TSTP Solution File: GEO089+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GEO089+1 : TPTP v8.2.0. Released v2.4.0.
% 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 : Mon Jun 24 06:13:04 EDT 2024
% Result : Theorem 103.16s 14.81s
% Output : CNFRefutation 103.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 22
% Syntax : Number of formulae : 235 ( 33 unt; 0 def)
% Number of atoms : 877 ( 113 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1003 ( 361 ~; 479 |; 125 &)
% ( 14 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 497 ( 14 sgn 227 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X3] :
( sum(X1,X3) = X0
<=> ! [X4] :
( incident_c(X4,X0)
<=> ( incident_c(X4,X3)
| incident_c(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).
fof(f3,axiom,
! [X2,X0] :
( end_point(X2,X0)
<=> ( ! [X1,X3] :
( ( incident_c(X2,X3)
& incident_c(X2,X1)
& part_of(X3,X0)
& part_of(X1,X0) )
=> ( part_of(X3,X1)
| part_of(X1,X3) ) )
& incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn) ).
fof(f4,axiom,
! [X2,X0] :
( inner_point(X2,X0)
<=> ( ~ end_point(X2,X0)
& incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f6,axiom,
! [X0] :
( closed(X0)
<=> ~ ? [X2] : end_point(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn) ).
fof(f9,axiom,
! [X0,X1,X3,X5] :
( ( ? [X2] :
( end_point(X2,X5)
& end_point(X2,X3)
& end_point(X2,X1) )
& part_of(X5,X0)
& part_of(X3,X0)
& part_of(X1,X0) )
=> ( part_of(X5,X1)
| part_of(X1,X5)
| part_of(X3,X1)
| part_of(X1,X3)
| part_of(X5,X3)
| part_of(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2) ).
fof(f10,axiom,
! [X0] :
? [X2] : inner_point(X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3) ).
fof(f11,axiom,
! [X0,X2] :
( inner_point(X2,X0)
=> ? [X1,X3] :
( sum(X1,X3) = X0
& meet(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4) ).
fof(f12,axiom,
! [X0,X2,X4,X6] :
( ( end_point(X6,X0)
& end_point(X4,X0)
& end_point(X2,X0) )
=> ( X4 = X6
| X2 = X6
| X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5) ).
fof(f13,axiom,
! [X0,X2] :
( end_point(X2,X0)
=> ? [X4] :
( X2 != X4
& end_point(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
fof(f17,conjecture,
! [X0,X2] :
( ? [X7] :
( inner_point(X2,X7)
& part_of(X7,X0) )
=> inner_point(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_11) ).
fof(f18,negated_conjecture,
~ ! [X0,X2] :
( ? [X7] :
( inner_point(X2,X7)
& part_of(X7,X0) )
=> inner_point(X2,X0) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( sum(X1,X2) = X0
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
inference(rectify,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
=> ( part_of(X3,X2)
| part_of(X2,X3) ) )
& incident_c(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f23,plain,
! [X0] :
( closed(X0)
<=> ~ ? [X1] : end_point(X1,X0) ),
inference(rectify,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( end_point(X4,X3)
& end_point(X4,X2)
& end_point(X4,X1) )
& part_of(X3,X0)
& part_of(X2,X0)
& part_of(X1,X0) )
=> ( part_of(X3,X1)
| part_of(X1,X3)
| part_of(X2,X1)
| part_of(X1,X2)
| part_of(X3,X2)
| part_of(X2,X3) ) ),
inference(rectify,[],[f9]) ).
fof(f26,plain,
! [X0] :
? [X1] : inner_point(X1,X0),
inference(rectify,[],[f10]) ).
fof(f27,plain,
! [X0,X1] :
( inner_point(X1,X0)
=> ? [X2,X3] :
( sum(X2,X3) = X0
& meet(X1,X2,X3) ) ),
inference(rectify,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( end_point(X3,X0)
& end_point(X2,X0)
& end_point(X1,X0) )
=> ( X2 = X3
| X1 = X3
| X1 = X2 ) ),
inference(rectify,[],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( end_point(X1,X0)
=> ? [X2] :
( X1 != X2
& end_point(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f32,plain,
~ ! [X0,X1] :
( ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) )
=> inner_point(X1,X0) ),
inference(rectify,[],[f18]) ).
