%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 01:21:30 PM UTC 2026
% Result : Theorem 50.13s 9.88s
% Output : CNFRefutation 50.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of formulae : 323 ( 34 unt; 0 def)
% Number of atoms : 842 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 955 ( 436 ~; 430 |; 56 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 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 : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 799 ( 0 sgn 783 !; 16 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD10) ).
fof(f11,axiom,
! [X0,X1,X2] :
( midp(X2,X1,X0)
=> midp(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD11) ).
fof(f12,axiom,
! [X0,X1,X2,X3] :
( ( cong(X3,X0,X3,X2)
& cong(X3,X0,X3,X1) )
=> circle(X3,X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD12) ).
fof(f13,axiom,
! [X0,X1,X2,X3,X4] :
( ( cong(X4,X0,X4,X3)
& cong(X4,X0,X4,X2)
& cong(X4,X0,X4,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD13) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD14) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD15) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD16) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
fof(f45,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X0,X2)
& midp(X3,X0,X1) )
=> para(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD44) ).
fof(f46,axiom,
! [X0,X1,X2,X3,X4] :
( ( coll(X4,X0,X2)
& para(X3,X4,X1,X2)
& midp(X3,X0,X1) )
=> midp(X4,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD45) ).
fof(f49,axiom,
! [X0,X1,X2,X3,X4] :
( ( perp(X3,X0,X0,X4)
& circle(X3,X0,X1,X2) )
=> eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD48) ).
fof(f50,axiom,
! [X0,X1,X2,X3,X4] :
( ( eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
& circle(X3,X0,X1,X2) )
=> perp(X3,X0,X0,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD49) ).
fof(f54,axiom,
! [X0,X1,X2,X3] :
( ( coll(X3,X0,X2)
& circle(X3,X0,X1,X2) )
=> perp(X0,X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD53) ).
fof(f56,axiom,
! [X0,X1,X2,X3] :
( ( perp(X3,X2,X0,X1)
& midp(X2,X0,X1) )
=> cong(X3,X0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD55) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(f64,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X2,X3)
& midp(X4,X0,X1) )
=> para(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD63) ).
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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(f68,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
fof(f69,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(f70,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD69) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( coll(X7,X0,X1)
& coll(X7,X3,X5)
& coll(X6,X0,X2)
& coll(X6,X3,X4)
& midp(X5,X2,X0)
& midp(X4,X1,X0)
& circle(X3,X0,X1,X2) )
=> cyclic(X7,X1,X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214031) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( coll(X7,X0,X1)
& coll(X7,X3,X5)
& coll(X6,X0,X2)
& coll(X6,X3,X4)
& midp(X5,X2,X0)
& midp(X4,X1,X0)
& circle(X3,X0,X1,X2) )
=> cyclic(X7,X1,X2,X6) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( coll(X7,X0,X1)
& coll(X7,X3,X5)
& coll(X6,X0,X2)
& coll(X6,X3,X4)
& midp(X5,X2,X0)
& midp(X4,X1,X0)
& circle(X3,X0,X1,X2)
& ~ cyclic(X7,X1,X2,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( coll(X7,X0,X1)
& coll(X7,X3,X5)
& coll(X6,X0,X2)
& coll(X6,X3,X4)
& midp(X5,X2,X0)
& midp(X4,X1,X0)
& circle(X3,X0,X1,X2)
& ~ cyclic(X7,X1,X2,X6) ),
inference(flattening,[],[f98]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f70]) ).
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(f126,plain,
! [X0,X1,X2,X3,X4] :
( ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1)
| midp(X4,X0,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4] :
( ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1)
| midp(X4,X0,X2) ),
inference(flattening,[],[f126]) ).
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(f136,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f137,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(f138,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,[],[f137]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(flattening,[],[f141]) ).
fof(f145,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(flattening,[],[f153]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2)
| perp(X3,X0,X0,X4) ),
inference(ennf_transformation,[],[f50]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2)
| perp(X3,X0,X0,X4) ),
inference(flattening,[],[f159]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( ~ perp(X3,X0,X0,X4)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( ~ perp(X3,X0,X0,X4)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
inference(flattening,[],[f161]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1)
| circle(X3,X0,X1,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1)
| circle(X3,X0,X1,X2) ),
inference(flattening,[],[f163]) ).
fof(f171,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(f172,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,[],[f171]) ).
fof(f173,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(f174,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,[],[f173]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f178,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(f179,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f178]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f183,plain,
! [X0,X1,X2,X3,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f13]) ).
fof(f184,plain,
! [X0,X1,X2,X3,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f183]) ).
fof(f193,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(f194,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(f195,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(f196,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(flattening,[],[f195]) ).
fof(f197,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(f198,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f197]) ).
