%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO542+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 : n013.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 01:21:25 PM UTC 2026
% Result : Theorem 16.62s 4.97s
% Output : CNFRefutation 16.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 251 ( 15 unt; 0 def)
% Number of atoms : 659 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 754 ( 346 ~; 340 |; 38 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 687 ( 0 sgn 671 !; 16 ?; 205 :)
% 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(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
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(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(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(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(f53,axiom,
! [X0,X1,X2,X3] :
( ( midp(X3,X0,X2)
& perp(X0,X1,X1,X2) )
=> cong(X0,X3,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD52) ).
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(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox/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/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(f74,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( para(X4,X5,X6,X7)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD73) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X6,X0,X1,X2)
& midp(X5,X1,X0)
& midp(X4,X2,X0)
& midp(X3,X2,X1) )
=> perp(X6,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012002) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X6,X0,X1,X2)
& midp(X5,X1,X0)
& midp(X4,X2,X0)
& midp(X3,X2,X1) )
=> perp(X6,X3,X4,X5) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( circle(X6,X0,X1,X2)
& midp(X5,X1,X0)
& midp(X4,X2,X0)
& midp(X3,X2,X1)
& ~ perp(X6,X3,X4,X5) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( circle(X6,X0,X1,X2)
& midp(X5,X1,X0)
& midp(X4,X2,X0)
& midp(X3,X2,X1)
& ~ perp(X6,X3,X4,X5) ),
inference(flattening,[],[f98]) ).
fof(f122,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(f123,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(ennf_transformation,[],[f53]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(flattening,[],[f126]) ).
fof(f128,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(f129,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(flattening,[],[f128]) ).
fof(f130,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(f131,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f70]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(ennf_transformation,[],[f68]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(flattening,[],[f142]) ).
fof(f144,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(f145,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,[],[f144]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(flattening,[],[f146]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(flattening,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
? [X4] :
( ~ circle(X3,X0,X1,X2)
| perp(X4,X0,X0,X3) ),
inference(ennf_transformation,[],[f87]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(flattening,[],[f158]) ).
fof(f164,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(f165,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,[],[f164]) ).
fof(f166,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(f167,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,[],[f166]) ).
fof(f168,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(f169,plain,
! [X0,X1,X2,X3] :
( ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1)
| circle(X3,X0,X1,X2) ),
inference(flattening,[],[f168]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f177]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f74]) ).
fof(f187,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(flattening,[],[f186]) ).
fof(f188,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(f192,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
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(f220,plain,
( circle(sK6,sK0,sK1,sK2)
& midp(sK5,sK1,sK0)
& midp(sK4,sK2,sK0)
& midp(sK3,sK2,sK1)
& ~ perp(sK6,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f99]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( ~ circle(X3,X0,X1,X2)
| perp(sK21(X0,X1,X2,X3),X0,X0,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X4,sK21(X0,X1,X2,X3))],[f157]) ).
fof(f239,plain,
circle(sK6,sK0,sK1,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f240,plain,
midp(sK5,sK1,sK0),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
midp(sK4,sK2,sK0),
inference(cnf_transformation,[],[f220]) ).
fof(f242,plain,
midp(sK3,sK2,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f243,plain,
~ perp(sK6,sK3,sK4,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(cnf_transformation,[],[f127]) ).
fof(f268,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,[],[f129]) ).
fof(f269,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,[],[f131]) ).
fof(f270,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f133]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f140]) ).
fof(f279,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f141]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
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,[],[f145]) ).
fof(f282,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f147]) ).
fof(f284,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f288,plain,
! [X2,X3,X0,X1] :
( ~ circle(X3,X0,X1,X2)
| perp(sK21(X0,X1,X2,X3),X0,X0,X3) ),
inference(cnf_transformation,[],[f235]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f159]) ).
fof(f292,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,[],[f165]) ).
fof(f293,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,[],[f167]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1)
| circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f169]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f174]) ).