fof(f34,plain,
! [X0] :
( ~ ? [X1] : end_point(X1,X0)
=> closed(X0) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1) )
& incident_c(X0,X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1) )
& incident_c(X0,X1) ) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0] :
( closed(X0)
| ? [X1] : end_point(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( part_of(X3,X1)
| part_of(X1,X3)
| part_of(X2,X1)
| part_of(X1,X2)
| part_of(X3,X2)
| part_of(X2,X3)
| ! [X4] :
( ~ end_point(X4,X3)
| ~ end_point(X4,X2)
| ~ end_point(X4,X1) )
| ~ part_of(X3,X0)
| ~ part_of(X2,X0)
| ~ part_of(X1,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( part_of(X3,X1)
| part_of(X1,X3)
| part_of(X2,X1)
| part_of(X1,X2)
| part_of(X3,X2)
| part_of(X2,X3)
| ! [X4] :
( ~ end_point(X4,X3)
| ~ end_point(X4,X2)
| ~ end_point(X4,X1) )
| ~ part_of(X3,X0)
| ~ part_of(X2,X0)
| ~ part_of(X1,X0) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X2,X3] :
( sum(X2,X3) = X0
& meet(X1,X2,X3) )
| ~ inner_point(X1,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ end_point(X3,X0)
| ~ end_point(X2,X0)
| ~ end_point(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ end_point(X3,X0)
| ~ end_point(X2,X0)
| ~ end_point(X1,X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ? [X2] :
( X1 != X2
& end_point(X2,X0) )
| ~ end_point(X1,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f54,plain,
? [X0,X1] :
( ~ inner_point(X1,X0)
& ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f55,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) )
=> ( ~ incident_c(sK0(X0,X1),X0)
& incident_c(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK0(X0,X1),X0)
& incident_c(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f56,f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) )
=> ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
& ~ incident_c(sK1(X0,X1,X2),X1) )
| ~ incident_c(sK1(X0,X1,X2),X0) )
& ( incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| incident_c(sK1(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
& ~ incident_c(sK1(X0,X1,X2),X1) )
| ~ incident_c(sK1(X0,X1,X2),X0) )
& ( incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| incident_c(sK1(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f61,f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ? [X2,X3] :
( ~ part_of(X3,X2)
& ~ part_of(X2,X3)
& incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
| ~ incident_c(X0,X1) )
& ( ( ! [X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1) )
& incident_c(X0,X1) )
| ~ end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ? [X2,X3] :
( ~ part_of(X3,X2)
& ~ part_of(X2,X3)
& incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
| ~ incident_c(X0,X1) )
& ( ( ! [X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1) )
& incident_c(X0,X1) )
| ~ end_point(X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ? [X2,X3] :
( ~ part_of(X3,X2)
& ~ part_of(X2,X3)
& incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
| ~ incident_c(X0,X1) )
& ( ( ! [X4,X5] :
( part_of(X5,X4)
| part_of(X4,X5)
| ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1) )
& incident_c(X0,X1) )
| ~ end_point(X0,X1) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ part_of(X3,X2)
& ~ part_of(X2,X3)
& incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
=> ( ~ part_of(sK3(X0,X1),sK2(X0,X1))
& ~ part_of(sK2(X0,X1),sK3(X0,X1))
& incident_c(X0,sK3(X0,X1))
& incident_c(X0,sK2(X0,X1))
& part_of(sK3(X0,X1),X1)
& part_of(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ( ~ part_of(sK3(X0,X1),sK2(X0,X1))
& ~ part_of(sK2(X0,X1),sK3(X0,X1))
& incident_c(X0,sK3(X0,X1))
& incident_c(X0,sK2(X0,X1))
& part_of(sK3(X0,X1),X1)
& part_of(sK2(X0,X1),X1) )
| ~ incident_c(X0,X1) )
& ( ( ! [X4,X5] :
( part_of(X5,X4)
| part_of(X4,X5)
| ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1) )
& incident_c(X0,X1) )
| ~ end_point(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f66,f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| end_point(X0,X1)
| ~ incident_c(X0,X1) )
& ( ( ~ end_point(X0,X1)
& incident_c(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f70,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| end_point(X0,X1)
| ~ incident_c(X0,X1) )
& ( ( ~ end_point(X0,X1)
& incident_c(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ? [X1] : end_point(X1,X0)
=> end_point(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( closed(X0)
| end_point(sK5(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f40,f76]) ).
fof(f80,plain,
! [X0] :
( ? [X1] : inner_point(X1,X0)
=> inner_point(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f80]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2,X3] :
( sum(X2,X3) = X0
& meet(X1,X2,X3) )
=> ( sum(sK8(X0,X1),sK9(X0,X1)) = X0
& meet(X1,sK8(X0,X1),sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1] :
( ( sum(sK8(X0,X1),sK9(X0,X1)) = X0
& meet(X1,sK8(X0,X1),sK9(X0,X1)) )
| ~ inner_point(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f46,f82]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2] :
( X1 != X2
& end_point(X2,X0) )
=> ( sK10(X0,X1) != X1
& end_point(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1] :
( ( sK10(X0,X1) != X1
& end_point(sK10(X0,X1),X0) )
| ~ end_point(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f49,f84]) ).
fof(f92,plain,
( ? [X0,X1] :
( ~ inner_point(X1,X0)
& ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) ) )
=> ( ~ inner_point(sK14,sK13)
& ? [X2] :
( inner_point(sK14,X2)
& part_of(X2,sK13) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ? [X2] :
( inner_point(sK14,X2)
& part_of(X2,sK13) )
=> ( inner_point(sK14,sK15)
& part_of(sK15,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ~ inner_point(sK14,sK13)
& inner_point(sK14,sK15)
& part_of(sK15,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f54,f93,f92]) ).
fof(f95,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f96,plain,
! [X0,X1] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f97,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( incident_c(X4,X0)
| ~ incident_c(X4,X1)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f63]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( incident_c(X4,X0)
| ~ incident_c(X4,X2)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f63]) ).