fof(f205,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(f206,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f220,plain,
( coll(sK7,sK0,sK1)
& coll(sK7,sK3,sK5)
& coll(sK6,sK0,sK2)
& coll(sK6,sK3,sK4)
& midp(sK5,sK2,sK0)
& midp(sK4,sK1,sK0)
& circle(sK3,sK0,sK1,sK2)
& ~ cyclic(sK7,sK1,sK2,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f99]) ).
fof(f239,plain,
coll(sK7,sK0,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
coll(sK6,sK0,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f243,plain,
midp(sK5,sK2,sK0),
inference(cnf_transformation,[],[f220]) ).
fof(f244,plain,
midp(sK4,sK1,sK0),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
circle(sK3,sK0,sK1,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f246,plain,
~ cyclic(sK7,sK1,sK2,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f272,plain,
! [X2,X3,X0,X1,X4] :
( ~ coll(X4,X0,X2)
| ~ para(X3,X4,X1,X2)
| ~ midp(X3,X0,X1)
| midp(X4,X0,X2) ),
inference(cnf_transformation,[],[f127]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f136]) ).
fof(f281,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,[],[f138]) ).
fof(f282,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f285,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f154]) ).
fof(f293,plain,
! [X2,X3,X0,X1,X4] :
( ~ eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2)
| perp(X3,X0,X0,X4) ),
inference(cnf_transformation,[],[f160]) ).
fof(f294,plain,
! [X2,X3,X0,X1,X4] :
( ~ perp(X3,X0,X0,X4)
| ~ circle(X3,X0,X1,X2)
| eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
inference(cnf_transformation,[],[f162]) ).
fof(f295,plain,
! [X2,X3,X0,X1] :
( ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1)
| circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f164]) ).
fof(f300,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,[],[f172]) ).
fof(f301,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,[],[f174]) ).
fof(f303,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f177]) ).
fof(f304,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f179]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f180]) ).
fof(f306,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f182]) ).
fof(f308,plain,
! [X2,X3,X0,X1,X4] :
( ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f184]) ).
fof(f315,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f193]) ).
fof(f316,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f194]) ).
fof(f317,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,[],[f196]) ).
fof(f318,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,[],[f198]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f206]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f325,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_49,negated_conjecture,
~ cyclic(sK7,sK1,sK2,sK6),
inference(cnf_transformation,[],[f246]) ).
tcf(c_50,negated_conjecture,
circle(sK3,sK0,sK1,sK2),
inference(cnf_transformation,[],[f245]) ).
tcf(c_51,negated_conjecture,
midp(sK4,sK1,sK0),
inference(cnf_transformation,[],[f244]) ).
tcf(c_52,negated_conjecture,
midp(sK5,sK2,sK0),
inference(cnf_transformation,[],[f243]) ).
tcf(c_54,negated_conjecture,
coll(sK6,sK0,sK2),
inference(cnf_transformation,[],[f241]) ).
tcf(c_56,negated_conjecture,
coll(sK7,sK0,sK1),
inference(cnf_transformation,[],[f239]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( midp(X1,X4,X3)
| ~ coll(X1,X4,X3)
| ~ midp(X0,X4,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_91,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,[],[f281]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X0,X2,X0,X3)
| ~ midp(X1,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X3,X0,X4,X2)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_100,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,[],[f290]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( perp(X4,X0,X0,X1)
| ~ circle(X4,X0,X2,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X0,X3,X2) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ perp(X0,X1,X1,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_110,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,[],[f300]) ).
tcf(c_111,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,[],[f301]) ).
tcf(c_113,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,[],[f303]) ).
tcf(c_114,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,[],[f304]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_125,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,[],[f315]) ).
tcf(c_126,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,[],[f316]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_128,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,[],[f318]) ).
tcf(c_133,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,[],[f323]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_151,plain,
( eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_154,plain,
( midp(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_156,plain,
( perp(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_195,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_110]) ).
tcf(c_814,plain,
! [X0: $i] :
( perp(sK3,sK0,sK0,X0)
| ~ eqangle(sK0,X0,sK0,sK1,sK2,sK0,sK2,sK1) ),
inference(resolution,[status(thm)],[c_50,c_103]) ).
tcf(c_815,plain,
( perp(sK3,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK1,sK2,sK0,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_814]) ).
tcf(c_2035,plain,
( coll(sK4,sK1,sK0)
| ~ midp(sK4,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_2036,plain,
( coll(sK5,sK2,sK0)
| ~ midp(sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_2042,plain,
( coll(sK6,sK2,sK0)
| ~ coll(sK6,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2044,plain,
( coll(sK7,sK1,sK0)
| ~ coll(sK7,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2045,plain,
( midp(sK4,sK0,sK1)
| ~ midp(sK4,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_2046,plain,
( midp(sK5,sK0,sK2)
| ~ midp(sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_2047,plain,
( cong(sK4,sK1,sK4,sK0)
| ~ midp(sK4,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_2048,plain,
( cong(sK5,sK2,sK5,sK0)
| ~ midp(sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_2065,plain,
! [X0: $i,X1: $i] :
( para(X0,sK4,X1,sK0)
| ~ midp(sK4,sK1,sK0)
| ~ midp(X0,sK1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2066,plain,
( para(sK0,sK4,sK0,sK0)
| ~ midp(sK4,sK1,sK0)
| ~ midp(sK0,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_2065]) ).
