%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 01:21:28 PM UTC 2026
% Result : Theorem 47.24s 11.38s
% Output : CNFRefutation 47.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 249 ( 19 unt; 0 def)
% Number of atoms : 633 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 695 ( 311 ~; 305 |; 52 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 669 ( 0 sgn 643 !; 26 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD4) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD6) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD7) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> perp(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD10) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( coll(X2,X3,X1)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
& cyclic(X0,X1,X2,X5)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
fof(f54,axiom,
! [X0,X1,X2,X3] :
( ( coll(X3,X0,X2)
& circle(X3,X0,X1,X2) )
=> perp(X0,X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD53) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(f65,axiom,
! [X0,X1,X2,X3,X4] :
( ( para(X0,X3,X1,X2)
& para(X0,X2,X1,X3)
& midp(X4,X0,X1) )
=> midp(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(f68,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
fof(f69,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( circle(X7,X2,X8,X11)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X1,X5)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X9)
& circle(X3,X0,X1,X2) )
=> perp(X5,X8,X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012018) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( circle(X7,X2,X8,X11)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X1,X5)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X9)
& circle(X3,X0,X1,X2) )
=> perp(X5,X8,X8,X3) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( circle(X7,X2,X8,X11)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X1,X5)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X9)
& circle(X3,X0,X1,X2)
& ~ perp(X5,X8,X8,X3) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( circle(X7,X2,X8,X11)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X1,X5)
& coll(X5,X1,X4)
& coll(X5,X0,X2)
& circle(X3,X0,X4,X9)
& circle(X3,X0,X1,X2)
& ~ perp(X5,X8,X8,X3) ),
inference(flattening,[],[f98]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(ennf_transformation,[],[f68]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f142]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f10]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
? [X4] :
( ~ circle(X3,X0,X1,X2)
| perp(X4,X0,X0,X3) ),
inference(ennf_transformation,[],[f87]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(flattening,[],[f159]) ).
fof(f175,plain,
! [X0,X1,X2,X3,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(ennf_transformation,[],[f65]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(flattening,[],[f175]) ).
fof(f181,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f40]) ).
fof(f182,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f39]) ).
fof(f183,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f6]) ).
fof(f184,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f183]) ).
fof(f185,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f196,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f197,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f206,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(ennf_transformation,[],[f44]) ).
fof(f207,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(flattening,[],[f206]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f43]) ).
fof(f209,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f208]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(ennf_transformation,[],[f17]) ).
fof(f214,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f213]) ).
fof(f220,plain,
( circle(sK7,sK2,sK8,sK11)
& circle(sK6,sK0,sK8,sK10)
& circle(sK7,sK2,sK4,sK5)
& circle(sK6,sK0,sK1,sK5)
& coll(sK5,sK1,sK4)
& coll(sK5,sK0,sK2)
& circle(sK3,sK0,sK4,sK9)
& circle(sK3,sK0,sK1,sK2)
& ~ perp(sK5,sK8,sK8,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8),skolemize(X9,sK9),skolemize(X10,sK10),skolemize(X11,sK11)],[f99]) ).
fof(f236,plain,
! [X0,X1,X2,X3] :
( ~ circle(X3,X0,X1,X2)
| perp(sK27(X0,X1,X2,X3),X0,X0,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X4,sK27(X0,X1,X2,X3))],[f158]) ).
fof(f240,plain,
circle(sK6,sK0,sK8,sK10),
inference(cnf_transformation,[],[f220]) ).
fof(f242,plain,
circle(sK6,sK0,sK1,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f244,plain,
coll(sK5,sK0,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f246,plain,
circle(sK3,sK0,sK1,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f247,plain,
~ perp(sK5,sK8,sK8,sK3),
inference(cnf_transformation,[],[f220]) ).
fof(f270,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f143]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f149]) ).
fof(f288,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f151]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( ~ circle(X3,X0,X1,X2)
| perp(sK27(X0,X1,X2,X3),X0,X0,X3) ),
inference(cnf_transformation,[],[f236]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f304,plain,
! [X2,X3,X0,X1,X4] :
( ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| midp(X4,X2,X3) ),
inference(cnf_transformation,[],[f176]) ).
fof(f307,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f181]) ).
fof(f308,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f182]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f184]) ).
fof(f310,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f187]) ).