fof(f101,plain,
! [X2,X0,X1] :
( sum(X1,X2) = X0
| incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| incident_c(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f102,plain,
! [X2,X0,X1] :
( sum(X1,X2) = X0
| ~ incident_c(sK1(X0,X1,X2),X1)
| ~ incident_c(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f103,plain,
! [X2,X0,X1] :
( sum(X1,X2) = X0
| ~ incident_c(sK1(X0,X1,X2),X2)
| ~ incident_c(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f104,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f105,plain,
! [X0,X1,X4,X5] :
( part_of(X5,X4)
| part_of(X4,X5)
| ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f106,plain,
! [X0,X1] :
( end_point(X0,X1)
| part_of(sK2(X0,X1),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f107,plain,
! [X0,X1] :
( end_point(X0,X1)
| part_of(sK3(X0,X1),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f108,plain,
! [X0,X1] :
( end_point(X0,X1)
| incident_c(X0,sK2(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f109,plain,
! [X0,X1] :
( end_point(X0,X1)
| incident_c(X0,sK3(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f110,plain,
! [X0,X1] :
( end_point(X0,X1)
| ~ part_of(sK2(X0,X1),sK3(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f111,plain,
! [X0,X1] :
( end_point(X0,X1)
| ~ part_of(sK3(X0,X1),sK2(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
! [X0,X1] :
( inner_point(X0,X1)
| end_point(X0,X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f122,plain,
! [X0] :
( closed(X0)
| end_point(sK5(X0),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X4] :
( part_of(X3,X1)
| part_of(X1,X3)
| part_of(X2,X1)
| part_of(X1,X2)
| part_of(X3,X2)
| part_of(X2,X3)
| ~ end_point(X4,X3)
| ~ end_point(X4,X2)
| ~ end_point(X4,X1)
| ~ part_of(X3,X0)
| ~ part_of(X2,X0)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f126,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f81]) ).
fof(f128,plain,
! [X0,X1] :
( sum(sK8(X0,X1),sK9(X0,X1)) = X0
| ~ inner_point(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ end_point(X3,X0)
| ~ end_point(X2,X0)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f130,plain,
! [X0,X1] :
( end_point(sK10(X0,X1),X0)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f131,plain,
! [X0,X1] :
( sK10(X0,X1) != X1
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f94]) ).
fof(f137,plain,
inner_point(sK14,sK15),
inference(cnf_transformation,[],[f94]) ).
fof(f138,plain,
~ inner_point(sK14,sK13),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
! [X2,X1,X4] :
( incident_c(X4,sum(X1,X2))
| ~ incident_c(X4,X2) ),
inference(equality_resolution,[],[f100]) ).
fof(f140,plain,
! [X2,X1,X4] :
( incident_c(X4,sum(X1,X2))
| ~ incident_c(X4,X1) ),
inference(equality_resolution,[],[f99]) ).
cnf(c_49,plain,
( ~ incident_c(sK0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_50,plain,
( incident_c(sK0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_51,plain,
( ~ part_of(X0,X1)
| ~ incident_c(X2,X0)
| incident_c(X2,X1) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_52,plain,
( ~ incident_c(sK1(X0,X1,X2),X0)
| ~ incident_c(sK1(X0,X1,X2),X2)
| sum(X1,X2) = X0 ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_53,plain,
( ~ incident_c(sK1(X0,X1,X2),X0)
| ~ incident_c(sK1(X0,X1,X2),X1)
| sum(X1,X2) = X0 ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_54,plain,
( sum(X0,X1) = X2
| incident_c(sK1(X2,X0,X1),X0)
| incident_c(sK1(X2,X0,X1),X1)
| incident_c(sK1(X2,X0,X1),X2) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_55,plain,
( ~ incident_c(X0,X1)
| incident_c(X0,sum(X2,X1)) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_56,plain,
( ~ incident_c(X0,X1)
| incident_c(X0,sum(X1,X2)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_58,plain,
( ~ part_of(sK3(X0,X1),sK2(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_59,plain,
( ~ part_of(sK2(X0,X1),sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_60,plain,
( ~ incident_c(X0,X1)
| incident_c(X0,sK3(X0,X1))
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_61,plain,
( ~ incident_c(X0,X1)
| incident_c(X0,sK2(X0,X1))
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_62,plain,
( ~ incident_c(X0,X1)
| part_of(sK3(X0,X1),X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_63,plain,
( ~ incident_c(X0,X1)
| part_of(sK2(X0,X1),X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_64,plain,
( ~ part_of(X0,X1)
| ~ part_of(X2,X1)
| ~ incident_c(X3,X0)
| ~ incident_c(X3,X2)
| ~ end_point(X3,X1)
| part_of(X0,X2)
| part_of(X2,X0) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_65,plain,
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_66,plain,
( ~ incident_c(X0,X1)
| end_point(X0,X1)
| inner_point(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_67,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_68,plain,
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_76,plain,
( end_point(sK5(X0),X0)
| closed(X0) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_79,plain,
( ~ part_of(X0,X1)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ end_point(X4,X0)
| ~ end_point(X4,X2)
| ~ end_point(X4,X3)
| part_of(X0,X2)
| part_of(X0,X3)
| part_of(X2,X0)
| part_of(X2,X3)
| part_of(X3,X0)
| part_of(X3,X2) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_80,plain,
inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f126]) ).