tcf(c_2067,plain,
! [X0: $i,X1: $i] :
( para(X0,sK5,X1,sK0)
| ~ midp(sK5,sK2,sK0)
| ~ midp(X0,sK2,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2068,plain,
( para(sK0,sK5,sK0,sK0)
| ~ midp(sK5,sK2,sK0)
| ~ midp(sK0,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2067]) ).
tcf(c_2086,plain,
! [X0: $i,X1: $i] :
( midp(X0,sK1,X1)
| ~ midp(sK4,sK1,sK0)
| ~ coll(X0,sK1,X1)
| ~ para(sK4,X0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2087,plain,
( midp(sK0,sK1,sK0)
| ~ coll(sK0,sK1,sK0)
| ~ midp(sK4,sK1,sK0)
| ~ para(sK4,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2086]) ).
tcf(c_2088,plain,
! [X0: $i,X1: $i] :
( midp(X0,sK2,X1)
| ~ midp(sK5,sK2,sK0)
| ~ coll(X0,sK2,X1)
| ~ para(sK5,X0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2089,plain,
( midp(sK0,sK2,sK0)
| ~ coll(sK0,sK2,sK0)
| ~ midp(sK5,sK2,sK0)
| ~ para(sK5,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2088]) ).
tcf(c_2102,plain,
! [X0: $i,X1: $i] :
( midp(sK4,X0,X1)
| ~ midp(sK4,sK1,sK0)
| ~ para(sK1,X1,sK0,X0)
| ~ para(sK1,X0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2103,plain,
( midp(sK4,sK0,sK0)
| ~ midp(sK4,sK1,sK0)
| ~ para(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2102]) ).
tcf(c_2104,plain,
! [X0: $i,X1: $i] :
( midp(sK5,X0,X1)
| ~ midp(sK5,sK2,sK0)
| ~ para(sK2,X1,sK0,X0)
| ~ para(sK2,X0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2105,plain,
( midp(sK5,sK0,sK0)
| ~ midp(sK5,sK2,sK0)
| ~ para(sK2,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2104]) ).
tcf(c_2194,plain,
! [X0: $i] :
( perp(sK1,X0,X0,sK0)
| ~ coll(sK4,sK1,sK0)
| ~ circle(sK4,sK1,X0,sK0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_2195,plain,
( perp(sK1,sK0,sK0,sK0)
| ~ coll(sK4,sK1,sK0)
| ~ circle(sK4,sK1,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2194]) ).
tcf(c_2212,plain,
! [X0: $i] :
( perp(sK2,X0,X0,sK0)
| ~ coll(sK5,sK2,sK0)
| ~ circle(sK5,sK2,X0,sK0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_2213,plain,
( perp(sK2,sK0,sK0,sK0)
| ~ coll(sK5,sK2,sK0)
| ~ circle(sK5,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2212]) ).
tcf(c_2322,plain,
! [X0: $i] :
( coll(sK0,X0,sK6)
| ~ coll(sK6,sK2,sK0)
| ~ coll(sK6,sK2,X0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2325,plain,
( coll(sK0,sK0,sK6)
| ~ coll(sK6,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2322]) ).
tcf(c_2360,plain,
! [X0: $i] :
( coll(sK0,X0,sK7)
| ~ coll(sK7,sK1,sK0)
| ~ coll(sK7,sK1,X0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2363,plain,
( coll(sK0,sK0,sK7)
| ~ coll(sK7,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_2360]) ).
tcf(c_2368,plain,
! [X0: $i] :
( cong(X0,sK0,X0,sK1)
| ~ midp(sK4,sK0,sK1)
| ~ perp(X0,sK4,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_2369,plain,
( cong(sK0,sK0,sK0,sK1)
| ~ midp(sK4,sK0,sK1)
| ~ perp(sK0,sK4,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_2368]) ).
tcf(c_2401,plain,
! [X0: $i] :
( cong(X0,sK0,X0,sK2)
| ~ midp(sK5,sK0,sK2)
| ~ perp(X0,sK5,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_2402,plain,
( cong(sK0,sK0,sK0,sK2)
| ~ midp(sK5,sK0,sK2)
| ~ perp(sK0,sK5,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] :
( cyclic(sK1,sK0,X0,X1)
| ~ cong(sK4,sK1,sK4,sK0)
| ~ cong(sK4,sK1,sK4,X1)
| ~ cong(sK4,sK1,sK4,X0) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_2443,plain,
! [X0: $i] :
( circle(sK4,sK1,sK0,X0)
| ~ cong(sK4,sK1,sK4,sK0)
| ~ cong(sK4,sK1,sK4,X0) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_2444,plain,
( circle(sK4,sK1,sK0,sK0)
| ~ cong(sK4,sK1,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_2443]) ).
