%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO121+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:51:36 AM UTC 2026
% Result : Theorem 23.25s 4.54s
% Output : Refutation 27.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 39
% Syntax : Number of formulae : 358 ( 41 unt; 22 def)
% Number of atoms : 1321 ( 177 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1580 ( 617 ~; 753 |; 155 &)
% ( 42 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 22 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-4 aty)
% Number of variables : 494 ( 0 sgn 455 !; 39 ?)
% 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(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( ( part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) )
=> ( part_of(X2,X3)
| part_of(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( incident_c(X0,X1)
& ~ end_point(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f7,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : end_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3] :
( ( end_point(X1,X0)
& end_point(X2,X0)
& end_point(X3,X0) )
=> ( X1 = X2
| X1 = X3
| X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5) ).
fof(f13,axiom,
! [X0,X1] :
( end_point(X1,X0)
=> ? [X2] :
( end_point(X2,X0)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2] :
( incident_c(X2,X0)
<=> incident_c(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9) ).
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn) ).
fof(f19,axiom,
! [X0,X1] :
( start_point(X0,X1)
<=> ( incident_o(X0,X1)
& ! [X2] :
( ( X0 != X2
& incident_o(X2,X1) )
=> ordered_by(X1,X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_point_defn) ).
fof(f20,axiom,
! [X0,X1] :
( finish_point(X0,X1)
<=> ( incident_o(X0,X1)
& ! [X2] :
( ( X0 != X2
& incident_o(X2,X1) )
=> ordered_by(X1,X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finish_point_defn) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ordered_by(X0,X1,X2)
=> ( incident_o(X1,X0)
& incident_o(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o1) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( open(X1)
& ! [X2] :
( incident_o(X2,X0)
<=> incident_c(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o2) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( ! [X0] :
( incident_o(X0,X3)
<=> incident_c(X0,X4) )
& between_c(X4,X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3) ).
fof(f24,axiom,
! [X0] :
? [X1] : start_point(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o4) ).
fof(f27,axiom,
! [X0,X1] :
( X0 = underlying_curve(X1)
<=> ! [X2] :
( incident_o(X2,X1)
<=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',underlying_curve_defn) ).
fof(f28,conjecture,
! [X0,X1] :
( end_point(X1,underlying_curve(X0))
=> ( start_point(X1,X0)
| finish_point(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_7) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( end_point(X1,underlying_curve(X0))
=> ( start_point(X1,X0)
| finish_point(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) )
& between_c(X4,X0,X1,X2) ) ),
inference(rectify,[],[f23]) ).
fof(f31,plain,
! [X0,X1] :
( ( incident_o(X0,X1)
& ! [X2] :
( ( X0 != X2
& incident_o(X2,X1) )
=> ordered_by(X1,X2,X0) ) )
=> finish_point(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(flattening,[],[f34]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| X1 = X3
| X2 = X3
| ~ end_point(X1,X0)
| ~ end_point(X2,X0)
| ~ end_point(X3,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| X1 = X3
| X2 = X3
| ~ end_point(X1,X0)
| ~ end_point(X2,X0)
| ~ end_point(X3,X0) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X2] :
( end_point(X2,X0)
& X1 != X2 )
| ~ end_point(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f50,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( incident_c(X2,X0)
<~> incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f51,plain,
! [X0,X1] :
( start_point(X0,X1)
<=> ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f52,plain,
! [X0,X1] :
( start_point(X0,X1)
<=> ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( finish_point(X0,X1)
| ~ incident_o(X0,X1)
| ? [X2] :
( ~ ordered_by(X1,X2,X0)
& X0 != X2
& incident_o(X2,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f54,plain,
! [X0,X1] :
( finish_point(X0,X1)
| ~ incident_o(X0,X1)
| ? [X2] :
( ~ ordered_by(X1,X2,X0)
& X0 != X2
& incident_o(X2,X1) ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( incident_o(X1,X0)
& incident_o(X2,X0) )
| ~ ordered_by(X0,X1,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f59,plain,
? [X0,X1] :
( ~ start_point(X1,X0)
& ~ finish_point(X1,X0)
& end_point(X1,underlying_curve(X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f60,plain,
? [X0,X1] :
( ~ start_point(X1,X0)
& ~ finish_point(X1,X0)
& end_point(X1,underlying_curve(X0)) ),
inference(flattening,[],[f59]) ).
fof(f61,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,[],[f33]) ).
fof(f62,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,[],[f61]) ).
fof(f63,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(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f68,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ( ~ part_of(sK2(X0,X1),sK3(X0,X1))
& ~ part_of(sK3(X0,X1),sK2(X0,X1))
& part_of(sK2(X0,X1),X1)
& part_of(sK3(X0,X1),X1)
& incident_c(X0,sK2(X0,X1))
& incident_c(X0,sK3(X0,X1)) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f73,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(flattening,[],[f72]) ).
fof(f79,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( ? [X1] : end_point(X1,X0)
| ~ open(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f80,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( ? [X2] : end_point(X2,X0)
| ~ open(X0) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( end_point(sK6(X0),X0)
| ~ open(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0))],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( ( end_point(sK10(X0,X1),X0)
& sK10(X0,X1) != X1 )
| ~ end_point(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f46]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ incident_c(X2,X1)
| ~ incident_c(X2,X0) )
& ( incident_c(X2,X1)
| incident_c(X2,X0) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f88,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ incident_c(sK12(X0,X1),X1)
| ~ incident_c(sK12(X0,X1),X0) )
& ( incident_c(sK12(X0,X1),X1)
| incident_c(sK12(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f87]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X5] :
( part_of(X5,X0)
& end_point(X1,X5)
& end_point(X3,X5)
& inner_point(X2,X5) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& part_of(sK13(X0,X1,X2,X3),X0)
& end_point(X1,sK13(X0,X1,X2,X3))
& end_point(X3,sK13(X0,X1,X2,X3))
& inner_point(X2,sK13(X0,X1,X2,X3)) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X5,sK13(X0,X1,X2,X3))],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( ( between_o(X0,X1,X2,X3)
| ( ( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) )
& ( ~ ordered_by(X0,X3,X2)
| ~ ordered_by(X0,X2,X1) ) ) )
& ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) )
| ~ between_o(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ( between_o(X0,X1,X2,X3)
| ( ( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) )
& ( ~ ordered_by(X0,X3,X2)
| ~ ordered_by(X0,X2,X1) ) ) )
& ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) )
| ~ between_o(X0,X1,X2,X3) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( start_point(X0,X1)
| ~ incident_o(X0,X1)
| ? [X2] :
( ~ ordered_by(X1,X0,X2)
& X0 != X2
& incident_o(X2,X1) ) )
& ( ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) )
| ~ start_point(X0,X1) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f96,plain,
! [X0,X1] :
( ( start_point(X0,X1)
| ~ incident_o(X0,X1)
| ? [X2] :
( ~ ordered_by(X1,X0,X2)
& X0 != X2
& incident_o(X2,X1) ) )
& ( ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) )
| ~ start_point(X0,X1) ) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ( start_point(X0,X1)
| ~ incident_o(X0,X1)
| ? [X2] :
( ~ ordered_by(X1,X0,X2)
& X0 != X2
& incident_o(X2,X1) ) )
& ( ( incident_o(X0,X1)
& ! [X3] :
( ordered_by(X1,X0,X3)
| X0 = X3
| ~ incident_o(X3,X1) ) )
| ~ start_point(X0,X1) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( start_point(X0,X1)
| ~ incident_o(X0,X1)
| ( ~ ordered_by(X1,X0,sK14(X0,X1))
& sK14(X0,X1) != X0
& incident_o(sK14(X0,X1),X1) ) )
& ( ( incident_o(X0,X1)
& ! [X3] :
( ordered_by(X1,X0,X3)
| X0 = X3
| ~ incident_o(X3,X1) ) )
| ~ start_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0,X1))],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( finish_point(X0,X1)
| ~ incident_o(X0,X1)
| ( ~ ordered_by(X1,sK15(X0,X1),X0)
& sK15(X0,X1) != X0
& incident_o(sK15(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X2,sK15(X0,X1))],[f54]) ).
fof(f100,plain,
! [X0] :
? [X1] :
( open(X1)
& ! [X2] :
( ( incident_o(X2,X0)
| ~ incident_c(X2,X1) )
& ( incident_c(X2,X1)
| ~ incident_o(X2,X0) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f101,plain,
! [X0] :
( open(sK16(X0))
& ! [X2] :
( ( incident_o(X2,X0)
| ~ incident_c(X2,sK16(X0)) )
& ( incident_c(X2,sK16(X0))
| ~ incident_o(X2,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ? [X4] :
( ! [X5] :
( ( incident_o(X5,X3)
| ~ incident_c(X5,X4) )
& ( incident_c(X5,X4)
| ~ incident_o(X5,X3) ) )
& between_c(X4,X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ? [X6] :
( ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,X6) )
& ( incident_c(X7,X6)
| ~ incident_o(X7,X3) ) )
& between_c(X6,X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ( ( ~ incident_c(sK17(X3,X4),X4)
| ~ incident_o(sK17(X3,X4),X3) )
& ( incident_c(sK17(X3,X4),X4)
| incident_o(sK17(X3,X4),X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ( ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,sK18(X0,X1,X2,X3)) )
& ( incident_c(X7,sK18(X0,X1,X2,X3))
| ~ incident_o(X7,X3) ) )
& between_c(sK18(X0,X1,X2,X3),X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X5,sK17(X3,X4)),skolemize(X6,sK18(X0,X1,X2,X3))],[f103]) ).