cnf(c_81,plain,
( ~ inner_point(X0,X1)
| sum(sK8(X1,X0),sK9(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_83,plain,
( ~ end_point(X0,X1)
| ~ end_point(X2,X1)
| ~ end_point(X3,X1)
| X0 = X2
| X0 = X3
| X2 = X3 ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_84,plain,
( sK10(X0,X1) != X1
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_85,plain,
( ~ end_point(X0,X1)
| end_point(sK10(X1,X0),X1) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_90,negated_conjecture,
~ inner_point(sK14,sK13),
inference(cnf_transformation,[],[f138]) ).
cnf(c_91,negated_conjecture,
inner_point(sK14,sK15),
inference(cnf_transformation,[],[f137]) ).
cnf(c_92,negated_conjecture,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f136]) ).
cnf(c_738,plain,
( X0 != sK14
| X1 != sK13
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_66,c_90]) ).
cnf(c_739,plain,
( ~ incident_c(sK14,sK13)
| end_point(sK14,sK13) ),
inference(unflattening,[status(thm)],[c_738]) ).
cnf(c_756,plain,
( X0 != sK14
| X1 != sK15
| incident_c(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_68,c_91]) ).
cnf(c_757,plain,
incident_c(sK14,sK15),
inference(unflattening,[status(thm)],[c_756]) ).
cnf(c_761,plain,
( X0 != sK14
| X1 != sK15
| ~ end_point(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_67,c_91]) ).
cnf(c_762,plain,
~ end_point(sK14,sK15),
inference(unflattening,[status(thm)],[c_761]) ).
cnf(c_797,negated_conjecture,
part_of(sK15,sK13),
inference(demodulation,[status(thm)],[c_92]) ).
cnf(c_798,negated_conjecture,
inner_point(sK14,sK15),
inference(demodulation,[status(thm)],[c_91]) ).
cnf(c_799,negated_conjecture,
~ inner_point(sK14,sK13),
inference(demodulation,[status(thm)],[c_90]) ).
cnf(c_800,plain,
X0 = X0,
theory(equality) ).
cnf(c_803,plain,
( X0 != X1
| X2 != X3
| ~ part_of(X1,X3)
| part_of(X0,X2) ),
theory(equality) ).
cnf(c_811,plain,
sK13 = sK13,
inference(instantiation,[status(thm)],[c_800]) ).
cnf(c_1479,plain,
( ~ part_of(sK15,X0)
| ~ incident_c(sK14,sK15)
| incident_c(sK14,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1480,plain,
( ~ part_of(sK15,sK13)
| ~ incident_c(sK14,sK15)
| incident_c(sK14,sK13) ),
inference(instantiation,[status(thm)],[c_1479]) ).
cnf(c_1481,plain,
( ~ incident_c(sK14,sK15)
| incident_c(sK14,sK2(sK14,sK15))
| end_point(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1482,plain,
( ~ incident_c(sK14,sK15)
| incident_c(sK14,sK3(sK14,sK15))
| end_point(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_1485,plain,
( ~ part_of(sK2(sK14,sK15),sK3(sK14,sK15))
| ~ incident_c(sK14,sK15)
| end_point(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_1486,plain,
( ~ part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| ~ incident_c(sK14,sK15)
| end_point(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_1542,plain,
part_of(X0,X0),
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_1543,plain,
part_of(sK13,sK13),
inference(instantiation,[status(thm)],[c_1542]) ).
cnf(c_1757,plain,
incident_c(sK7(X0),X0),
inference(superposition,[status(thm)],[c_80,c_68]) ).
cnf(c_1814,plain,
( ~ part_of(X0,X1)
| incident_c(sK7(X0),X1) ),
inference(superposition,[status(thm)],[c_1757,c_51]) ).
cnf(c_1854,plain,
( ~ part_of(X0,X1)
| ~ part_of(X1,X2)
| incident_c(sK7(X0),X2) ),
inference(superposition,[status(thm)],[c_1814,c_51]) ).
cnf(c_1938,plain,
( ~ part_of(sK13,X0)
| incident_c(sK7(sK15),X0) ),
inference(superposition,[status(thm)],[c_797,c_1854]) ).
cnf(c_1940,plain,
( ~ part_of(sK13,sK13)
| incident_c(sK7(sK15),sK13) ),
inference(instantiation,[status(thm)],[c_1938]) ).
cnf(c_2029,plain,
( ~ part_of(sK3(sK14,sK15),X0)
| ~ part_of(sK2(sK14,sK15),X0)
| ~ incident_c(X1,sK3(sK14,sK15))
| ~ incident_c(X1,sK2(sK14,sK15))
| ~ end_point(X1,X0)
| part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_3904,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X0)
| incident_c(sK1(X0,X0,X1),X1) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
cnf(c_5989,plain,
( ~ incident_c(sK0(X0,sK2(sK14,sK15)),X0)
| part_of(sK2(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_5990,plain,
( ~ incident_c(sK0(sK13,sK2(sK14,sK15)),sK13)
| part_of(sK2(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_5989]) ).