tcf(c_2447,plain,
( cyclic(sK1,sK0,sK0,sK0)
| ~ cong(sK4,sK1,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_2439]) ).
tcf(c_2468,plain,
! [X0: $i] :
( circle(sK5,sK2,sK0,X0)
| ~ cong(sK5,sK2,sK5,sK0)
| ~ cong(sK5,sK2,sK5,X0) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_2469,plain,
( circle(sK5,sK2,sK0,sK0)
| ~ cong(sK5,sK2,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_2468]) ).
tcf(c_2742,plain,
coll(sK4,sK1,sK0),
inference(superposition,[status(thm)],[c_51,c_78]) ).
tcf(c_2743,plain,
coll(sK5,sK2,sK0),
inference(superposition,[status(thm)],[c_52,c_78]) ).
tcf(c_2748,plain,
coll(sK4,sK1,sK0),
inference(superposition,[status(thm)],[c_51,c_78]) ).
tcf(c_2880,plain,
coll(sK4,sK0,sK1),
inference(superposition,[status(thm)],[c_2742,c_85]) ).
tcf(c_2882,plain,
coll(sK4,sK0,sK1),
inference(superposition,[status(thm)],[c_2748,c_85]) ).
tcf(c_2883,plain,
coll(sK1,sK4,sK0),
inference(superposition,[status(thm)],[c_2748,c_84]) ).
tcf(c_2884,plain,
coll(sK5,sK0,sK2),
inference(superposition,[status(thm)],[c_2743,c_85]) ).
tcf(c_3018,plain,
coll(sK0,sK4,sK1),
inference(superposition,[status(thm)],[c_2880,c_84]) ).
tcf(c_3076,plain,
coll(sK0,sK5,sK2),
inference(superposition,[status(thm)],[c_2884,c_84]) ).
tcf(c_3401,plain,
! [X0: $i] :
( coll(sK0,X0,sK4)
| ~ coll(sK4,sK1,X0) ),
inference(superposition,[status(thm)],[c_2742,c_83]) ).
tcf(c_3402,plain,
! [X0: $i] :
( coll(sK0,X0,sK5)
| ~ coll(sK5,sK2,X0) ),
inference(superposition,[status(thm)],[c_2743,c_83]) ).
tcf(c_3425,plain,
! [X0: $i] :
( coll(sK1,X0,sK0)
| ~ coll(sK0,sK4,X0) ),
inference(superposition,[status(thm)],[c_3018,c_83]) ).
tcf(c_3427,plain,
! [X0: $i] :
( coll(sK2,X0,sK0)
| ~ coll(sK0,sK5,X0) ),
inference(superposition,[status(thm)],[c_3076,c_83]) ).
tcf(c_3509,plain,
( coll(sK2,sK0,sK0)
| ~ coll(sK0,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_3427]) ).
tcf(c_3510,plain,
( coll(sK1,sK0,sK0)
| ~ coll(sK0,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_3425]) ).
tcf(c_3550,plain,
! [X0: $i] :
( coll(sK1,X0,sK4)
| ~ coll(sK4,sK0,X0) ),
inference(superposition,[status(thm)],[c_2882,c_83]) ).
tcf(c_3551,plain,
! [X0: $i] :
( coll(sK0,X0,sK1)
| ~ coll(sK1,sK4,X0) ),
inference(superposition,[status(thm)],[c_2883,c_83]) ).
tcf(c_4095,plain,
! [X0: $i,X1: $i] :
( para(X0,sK4,X1,sK0)
| ~ midp(X0,sK1,X1) ),
inference(superposition,[status(thm)],[c_51,c_95]) ).
tcf(c_4513,plain,
coll(sK0,sK0,sK4),
inference(superposition,[status(thm)],[c_2742,c_3401]) ).
tcf(c_4600,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(superposition,[status(thm)],[c_113,c_126]) ).
tcf(c_4604,plain,
( para(sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_4600]) ).
tcf(c_4687,plain,
coll(sK0,sK4,sK0),
inference(superposition,[status(thm)],[c_4513,c_85]) ).
tcf(c_4837,plain,
coll(sK0,sK0,sK5),
inference(superposition,[status(thm)],[c_2743,c_3402]) ).
tcf(c_4844,plain,
coll(sK0,sK5,sK0),
inference(superposition,[status(thm)],[c_4837,c_85]) ).
tcf(c_5125,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK6,sK0,X1)
| ~ coll(sK0,X1,sK6)
| ~ eqangle(sK0,X0,sK0,sK6,X1,X0,X1,sK6) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_5126,plain,
( cyclic(sK0,sK6,sK0,sK0)
| ~ coll(sK0,sK0,sK6)
| ~ eqangle(sK0,sK0,sK0,sK6,sK0,sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_5125]) ).