fof(f319,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f196]) ).
fof(f320,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f197]) ).
fof(f327,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f207]) ).
fof(f328,plain,
! [X2,X3,X0,X1] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f209]) ).
fof(f330,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f331,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_49,negated_conjecture,
~ perp(sK5,sK8,sK8,sK3),
inference(cnf_transformation,[],[f247]) ).
tcf(c_50,negated_conjecture,
circle(sK3,sK0,sK1,sK2),
inference(cnf_transformation,[],[f246]) ).
tcf(c_52,negated_conjecture,
coll(sK5,sK0,sK2),
inference(cnf_transformation,[],[f244]) ).
tcf(c_54,negated_conjecture,
circle(sK6,sK0,sK1,sK5),
inference(cnf_transformation,[],[f242]) ).
tcf(c_56,negated_conjecture,
circle(sK6,sK0,sK8,sK10),
inference(cnf_transformation,[],[f240]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( perp(X4,X5,X2,X3)
| ~ para(X4,X5,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(sK27(X1,X2,X3,X0),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( midp(X4,X1,X3)
| ~ midp(X4,X0,X2)
| ~ para(X0,X3,X2,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f304]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f319]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( cong(X1,X2,X4,X5)
| ~ cyclic(X1,X2,X0,X5)
| ~ cyclic(X1,X2,X0,X4)
| ~ cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_149,plain,
( eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_155,plain,
( midp(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_159,plain,
( perp(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_197,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_781,plain,
perp(sK27(sK0,sK1,sK2,sK3),sK0,sK0,sK3),
inference(resolution,[status(thm)],[c_50,c_103]) ).
tcf(c_873,plain,
perp(sK27(sK0,sK1,sK5,sK6),sK0,sK0,sK6),
inference(resolution,[status(thm)],[c_54,c_103]) ).
tcf(c_2604,plain,
( coll(sK5,sK2,sK0)
| ~ coll(sK5,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_2736,plain,
! [X0: $i] :
( coll(sK0,X0,sK5)
| ~ coll(sK5,sK2,sK0)
| ~ coll(sK5,sK2,X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2738,plain,
( coll(sK2,sK5,sK0)
| ~ coll(sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2739,plain,
( coll(sK0,sK0,sK5)
| ~ coll(sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2736]) ).
tcf(c_2796,plain,
( perp(sK27(sK0,sK1,sK2,sK3),sK0,sK3,sK0)
| ~ perp(sK27(sK0,sK1,sK2,sK3),sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_2797,plain,
( perp(sK0,sK3,sK27(sK0,sK1,sK2,sK3),sK0)
| ~ perp(sK27(sK0,sK1,sK2,sK3),sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_2860,plain,
( perp(sK27(sK0,sK1,sK5,sK6),sK0,sK6,sK0)
| ~ perp(sK27(sK0,sK1,sK5,sK6),sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_2861,plain,
( perp(sK0,sK6,sK27(sK0,sK1,sK5,sK6),sK0)
| ~ perp(sK27(sK0,sK1,sK5,sK6),sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_3162,plain,
! [X0: $i] :
( coll(sK0,X0,sK2)
| ~ coll(sK2,sK5,sK0)
| ~ coll(sK2,sK5,X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_3165,plain,
( coll(sK0,sK0,sK2)
| ~ coll(sK2,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_3162]) ).
tcf(c_3226,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK3,X0,X1)
| ~ perp(sK0,sK3,sK27(sK0,sK1,sK2,sK3),sK0)
| ~ perp(sK27(sK0,sK1,sK2,sK3),sK0,X0,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_3272,plain,
coll(sK5,sK2,sK0),
inference(superposition,[status(thm)],[c_52,c_86]) ).
tcf(c_3327,plain,
! [X0: $i] :
( coll(sK0,sK5,X0)
| ~ coll(sK0,X0,sK5) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_3329,plain,
( coll(sK0,sK5,sK0)
| ~ coll(sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_3327]) ).
tcf(c_3530,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK6,X0,X1)
| ~ perp(sK0,sK6,sK27(sK0,sK1,sK5,sK6),sK0)
| ~ perp(sK27(sK0,sK1,sK5,sK6),sK0,X0,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_3739,plain,
! [X0: $i] :
( coll(sK0,X0,sK5)
| ~ coll(sK5,sK2,X0) ),
inference(superposition,[status(thm)],[c_3272,c_84]) ).