cnf(c_6028,plain,
( ~ incident_c(sK0(X0,sK3(sK14,sK15)),X0)
| part_of(sK3(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_6029,plain,
( ~ incident_c(sK0(sK13,sK3(sK14,sK15)),sK13)
| part_of(sK3(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_6028]) ).
cnf(c_6617,plain,
( sK10(X0,sK14) != sK14
| ~ end_point(sK14,X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_6618,plain,
( sK10(sK13,sK14) != sK14
| ~ end_point(sK14,sK13) ),
inference(instantiation,[status(thm)],[c_6617]) ).
cnf(c_7175,plain,
( sum(X0,sK15) != X1
| X2 != X3
| ~ part_of(X1,X3)
| part_of(sum(X0,sK15),X2) ),
inference(instantiation,[status(thm)],[c_803]) ).
cnf(c_7176,plain,
( sum(sK13,sK15) != sK13
| sK13 != sK13
| ~ part_of(sK13,sK13)
| part_of(sum(sK13,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_7175]) ).
cnf(c_9164,plain,
( ~ part_of(sK3(sK14,sK15),X0)
| ~ part_of(sK2(sK14,sK15),X0)
| ~ incident_c(sK14,sK3(sK14,sK15))
| ~ incident_c(sK14,sK2(sK14,sK15))
| ~ end_point(sK14,X0)
| part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_2029]) ).
cnf(c_9167,plain,
( ~ part_of(sK3(sK14,sK15),sK13)
| ~ part_of(sK2(sK14,sK15),sK13)
| ~ incident_c(sK14,sK3(sK14,sK15))
| ~ incident_c(sK14,sK2(sK14,sK15))
| ~ end_point(sK14,sK13)
| part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_9164]) ).
cnf(c_9362,plain,
incident_c(sK14,sK15),
inference(superposition,[status(thm)],[c_798,c_68]) ).
cnf(c_9956,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X0)
| incident_c(sK1(X0,X0,X1),X1) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
cnf(c_10021,plain,
( ~ incident_c(X0,X1)
| ~ part_of(X1,sK13)
| ~ incident_c(X0,sK15)
| ~ end_point(X0,sK13)
| part_of(X1,sK15)
| part_of(sK15,X1) ),
inference(superposition,[status(thm)],[c_797,c_64]) ).
cnf(c_10078,plain,
( ~ incident_c(sK1(X0,X0,X1),X0)
| sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_9956,c_53]) ).
cnf(c_10186,plain,
( ~ incident_c(sK1(X0,X0,X1),sK15)
| ~ end_point(sK1(X0,X0,X1),sK13)
| ~ part_of(X0,sK13)
| sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X1)
| part_of(X0,sK15)
| part_of(sK15,X0) ),
inference(superposition,[status(thm)],[c_9956,c_10021]) ).
cnf(c_12626,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_10186,c_3904,c_10078]) ).
cnf(c_18646,plain,
( ~ incident_c(sK0(sum(X0,X1),X2),X0)
| part_of(X2,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_49]) ).
cnf(c_18690,plain,
( ~ part_of(X0,X1)
| incident_c(sK0(X2,X0),X1)
| part_of(X0,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
cnf(c_19852,plain,
( ~ part_of(X0,X1)
| ~ part_of(X1,X2)
| incident_c(sK0(X3,X0),X2)
| part_of(X0,X3) ),
inference(superposition,[status(thm)],[c_18690,c_51]) ).
cnf(c_20388,plain,
( ~ part_of(sK13,X0)
| incident_c(sK0(X1,sK15),X0)
| part_of(sK15,X1) ),
inference(superposition,[status(thm)],[c_797,c_19852]) ).
cnf(c_20519,plain,
( ~ part_of(sK13,X0)
| part_of(sK15,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_20388,c_18646]) ).
cnf(c_36867,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X0)
| incident_c(sK1(X0,X0,X1),X1) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
cnf(c_37329,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_36867,c_3904,c_10078]) ).
cnf(c_37333,plain,
( ~ part_of(X0,X1)
| sum(X2,X0) = X2
| incident_c(sK1(X2,X2,X0),X1) ),
inference(superposition,[status(thm)],[c_37329,c_51]) ).
cnf(c_47368,plain,
( ~ incident_c(sK1(X0,X0,X1),X1)
| ~ part_of(X1,X0)
| sum(X0,X1) = X0 ),
inference(superposition,[status(thm)],[c_37333,c_52]) ).
cnf(c_107151,plain,
( incident_c(sK5(X0),X0)
| closed(X0) ),
inference(superposition,[status(thm)],[c_76,c_65]) ).
cnf(c_107154,plain,
incident_c(sK7(X0),X0),
inference(superposition,[status(thm)],[c_80,c_68]) ).
cnf(c_107182,plain,
( ~ incident_c(sK0(sum(X0,X1),X2),X1)
| part_of(X2,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_49]) ).