tcf(c_5153,plain,
! [X0: $i] :
( coll(sK0,X0,sK0)
| ~ coll(sK0,sK4,X0) ),
inference(superposition,[status(thm)],[c_4687,c_83]) ).
tcf(c_5158,plain,
( coll(sK0,sK0,sK0)
| ~ coll(sK0,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_5153]) ).
tcf(c_5221,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK7,sK0,X1)
| ~ coll(sK0,X1,sK7)
| ~ eqangle(sK0,X0,sK0,sK7,X1,X0,X1,sK7) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_5222,plain,
( cyclic(sK0,sK7,sK0,sK0)
| ~ coll(sK0,sK0,sK7)
| ~ eqangle(sK0,sK0,sK0,sK7,sK0,sK0,sK0,sK7) ),
inference(instantiation,[status(thm)],[c_5221]) ).
tcf(c_5326,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK1,X0,X1,X2)
| ~ perp(sK1,X0,X0,sK0)
| ~ perp(X0,sK0,X1,X2) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_5328,plain,
! [X0: $i] :
( perp(X0,sK0,sK1,X0)
| ~ perp(sK1,X0,X0,sK0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_5333,plain,
( perp(sK0,sK0,sK1,sK0)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5328]) ).
tcf(c_5334,plain,
( para(sK1,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5326]) ).
tcf(c_5442,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK2,X0,X1,X2)
| ~ perp(sK2,X0,X0,sK0)
| ~ perp(X0,sK0,X1,X2) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_5444,plain,
! [X0: $i] :
( perp(X0,sK0,sK2,X0)
| ~ perp(sK2,X0,X0,sK0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_5449,plain,
( perp(sK0,sK0,sK2,sK0)
| ~ perp(sK2,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5444]) ).
tcf(c_5450,plain,
( para(sK2,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK2,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5442]) ).
tcf(c_5662,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(sK0,X0,X2,X1)
| ~ cyclic(sK1,sK0,X0,X2)
| ~ cyclic(sK1,sK0,X0,X1) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_5669,plain,
( cyclic(sK0,sK0,sK0,sK0)
| ~ cyclic(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5662]) ).
tcf(c_6048,plain,
! [X0: $i,X1: $i] :
( coll(X0,sK1,X1)
| ~ coll(sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_6049,plain,
( coll(sK0,sK1,sK0)
| ~ coll(sK1,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6048]) ).
tcf(c_6050,plain,
! [X0: $i,X1: $i] :
( coll(X0,sK2,X1)
| ~ coll(sK2,X0,X1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_6051,plain,
( coll(sK0,sK2,sK0)
| ~ coll(sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6050]) ).
tcf(c_6392,plain,
! [X0: $i] :
( midp(sK4,sK2,X0)
| ~ midp(sK4,sK1,sK0)
| ~ para(sK1,sK2,sK0,X0)
| ~ para(sK1,X0,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_2102]) ).
tcf(c_6394,plain,
( midp(sK4,sK2,sK0)
| ~ midp(sK4,sK1,sK0)
| ~ para(sK1,sK0,sK0,sK2)
| ~ para(sK1,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6392]) ).
tcf(c_7020,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK4,X0,sK0,X2)
| ~ midp(sK4,X1,sK0)
| ~ midp(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_7021,plain,
( para(sK4,sK0,sK0,sK0)
| ~ midp(sK4,sK0,sK0)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_7020]) ).
tcf(c_7022,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK5,X0,sK0,X2)
| ~ midp(sK5,X1,sK0)
| ~ midp(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_7023,plain,
( para(sK5,sK0,sK0,sK0)
| ~ midp(sK5,sK0,sK0)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_7022]) ).
tcf(c_7199,plain,
! [X0: $i] :
( perp(sK0,X0,X0,sK2)
| ~ perp(sK0,X0,sK2,X0) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_7200,plain,
( perp(sK0,sK0,sK0,sK2)
| ~ perp(sK0,sK0,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_7199]) ).
tcf(c_7215,plain,
! [X0: $i] :
( perp(X0,sK4,sK0,sK1)
| ~ perp(X0,sK4,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_7216,plain,
( perp(sK0,sK4,sK0,sK1)
| ~ perp(sK0,sK4,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_7215]) ).
tcf(c_7217,plain,
! [X0: $i] :
( perp(X0,sK5,sK0,sK2)
| ~ perp(X0,sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_7218,plain,
( perp(sK0,sK5,sK0,sK2)
| ~ perp(sK0,sK5,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_7217]) ).
tcf(c_9158,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,sK4,sK1,sK0)
| ~ perp(X1,X2,sK1,sK0)
| ~ para(X0,sK4,X1,X2) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_9159,plain,
( perp(sK0,sK4,sK1,sK0)
| ~ perp(sK0,sK0,sK1,sK0)
| ~ para(sK0,sK4,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_9158]) ).