fof(f105,plain,
! [X0] : start_point(sK19(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19(X0))],[f24]) ).
fof(f110,plain,
! [X0,X1] :
( ( X0 = underlying_curve(X1)
| ? [X2] :
( ( ~ incident_c(X2,X0)
| ~ incident_o(X2,X1) )
& ( incident_c(X2,X0)
| incident_o(X2,X1) ) ) )
& ( ! [X2] :
( ( incident_o(X2,X1)
| ~ incident_c(X2,X0) )
& ( incident_c(X2,X0)
| ~ incident_o(X2,X1) ) )
| underlying_curve(X1) != X0 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f111,plain,
! [X0,X1] :
( ( X0 = underlying_curve(X1)
| ? [X2] :
( ( ~ incident_c(X2,X0)
| ~ incident_o(X2,X1) )
& ( incident_c(X2,X0)
| incident_o(X2,X1) ) ) )
& ( ! [X3] :
( ( incident_o(X3,X1)
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X0)
| ~ incident_o(X3,X1) ) )
| underlying_curve(X1) != X0 ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( X0 = underlying_curve(X1)
| ( ( ~ incident_c(sK23(X0,X1),X0)
| ~ incident_o(sK23(X0,X1),X1) )
& ( incident_c(sK23(X0,X1),X0)
| incident_o(sK23(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( incident_o(X3,X1)
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X0)
| ~ incident_o(X3,X1) ) )
| underlying_curve(X1) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X2,sK23(X0,X1))],[f111]) ).
fof(f113,plain,
( ~ start_point(sK25,sK24)
& ~ finish_point(sK25,sK24)
& end_point(sK25,underlying_curve(sK24)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X0,sK24),skolemize(X1,sK25)],[f60]) ).
fof(f114,plain,
! [X3,X0,X1] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f115,plain,
! [X0,X1] :
( incident_c(sK0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f116,plain,
! [X0,X1] :
( ~ incident_c(sK0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f124,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f133,plain,
! [X0,X1] :
( ~ incident_c(X0,X1)
| inner_point(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f142,plain,
! [X0] :
( end_point(sK6(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f143,plain,
! [X0,X1] :
( ~ end_point(X1,X0)
| open(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ end_point(X3,X0)
| X1 = X3
| X2 = X3
| ~ end_point(X1,X0)
| ~ end_point(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f45]) ).
fof(f150,plain,
! [X0,X1] :
( sK10(X0,X1) != X1
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f151,plain,
! [X0,X1] :
( end_point(sK10(X0,X1),X0)
| ~ end_point(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f154,plain,
! [X0,X1] :
( incident_c(sK12(X0,X1),X1)
| incident_c(sK12(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f88]) ).
fof(f155,plain,
! [X0,X1] :
( ~ incident_c(sK12(X0,X1),X1)
| X0 = X1
| ~ incident_c(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X4] :
( ~ inner_point(X2,X4)
| X1 = X3
| ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( ~ between_o(X0,X1,X2,X3)
| ordered_by(X0,X2,X1)
| ordered_by(X0,X2,X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ between_o(X0,X1,X2,X3)
| ordered_by(X0,X3,X2)
| ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X3,X2)
| ~ ordered_by(X0,X2,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f168,plain,
! [X3,X0,X1] :
( ordered_by(X1,X0,X3)
| X0 = X3
| ~ incident_o(X3,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f169,plain,
! [X0,X1] :
( ~ start_point(X0,X1)
| incident_o(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f173,plain,
! [X0,X1] :
( incident_o(sK15(X0,X1),X1)
| ~ incident_o(X0,X1)
| finish_point(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f174,plain,
! [X0,X1] :
( sK15(X0,X1) != X0
| ~ incident_o(X0,X1)
| finish_point(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f175,plain,
! [X0,X1] :
( finish_point(X0,X1)
| ~ incident_o(X0,X1)
| ~ ordered_by(X1,sK15(X0,X1),X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| incident_o(X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| incident_o(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f178,plain,
! [X2,X0] :
( incident_c(X2,sK16(X0))
| ~ incident_o(X2,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f179,plain,
! [X2,X0] :
( ~ incident_c(X2,sK16(X0))
| incident_o(X2,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( between_c(sK18(X0,X1,X2,X3),X0,X1,X2)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f184,plain,
! [X2,X3,X0,X1,X4] :
( ~ between_c(X4,X0,X1,X2)
| incident_c(sK17(X3,X4),X4)
| incident_o(sK17(X3,X4),X3)
| between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f185,plain,
! [X2,X3,X0,X1,X4] :
( ~ incident_o(sK17(X3,X4),X3)
| ~ incident_c(sK17(X3,X4),X4)
| between_o(X3,X0,X1,X2)
| ~ between_c(X4,X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f186,plain,
! [X0] : start_point(sK19(X0),X0),
inference(cnf_transformation,[],[f105]) ).
fof(f192,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_o(X3,X1)
| underlying_curve(X1) != X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f193,plain,
! [X3,X0,X1] :
( incident_o(X3,X1)
| ~ incident_c(X3,X0)
| underlying_curve(X1) != X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f196,plain,
end_point(sK25,underlying_curve(sK24)),
inference(cnf_transformation,[],[f113]) ).
fof(f197,plain,
~ finish_point(sK25,sK24),
inference(cnf_transformation,[],[f113]) ).
fof(f198,plain,
~ start_point(sK25,sK24),
inference(cnf_transformation,[],[f113]) ).
fof(f203,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f160]) ).
fof(f204,plain,
! [X3,X1] :
( ~ incident_c(X3,underlying_curve(X1))
| incident_o(X3,X1) ),
inference(equality_resolution,[],[f193]) ).
fof(f205,plain,
! [X3,X1] :
( incident_c(X3,underlying_curve(X1))
| ~ incident_o(X3,X1) ),
inference(equality_resolution,[],[f192]) ).
fof(f206,definition,
sF26 = underlying_curve(sK24),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f207,plain,
underlying_curve(sK24) = sF26,
inference(reorient_equations,[],[f206]) ).
fof(f208,plain,
end_point(sK25,sF26),
inference(definition_folding,[],[f196,f207]) ).
fof(f209,plain,
! [X0,X1] :
( ~ ordered_by(X1,sK15(X0,X1),X0)
| finish_point(X0,X1) ),
inference(forward_subsumption_resolution,[],[f175,f176]) ).
fof(f211,plain,
! [X0] :
( ~ incident_c(X0,sF26)
| incident_o(X0,sK24) ),
inference(superposition,[],[f204,f207]) ).
fof(f213,plain,
! [X0] :
( ~ incident_o(X0,sK24)
| incident_c(X0,sF26) ),
inference(superposition,[],[f205,f207]) ).
fof(f216,plain,
! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[],[f203,f181]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[],[f216,f166]) ).
fof(f219,plain,
! [X0] :
( incident_c(sK15(X0,sK24),sF26)
| finish_point(X0,sK24)
| ~ incident_o(X0,sK24) ),
inference(resolution,[],[f173,f213]) ).
fof(f221,plain,
incident_c(sK25,sF26),
inference(resolution,[],[f124,f208]) ).
fof(f222,plain,
incident_o(sK25,sK24),
inference(resolution,[],[f221,f211]) ).
fof(f225,plain,
open(sF26),
inference(resolution,[],[f143,f208]) ).
fof(f228,plain,
! [X0] :
( incident_o(sK0(X0,sF26),sK24)
| part_of(sF26,X0) ),
inference(resolution,[],[f115,f211]) ).
fof(f233,plain,
! [X0] :
( part_of(X0,X0)
| part_of(X0,X0) ),
inference(resolution,[],[f116,f115]) ).
fof(f235,plain,
! [X0] : part_of(X0,X0),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f243,plain,
! [X0,X1] :
( sK15(X0,X1) = X0
| ~ incident_o(X0,X1)
| ~ start_point(sK15(X0,X1),X1)
| finish_point(X0,X1) ),
inference(resolution,[],[f168,f209]) ).
fof(f247,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ incident_o(X1,X2)
| ~ start_point(X0,X2)
| ~ ordered_by(X2,X1,X0) ),
inference(resolution,[],[f168,f218]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ ordered_by(X2,X1,X0)
| ~ start_point(X0,X2)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f247,f177]) ).
fof(f249,plain,
! [X0,X1] :
( ~ start_point(sK15(X0,X1),X1)
| ~ incident_o(X0,X1)
| finish_point(X0,X1) ),
inference(forward_subsumption_resolution,[],[f243,f174]) ).
fof(f250,plain,
! [X0,X1] :
( incident_o(sK0(X0,sK16(X1)),X1)
| part_of(sK16(X1),X0) ),
inference(resolution,[],[f179,f115]) ).
fof(f270,plain,
! [X0,X1] :
( ~ incident_o(sK0(sK16(X0),X1),X0)
| part_of(X1,sK16(X0)) ),
inference(resolution,[],[f178,f116]) ).
fof(f298,plain,
! [X0] : incident_o(sK19(X0),X0),
inference(resolution,[],[f186,f169]) ).
fof(f299,plain,
incident_c(sK19(sK24),sF26),
inference(resolution,[],[f298,f213]) ).