cnf(c_107185,plain,
( ~ incident_c(sK0(sum(X0,X1),X2),X0)
| part_of(X2,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_49]) ).
cnf(c_107234,plain,
( ~ part_of(X0,X1)
| incident_c(sK0(X2,X0),X1)
| part_of(X0,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
cnf(c_107237,plain,
( ~ part_of(X0,X1)
| incident_c(sK7(X0),X1) ),
inference(superposition,[status(thm)],[c_107154,c_51]) ).
cnf(c_107238,plain,
( ~ part_of(sK15,X0)
| incident_c(sK14,X0) ),
inference(superposition,[status(thm)],[c_9362,c_51]) ).
cnf(c_107239,plain,
( ~ part_of(X0,X1)
| incident_c(sK5(X0),X1)
| closed(X0) ),
inference(superposition,[status(thm)],[c_107151,c_51]) ).
cnf(c_107298,plain,
incident_c(sK14,sK13),
inference(superposition,[status(thm)],[c_797,c_107238]) ).
cnf(c_107301,plain,
( end_point(sK14,sK13)
| inner_point(sK14,sK13) ),
inference(superposition,[status(thm)],[c_107298,c_66]) ).
cnf(c_107302,plain,
end_point(sK14,sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_107301,c_799]) ).
cnf(c_107662,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X0)
| incident_c(sK1(X0,X0,X1),X1) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
cnf(c_107673,plain,
( ~ end_point(X0,sK13)
| ~ end_point(X1,sK13)
| X0 = X1
| X0 = sK14
| X1 = sK14 ),
inference(superposition,[status(thm)],[c_107302,c_83]) ).
cnf(c_107683,plain,
( ~ incident_c(X0,X1)
| ~ part_of(X1,sK13)
| ~ incident_c(X0,sK15)
| ~ end_point(X0,sK13)
| part_of(X1,sK15)
| part_of(sK15,X1) ),
inference(superposition,[status(thm)],[c_797,c_64]) ).
cnf(c_107691,plain,
( sum(X0,X1) = X0
| incident_c(sK1(X0,X0,X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_107662,c_12626]) ).
cnf(c_107695,plain,
( ~ part_of(X0,X1)
| sum(X2,X0) = X2
| incident_c(sK1(X2,X2,X0),X1) ),
inference(superposition,[status(thm)],[c_107691,c_51]) ).
cnf(c_107774,plain,
( ~ end_point(X0,sK13)
| ~ end_point(X1,sK13)
| sK10(sK13,X0) = X1
| sK10(sK13,X0) = sK14
| X1 = sK14 ),
inference(superposition,[status(thm)],[c_85,c_107673]) ).
cnf(c_107849,plain,
( ~ end_point(X0,X1)
| ~ end_point(X0,X2)
| ~ part_of(X1,sK13)
| ~ part_of(X2,sK13)
| ~ end_point(X0,sK15)
| part_of(X1,X2)
| part_of(X2,X1)
| part_of(X1,sK15)
| part_of(X2,sK15)
| part_of(sK15,X1)
| part_of(sK15,X2) ),
inference(superposition,[status(thm)],[c_797,c_79]) ).
cnf(c_107855,plain,
( ~ part_of(X0,X1)
| ~ part_of(X1,X2)
| incident_c(sK7(X0),X2) ),
inference(superposition,[status(thm)],[c_107237,c_51]) ).
cnf(c_107963,plain,
( ~ part_of(X0,X1)
| ~ part_of(X1,X2)
| incident_c(sK5(X0),X2)
| closed(X0) ),
inference(superposition,[status(thm)],[c_107239,c_51]) ).
cnf(c_108273,plain,
( ~ part_of(X0,X1)
| ~ part_of(X1,X2)
| incident_c(sK0(X3,X0),X2)
| part_of(X0,X3) ),
inference(superposition,[status(thm)],[c_107234,c_51]) ).
cnf(c_108502,plain,
( ~ part_of(sK13,X0)
| incident_c(sK7(sK15),X0) ),
inference(superposition,[status(thm)],[c_797,c_107855]) ).
cnf(c_108516,plain,
( ~ part_of(X0,X1)
| ~ part_of(sK13,X0)
| incident_c(sK7(sK15),X1) ),
inference(superposition,[status(thm)],[c_108502,c_51]) ).
cnf(c_108536,plain,
( ~ part_of(sK13,sK15)
| incident_c(sK7(sK15),sK13) ),
inference(superposition,[status(thm)],[c_797,c_108516]) ).
cnf(c_108540,plain,
incident_c(sK7(sK15),sK13),
inference(global_subsumption_just,[status(thm)],[c_108536,c_1543,c_1940]) ).
cnf(c_108544,plain,
( end_point(sK7(sK15),sK13)
| inner_point(sK7(sK15),sK13) ),
inference(superposition,[status(thm)],[c_108540,c_66]) ).
cnf(c_108547,plain,
( sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))) = sK13
| end_point(sK7(sK15),sK13) ),
inference(superposition,[status(thm)],[c_108544,c_81]) ).