tcf(c_9160,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,sK5,sK2,sK0)
| ~ perp(X1,X2,sK2,sK0)
| ~ para(X0,sK5,X1,X2) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_9161,plain,
( perp(sK0,sK5,sK2,sK0)
| ~ perp(sK0,sK0,sK2,sK0)
| ~ para(sK0,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_9160]) ).
tcf(c_9486,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK1,sK2,X1,X2)
| ~ midp(X0,sK2,X2)
| ~ midp(X0,sK1,X1) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_9487,plain,
( para(sK1,sK2,sK0,sK0)
| ~ midp(sK0,sK2,sK0)
| ~ midp(sK0,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_9486]) ).
tcf(c_9607,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(sK4,X1,sK0)
| ~ coll(sK4,X1,sK0)
| ~ midp(X0,sK1,X2)
| ~ midp(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_4095,c_82]) ).
tcf(c_13189,plain,
( cyclic(sK7,sK1,sK2,sK6)
| ~ cyclic(sK1,sK7,sK2,sK6) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_14283,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK1,X0,sK0,sK2)
| ~ perp(X1,X2,sK0,sK2)
| ~ perp(sK1,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_14286,plain,
( para(sK1,sK0,sK0,sK2)
| ~ perp(sK0,sK0,sK0,sK2)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_14283]) ).
tcf(c_16148,plain,
! [X0: $i] :
( cyclic(sK1,sK7,sK2,sK6)
| ~ cyclic(X0,sK1,sK7,sK6)
| ~ cyclic(X0,sK1,sK7,sK2) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_16149,plain,
( cyclic(sK1,sK7,sK2,sK6)
| ~ cyclic(sK0,sK1,sK7,sK6)
| ~ cyclic(sK0,sK1,sK7,sK2) ),
inference(instantiation,[status(thm)],[c_16148]) ).
tcf(c_16553,plain,
! [X0: $i,X1: $i] :
( eqangle(sK0,X1,sK0,sK1,sK2,sK0,sK2,sK1)
| ~ circle(X0,sK0,sK1,sK2)
| ~ perp(X0,sK0,sK0,X1) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_16554,plain,
( eqangle(sK0,sK0,sK0,sK1,sK2,sK0,sK2,sK1)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ circle(sK0,sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_16553]) ).
tcf(c_18652,plain,
! [X0: $i] :
( eqangle(sK0,X0,sK0,sK1,sK2,sK0,sK2,sK1)
| ~ perp(sK3,sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_50,c_104]) ).
tcf(c_19276,plain,
( cyclic(sK0,sK1,sK0,sK2)
| ~ coll(sK0,sK2,sK1)
| ~ perp(sK3,sK0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_18652,c_111]) ).
tcf(c_21333,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK1,sK7,sK2)
| ~ cyclic(X0,X1,sK1,sK2)
| ~ cyclic(X0,X1,sK1,sK7) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_21334,plain,
( cyclic(sK0,sK1,sK7,sK2)
| ~ cyclic(sK0,sK0,sK1,sK2)
| ~ cyclic(sK0,sK0,sK1,sK7) ),
inference(instantiation,[status(thm)],[c_21333]) ).
tcf(c_23955,plain,
! [X0: $i] :
( circle(X0,sK0,sK1,sK2)
| ~ cong(X0,sK0,X0,sK2)
| ~ cong(X0,sK0,X0,sK1) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_23956,plain,
( circle(sK0,sK0,sK1,sK2)
| ~ cong(sK0,sK0,sK0,sK2)
| ~ cong(sK0,sK0,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_23955]) ).
tcf(c_24375,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK7,sK1)
| ~ cyclic(X0,X1,X2,sK1)
| ~ cyclic(X0,X1,X2,sK7) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_24376,plain,
( cyclic(sK0,sK0,sK7,sK1)
| ~ cyclic(sK0,sK0,sK0,sK1)
| ~ cyclic(sK0,sK0,sK0,sK7) ),
inference(instantiation,[status(thm)],[c_24375]) ).
tcf(c_26983,plain,
! [X0: $i] :
( eqangle(sK0,X0,sK0,sK1,sK2,sK0,sK2,sK1)
| ~ perp(sK3,sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_50,c_104]) ).
tcf(c_28707,plain,
( cyclic(sK0,sK1,sK0,sK2)
| ~ coll(sK0,sK2,sK1)
| ~ perp(sK3,sK0,sK0,sK0) ),
inference(superposition,[status(thm)],[c_26983,c_111]) ).
tcf(c_32260,plain,
( midp(sK4,sK2,sK0)
| ~ coll(sK4,sK2,sK0)
| ~ midp(sK5,sK1,sK0) ),
inference(superposition,[status(thm)],[c_52,c_9607]) ).