tcf(c_4343,plain,
coll(sK0,sK0,sK5),
inference(superposition,[status(thm)],[c_3272,c_3739]) ).
tcf(c_4530,plain,
coll(sK0,sK5,sK0),
inference(superposition,[status(thm)],[c_4343,c_86]) ).
tcf(c_4737,plain,
! [X0: $i] :
( coll(sK0,X0,sK0)
| ~ coll(sK0,sK5,X0) ),
inference(superposition,[status(thm)],[c_4530,c_84]) ).
tcf(c_4743,plain,
( coll(sK0,sK0,sK0)
| ~ coll(sK0,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_4737]) ).
tcf(c_4880,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(superposition,[status(thm)],[c_140,c_118]) ).
tcf(c_4883,plain,
( para(sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_4880]) ).
tcf(c_5123,plain,
( perp(sK0,sK1,sK1,sK2)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_50,c_104]) ).
tcf(c_5127,plain,
( perp(sK0,sK8,sK8,sK10)
| ~ coll(sK6,sK0,sK10) ),
inference(superposition,[status(thm)],[c_56,c_104]) ).
tcf(c_5147,plain,
( perp(sK0,sK1,sK1,sK2)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_50,c_104]) ).
tcf(c_5149,plain,
( perp(sK0,sK1,sK1,sK5)
| ~ coll(sK6,sK0,sK5) ),
inference(superposition,[status(thm)],[c_54,c_104]) ).
tcf(c_5367,plain,
( perp(sK1,sK2,sK0,sK1)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_5123,c_99]) ).
tcf(c_5386,plain,
( perp(sK1,sK2,sK0,sK1)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_5147,c_99]) ).
tcf(c_5645,plain,
( perp(sK8,sK10,sK0,sK8)
| ~ coll(sK6,sK0,sK10) ),
inference(superposition,[status(thm)],[c_5127,c_99]) ).
tcf(c_6378,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK1,X0,X1)
| ~ coll(sK3,sK0,sK2)
| ~ perp(sK1,sK2,X0,X1) ),
inference(superposition,[status(thm)],[c_5123,c_98]) ).
tcf(c_6382,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK8,X0,X1)
| ~ coll(sK6,sK0,sK10)
| ~ perp(sK8,sK10,X0,X1) ),
inference(superposition,[status(thm)],[c_5127,c_98]) ).
tcf(c_6388,plain,
! [X0: $i,X1: $i] :
( para(sK1,sK2,X0,X1)
| ~ coll(sK3,sK0,sK2)
| ~ perp(sK0,sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_5367,c_98]) ).
tcf(c_6459,plain,
! [X0: $i,X1: $i] :
( para(sK1,sK2,X0,X1)
| ~ coll(sK3,sK0,sK2)
| ~ perp(sK0,sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_5386,c_98]) ).
tcf(c_6631,plain,
( perp(sK5,sK8,sK8,sK3)
| ~ perp(sK8,sK3,sK5,sK8) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_7284,plain,
( para(sK0,sK3,sK3,sK0)
| ~ perp(sK0,sK3,sK27(sK0,sK1,sK2,sK3),sK0)
| ~ perp(sK27(sK0,sK1,sK2,sK3),sK0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_3226]) ).
tcf(c_7598,plain,
( para(sK0,sK6,sK6,sK0)
| ~ perp(sK0,sK6,sK27(sK0,sK1,sK5,sK6),sK0)
| ~ perp(sK27(sK0,sK1,sK5,sK6),sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_3530]) ).
tcf(c_11434,plain,
( para(sK0,sK1,sK0,sK1)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_5367,c_6378]) ).
tcf(c_12862,plain,
( para(sK0,sK8,sK0,sK8)
| ~ coll(sK6,sK0,sK10) ),
inference(superposition,[status(thm)],[c_5645,c_6382]) ).
tcf(c_14001,plain,
( coll(sK6,sK0,sK10)
| ~ coll(sK6,sK10,sK0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_14017,plain,
( coll(sK6,sK0,sK5)
| ~ coll(sK6,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_18204,plain,
! [X0: $i,X1: $i] :
( coll(sK0,X1,sK3)
| ~ coll(sK3,X0,sK0)
| ~ coll(sK3,X0,X1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_18205,plain,
( coll(sK0,sK0,sK3)
| ~ coll(sK3,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_18204]) ).
