TSTP Solution File: GEO172+3 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GEO172+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 02:16:39 EDT 2024
% Result : Theorem 2.68s 1.11s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 16 unt; 0 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 163 ( 62 ~; 68 |; 21 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 68 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f11,axiom,
! [X0,X1,X3,X4] :
( ( distinct_lines(X3,X4)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X4)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> equal_points(X2,intersection_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> equal_points(X2,intersection_point(X0,X1)) ),
inference(negated_conjecture,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f51,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f52,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f61,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f69,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f70,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f91,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f92,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f93,plain,
? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f94,plain,
? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
( ? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> ( ~ equal_points(sK2,intersection_point(sK0,sK1))
& incident_point_and_line(sK2,sK1)
& incident_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
( ~ equal_points(sK2,intersection_point(sK0,sK1))
& incident_point_and_line(sK2,sK1)
& incident_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f94,f95]) ).
fof(f99,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f105,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f106,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f110,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f133,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f135,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f96]) ).
fof(f136,plain,
incident_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f96]) ).
fof(f137,plain,
incident_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f96]) ).
fof(f138,plain,
~ equal_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f96]) ).
cnf(c_51,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f99]) ).
cnf(c_57,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_58,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_59,plain,
( ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_62,plain,
( ~ convergent_lines(X0,X1)
| distinct_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_85,plain,
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_86,plain,
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_87,negated_conjecture,
~ equal_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f138]) ).
cnf(c_88,negated_conjecture,
incident_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f137]) ).
cnf(c_89,negated_conjecture,
incident_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f136]) ).
cnf(c_90,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f135]) ).
cnf(c_91,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_303,plain,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(resolution,[status(thm)],[c_85,c_87]) ).
cnf(c_308,plain,
~ apart_point_and_line(sK2,sK1),
inference(resolution,[status(thm)],[c_86,c_88]) ).
cnf(c_312,plain,
~ apart_point_and_line(sK2,sK0),
inference(resolution,[status(thm)],[c_86,c_89]) ).
cnf(c_477,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_478,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_481,plain,
( ~ convergent_lines(sK0,sK1)
| distinct_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_482,plain,
( ~ convergent_lines(sK0,sK1)
| distinct_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_481]) ).
cnf(c_499,plain,
( ~ distinct_points(sK2,intersection_point(sK0,sK1))
| ~ distinct_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK2,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_530,plain,
( ~ distinct_points(sK2,intersection_point(sK0,sK1))
| ~ distinct_lines(sK1,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_499]) ).
cnf(c_531,plain,
( ~ distinct_points(sK2,intersection_point(sK0,sK1))
| ~ distinct_lines(sK1,sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(sK2,sK0)
| apart_point_and_line(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_530]) ).
cnf(c_532,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_531,c_482,c_478,c_477,c_312,c_308,c_303,c_91,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO172+3 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 01:18:29 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.68/1.11 % SZS status Started for theBenchmark.p
% 2.68/1.11 % SZS status Theorem for theBenchmark.p
% 2.68/1.11
% 2.68/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.68/1.11
% 2.68/1.11 ------ iProver source info
% 2.68/1.11
% 2.68/1.11 git: date: 2024-05-02 19:28:25 +0000
% 2.68/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.68/1.11 git: non_committed_changes: false
% 2.68/1.11
% 2.68/1.11 ------ Parsing...
% 2.68/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.68/1.11
% 2.68/1.11 ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 2.68/1.11
% 2.68/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.68/1.11 ------ Proving...
% 2.68/1.11 ------ Problem Properties
% 2.68/1.11
% 2.68/1.11
% 2.68/1.11 clauses 32
% 2.68/1.11 conjectures 1
% 2.68/1.11 EPR 23
% 2.68/1.11 Horn 16
% 2.68/1.11 unary 11
% 2.68/1.11 binary 6
% 2.68/1.11 lits 79
% 2.68/1.11 lits eq 0
% 2.68/1.11 fd_pure 0
% 2.68/1.11 fd_pseudo 0
% 2.68/1.12 fd_cond 0
% 2.68/1.12 fd_pseudo_cond 0
% 2.68/1.12 AC symbols 0
% 2.68/1.12
% 2.68/1.12 ------ Schedule dynamic 5 is on
% 2.68/1.12
% 2.68/1.12 ------ no equalities: superposition off
% 2.68/1.12
% 2.68/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.68/1.12
% 2.68/1.12
% 2.68/1.12 ------
% 2.68/1.12 Current options:
% 2.68/1.12 ------
% 2.68/1.12
% 2.68/1.12
% 2.68/1.12
% 2.68/1.12
% 2.68/1.12 ------ Proving...
% 2.68/1.12
% 2.68/1.12
% 2.68/1.12 % SZS status Theorem for theBenchmark.p
% 2.68/1.12
% 2.68/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.68/1.12
% 2.68/1.12
%------------------------------------------------------------------------------