tcf(c_32470,plain,
midp(sK4,sK2,sK0),
inference(global_subsumption_just,[status(thm)],[c_32260,c_52,c_51,c_151,c_154,c_156,c_195,c_2035,c_2036,c_2047,c_2048,c_2087,c_2089,c_2103,c_2105,c_2195,c_2213,c_2444,c_2447,c_2469,c_3509,c_3510,c_4687,c_4844,c_5158,c_5334,c_5449,c_5450,c_5669,c_6049,c_6051,c_6394,c_7021,c_7023,c_7200,c_9487,c_14286]) ).
tcf(c_32475,plain,
midp(sK4,sK0,sK2),
inference(superposition,[status(thm)],[c_32470,c_96]) ).
tcf(c_32501,plain,
coll(sK4,sK0,sK2),
inference(superposition,[status(thm)],[c_32475,c_78]) ).
tcf(c_37847,plain,
coll(sK1,sK2,sK4),
inference(superposition,[status(thm)],[c_32501,c_3550]) ).
tcf(c_42244,plain,
coll(sK1,sK4,sK2),
inference(superposition,[status(thm)],[c_37847,c_85]) ).
tcf(c_44560,plain,
coll(sK0,sK2,sK1),
inference(superposition,[status(thm)],[c_42244,c_3551]) ).
tcf(c_52467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X1,sK6,X2,X3,X1,sK6)
| ~ para(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_52468,plain,
( eqangle(sK0,sK0,sK0,sK6,sK0,sK0,sK0,sK6)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_52467]) ).
tcf(c_52517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X1,sK7,X2,X3,X1,sK7)
| ~ para(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_52518,plain,
( eqangle(sK0,sK0,sK0,sK7,sK0,sK0,sK0,sK7)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_52517]) ).
tcf(c_56938,plain,
cyclic(sK0,sK1,sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_28707,c_52,c_51,c_151,c_154,c_156,c_195,c_815,c_2035,c_2036,c_2045,c_2046,c_2047,c_2048,c_2066,c_2068,c_2087,c_2089,c_2103,c_2105,c_2195,c_2213,c_2369,c_2402,c_2444,c_2447,c_2469,c_3509,c_3510,c_4687,c_4844,c_5158,c_5333,c_5334,c_5449,c_5450,c_5669,c_6049,c_6051,c_7021,c_7023,c_7216,c_7218,c_9159,c_9161,c_16554,c_19276,c_23956,c_44560]) ).
tcf(c_56943,plain,
cyclic(sK0,sK0,sK1,sK2),
inference(superposition,[status(thm)],[c_56938,c_116]) ).
tcf(c_67123,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,sK7,X2,sK1)
| ~ cyclic(X0,X1,sK7,sK1)
| ~ cyclic(X0,X1,sK7,X2) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_67829,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK1,sK7)
| ~ cyclic(X0,X1,X2,sK1)
| ~ cyclic(X0,X1,X2,sK7) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_67830,plain,
( cyclic(sK0,sK0,sK1,sK7)
| ~ cyclic(sK0,sK0,sK0,sK1)
| ~ cyclic(sK0,sK0,sK0,sK7) ),
inference(instantiation,[status(thm)],[c_67829]) ).
tcf(c_67909,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK7,sK1,X1)
| ~ cyclic(X0,sK7,X1,sK1) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_68288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,X3,sK7)
| ~ cyclic(X0,X1,X2,sK7)
| ~ cyclic(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_68291,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK7)
| ~ cyclic(X0,X1,sK7,X2) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_68292,plain,
( cyclic(sK0,sK0,sK0,sK7)
| ~ cyclic(sK0,sK0,sK7,sK0) ),
inference(instantiation,[status(thm)],[c_68291]) ).
tcf(c_69457,plain,
! [X0: $i] :
( cyclic(X0,sK1,sK7,sK6)
| ~ cyclic(X0,sK7,sK1,sK6) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_69458,plain,
( cyclic(sK0,sK1,sK7,sK6)
| ~ cyclic(sK0,sK7,sK1,sK6) ),
inference(instantiation,[status(thm)],[c_69457]) ).
tcf(c_70861,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK7,X2)
| ~ cyclic(X0,sK7,X1,X2) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_70862,plain,
( cyclic(sK0,sK0,sK7,sK0)
| ~ cyclic(sK0,sK7,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_70861]) ).
tcf(c_70863,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK7,X2)
| ~ cyclic(X0,X1,X2,sK7) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_72344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cyclic(X1,X2,X3,sK1)
| ~ cong(X0,X1,X0,sK1)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_72345,plain,
( cyclic(sK0,sK0,sK0,sK1)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_72344]) ).
tcf(c_73953,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK7,sK6,sK1)
| ~ cyclic(X0,X1,sK7,sK6)
| ~ cyclic(X0,X1,sK7,sK1) ),
inference(instantiation,[status(thm)],[c_67123]) ).