cnf(c_108585,plain,
( ~ incident_c(sK0(sum(X0,sum(X1,X2)),X3),X2)
| part_of(X3,sum(X0,sum(X1,X2))) ),
inference(superposition,[status(thm)],[c_55,c_107182]) ).
cnf(c_108698,plain,
part_of(X0,sum(X0,X1)),
inference(superposition,[status(thm)],[c_50,c_107185]) ).
cnf(c_110310,plain,
( ~ part_of(sK13,X0)
| incident_c(sK5(sK15),X0)
| closed(sK15) ),
inference(superposition,[status(thm)],[c_797,c_107963]) ).
cnf(c_110321,plain,
( ~ part_of(X0,X1)
| ~ part_of(sK13,X0)
| incident_c(sK5(sK15),X1)
| closed(sK15) ),
inference(superposition,[status(thm)],[c_110310,c_51]) ).
cnf(c_110370,plain,
( ~ part_of(sK13,X0)
| incident_c(sK5(sK15),sum(X0,X1))
| closed(sK15) ),
inference(superposition,[status(thm)],[c_108698,c_110321]) ).
cnf(c_110542,plain,
( ~ part_of(sum(X0,X1),sK13)
| ~ incident_c(sK5(sK15),sK15)
| ~ end_point(sK5(sK15),sK13)
| ~ part_of(sK13,X0)
| part_of(sum(X0,X1),sK15)
| part_of(sK15,sum(X0,X1))
| closed(sK15) ),
inference(superposition,[status(thm)],[c_110370,c_107683]) ).
cnf(c_110608,plain,
( part_of(sK15,sum(X0,X1))
| ~ part_of(sK13,X0) ),
inference(global_subsumption_just,[status(thm)],[c_110542,c_20519]) ).
cnf(c_110609,plain,
( ~ part_of(sK13,X0)
| part_of(sK15,sum(X0,X1)) ),
inference(renaming,[status(thm)],[c_110608]) ).
cnf(c_110628,plain,
( ~ part_of(sK13,X0)
| incident_c(sK14,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_110609,c_107238]) ).
cnf(c_110692,plain,
( ~ part_of(sK13,X0)
| end_point(sK14,sum(X0,X1))
| inner_point(sK14,sum(X0,X1)) ),
inference(superposition,[status(thm)],[c_110628,c_66]) ).
cnf(c_112176,plain,
( ~ end_point(X0,sK13)
| sK10(sK13,sK14) = X0
| sK10(sK13,sK14) = sK14
| X0 = sK14 ),
inference(superposition,[status(thm)],[c_107302,c_107774]) ).
cnf(c_112189,plain,
( sK10(sK13,sK14) = X0
| ~ end_point(X0,sK13)
| X0 = sK14 ),
inference(global_subsumption_just,[status(thm)],[c_112176,c_92,c_739,c_757,c_1480,c_6618,c_112176]) ).
cnf(c_112190,plain,
( ~ end_point(X0,sK13)
| sK10(sK13,sK14) = X0
| X0 = sK14 ),
inference(renaming,[status(thm)],[c_112189]) ).
cnf(c_112200,plain,
( sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))) = sK13
| sK10(sK13,sK14) = sK7(sK15)
| sK7(sK15) = sK14 ),
inference(superposition,[status(thm)],[c_108547,c_112190]) ).
cnf(c_113524,plain,
( ~ part_of(sK13,sK8(sK13,sK7(sK15)))
| sK10(sK13,sK14) = sK7(sK15)
| sK7(sK15) = sK14
| end_point(sK14,sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))))
| inner_point(sK14,sK13) ),
inference(superposition,[status(thm)],[c_112200,c_110692]) ).
cnf(c_113597,plain,
( ~ part_of(sK13,sK8(sK13,sK7(sK15)))
| sK10(sK13,sK14) = sK7(sK15)
| sK7(sK15) = sK14
| end_point(sK14,sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_113524,c_799]) ).
cnf(c_113705,plain,
( ~ incident_c(sK1(X0,X0,X1),X0)
| ~ part_of(X1,X0)
| sum(X0,X1) = X0 ),
inference(superposition,[status(thm)],[c_107695,c_53]) ).
cnf(c_113786,plain,
( ~ part_of(sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))),sK13)
| ~ part_of(sK13,sK8(sK13,sK7(sK15)))
| ~ part_of(X0,sK13)
| ~ end_point(sK14,X0)
| ~ end_point(sK14,sK15)
| sK10(sK13,sK14) = sK7(sK15)
| sK7(sK15) = sK14
| part_of(sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))),X0)
| part_of(X0,sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))))
| part_of(sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))),sK15)
| part_of(sK15,sum(sK8(sK13,sK7(sK15)),sK9(sK13,sK7(sK15))))
| part_of(X0,sK15)
| part_of(sK15,X0) ),
inference(superposition,[status(thm)],[c_113597,c_107849]) ).
cnf(c_113959,plain,
~ end_point(sK14,sK15),
inference(global_subsumption_just,[status(thm)],[c_113786,c_762]) ).
cnf(c_120099,plain,
part_of(X0,sum(X1,sum(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_108585]) ).