fof(f301,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f179]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f308,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f187]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f188]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f323,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(f324,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]) ).
tcf(c_49,negated_conjecture,
~ perp(sK6,sK3,sK4,sK5),
inference(cnf_transformation,[],[f243]) ).
tcf(c_50,negated_conjecture,
midp(sK3,sK2,sK1),
inference(cnf_transformation,[],[f242]) ).
tcf(c_51,negated_conjecture,
midp(sK4,sK2,sK0),
inference(cnf_transformation,[],[f241]) ).
tcf(c_52,negated_conjecture,
midp(sK5,sK1,sK0),
inference(cnf_transformation,[],[f240]) ).
tcf(c_53,negated_conjecture,
circle(sK6,sK0,sK1,sK2),
inference(cnf_transformation,[],[f239]) ).
tcf(c_75,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,[],[f265]) ).
tcf(c_76,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,[],[f266]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_78,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,[],[f268]) ).
tcf(c_79,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,[],[f269]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,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_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(sK21(X1,X2,X3,X0),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_99,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,[],[f289]) ).
tcf(c_102,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,[],[f292]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( eqangle(X1,X2,X1,X3,X4,X1,X4,X3)
| ~ circle(X0,X1,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_119,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,[],[f309]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_133,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,[],[f323]) ).
tcf(c_134,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,[],[f324]) ).
tcf(c_147,plain,
( eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_151,plain,
( midp(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_155,plain,
( perp(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_159,plain,
( cyclic(sK0,sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_193,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_133]) ).
tcf(c_732,plain,
perp(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK6),
inference(resolution,[status(thm)],[c_53,c_98]) ).
tcf(c_747,plain,
! [X0: $i] :
( perp(sK6,sK0,sK0,X0)
| ~ eqangle(sK0,X0,sK0,sK1,sK2,sK0,sK2,sK1) ),
inference(resolution,[status(thm)],[c_53,c_102]) ).
tcf(c_748,plain,
( perp(sK6,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK1,sK2,sK0,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_747]) ).
tcf(c_2023,plain,
( coll(sK4,sK2,sK0)
| ~ midp(sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_2024,plain,
( coll(sK5,sK1,sK0)
| ~ midp(sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_2025,plain,
( midp(sK3,sK1,sK2)
| ~ midp(sK3,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2026,plain,
( midp(sK4,sK0,sK2)
| ~ midp(sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2027,plain,
( midp(sK5,sK0,sK1)
| ~ midp(sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_2029,plain,
( cong(sK4,sK2,sK4,sK0)
| ~ midp(sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_2030,plain,
( cong(sK5,sK1,sK5,sK0)
| ~ midp(sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i] :
( para(sK2,X0,sK0,X1)
| ~ midp(sK4,sK2,sK0)
| ~ midp(sK4,X0,X1) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_2151,plain,
! [X0: $i] :
( perp(sK2,X0,X0,sK0)
| ~ coll(sK4,sK2,sK0)
| ~ circle(sK4,sK2,X0,sK0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_2152,plain,
( perp(sK2,sK0,sK0,sK0)
| ~ coll(sK4,sK2,sK0)
| ~ circle(sK4,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2151]) ).
tcf(c_2169,plain,
! [X0: $i] :
( perp(sK1,X0,X0,sK0)
| ~ coll(sK5,sK1,sK0)
| ~ circle(sK5,sK1,X0,sK0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_2170,plain,
( perp(sK1,sK0,sK0,sK0)
| ~ coll(sK5,sK1,sK0)
| ~ circle(sK5,sK1,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2169]) ).
tcf(c_2189,plain,
! [X0: $i,X1: $i] :
( midp(sK3,X0,X1)
| ~ midp(sK3,sK1,sK2)
| ~ para(sK1,X1,sK2,X0)
| ~ para(sK1,X0,sK2,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2190,plain,
( midp(sK3,sK0,sK0)
| ~ midp(sK3,sK1,sK2)
| ~ para(sK1,sK0,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2189]) ).