tcf(c_19961,plain,
! [X0: $i] :
( coll(sK6,sK10,sK0)
| ~ coll(sK0,X0,sK10)
| ~ coll(sK0,X0,sK6) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_19962,plain,
( coll(sK6,sK10,sK0)
| ~ coll(sK0,sK0,sK10)
| ~ coll(sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_19961]) ).
tcf(c_20029,plain,
! [X0: $i] :
( coll(sK6,sK5,sK0)
| ~ coll(sK0,X0,sK6)
| ~ coll(sK0,X0,sK5) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_20030,plain,
( coll(sK6,sK5,sK0)
| ~ coll(sK0,sK0,sK6)
| ~ coll(sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_20029]) ).
tcf(c_20505,plain,
! [X0: $i] :
( coll(sK10,X0,sK0)
| ~ para(sK10,X0,sK10,sK0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_20506,plain,
( coll(sK10,sK0,sK0)
| ~ para(sK10,sK0,sK10,sK0) ),
inference(instantiation,[status(thm)],[c_20505]) ).
tcf(c_20978,plain,
! [X0: $i,X1: $i] :
( coll(sK3,X0,X1)
| ~ para(sK3,X0,sK3,X1) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_20979,plain,
( coll(sK3,sK0,sK0)
| ~ para(sK3,sK0,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_20978]) ).
tcf(c_21095,plain,
! [X0: $i,X1: $i] :
( coll(sK6,X0,X1)
| ~ para(sK6,X0,sK6,X1) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_21096,plain,
( coll(sK6,sK0,sK0)
| ~ para(sK6,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_21095]) ).
tcf(c_27848,plain,
! [X0: $i] :
( midp(X0,sK1,sK1)
| ~ coll(sK3,sK0,sK2)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK1,sK0,sK1) ),
inference(superposition,[status(thm)],[c_11434,c_114]) ).
tcf(c_27866,plain,
( midp(sK0,sK1,sK1)
| ~ midp(sK0,sK0,sK0)
| ~ coll(sK3,sK0,sK2)
| ~ para(sK0,sK1,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_27848]) ).
tcf(c_28029,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X2,sK10)
| ~ coll(sK10,X0,X2)
| ~ coll(sK10,X0,X1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_28030,plain,
( coll(sK0,sK0,sK10)
| ~ coll(sK10,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_28029]) ).
tcf(c_29055,plain,
! [X0: $i] :
( midp(X0,sK8,sK8)
| ~ coll(sK6,sK0,sK10)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK8,sK0,sK8) ),
inference(superposition,[status(thm)],[c_12862,c_114]) ).
tcf(c_29072,plain,
( midp(sK0,sK8,sK8)
| ~ midp(sK0,sK0,sK0)
| ~ coll(sK6,sK0,sK10)
| ~ para(sK0,sK8,sK0,sK8) ),
inference(instantiation,[status(thm)],[c_29055]) ).
tcf(c_31728,plain,
! [X0: $i,X1: $i] :
( coll(sK0,X1,sK6)
| ~ coll(sK6,X0,sK0)
| ~ coll(sK6,X0,X1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_31729,plain,
( coll(sK0,sK0,sK6)
| ~ coll(sK6,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_31728]) ).
tcf(c_33734,plain,
( perp(sK0,sK1,sK1,sK2)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_50,c_104]) ).
tcf(c_33736,plain,
( perp(sK0,sK1,sK1,sK5)
| ~ coll(sK6,sK0,sK5) ),
inference(superposition,[status(thm)],[c_54,c_104]) ).
tcf(c_33769,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,X0,X2,X1)
| ~ midp(X0,X2,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_94]) ).
tcf(c_33796,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,X0,X2,X1)
| ~ midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_122,c_33769]) ).
tcf(c_33885,plain,
( perp(sK1,sK2,sK0,sK1)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_33734,c_99]) ).
tcf(c_34166,plain,
! [X0: $i,X1: $i] :
( para(sK1,sK2,X0,X1)
| ~ coll(sK3,sK0,sK2)
| ~ perp(sK0,sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_33885,c_98]) ).