cnf(c_120427,plain,
( ~ part_of(sum(X0,sum(X1,X2)),X3)
| incident_c(sK0(X4,X2),X3)
| part_of(X2,X4) ),
inference(superposition,[status(thm)],[c_120099,c_108273]) ).
cnf(c_124028,plain,
( ~ part_of(X1,X0)
| sum(X0,X1) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_113705,c_12626,c_47368]) ).
cnf(c_124029,plain,
( ~ part_of(X0,X1)
| sum(X1,X0) = X1 ),
inference(renaming,[status(thm)],[c_124028]) ).
cnf(c_124032,plain,
( ~ incident_c(X0,X1)
| sum(X1,sK3(X0,X1)) = X1
| end_point(X0,X1) ),
inference(superposition,[status(thm)],[c_62,c_124029]) ).
cnf(c_124033,plain,
( ~ incident_c(X0,X1)
| sum(X1,sK2(X0,X1)) = X1
| end_point(X0,X1) ),
inference(superposition,[status(thm)],[c_63,c_124029]) ).
cnf(c_124034,plain,
sum(sK13,sK15) = sK13,
inference(superposition,[status(thm)],[c_797,c_124029]) ).
cnf(c_128462,plain,
( sum(sK15,sK3(sK14,sK15)) = sK15
| end_point(sK14,sK15) ),
inference(superposition,[status(thm)],[c_9362,c_124032]) ).
cnf(c_128949,plain,
sum(sK15,sK3(sK14,sK15)) = sK15,
inference(forward_subsumption_resolution,[status(thm)],[c_128462,c_113959]) ).
cnf(c_133703,plain,
( sum(sK15,sK2(sK14,sK15)) = sK15
| end_point(sK14,sK15) ),
inference(superposition,[status(thm)],[c_9362,c_124033]) ).
cnf(c_134190,plain,
sum(sK15,sK2(sK14,sK15)) = sK15,
inference(forward_subsumption_resolution,[status(thm)],[c_133703,c_113959]) ).
cnf(c_178384,plain,
( ~ part_of(sum(X0,sK15),X1)
| incident_c(sK0(X2,sK3(sK14,sK15)),X1)
| part_of(sK3(sK14,sK15),X2) ),
inference(superposition,[status(thm)],[c_128949,c_120427]) ).
cnf(c_178747,plain,
( ~ part_of(sum(sK13,sK15),sK13)
| incident_c(sK0(sK13,sK3(sK14,sK15)),sK13)
| part_of(sK3(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_178384]) ).
cnf(c_179698,plain,
( ~ part_of(sum(X0,sK15),X1)
| incident_c(sK0(X2,sK2(sK14,sK15)),X1)
| part_of(sK2(sK14,sK15),X2) ),
inference(superposition,[status(thm)],[c_134190,c_120427]) ).
cnf(c_180061,plain,
( ~ part_of(sum(sK13,sK15),sK13)
| incident_c(sK0(sK13,sK2(sK14,sK15)),sK13)
| part_of(sK2(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_179698]) ).
cnf(c_181469,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_180061,c_178747,c_124034,c_9167,c_7176,c_6029,c_5990,c_1543,c_1481,c_1482,c_1485,c_1486,c_1480,c_811,c_762,c_757,c_739,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO089+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 06:49:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 103.16/14.81 % SZS status Started for theBenchmark.p
% 103.16/14.81 % SZS status Theorem for theBenchmark.p
% 103.16/14.81
% 103.16/14.81 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 103.16/14.81
% 103.16/14.81 ------ iProver source info
% 103.16/14.81
% 103.16/14.81 git: date: 2024-06-12 09:56:46 +0000
% 103.16/14.81 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 103.16/14.81 git: non_committed_changes: false
% 103.16/14.81
% 103.16/14.81 ------ Parsing...
% 103.16/14.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 103.16/14.81
% 103.16/14.81 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 103.16/14.81
% 103.16/14.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 103.16/14.81
% 103.16/14.81 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 103.16/14.81 ------ Proving...
% 103.16/14.81 ------ Problem Properties
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81 clauses 44
% 103.16/14.81 conjectures 3
% 103.16/14.81 EPR 16
% 103.16/14.81 Horn 28
% 103.16/14.81 unary 4
% 103.16/14.81 binary 16
% 103.16/14.81 lits 132
% 103.16/14.81 lits eq 12
% 103.16/14.81 fd_pure 0
% 103.16/14.81 fd_pseudo 0
% 103.16/14.81 fd_cond 0
% 103.16/14.81 fd_pseudo_cond 7
% 103.16/14.81 AC symbols 0
% 103.16/14.81
% 103.16/14.81 ------ Input Options Time Limit: Unbounded
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81 ------
% 103.16/14.81 Current options:
% 103.16/14.81 ------
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81 ------ Proving...
% 103.16/14.81
% 103.16/14.81
% 103.16/14.81 % SZS status Theorem for theBenchmark.p
% 103.16/14.81
% 103.16/14.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 103.16/14.81
% 103.16/14.82
%------------------------------------------------------------------------------