fof(f313,plain,
! [X0] :
( end_point(sK15(X0,sK24),sF26)
| inner_point(sK15(X0,sK24),sF26)
| finish_point(X0,sK24)
| ~ incident_o(X0,sK24) ),
inference(resolution,[],[f133,f219]) ).
fof(f315,plain,
( inner_point(sK19(sK24),sF26)
| end_point(sK19(sK24),sF26) ),
inference(resolution,[],[f133,f299]) ).
fof(f318,definition,
( spl27_1
<=> end_point(sK19(sK24),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f319,plain,
( ~ end_point(sK19(sK24),sF26)
| spl27_1 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f320,plain,
( end_point(sK19(sK24),sF26)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f322,definition,
( spl27_2
<=> inner_point(sK19(sK24),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f324,plain,
( inner_point(sK19(sK24),sF26)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f325,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f315,f322,f318]) ).
fof(f333,plain,
! [X0] :
( incident_c(sK0(X0,sK16(sK24)),sF26)
| part_of(sK16(sK24),X0) ),
inference(resolution,[],[f250,f213]) ).
fof(f335,plain,
( part_of(sK16(sK24),sF26)
| part_of(sK16(sK24),sF26) ),
inference(resolution,[],[f333,f116]) ).
fof(f339,plain,
part_of(sK16(sK24),sF26),
inference(duplicate_literal_removal,[],[f335]) ).
fof(f367,definition,
( spl27_5
<=> ! [X0] :
( incident_c(sK17(sK24,X0),X0)
| ~ part_of(sF26,X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f368,plain,
( ! [X0] :
( incident_c(sK17(sK24,X0),X0)
| ~ part_of(sF26,X0) )
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f500,definition,
( spl27_19
<=> sK25 = sK19(sK24) ),
introduced(definition,[new_symbols(definition,[spl27_19])],[avatar_definition]) ).
fof(f501,plain,
( sK25 != sK19(sK24)
| spl27_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f502,plain,
( sK25 = sK19(sK24)
| ~ spl27_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f539,definition,
( spl27_21
<=> sK25 = sK6(sF26) ),
introduced(definition,[new_symbols(definition,[spl27_21])],[avatar_definition]) ).
fof(f540,plain,
( sK25 != sK6(sF26)
| spl27_21 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f541,plain,
( sK25 = sK6(sF26)
| ~ spl27_21 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f605,definition,
( spl27_27
<=> part_of(sF26,sK16(sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_27])],[avatar_definition]) ).
fof(f606,plain,
( part_of(sF26,sK16(sK24))
| ~ spl27_27 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f607,plain,
( ~ part_of(sF26,sK16(sK24))
| spl27_27 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f753,definition,
( spl27_36
<=> ordered_by(sK24,sK25,sK19(sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_36])],[avatar_definition]) ).
fof(f755,plain,
( ordered_by(sK24,sK25,sK19(sK24))
| ~ spl27_36 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f782,plain,
( ! [X0,X1] :
( incident_c(sK17(sK24,X0),X1)
| ~ part_of(sF26,X0)
| ~ part_of(X0,X1) )
| ~ spl27_5 ),
inference(resolution,[],[f368,f114]) ).
fof(f784,plain,
( ! [X0] :
( incident_o(sK17(sK24,sK16(X0)),X0)
| ~ part_of(sF26,sK16(X0)) )
| ~ spl27_5 ),
inference(resolution,[],[f368,f179]) ).
fof(f791,plain,
( ! [X2,X0,X1] :
( ~ part_of(sF26,sK16(sK24))
| ~ incident_c(sK17(sK24,sK16(sK24)),sK16(sK24))
| between_o(sK24,X0,X1,X2)
| ~ between_c(sK16(sK24),X0,X1,X2) )
| ~ spl27_5 ),
inference(resolution,[],[f784,f185]) ).
fof(f821,plain,
( part_of(sF26,sK16(sK24))
| part_of(sF26,sK16(sK24)) ),
inference(resolution,[],[f270,f228]) ).
fof(f822,plain,
part_of(sF26,sK16(sK24)),
inference(duplicate_literal_removal,[],[f821]) ).
fof(f825,plain,
( $false
| spl27_27 ),
inference(forward_subsumption_resolution,[],[f822,f607]) ).
fof(f826,plain,
spl27_27,
inference(avatar_contradiction_clause,[],[f825]) ).
fof(f827,plain,
( ! [X2,X0,X1] :
( ~ incident_c(sK17(sK24,sK16(sK24)),sK16(sK24))
| between_o(sK24,X0,X1,X2)
| ~ between_c(sK16(sK24),X0,X1,X2) )
| ~ spl27_5
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f791,f606]) ).
fof(f829,definition,
( spl27_42
<=> ! [X2,X0,X1] :
( between_o(sK24,X0,X1,X2)
| ~ between_c(sK16(sK24),X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl27_42])],[avatar_definition]) ).
fof(f830,plain,
( ! [X2,X0,X1] :
( ~ between_c(sK16(sK24),X0,X1,X2)
| between_o(sK24,X0,X1,X2) )
| ~ spl27_42 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f832,definition,
( spl27_43
<=> incident_c(sK17(sK24,sK16(sK24)),sK16(sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_43])],[avatar_definition]) ).
fof(f833,plain,
( incident_c(sK17(sK24,sK16(sK24)),sK16(sK24))
| ~ spl27_43 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f834,plain,
( ~ incident_c(sK17(sK24,sK16(sK24)),sK16(sK24))
| spl27_43 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f835,plain,
( spl27_42
| ~ spl27_43
| ~ spl27_5
| ~ spl27_27 ),
inference(avatar_split_clause,[],[f827,f605,f367,f832,f829]) ).
fof(f837,plain,
( ~ part_of(sF26,sK16(sK24))
| ~ part_of(sK16(sK24),sK16(sK24))
| ~ spl27_5
| spl27_43 ),
inference(resolution,[],[f834,f782]) ).
fof(f839,plain,
( ~ incident_o(sK17(sK24,sK16(sK24)),sK24)
| spl27_43 ),
inference(resolution,[],[f834,f178]) ).
fof(f840,plain,
( ~ part_of(sK16(sK24),sK16(sK24))
| ~ spl27_5
| ~ spl27_27
| spl27_43 ),
inference(forward_subsumption_resolution,[],[f837,f606]) ).
fof(f843,plain,
( $false
| ~ spl27_5
| ~ spl27_27
| spl27_43 ),
inference(forward_subsumption_resolution,[],[f840,f235]) ).
fof(f844,plain,
( ~ spl27_5
| ~ spl27_27
| spl27_43 ),
inference(avatar_contradiction_clause,[],[f843]) ).
fof(f1081,plain,
! [X2,X0,X1] :
( incident_c(sK12(X0,X1),X2)
| incident_c(sK12(X0,X1),X0)
| X0 = X1
| ~ part_of(X1,X2) ),
inference(resolution,[],[f154,f114]) ).
fof(f1086,plain,
! [X2,X0,X1] :
( incident_c(sK12(X0,X1),X2)
| incident_c(sK12(X0,X1),X1)
| X0 = X1
| ~ part_of(X0,X2) ),
inference(resolution,[],[f154,f114]) ).
fof(f1208,plain,
! [X2,X0,X1] :
( sK6(X1) = X0
| sK6(X1) = X2
| ~ end_point(X0,X1)
| ~ end_point(X2,X1)
| X0 = X2
| ~ open(X1) ),
inference(resolution,[],[f149,f142]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ end_point(X1,sF26)
| sK25 = X1
| ~ end_point(X0,sF26)
| sK25 = X0
| X0 = X1 ),
inference(resolution,[],[f149,f208]) ).
fof(f1217,plain,
! [X2,X0,X1] :
( ~ end_point(X2,X1)
| sK6(X1) = X2
| ~ end_point(X0,X1)
| sK6(X1) = X0
| X0 = X2 ),
inference(forward_subsumption_resolution,[],[f1208,f143]) ).
fof(f1358,definition,
( spl27_61
<=> sK25 = sK10(sK16(sK24),sK25) ),
introduced(definition,[new_symbols(definition,[spl27_61])],[avatar_definition]) ).
fof(f1359,plain,
( sK25 != sK10(sK16(sK24),sK25)
| spl27_61 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1360,plain,
( sK25 = sK10(sK16(sK24),sK25)
| ~ spl27_61 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1382,plain,
( sK25 != sK25
| ~ end_point(sK25,sK16(sK24))
| ~ spl27_61 ),
inference(superposition,[],[f150,f1360]) ).
fof(f1383,plain,
( ~ end_point(sK25,sK16(sK24))
| ~ spl27_61 ),
inference(trivial_inequality_removal,[],[f1382]) ).
fof(f1739,definition,
( spl27_81
<=> start_point(sK6(sF26),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_81])],[avatar_definition]) ).
fof(f1740,plain,
( ~ start_point(sK6(sF26),sK24)
| spl27_81 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f1741,plain,
( start_point(sK6(sF26),sK24)
| ~ spl27_81 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f2288,definition,
( spl27_119
<=> end_point(sK15(sK25,sK24),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_119])],[avatar_definition]) ).
fof(f2289,plain,
( end_point(sK15(sK25,sK24),sF26)
| ~ spl27_119 ),
inference(avatar_component_clause,[],[f2288]) ).
fof(f2290,plain,
( ~ end_point(sK15(sK25,sK24),sF26)
| spl27_119 ),
inference(avatar_component_clause,[],[f2288]) ).