tcf(c_36115,plain,
( para(sK1,sK2,sK1,sK5)
| ~ coll(sK6,sK0,sK5)
| ~ coll(sK3,sK0,sK2) ),
inference(superposition,[status(thm)],[c_33736,c_34166]) ).
tcf(c_53809,plain,
( coll(sK3,sK0,sK2)
| ~ coll(sK3,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_53988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X3,X4,X5)
| ~ perp(X0,X3,sK27(X0,X1,X2,X3),X0)
| ~ perp(sK27(X0,X1,X2,X3),X0,X4,X5) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_54294,plain,
! [X0: $i] :
( coll(sK3,sK2,sK0)
| ~ coll(sK0,X0,sK2)
| ~ coll(sK0,X0,sK3) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_54295,plain,
( coll(sK3,sK2,sK0)
| ~ coll(sK0,sK0,sK2)
| ~ coll(sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_54294]) ).
tcf(c_55519,plain,
( para(sK0,sK3,sK0,sK3)
| ~ perp(sK0,sK3,sK27(sK0,sK1,sK2,sK3),sK0)
| ~ perp(sK27(sK0,sK1,sK2,sK3),sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_53988]) ).
tcf(c_55707,plain,
! [X0: $i,X1: $i] :
( eqangle(sK0,sK3,X0,X1,sK0,sK3,X0,X1)
| ~ para(sK0,sK3,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_55710,plain,
( eqangle(sK0,sK3,sK0,sK0,sK0,sK3,sK0,sK0)
| ~ para(sK0,sK3,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_55707]) ).
tcf(c_59728,plain,
( para(sK3,sK0,sK0,sK3)
| ~ para(sK0,sK3,sK3,sK0) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_59923,plain,
( para(sK6,sK0,sK0,sK6)
| ~ para(sK0,sK6,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_60676,plain,
! [X0: $i] :
( cyclic(sK3,X0,sK0,sK0)
| ~ coll(sK0,sK0,X0)
| ~ eqangle(sK0,sK3,sK0,X0,sK0,sK3,sK0,X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_60677,plain,
( cyclic(sK3,sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ eqangle(sK0,sK3,sK0,sK0,sK0,sK3,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_60676]) ).
tcf(c_63087,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,sK0,X2,X1)
| ~ cyclic(sK3,X0,sK0,X2)
| ~ cyclic(sK3,X0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_63094,plain,
( cyclic(sK0,sK0,sK0,sK0)
| ~ cyclic(sK3,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_63087]) ).
tcf(c_67030,plain,
! [X0: $i,X1: $i] :
( para(sK3,X0,sK3,X1)
| ~ para(sK3,X0,X1,sK3) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_67031,plain,
( para(sK3,sK0,sK3,sK0)
| ~ para(sK3,sK0,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_67030]) ).
tcf(c_67032,plain,
! [X0: $i,X1: $i] :
( para(sK6,X0,sK6,X1)
| ~ para(sK6,X0,X1,sK6) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_67033,plain,
( para(sK6,sK0,sK6,sK0)
| ~ para(sK6,sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_67032]) ).
tcf(c_67533,plain,
! [X0: $i,X1: $i,X2: $i] :
( eqangle(X0,X1,sK10,X1,X0,X2,sK10,X1)
| ~ para(X0,X1,X0,X2) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_67534,plain,
( eqangle(sK0,sK0,sK10,sK0,sK0,sK0,sK10,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_67533]) ).
tcf(c_67838,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK10,X0,sK10,sK0)
| ~ eqangle(sK10,X0,X1,X2,sK10,sK0,X1,X2) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_67839,plain,
( para(sK10,sK0,sK10,sK0)
| ~ eqangle(sK10,sK0,sK0,sK0,sK10,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_67838]) ).
tcf(c_68046,plain,
! [X0: $i,X1: $i] :
( perp(sK8,sK3,sK5,sK8)
| ~ para(sK8,sK3,X0,X1)
| ~ perp(X0,X1,sK5,sK8) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_68047,plain,
( perp(sK8,sK3,sK5,sK8)
| ~ para(sK8,sK3,sK0,sK0)
| ~ perp(sK0,sK0,sK5,sK8) ),
inference(instantiation,[status(thm)],[c_68046]) ).