tcf(c_73954,plain,
( cyclic(sK0,sK7,sK6,sK1)
| ~ cyclic(sK0,sK0,sK7,sK6)
| ~ cyclic(sK0,sK0,sK7,sK1) ),
inference(instantiation,[status(thm)],[c_73953]) ).
tcf(c_74418,plain,
! [X0: $i] :
( cyclic(X0,sK7,sK1,sK6)
| ~ cyclic(X0,sK7,sK6,sK1) ),
inference(instantiation,[status(thm)],[c_67909]) ).
tcf(c_74419,plain,
( cyclic(sK0,sK7,sK1,sK6)
| ~ cyclic(sK0,sK7,sK6,sK1) ),
inference(instantiation,[status(thm)],[c_74418]) ).
tcf(c_87100,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK6,sK7)
| ~ cyclic(X0,X1,X2,sK6)
| ~ cyclic(X0,X1,X2,sK7) ),
inference(instantiation,[status(thm)],[c_68288]) ).
tcf(c_87101,plain,
( cyclic(sK0,sK0,sK6,sK7)
| ~ cyclic(sK0,sK0,sK0,sK6)
| ~ cyclic(sK0,sK0,sK0,sK7) ),
inference(instantiation,[status(thm)],[c_87100]) ).
tcf(c_88622,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,X2,sK6)
| ~ cyclic(X0,X1,sK6,X2) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_88623,plain,
( cyclic(sK0,sK0,sK0,sK6)
| ~ cyclic(sK0,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_88622]) ).
tcf(c_100157,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK7,sK6)
| ~ cyclic(X0,X1,sK6,sK7) ),
inference(instantiation,[status(thm)],[c_70863]) ).
tcf(c_100158,plain,
( cyclic(sK0,sK0,sK7,sK6)
| ~ cyclic(sK0,sK0,sK6,sK7) ),
inference(instantiation,[status(thm)],[c_100157]) ).
tcf(c_136009,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X0,X1,sK6,X2)
| ~ cyclic(X0,sK6,X1,X2) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_136010,plain,
( cyclic(sK0,sK0,sK6,sK0)
| ~ cyclic(sK0,sK6,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_136009]) ).
tcf(c_136011,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_136010,c_100158,c_88623,c_87101,c_74419,c_73954,c_72345,c_70862,c_69458,c_68292,c_67830,c_56943,c_52518,c_52468,c_24376,c_21334,c_16149,c_13189,c_9159,c_7216,c_7021,c_6049,c_5669,c_5334,c_5333,c_5222,c_5158,c_5126,c_4687,c_4604,c_3510,c_2447,c_2444,c_2369,c_2363,c_2325,c_2195,c_2103,c_2087,c_2066,c_2047,c_2045,c_2044,c_2042,c_2035,c_195,c_156,c_154,c_151,c_49,c_51,c_54,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 12:23:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 50.13/9.88 % SZS status Started for theBenchmark.p
% 50.13/9.88 % SZS status Theorem for theBenchmark.p
% 50.13/9.88
% 50.13/9.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.13/9.88
% 50.13/9.88 % ------ iProver source info
% 50.13/9.88
% 50.13/9.88 % git: date: 2026-07-19 20:42:38 +0200
% 50.13/9.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.13/9.88 % git: non_committed_changes: false
% 50.13/9.88
% 50.13/9.88 % ------ Parsing...
% 50.13/9.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.13/9.88
% 50.13/9.88 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 50.13/9.88
% 50.13/9.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 50.13/9.88 % ------ Proving...
% 50.13/9.88 % ------ Problem Properties
% 50.13/9.88
% 50.13/9.88 %
% 50.13/9.88 % clauses 95
% 50.13/9.88 % conjectures 8
% 50.13/9.88 % EPR 62
% 50.13/9.88 % Horn 90
% 50.13/9.88 % unary 8
% 50.13/9.88 % binary 24
% 50.13/9.88 % lits 264
% 50.13/9.88 % lits eq 0
% 50.13/9.88 % fd_pure 0
% 50.13/9.88 % fd_pseudo 0
% 50.13/9.88 % fd_cond 0
% 50.13/9.88 % fd_pseudo_cond 0
% 50.13/9.88 % AC symbols 0
% 50.13/9.88
% 50.13/9.88 % ------ Schedule dynamic 5 is on
% 50.13/9.88
% 50.13/9.88 % ------ no equalities: superposition off
% 50.13/9.88
% 50.13/9.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 50.13/9.88
% 50.13/9.88
% 50.13/9.88 % ------
% 50.13/9.88 % Current options:
% 50.13/9.88 % ------
% 50.13/9.88
% 50.13/9.88
% 50.13/9.88 %
% 50.13/9.88
% 50.13/9.88 % ------ Proving...
% 50.13/9.88 %
% 50.13/9.88
% 50.13/9.88 % SZS status Theorem for theBenchmark.p
% 50.13/9.88
% 50.13/9.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.13/9.89
% 50.13/9.89
%------------------------------------------------------------------------------