fof(f2297,plain,
( inner_point(sK15(sK25,sK24),sF26)
| finish_point(sK25,sK24)
| ~ incident_o(sK25,sK24)
| spl27_119 ),
inference(resolution,[],[f2290,f313]) ).
fof(f2298,plain,
( inner_point(sK15(sK25,sK24),sF26)
| ~ incident_o(sK25,sK24)
| spl27_119 ),
inference(forward_subsumption_resolution,[],[f2297,f197]) ).
fof(f2299,plain,
( inner_point(sK15(sK25,sK24),sF26)
| spl27_119 ),
inference(forward_subsumption_resolution,[],[f2298,f222]) ).
fof(f2301,plain,
( ! [X2,X0,X1] :
( between_c(X2,X0,sK15(sK25,sK24),X1)
| ~ part_of(sF26,X2)
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1 )
| spl27_119 ),
inference(resolution,[],[f2299,f161]) ).
fof(f2323,plain,
( ! [X2,X3,X0,X1] :
( between_o(X3,X1,sK15(sK25,sK24),X2)
| incident_o(sK17(X3,X0),X3)
| incident_c(sK17(X3,X0),X0)
| X1 = X2
| ~ end_point(X2,sF26)
| ~ end_point(X1,sF26)
| ~ part_of(sF26,X0) )
| spl27_119 ),
inference(resolution,[],[f2301,f184]) ).
fof(f2363,plain,
( ! [X2,X0,X1] :
( between_o(sK24,X1,sK15(sK25,sK24),X2)
| incident_c(sK17(sK24,X0),X0)
| X1 = X2
| ~ end_point(X2,sF26)
| ~ end_point(X1,sF26)
| ~ part_of(sF26,X0)
| incident_c(sK17(sK24,X0),sF26) )
| spl27_119 ),
inference(resolution,[],[f2323,f213]) ).
fof(f2371,plain,
( ! [X2,X0,X1] :
( between_o(sK24,X1,sK15(sK25,sK24),X2)
| incident_c(sK17(sK24,X0),X0)
| X1 = X2
| ~ end_point(X2,sF26)
| ~ end_point(X1,sF26)
| ~ part_of(sF26,X0) )
| spl27_119 ),
inference(forward_subsumption_resolution,[],[f2363,f114]) ).
fof(f2373,definition,
( spl27_125
<=> ! [X2,X1] :
( between_o(sK24,X1,sK15(sK25,sK24),X2)
| ~ end_point(X1,sF26)
| ~ end_point(X2,sF26)
| X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[spl27_125])],[avatar_definition]) ).
fof(f2374,plain,
( ! [X2,X1] :
( between_o(sK24,X1,sK15(sK25,sK24),X2)
| ~ end_point(X1,sF26)
| ~ end_point(X2,sF26)
| X1 = X2 )
| ~ spl27_125 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f2377,plain,
( spl27_5
| spl27_125
| spl27_119 ),
inference(avatar_split_clause,[],[f2371,f2288,f2373,f367]) ).
fof(f2382,plain,
( ! [X0,X1] :
( ordered_by(sK24,sK15(sK25,sK24),X1)
| ordered_by(sK24,sK15(sK25,sK24),X0)
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26) )
| ~ spl27_125 ),
inference(resolution,[],[f2374,f162]) ).
fof(f2423,plain,
( ! [X0] :
( ordered_by(sK24,sK15(sK25,sK24),X0)
| sK25 = X0
| ~ end_point(X0,sF26)
| ~ end_point(sK25,sF26)
| finish_point(sK25,sK24) )
| ~ spl27_125 ),
inference(resolution,[],[f2382,f209]) ).
fof(f2436,plain,
( ! [X0] :
( ordered_by(sK24,sK15(sK25,sK24),X0)
| sK25 = X0
| ~ end_point(X0,sF26)
| finish_point(sK25,sK24) )
| ~ spl27_125 ),
inference(forward_subsumption_resolution,[],[f2423,f208]) ).
fof(f2444,plain,
( ! [X0] :
( ordered_by(sK24,sK15(sK25,sK24),X0)
| sK25 = X0
| ~ end_point(X0,sF26) )
| ~ spl27_125 ),
inference(forward_subsumption_resolution,[],[f2436,f197]) ).
fof(f2451,plain,
( ! [X0] :
( ~ start_point(X0,sK24)
| ~ end_point(X0,sF26)
| sK25 = X0
| sK15(sK25,sK24) = X0 )
| ~ spl27_125 ),
inference(resolution,[],[f2444,f248]) ).
fof(f2468,plain,
( ~ end_point(sK19(sK24),sF26)
| sK25 = sK19(sK24)
| sK19(sK24) = sK15(sK25,sK24)
| ~ spl27_125 ),
inference(resolution,[],[f2451,f186]) ).
fof(f2471,plain,
( sK25 = sK19(sK24)
| sK19(sK24) = sK15(sK25,sK24)
| ~ spl27_1
| ~ spl27_125 ),
inference(forward_subsumption_resolution,[],[f2468,f320]) ).
fof(f2474,definition,
( spl27_128
<=> sK19(sK24) = sK15(sK25,sK24) ),
introduced(definition,[new_symbols(definition,[spl27_128])],[avatar_definition]) ).
fof(f2475,plain,
( sK19(sK24) != sK15(sK25,sK24)
| spl27_128 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f2476,plain,
( sK19(sK24) = sK15(sK25,sK24)
| ~ spl27_128 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f2560,definition,
( spl27_134
<=> sK25 = sK15(sK25,sK24) ),
introduced(definition,[new_symbols(definition,[spl27_134])],[avatar_definition]) ).
fof(f2561,plain,
( sK25 = sK15(sK25,sK24)
| ~ spl27_134 ),
inference(avatar_component_clause,[],[f2560]) ).
fof(f2562,plain,
( sK25 != sK15(sK25,sK24)
| spl27_134 ),
inference(avatar_component_clause,[],[f2560]) ).
fof(f2651,plain,
( ! [X0] :
( sK6(sF26) = sK15(sK25,sK24)
| ~ end_point(X0,sF26)
| sK6(sF26) = X0
| sK15(sK25,sK24) = X0 )
| ~ spl27_119 ),
inference(resolution,[],[f2289,f1217]) ).
fof(f2657,definition,
( spl27_135
<=> ! [X0] :
( ~ end_point(X0,sF26)
| sK15(sK25,sK24) = X0
| sK6(sF26) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl27_135])],[avatar_definition]) ).
fof(f2658,plain,
( ! [X0] :
( ~ end_point(X0,sF26)
| sK15(sK25,sK24) = X0
| sK6(sF26) = X0 )
| ~ spl27_135 ),
inference(avatar_component_clause,[],[f2657]) ).
fof(f2660,definition,
( spl27_136
<=> sK6(sF26) = sK15(sK25,sK24) ),
introduced(definition,[new_symbols(definition,[spl27_136])],[avatar_definition]) ).
fof(f2662,plain,
( sK6(sF26) = sK15(sK25,sK24)
| ~ spl27_136 ),
inference(avatar_component_clause,[],[f2660]) ).
fof(f2663,plain,
( spl27_135
| spl27_136
| ~ spl27_119 ),
inference(avatar_split_clause,[],[f2651,f2288,f2660,f2657]) ).
fof(f2724,plain,
( ~ start_point(sK6(sF26),sK24)
| ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_136 ),
inference(superposition,[],[f249,f2662]) ).
fof(f2729,plain,
( ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_81
| ~ spl27_136 ),
inference(forward_subsumption_resolution,[],[f2724,f1741]) ).
fof(f2735,plain,
( finish_point(sK25,sK24)
| ~ spl27_81
| ~ spl27_136 ),
inference(forward_subsumption_resolution,[],[f2729,f222]) ).
fof(f2736,plain,
( $false
| ~ spl27_81
| ~ spl27_136 ),
inference(forward_subsumption_resolution,[],[f2735,f197]) ).
fof(f2737,plain,
( ~ spl27_81
| ~ spl27_136 ),
inference(avatar_contradiction_clause,[],[f2736]) ).
fof(f2820,plain,
( sK25 != sK25
| ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_134 ),
inference(superposition,[],[f174,f2561]) ).
fof(f2822,plain,
( ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_134 ),
inference(trivial_inequality_removal,[],[f2820]) ).
fof(f2824,plain,
( finish_point(sK25,sK24)
| ~ spl27_134 ),
inference(forward_subsumption_resolution,[],[f2822,f222]) ).
fof(f2827,plain,
( $false
| ~ spl27_134 ),
inference(forward_subsumption_resolution,[],[f2824,f197]) ).
fof(f2828,plain,
~ spl27_134,
inference(avatar_contradiction_clause,[],[f2827]) ).
fof(f2875,plain,
( incident_o(sK17(sK24,sK16(sK24)),sK24)
| ~ spl27_43 ),
inference(resolution,[],[f833,f179]) ).
fof(f2930,plain,
( ! [X2,X0,X1] :
( between_c(X2,X0,sK15(sK25,sK24),X1)
| ~ part_of(sF26,X2)
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1 )
| spl27_119 ),
inference(resolution,[],[f2299,f161]) ).
fof(f2973,plain,
( ! [X0,X1] :
( ~ part_of(sF26,sK16(sK24))
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1
| between_o(sK24,X0,sK15(sK25,sK24),X1) )
| ~ spl27_42
| spl27_119 ),
inference(resolution,[],[f2930,f830]) ).