tcf(c_69420,plain,
! [X0: $i,X1: $i,X2: $i] :
( eqangle(sK10,sK0,X1,sK0,sK10,X0,X1,X2)
| ~ eqangle(sK10,sK0,sK10,X0,X1,sK0,X1,X2) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_69421,plain,
( eqangle(sK10,sK0,sK0,sK0,sK10,sK0,sK0,sK0)
| ~ eqangle(sK10,sK0,sK10,sK0,sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_69420]) ).
tcf(c_69488,plain,
! [X0: $i,X1: $i,X2: $i] :
( eqangle(X0,X1,X0,X2,sK10,X1,sK10,X2)
| ~ eqangle(X0,X1,sK10,X1,X0,X2,sK10,X2) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_69489,plain,
( eqangle(sK0,sK0,sK0,sK0,sK10,sK0,sK10,sK0)
| ~ eqangle(sK0,sK0,sK10,sK0,sK0,sK0,sK10,sK0) ),
inference(instantiation,[status(thm)],[c_69488]) ).
tcf(c_69870,plain,
! [X0: $i,X1: $i] :
( eqangle(sK10,sK0,sK10,X1,X0,sK0,X0,X1)
| ~ eqangle(X0,sK0,X0,X1,sK10,sK0,sK10,X1) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_69871,plain,
( eqangle(sK10,sK0,sK10,sK0,sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK10,sK0,sK10,sK0) ),
inference(instantiation,[status(thm)],[c_69870]) ).
tcf(c_77413,plain,
! [X0: $i,X1: $i] :
( para(sK1,sK2,X0,X1)
| ~ perp(sK0,sK1,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_6459,c_52,c_781,c_2604,c_2738,c_2797,c_2796,c_3165,c_6388,c_7284,c_18205,c_20979,c_53809,c_54295,c_59728,c_67031]) ).
tcf(c_77421,plain,
( para(sK1,sK2,sK1,sK5)
| ~ coll(sK6,sK0,sK5) ),
inference(superposition,[status(thm)],[c_5149,c_77413]) ).
tcf(c_77651,plain,
para(sK1,sK2,sK1,sK5),
inference(global_subsumption_just,[status(thm)],[c_77421,c_52,c_781,c_873,c_2604,c_2738,c_2739,c_2797,c_2796,c_2861,c_2860,c_3165,c_7284,c_7598,c_14017,c_18205,c_20030,c_20979,c_21096,c_31729,c_36115,c_53809,c_54295,c_59728,c_59923,c_67031,c_67033]) ).
tcf(c_77653,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK1,sK5)
| ~ para(X0,X1,sK1,sK2) ),
inference(superposition,[status(thm)],[c_77651,c_119]) ).
tcf(c_77657,plain,
para(sK1,sK5,sK1,sK2),
inference(superposition,[status(thm)],[c_77651,c_120]) ).
tcf(c_78613,plain,
para(sK1,sK5,sK1,sK5),
inference(superposition,[status(thm)],[c_77657,c_77653]) ).
tcf(c_81587,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK1,sK1)
| ~ para(sK1,sK5,sK1,sK5) ),
inference(superposition,[status(thm)],[c_78613,c_114]) ).
tcf(c_81595,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_81587,c_78613]) ).
tcf(c_81598,plain,
( midp(sK0,sK5,sK5)
| ~ midp(sK0,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_81595]) ).
tcf(c_112074,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X2,sK3,sK3)
| ~ midp(X2,X0,X1)
| ~ para(X0,sK3,X1,sK3) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_112075,plain,
( midp(sK0,sK3,sK3)
| ~ midp(sK0,sK0,sK0)
| ~ para(sK0,sK3,sK0,sK3) ),
inference(instantiation,[status(thm)],[c_112074]) ).
tcf(c_112118,plain,
! [X0: $i,X1: $i] :
( para(sK8,sK3,X0,X1)
| ~ para(X0,X1,sK8,sK3) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_112119,plain,
( para(sK8,sK3,sK0,sK0)
| ~ para(sK0,sK0,sK8,sK3) ),
inference(instantiation,[status(thm)],[c_112118]) ).
tcf(c_113623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,sK8,sK3)
| ~ perp(X2,X3,sK8,sK3)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_113624,plain,
( para(sK0,sK0,sK8,sK3)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK8,sK3) ),
inference(instantiation,[status(thm)],[c_113623]) ).
