.19 ------ Input Options Time Limit: Unbounded
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19 ------
% 17.70/3.19 Current options:
% 17.70/3.19 ------
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19 ------ Proving...
% 17.70/3.19
% 17.70/3.19
% 17.70/3.19 % SZS status Theorem for theBenchmark.p
% 17.70/3.19
% 17.70/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.70/3.19
% 17.70/3.19
%------------------------------------------------------------------------------