fof(f2976,plain,
( ! [X0,X1] :
( ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1
| between_o(sK24,X0,sK15(sK25,sK24),X1) )
| ~ spl27_27
| ~ spl27_42
| spl27_119 ),
inference(forward_subsumption_resolution,[],[f2973,f606]) ).
fof(f2977,plain,
( spl27_125
| ~ spl27_27
| ~ spl27_42
| spl27_119 ),
inference(avatar_split_clause,[],[f2976,f2288,f829,f605,f2373]) ).
fof(f2982,plain,
( spl27_128
| spl27_19
| ~ spl27_1
| ~ spl27_125 ),
inference(avatar_split_clause,[],[f2471,f2373,f318,f500,f2474]) ).
fof(f2989,plain,
( ! [X2,X0,X1] :
( ~ incident_c(sK17(sK24,sK16(sK24)),sK16(sK24))
| between_o(sK24,X0,X1,X2)
| ~ between_c(sK16(sK24),X0,X1,X2) )
| ~ spl27_43 ),
inference(resolution,[],[f2875,f185]) ).
fof(f2995,plain,
( ! [X2,X0,X1] :
( between_o(sK24,X0,X1,X2)
| ~ between_c(sK16(sK24),X0,X1,X2) )
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f2989,f833]) ).
fof(f2996,plain,
( spl27_42
| ~ spl27_43 ),
inference(avatar_split_clause,[],[f2995,f832,f829]) ).
fof(f3103,plain,
( ~ start_point(sK19(sK24),sK24)
| ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_128 ),
inference(superposition,[],[f249,f2476]) ).
fof(f3108,plain,
( ~ incident_o(sK25,sK24)
| finish_point(sK25,sK24)
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3103,f186]) ).
fof(f3117,plain,
( finish_point(sK25,sK24)
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3108,f222]) ).
fof(f3119,plain,
( $false
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3117,f197]) ).
fof(f3120,plain,
~ spl27_128,
inference(avatar_contradiction_clause,[],[f3119]) ).
fof(f3165,plain,
( start_point(sK25,sK24)
| ~ spl27_19 ),
inference(superposition,[],[f186,f502]) ).
fof(f3166,plain,
( $false
| ~ spl27_19 ),
inference(forward_subsumption_resolution,[],[f3165,f198]) ).
fof(f3167,plain,
~ spl27_19,
inference(avatar_contradiction_clause,[],[f3166]) ).
fof(f3256,plain,
( sK25 = sK15(sK25,sK24)
| sK25 = sK6(sF26)
| ~ spl27_135 ),
inference(resolution,[],[f2658,f208]) ).
fof(f3257,plain,
( sK25 = sK6(sF26)
| spl27_134
| ~ spl27_135 ),
inference(forward_subsumption_resolution,[],[f3256,f2562]) ).
fof(f3259,plain,
( $false
| spl27_21
| spl27_134
| ~ spl27_135 ),
inference(forward_subsumption_resolution,[],[f3257,f540]) ).
fof(f3260,plain,
( spl27_21
| spl27_134
| ~ spl27_135 ),
inference(avatar_contradiction_clause,[],[f3259]) ).
fof(f3672,plain,
( ! [X2,X0,X1] :
( between_c(X2,X0,sK19(sK24),X1)
| ~ part_of(sF26,X2)
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1 )
| ~ spl27_2 ),
inference(resolution,[],[f324,f161]) ).
fof(f3676,plain,
( ! [X2,X3,X0,X1] :
( between_o(X3,X1,sK19(sK24),X2)
| incident_o(sK17(X3,X0),X3)
| incident_c(sK17(X3,X0),X0)
| X1 = X2
| ~ end_point(X2,sF26)
| ~ end_point(X1,sF26)
| ~ part_of(sF26,X0) )
| ~ spl27_2 ),
inference(resolution,[],[f3672,f184]) ).
fof(f5096,plain,
( ! [X0,X1] :
( between_o(sK24,X0,sK19(sK24),X1)
| incident_o(sK17(sK24,sK16(sK24)),sK24)
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26)
| ~ part_of(sF26,sK16(sK24)) )
| ~ spl27_2
| spl27_43 ),
inference(resolution,[],[f3676,f834]) ).
fof(f7427,plain,
! [X0,X1] :
( incident_c(sK12(X0,X1),X0)
| X0 = X1
| ~ part_of(X1,X0) ),
inference(factoring,[],[f1081]) ).
fof(f7457,plain,
! [X0,X1] :
( incident_c(sK12(X0,X1),X1)
| X0 = X1
| ~ part_of(X0,X1) ),
inference(factoring,[],[f1086]) ).
fof(f7459,plain,
! [X0,X1] :
( X0 = X1
| ~ part_of(X0,X1)
| X0 = X1
| ~ incident_c(sK12(X0,X1),X0) ),
inference(resolution,[],[f7457,f155]) ).
fof(f7468,plain,
! [X0,X1] :
( ~ incident_c(sK12(X0,X1),X0)
| ~ part_of(X0,X1)
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f7459]) ).
fof(f7471,plain,
! [X0,X1] :
( ~ part_of(X0,X1)
| X0 = X1
| X0 = X1
| ~ part_of(X1,X0) ),
inference(resolution,[],[f7468,f7427]) ).
fof(f7483,plain,
! [X0,X1] :
( ~ part_of(X1,X0)
| X0 = X1
| ~ part_of(X0,X1) ),
inference(duplicate_literal_removal,[],[f7471]) ).
fof(f7496,plain,
( sF26 = sK16(sK24)
| ~ part_of(sF26,sK16(sK24)) ),
inference(resolution,[],[f7483,f339]) ).
fof(f7497,plain,
( sF26 = sK16(sK24)
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f7496,f606]) ).
fof(f7522,plain,
( sK25 != sK10(sF26,sK25)
| ~ spl27_27
| spl27_61 ),
inference(superposition,[],[f1359,f7497]) ).
fof(f7701,plain,
( ! [X0,X1] :
( between_o(sK24,X0,sK19(sK24),X1)
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26)
| ~ part_of(sF26,sK16(sK24)) )
| ~ spl27_2
| spl27_43 ),
inference(forward_subsumption_resolution,[],[f5096,f839]) ).
fof(f7703,definition,
( spl27_204
<=> ! [X2,X1] :
( between_o(sK24,X1,sK19(sK24),X2)
| ~ end_point(X1,sF26)
| ~ end_point(X2,sF26)
| X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[spl27_204])],[avatar_definition]) ).
fof(f7704,plain,
( ! [X2,X1] :
( between_o(sK24,X1,sK19(sK24),X2)
| ~ end_point(X1,sF26)
| ~ end_point(X2,sF26)
| X1 = X2 )
| ~ spl27_204 ),
inference(avatar_component_clause,[],[f7703]) ).
fof(f7825,plain,
( ! [X0,X1] :
( between_o(sK24,X0,sK19(sK24),X1)
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26) )
| ~ spl27_2
| ~ spl27_27
| spl27_43 ),
inference(forward_subsumption_resolution,[],[f7701,f606]) ).
fof(f7898,plain,
( spl27_204
| ~ spl27_2
| ~ spl27_27
| spl27_43 ),
inference(avatar_split_clause,[],[f7825,f832,f605,f322,f7703]) ).
fof(f8256,plain,
( ! [X0,X1] :
( ordered_by(sK24,X1,sK19(sK24))
| ordered_by(sK24,X0,sK19(sK24))
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26) )
| ~ spl27_204 ),
inference(resolution,[],[f7704,f165]) ).
fof(f8312,plain,
( ! [X0,X1] :
( ordered_by(sK24,X1,sK19(sK24))
| X0 = X1
| ~ end_point(X1,sF26)
| ~ end_point(X0,sF26)
| ~ start_point(sK19(sK24),sK24)
| sK19(sK24) = X0 )
| ~ spl27_204 ),
inference(resolution,[],[f8256,f248]) ).
fof(f8322,plain,
( ! [X0,X1] :
( ~ end_point(X1,sF26)
| X0 = X1
| ordered_by(sK24,X1,sK19(sK24))
| ~ end_point(X0,sF26)
| sK19(sK24) = X0 )
| ~ spl27_204 ),
inference(forward_subsumption_resolution,[],[f8312,f186]) ).
fof(f8396,plain,
( ! [X0] :
( sK25 = X0
| ordered_by(sK24,sK25,sK19(sK24))
| ~ end_point(X0,sF26)
| sK19(sK24) = X0 )
| ~ spl27_204 ),
inference(resolution,[],[f8322,f208]) ).
fof(f8398,definition,
( spl27_226
<=> ! [X0] :
( sK25 = X0
| sK19(sK24) = X0
| ~ end_point(X0,sF26) ) ),
introduced(definition,[new_symbols(definition,[spl27_226])],[avatar_definition]) ).
fof(f8399,plain,
( ! [X0] :
( ~ end_point(X0,sF26)
| sK19(sK24) = X0
| sK25 = X0 )
| ~ spl27_226 ),
inference(avatar_component_clause,[],[f8398]) ).
fof(f8400,plain,
( spl27_36
| spl27_226
| ~ spl27_204 ),
inference(avatar_split_clause,[],[f8396,f7703,f8398,f753]) ).
fof(f8415,plain,
( ~ start_point(sK19(sK24),sK24)
| sK25 = sK19(sK24)
| ~ spl27_36 ),
inference(resolution,[],[f755,f248]) ).