tcf(c_114145,plain,
! [X0: $i] :
( perp(X0,X0,sK5,sK8)
| ~ midp(X0,sK8,sK8)
| ~ midp(X0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_33796]) ).
tcf(c_114146,plain,
( perp(sK0,sK0,sK5,sK8)
| ~ midp(sK0,sK8,sK8)
| ~ midp(sK0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_114145]) ).
tcf(c_115755,plain,
! [X0: $i] :
( perp(X0,X0,sK8,sK3)
| ~ midp(X0,sK3,sK3)
| ~ midp(X0,sK8,sK8) ),
inference(instantiation,[status(thm)],[c_33796]) ).
tcf(c_115756,plain,
( perp(sK0,sK0,sK8,sK3)
| ~ midp(sK0,sK3,sK3)
| ~ midp(sK0,sK8,sK8) ),
inference(instantiation,[status(thm)],[c_115755]) ).
tcf(c_115757,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_115756,c_114146,c_113624,c_112119,c_112075,c_81598,c_69871,c_69489,c_69421,c_68047,c_67839,c_67534,c_67033,c_67031,c_63094,c_60677,c_59923,c_59728,c_55710,c_55519,c_54295,c_53809,c_31729,c_29072,c_28030,c_27866,c_21096,c_20979,c_20506,c_19962,c_18205,c_14001,c_12862,c_11434,c_7598,c_7284,c_6631,c_4883,c_4743,c_3329,c_3165,c_2860,c_2861,c_2796,c_2797,c_2739,c_2738,c_2604,c_873,c_781,c_197,c_159,c_155,c_149,c_49,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 12:26:38 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 47.24/11.38 % SZS status Started for theBenchmark.p
% 47.24/11.38 % SZS status Theorem for theBenchmark.p
% 47.24/11.38
% 47.24/11.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 47.24/11.38
% 47.24/11.38 % ------ iProver source info
% 47.24/11.38
% 47.24/11.38 % git: date: 2026-07-19 20:42:38 +0200
% 47.24/11.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 47.24/11.38 % git: non_committed_changes: false
% 47.24/11.38
% 47.24/11.38 % ------ Parsing...
% 47.24/11.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 47.24/11.38
% 47.24/11.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 47.24/11.38
% 47.24/11.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 47.24/11.38 % ------ Proving...
% 47.24/11.38 % ------ Problem Properties
% 47.24/11.38
% 47.24/11.38 %
% 47.24/11.38 % clauses 96
% 47.24/11.38 % conjectures 9
% 47.24/11.38 % EPR 63
% 47.24/11.38 % Horn 91
% 47.24/11.38 % unary 9
% 47.24/11.38 % binary 24
% 47.24/11.38 % lits 265
% 47.24/11.38 % lits eq 0
% 47.24/11.38 % fd_pure 0
% 47.24/11.38 % fd_pseudo 0
% 47.24/11.38 % fd_cond 0
% 47.24/11.38 % fd_pseudo_cond 0
% 47.24/11.38 % AC symbols 0
% 47.24/11.38
% 47.24/11.38 % ------ Schedule dynamic 5 is on
% 47.24/11.38
% 47.24/11.38 % ------ no equalities: superposition off
% 47.24/11.38
% 47.24/11.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 47.24/11.38
% 47.24/11.38
% 47.24/11.38 % ------
% 47.24/11.38 % Current options:
% 47.24/11.38 % ------
% 47.24/11.38
% 47.24/11.38
% 47.24/11.38 %
% 47.24/11.38
% 47.24/11.38 % ------ Proving...
% 47.24/11.38 % Proof_search_loop: time out after: 7594 full_loop iterations
% 47.24/11.38
% 47.24/11.38 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 47.24/11.38
% 47.24/11.38
% 47.24/11.38 % ------
% 47.24/11.38 % Current options:
% 47.24/11.38 % ------
% 47.24/11.38
% 47.24/11.38
% 47.24/11.38 %
% 47.24/11.38
% 47.24/11.38 % ------ Proving...
% 47.24/11.38 %
% 47.24/11.38
% 47.24/11.38 % SZS status Theorem for theBenchmark.p
% 47.24/11.38
% 47.24/11.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 47.24/11.39
% 47.24/11.39
%------------------------------------------------------------------------------