fof(f8419,plain,
( sK25 = sK19(sK24)
| ~ spl27_36 ),
inference(forward_subsumption_resolution,[],[f8415,f186]) ).
fof(f8420,plain,
( $false
| spl27_19
| ~ spl27_36 ),
inference(forward_subsumption_resolution,[],[f8419,f501]) ).
fof(f8421,plain,
( spl27_19
| ~ spl27_36 ),
inference(avatar_contradiction_clause,[],[f8420]) ).
fof(f8425,plain,
( sK19(sK24) = sK6(sF26)
| sK25 = sK6(sF26)
| ~ open(sF26)
| ~ spl27_226 ),
inference(resolution,[],[f8399,f142]) ).
fof(f8432,plain,
( sK19(sK24) = sK6(sF26)
| ~ open(sF26)
| spl27_21
| ~ spl27_226 ),
inference(forward_subsumption_resolution,[],[f8425,f540]) ).
fof(f8436,plain,
( sK19(sK24) = sK6(sF26)
| spl27_21
| ~ spl27_226 ),
inference(forward_subsumption_resolution,[],[f8432,f225]) ).
fof(f8496,plain,
( ! [X2,X0,X1] :
( ~ between_c(sF26,X0,X1,X2)
| between_o(sK24,X0,X1,X2) )
| ~ spl27_27
| ~ spl27_42 ),
inference(forward_demodulation,[],[f830,f7497]) ).
fof(f8678,plain,
( ! [X0,X1] :
( between_o(sK24,X0,sK19(sK24),X1)
| ~ part_of(sF26,sF26)
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1 )
| ~ spl27_2
| ~ spl27_27
| ~ spl27_42 ),
inference(resolution,[],[f8496,f3672]) ).
fof(f8679,plain,
( ! [X0,X1] :
( between_o(sK24,X0,sK19(sK24),X1)
| ~ end_point(X0,sF26)
| ~ end_point(X1,sF26)
| X0 = X1 )
| ~ spl27_2
| ~ spl27_27
| ~ spl27_42 ),
inference(forward_subsumption_resolution,[],[f8678,f235]) ).
fof(f8680,plain,
( spl27_204
| ~ spl27_2
| ~ spl27_27
| ~ spl27_42 ),
inference(avatar_split_clause,[],[f8679,f829,f605,f322,f7703]) ).
fof(f8859,definition,
( spl27_257
<=> end_point(sK10(sF26,sK25),sF26) ),
introduced(definition,[new_symbols(definition,[spl27_257])],[avatar_definition]) ).
fof(f8860,plain,
( end_point(sK10(sF26,sK25),sF26)
| ~ spl27_257 ),
inference(avatar_component_clause,[],[f8859]) ).
fof(f8861,plain,
( ~ end_point(sK10(sF26,sK25),sF26)
| spl27_257 ),
inference(avatar_component_clause,[],[f8859]) ).
fof(f9153,plain,
( start_point(sK6(sF26),sK24)
| spl27_21
| ~ spl27_226 ),
inference(superposition,[],[f186,f8436]) ).
fof(f9154,plain,
( $false
| spl27_21
| spl27_81
| ~ spl27_226 ),
inference(forward_subsumption_resolution,[],[f9153,f1740]) ).
fof(f9155,plain,
( spl27_21
| spl27_81
| ~ spl27_226 ),
inference(avatar_contradiction_clause,[],[f9154]) ).
fof(f10851,plain,
( ~ end_point(sK25,sF26)
| ~ spl27_27
| ~ spl27_61 ),
inference(forward_demodulation,[],[f1383,f7497]) ).
fof(f10854,definition,
( spl27_353
<=> sK25 = sK10(sF26,sK25) ),
introduced(definition,[new_symbols(definition,[spl27_353])],[avatar_definition]) ).
fof(f10855,plain,
( sK25 != sK10(sF26,sK25)
| spl27_353 ),
inference(avatar_component_clause,[],[f10854]) ).
fof(f10867,plain,
( $false
| ~ spl27_27
| ~ spl27_61 ),
inference(forward_subsumption_resolution,[],[f10851,f208]) ).
fof(f10868,plain,
( ~ spl27_27
| ~ spl27_61 ),
inference(avatar_contradiction_clause,[],[f10867]) ).
fof(f10875,plain,
( ~ spl27_353
| ~ spl27_27
| spl27_61 ),
inference(avatar_split_clause,[],[f7522,f1358,f605,f10854]) ).
fof(f12521,plain,
( ~ end_point(sK25,sF26)
| spl27_257 ),
inference(resolution,[],[f8861,f151]) ).
fof(f12522,plain,
( $false
| spl27_257 ),
inference(forward_subsumption_resolution,[],[f12521,f208]) ).
fof(f12523,plain,
spl27_257,
inference(avatar_contradiction_clause,[],[f12522]) ).
fof(f12681,plain,
( sK19(sK24) = sK10(sF26,sK25)
| sK25 = sK10(sF26,sK25)
| ~ spl27_226
| ~ spl27_257 ),
inference(resolution,[],[f8860,f8399]) ).
fof(f12772,plain,
( sK19(sK24) = sK10(sF26,sK25)
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(forward_subsumption_resolution,[],[f12681,f10855]) ).
fof(f12908,plain,
( end_point(sK19(sK24),sF26)
| ~ end_point(sK25,sF26)
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(superposition,[],[f151,f12772]) ).
fof(f12910,plain,
( ~ end_point(sK25,sF26)
| spl27_1
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(forward_subsumption_resolution,[],[f12908,f319]) ).
fof(f12913,plain,
( $false
| spl27_1
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(forward_subsumption_resolution,[],[f12910,f208]) ).
fof(f12914,plain,
( spl27_1
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(avatar_contradiction_clause,[],[f12913]) ).
fof(f12916,plain,
( ! [X0] :
( ~ end_point(X0,sF26)
| sK25 = X0
| sK15(sK25,sK24) = X0 )
| ~ spl27_21
| ~ spl27_135 ),
inference(forward_demodulation,[],[f2658,f541]) ).
fof(f17362,plain,
( ! [X0] :
( sK25 = sK19(sK24)
| ~ end_point(X0,sF26)
| sK25 = X0
| sK19(sK24) = X0 )
| ~ spl27_1 ),
inference(resolution,[],[f320,f1215]) ).
fof(f17385,plain,
( sK25 = sK19(sK24)
| sK19(sK24) = sK15(sK25,sK24)
| ~ spl27_1
| ~ spl27_21
| ~ spl27_135 ),
inference(resolution,[],[f320,f12916]) ).
fof(f17533,plain,
( sK19(sK24) = sK15(sK25,sK24)
| ~ spl27_1
| spl27_19
| ~ spl27_21
| ~ spl27_135 ),
inference(forward_subsumption_resolution,[],[f17385,f501]) ).
fof(f17590,plain,
( ! [X0] :
( ~ end_point(X0,sF26)
| sK25 = X0
| sK19(sK24) = X0 )
| ~ spl27_1
| spl27_19 ),
inference(forward_subsumption_resolution,[],[f17362,f501]) ).
fof(f17597,plain,
( $false
| ~ spl27_1
| spl27_19
| ~ spl27_21
| spl27_128
| ~ spl27_135 ),
inference(forward_subsumption_resolution,[],[f17533,f2475]) ).
fof(f17598,plain,
( ~ spl27_1
| spl27_19
| ~ spl27_21
| spl27_128
| ~ spl27_135 ),
inference(avatar_contradiction_clause,[],[f17597]) ).
fof(f17605,plain,
( spl27_226
| ~ spl27_1
| spl27_19 ),
inference(avatar_split_clause,[],[f17590,f500,f318,f8398]) ).
fof(f17626,plain,
( sK25 = sK15(sK25,sK24)
| ~ spl27_21
| ~ spl27_136 ),
inference(forward_demodulation,[],[f2662,f541]) ).
fof(f17663,plain,
( $false
| ~ spl27_21
| spl27_134
| ~ spl27_136 ),
inference(forward_subsumption_resolution,[],[f17626,f2562]) ).
fof(f17664,plain,
( ~ spl27_21
| spl27_134
| ~ spl27_136 ),
inference(avatar_contradiction_clause,[],[f17663]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f325]) ).
cnf(s31,plain,
spl27_27,
inference(sat_conversion,[],[f826]) ).
cnf(s32,plain,
( ~ spl27_5
| ~ spl27_27
| spl27_42
| ~ spl27_43 ),
inference(sat_conversion,[],[f835]) ).
cnf(s34,plain,
( ~ spl27_5
| ~ spl27_27
| spl27_43 ),
inference(sat_conversion,[],[f844]) ).
cnf(s144,plain,
( spl27_5
| spl27_119
| spl27_125 ),
inference(sat_conversion,[],[f2377]) ).
cnf(s162,plain,
( ~ spl27_119
| spl27_135
| spl27_136 ),
inference(sat_conversion,[],[f2663]) ).
cnf(s177,plain,
( ~ spl27_81
| ~ spl27_136 ),
inference(sat_conversion,[],[f2737]) ).
cnf(s185,plain,
~ spl27_134,
inference(sat_conversion,[],[f2828]) ).
cnf(s198,plain,
( ~ spl27_27
| ~ spl27_42
| spl27_119
| spl27_125 ),
inference(sat_conversion,[],[f2977]) ).
cnf(s199,plain,
( ~ spl27_1
| spl27_19
| ~ spl27_125
| spl27_128 ),
inference(sat_conversion,[],[f2982]) ).
cnf(s203,plain,
( spl27_42
| ~ spl27_43 ),
inference(sat_conversion,[],[f2996]) ).
cnf(s210,plain,
~ spl27_128,
inference(sat_conversion,[],[f3120]) ).
cnf(s211,plain,
~ spl27_19,
inference(sat_conversion,[],[f3167]) ).
cnf(s223,plain,
( spl27_21
| spl27_134
| ~ spl27_135 ),
inference(sat_conversion,[],[f3260]) ).
cnf(s362,plain,
( ~ spl27_2
| ~ spl27_27
| spl27_43
| spl27_204 ),
inference(sat_conversion,[],[f7898]) ).
cnf(s389,plain,
( spl27_36
| ~ spl27_204
| spl27_226 ),
inference(sat_conversion,[],[f8400]) ).
cnf(s393,plain,
( spl27_19
| ~ spl27_36 ),
inference(sat_conversion,[],[f8421]) ).
cnf(s423,plain,
( ~ spl27_2
| ~ spl27_27
| ~ spl27_42
| spl27_204 ),
inference(sat_conversion,[],[f8680]) ).
cnf(s453,plain,
( spl27_21
| spl27_81
| ~ spl27_226 ),
inference(sat_conversion,[],[f9155]) ).
cnf(s592,plain,
( ~ spl27_27
| ~ spl27_61 ),
inference(sat_conversion,[],[f10868]) ).
cnf(s595,plain,
( ~ spl27_27
| spl27_61
| ~ spl27_353 ),
inference(sat_conversion,[],[f10875]) ).
cnf(s677,plain,
spl27_257,
inference(sat_conversion,[],[f12523]) ).
cnf(s725,plain,
( spl27_1
| ~ spl27_226
| ~ spl27_257
| spl27_353 ),
inference(sat_conversion,[],[f12914]) ).
cnf(s898,plain,
( ~ spl27_1
| spl27_19
| ~ spl27_21
| spl27_128
| ~ spl27_135 ),
inference(sat_conversion,[],[f17598]) ).
cnf(s899,plain,
( ~ spl27_1
| spl27_19
| spl27_226 ),
inference(sat_conversion,[],[f17605]) ).
cnf(s913,plain,
( ~ spl27_21
| spl27_134
| ~ spl27_136 ),
inference(sat_conversion,[],[f17664]) ).
cnf(s922,plain,
~ spl27_36,
inference(rat,[],[s393,s211]) ).
cnf(s923,plain,
( ~ spl27_1
| ~ spl27_125 ),
inference(rat,[],[s199,s210,s211]) ).
cnf(s934,plain,
~ spl27_61,
inference(rat,[],[s592,s31]) ).
cnf(s939,plain,
~ spl27_353,
inference(rat,[],[s595,s31,s934]) ).
cnf(s948,plain,
( spl27_204
| ~ spl27_2 ),
inference(rat,[],[s203,s362,s423,s31]) ).
cnf(s949,plain,
spl27_1,
inference(rat,[],[s948,s389,s1,s725,s922,s677,s939]) ).
cnf(s951,plain,
spl27_226,
inference(rat,[],[s899,s211,s949]) ).
cnf(s952,plain,
~ spl27_125,
inference(rat,[],[s923,s949]) ).
cnf(s955,plain,
( spl27_21
| ~ spl27_119 ),
inference(rat,[],[s177,s162,s453,s223,s951,s185]) ).
cnf(s956,plain,
~ spl27_119,
inference(rat,[],[s162,s898,s913,s955,s211,s210,s949,s185]) ).
cnf(s961,plain,
spl27_5,
inference(rat,[],[s144,s952,s956]) ).
cnf(s964,plain,
~ spl27_42,
inference(rat,[],[s198,s952,s31,s956]) ).
cnf(s965,plain,
spl27_43,
inference(rat,[],[s34,s31,s961]) ).
cnf(s966,plain,
$false,
inference(rat,[],[s32,s965,s31,s964,s961]) ).
fof(f17682,plain,
$false,
inference(avatar_sat_refutation,[],[s966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO121+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 07:01:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.11/3.26 % (2203613)Detected formulas, will run a generic FOF schedule.
% 18.11/3.26 % (2203679)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1484042267:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 18.11/3.26 % (2203684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2604471120:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 18.11/3.26 % (2203681)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2666051768:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 18.11/3.26 % (2203685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2149701432:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 18.11/3.26 % (2203682)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=133858460:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 18.11/3.26 % (2203683)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3723284426:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 18.11/3.26 % (2203686)dis-21_1_sil=8000:lcm=predicate:random_seed=3113296187:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 18.11/3.26 % (2203683)Instruction limit reached!
% 18.11/3.26 % (2203683)------------------------------
% 18.11/3.26 % (2203683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.11/3.26 % (2203683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.11/3.26 % (2203683)CaDiCaL version: 2.1.3
% 18.11/3.26 % (2203683)Termination reason: Instruction limit
% 18.11/3.26 % (2203683)Termination phase: Saturation
% 18.11/3.26 % (2203683)Time elapsed: 0.053 s
% 18.11/3.26 % (2203683)Peak memory usage: 88 MB
% 18.11/3.26 % (2203683)Instructions burned: 110 (million)
% 18.11/3.26 % (2203684)Instruction limit reached!
% 18.11/3.26 % (2203684)------------------------------
% 18.11/3.26 % (2203684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.11/3.26 % (2203684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.11/3.26 % (2203684)CaDiCaL version: 2.1.3
% 18.11/3.26 % (2203684)Termination reason: Instruction limit
% 18.11/3.26 % (2203684)Termination phase: Saturation
% 18.11/3.26 % (2203684)Time elapsed: 0.054 s
% 18.11/3.26 % (2203684)Peak memory usage: 87 MB
% 18.11/3.26 % (2203684)Instructions burned: 120 (million)
% 18.11/3.26 % (2203686)Instruction limit reached!
% 18.11/3.26 % (2203686)------------------------------
% 18.11/3.26 % (2203686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.11/3.26 % (2203686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.11/3.26 % (2203686)CaDiCaL version: 2.1.3
% 18.11/3.26 % (2203686)Termination reason: Instruction limit
% 18.11/3.26 % (2203686)Termination phase: Saturation
% 18.11/3.26 % (2203686)Time elapsed: 0.078 s
% 18.11/3.26 % (2203686)Peak memory usage: 89 MB
% 18.11/3.26 % (2203686)Instructions burned: 130 (million)
% 18.11/3.26 % (2203685)Instruction limit reached!
% 18.11/3.26 % (2203685)------------------------------
% 18.11/3.26 % (2203685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.11/3.26 % (2203685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.11/3.26 % (2203685)CaDiCaL version: 2.1.3
% 18.11/3.26 % (2203685)Termination reason: Instruction limit
% 18.11/3.26 % (2203685)Termination phase: Saturation
% 18.11/3.26 % (2203685)Time elapsed: 0.088 s
% 18.11/3.26 % (2203685)Peak memory usage: 89 MB
% 18.11/3.26 % (2203685)Instructions burned: 139 (million)
% 18.11/3.26 % (2203701)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1624837431:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 18.11/3.26 % (2203700)lrs+10_1_sil=8000:sp=occurrence:random_seed=3944069914:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 18.11/3.26 % (2203702)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2121857049:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 18.11/3.26 % (2203701)Refutation not found, incomplete strategy
% 18.11/3.26 % (2203701)------------------------------
% 18.11/3.26 % (2203701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.11/3.26 % (2203701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203701)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203701)Termination reason: Refutation not found, incomplete strategy
% 23.25/4.54 % (2203701)Time elapsed: 0.022 s
% 23.25/4.54 % (2203701)Peak memory usage: 89 MB
% 23.25/4.54 % (2203701)Instructions burned: 22 (million)
% 23.25/4.54 % (2203703)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3074725027:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 23.25/4.54 % (2203702)Instruction limit reached!
% 23.25/4.54 % (2203702)------------------------------
% 23.25/4.54 % (2203702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203702)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203702)Termination reason: Instruction limit
% 23.25/4.54 % (2203702)Termination phase: Saturation
% 23.25/4.54 % (2203702)Time elapsed: 0.174 s
% 23.25/4.54 % (2203702)Peak memory usage: 91 MB
% 23.25/4.54 % (2203702)Instructions burned: 325 (million)
% 23.25/4.54 % (2203700)Instruction limit reached!
% 23.25/4.54 % (2203700)------------------------------
% 23.25/4.54 % (2203700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203700)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203700)Termination reason: Instruction limit
% 23.25/4.54 % (2203700)Termination phase: Saturation
% 23.25/4.54 % (2203700)Time elapsed: 0.218 s
% 23.25/4.54 % (2203700)Peak memory usage: 89 MB
% 23.25/4.54 % (2203700)Instructions burned: 285 (million)
% 23.25/4.54 % (2203703)Instruction limit reached!
% 23.25/4.54 % (2203703)------------------------------
% 23.25/4.54 % (2203703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203703)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203703)Termination reason: Instruction limit
% 23.25/4.54 % (2203703)Termination phase: Saturation
% 23.25/4.54 % (2203703)Time elapsed: 0.227 s
% 23.25/4.54 % (2203703)Peak memory usage: 90 MB
% 23.25/4.54 % (2203703)Instructions burned: 248 (million)
% 23.25/4.54 % (2203701)------------------------------
% 23.25/4.54 % (2203701)------------------------------
% 23.25/4.54 % (2203743)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3399930348:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 23.25/4.54 % (2203745)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3683206135:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 23.25/4.54 % (2203747)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2178398125:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 23.25/4.54 % (2203749)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1987982406:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 23.25/4.54 % (2203743)Instruction limit reached!
% 23.25/4.54 % (2203743)------------------------------
% 23.25/4.54 % (2203743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203743)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203743)Termination reason: Instruction limit
% 23.25/4.54 % (2203743)Termination phase: Saturation
% 23.25/4.54 % (2203743)Time elapsed: 0.155 s
% 23.25/4.54 % (2203743)Peak memory usage: 89 MB
% 23.25/4.54 % (2203743)Instructions burned: 295 (million)
% 23.25/4.54 % (2203749)Instruction limit reached!
% 23.25/4.54 % (2203749)------------------------------
% 23.25/4.54 % (2203749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203749)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203749)Termination reason: Instruction limit
% 23.25/4.54 % (2203749)Termination phase: Saturation
% 23.25/4.54 % (2203749)Time elapsed: 0.107 s
% 23.25/4.54 % (2203749)Peak memory usage: 89 MB
% 23.25/4.54 % (2203749)Instructions burned: 128 (million)
% 23.25/4.54 % (2203747)Instruction limit reached!
% 23.25/4.54 % (2203747)------------------------------
% 23.25/4.54 % (2203747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203747)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203747)Termination reason: Instruction limit
% 23.25/4.54 % (2203747)Termination phase: Saturation
% 23.25/4.54 % (2203747)Time elapsed: 0.124 s
% 23.25/4.54 % (2203747)Peak memory usage: 89 MB
% 23.25/4.54 % (2203747)Instructions burned: 114 (million)
% 23.25/4.54 % (2203756)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2061710889:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 23.25/4.54 % (2203756)Instruction limit reached!
% 23.25/4.54 % (2203756)------------------------------
% 23.25/4.54 % (2203756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203756)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203756)Termination reason: Instruction limit
% 23.25/4.54 % (2203756)Termination phase: Saturation
% 23.25/4.54 % (2203756)Time elapsed: 0.057 s
% 23.25/4.54 % (2203756)Peak memory usage: 89 MB
% 23.25/4.54 % (2203756)Instructions burned: 114 (million)
% 23.25/4.54 % (2203758)lrs+10_1_sil=8000:sp=occurrence:random_seed=1631553431:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 23.25/4.54 % (2203759)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1678184483:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 23.25/4.54 % (2203759)Refutation not found, incomplete strategy
% 23.25/4.54 % (2203759)------------------------------
% 23.25/4.54 % (2203759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203759)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203759)Termination reason: Refutation not found, incomplete strategy
% 23.25/4.54 % (2203759)Time elapsed: 0.004 s
% 23.25/4.54 % (2203759)Peak memory usage: 88 MB
% 23.25/4.54 % (2203759)Instructions burned: 2 (million)
% 23.25/4.54 % (2203766)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=364794766:i=5202:ss=axioms:sgt=16_2986 on theBenchmark for (2986ds/5202Mi)
% 23.25/4.54 % (2203759)------------------------------
% 23.25/4.54 % (2203759)------------------------------
% 23.25/4.54 % (2203758)Instruction limit reached!
% 23.25/4.54 % (2203758)------------------------------
% 23.25/4.54 % (2203758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203758)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203758)Termination reason: Instruction limit
% 23.25/4.54 % (2203758)Termination phase: Saturation
% 23.25/4.54 % (2203758)Time elapsed: 0.476 s
% 23.25/4.54 % (2203758)Peak memory usage: 96 MB
% 23.25/4.54 % (2203758)Instructions burned: 908 (million)
% 23.25/4.54 % (2203772)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2378681616:st=8:i=592:sd=3:ep=RST:ss=axioms_2981 on theBenchmark for (2981ds/592Mi)
% 23.25/4.54 % (2203771)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=328516029:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2982 on theBenchmark for (2982ds/134Mi)
% 23.25/4.54 % (2203771)Instruction limit reached!
% 23.25/4.54 % (2203771)------------------------------
% 23.25/4.54 % (2203771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203771)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203771)Termination reason: Instruction limit
% 23.25/4.54 % (2203771)Termination phase: Saturation
% 23.25/4.54 % (2203771)Time elapsed: 0.075 s
% 23.25/4.54 % (2203771)Peak memory usage: 89 MB
% 23.25/4.54 % (2203771)Instructions burned: 135 (million)
% 23.25/4.54 % (2203772)Instruction limit reached!
% 23.25/4.54 % (2203772)------------------------------
% 23.25/4.54 % (2203772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203772)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203772)Termination reason: Instruction limit
% 23.25/4.54 % (2203772)Termination phase: Saturation
% 23.25/4.54 % (2203772)Time elapsed: 0.270 s
% 23.25/4.54 % (2203772)Peak memory usage: 93 MB
% 23.25/4.54 % (2203772)Instructions burned: 594 (million)
% 23.25/4.54 % (2203781)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3716698173:st=3:i=13193:sd=3:ss=axioms_2978 on theBenchmark for (2978ds/13193Mi)
% 23.25/4.54 % (2203784)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1102725780:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2976 on theBenchmark for (2976ds/125Mi)
% 23.25/4.54 % (2203784)Instruction limit reached!
% 23.25/4.54 % (2203784)------------------------------
% 23.25/4.54 % (2203784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203784)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203784)Termination reason: Instruction limit
% 23.25/4.54 % (2203784)Termination phase: Saturation
% 23.25/4.54 % (2203784)Time elapsed: 0.134 s
% 23.25/4.54 % (2203784)Peak memory usage: 90 MB
% 23.25/4.54 % (2203784)Instructions burned: 126 (million)
% 23.25/4.54 % (2203788)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=912022083:i=134:gtgl=5:slsql=off:gtg=exists_sym_2972 on theBenchmark for (2972ds/134Mi)
% 23.25/4.54 % (2203788)Instruction limit reached!
% 23.25/4.54 % (2203788)------------------------------
% 23.25/4.54 % (2203788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203788)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203788)Termination reason: Instruction limit
% 23.25/4.54 % (2203788)Termination phase: Saturation
% 23.25/4.54 % (2203788)Time elapsed: 0.144 s
% 23.25/4.54 % (2203788)Peak memory usage: 90 MB
% 23.25/4.54 % (2203788)Instructions burned: 135 (million)
% 23.25/4.54 % (2203745)Instruction limit reached!
% 23.25/4.54 % (2203745)------------------------------
% 23.25/4.54 % (2203745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203745)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203745)Termination reason: Instruction limit
% 23.25/4.54 % (2203745)Termination phase: Saturation
% 23.25/4.54 % (2203745)Time elapsed: 2.406 s
% 23.25/4.54 % (2203745)Peak memory usage: 138 MB
% 23.25/4.54 % (2203745)Instructions burned: 2350 (million)
% 23.25/4.54 % (2203679)First to succeed.
% 23.25/4.54 % (2203679)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2203613"
% 23.25/4.54 % (2203791)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1769717720:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2967 on theBenchmark for (2967ds/141Mi)
% 23.25/4.54 % (2203791)Instruction limit reached!
% 23.25/4.54 % (2203791)------------------------------
% 23.25/4.54 % (2203791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203791)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203791)Termination reason: Instruction limit
% 23.25/4.54 % (2203791)Termination phase: Saturation
% 23.25/4.54 % (2203791)Time elapsed: 0.103 s
% 23.25/4.54 % (2203791)Peak memory usage: 89 MB
% 23.25/4.54 % (2203791)Instructions burned: 142 (million)
% 23.25/4.54 % (2203792)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=3523336810:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2966 on theBenchmark for (2966ds/431Mi)
% 23.25/4.54 % (2203792)Refutation not found, incomplete strategy
% 23.25/4.54 % (2203792)------------------------------
% 23.25/4.54 % (2203792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.25/4.54 % (2203792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.25/4.54 % (2203792)CaDiCaL version: 2.1.3
% 23.25/4.54 % (2203792)Termination reason: Refutation not found, incomplete strategy
% 23.25/4.54 % (2203792)Time elapsed: 0.005 s
% 23.25/4.54 % (2203792)Peak memory usage: 88 MB
% 23.25/4.54 % (2203792)Instructions burned: 3 (million)
% 23.25/4.54 % (2203679)Refutation found. Thanks to Tanya!
% 23.25/4.54 % SZS status Theorem for theBenchmark
% 23.25/4.54 % SZS output start Proof for theBenchmark
% See solution above
% 27.78/4.77 % (2203679)------------------------------
% 27.78/4.77 % (2203679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 27.78/4.77 % (2203679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.78/4.77 % (2203679)CaDiCaL version: 2.1.3
% 27.78/4.77 % (2203679)Termination reason: Refutation
% 27.78/4.77 % (2203679)Time elapsed: 3.278 s
% 27.78/4.77 % (2203679)Peak memory usage: 143 MB
% 27.78/4.77 % (2203679)Instructions burned: 3271 (million)
% 27.78/4.77 % (2203679)------------------------------
% 27.78/4.77 % (2203679)------------------------------
% 27.78/4.77 % (2203613)Success in time 3.885 s
% 27.78/4.77 % Vampire exiting
%------------------------------------------------------------------------------