tcf(c_2214,plain,
! [X0: $i] :
( cong(X0,sK0,X0,sK2)
| ~ midp(sK4,sK0,sK2)
| ~ perp(X0,sK4,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2215,plain,
( cong(sK0,sK0,sK0,sK2)
| ~ midp(sK4,sK0,sK2)
| ~ perp(sK0,sK4,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_2214]) ).
tcf(c_2216,plain,
! [X0: $i] :
( cong(sK0,sK4,X0,sK4)
| ~ midp(sK4,sK0,sK2)
| ~ perp(sK0,X0,X0,sK2) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_2217,plain,
( cong(sK0,sK4,sK0,sK4)
| ~ midp(sK4,sK0,sK2)
| ~ perp(sK0,sK0,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_2216]) ).
tcf(c_2247,plain,
! [X0: $i] :
( cong(X0,sK0,X0,sK1)
| ~ midp(sK5,sK0,sK1)
| ~ perp(X0,sK5,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2248,plain,
( cong(sK0,sK0,sK0,sK1)
| ~ midp(sK5,sK0,sK1)
| ~ perp(sK0,sK5,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_2247]) ).
tcf(c_2249,plain,
! [X0: $i] :
( cong(sK0,sK5,X0,sK5)
| ~ midp(sK5,sK0,sK1)
| ~ perp(sK0,X0,X0,sK1) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_2250,plain,
( cong(sK0,sK5,sK0,sK5)
| ~ midp(sK5,sK0,sK1)
| ~ perp(sK0,sK0,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_2249]) ).
tcf(c_2291,plain,
! [X0: $i] :
( circle(sK4,sK2,X0,sK0)
| ~ cong(sK4,sK2,sK4,sK0)
| ~ cong(sK4,sK2,sK4,X0) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2292,plain,
( circle(sK4,sK2,sK0,sK0)
| ~ cong(sK4,sK2,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_2291]) ).
tcf(c_2304,plain,
! [X0: $i] :
( circle(sK5,sK1,X0,sK0)
| ~ cong(sK5,sK1,sK5,sK0)
| ~ cong(sK5,sK1,sK5,X0) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2305,plain,
( circle(sK5,sK1,sK0,sK0)
| ~ cong(sK5,sK1,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_2304]) ).
tcf(c_2334,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,sK0,sK6)
| ~ perp(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK6)
| ~ para(X0,X1,sK21(sK0,sK1,sK2,sK6),sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_2335,plain,
( perp(sK21(sK0,sK1,sK2,sK6),sK0,sK6,sK0)
| ~ perp(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_2337,plain,
( perp(sK0,sK0,sK0,sK6)
| ~ para(sK0,sK0,sK21(sK0,sK1,sK2,sK6),sK0)
| ~ perp(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_2334]) ).
tcf(c_2349,plain,
( para(sK2,sK2,sK0,sK0)
| ~ midp(sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2033]) ).
tcf(c_2438,plain,
( para(sK0,sK0,sK2,sK2)
| ~ para(sK2,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_2440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X2,X3)
| ~ para(sK2,sK2,sK0,sK0)
| ~ eqangle(X0,X1,X2,X3,sK2,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_2441,plain,
( para(sK0,sK0,sK0,sK0)
| ~ para(sK2,sK2,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK2,sK2,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_2440]) ).
tcf(c_2630,plain,
coll(sK4,sK2,sK0),
inference(superposition,[status(thm)],[c_51,c_88]) ).
tcf(c_3315,plain,
! [X0: $i] :
( coll(sK0,X0,sK4)
| ~ coll(sK4,sK2,X0) ),
inference(superposition,[status(thm)],[c_2630,c_111]) ).
tcf(c_3668,plain,
coll(sK0,sK0,sK4),
inference(superposition,[status(thm)],[c_2630,c_3315]) ).
tcf(c_3692,plain,
coll(sK0,sK4,sK0),
inference(superposition,[status(thm)],[c_3668,c_113]) ).
tcf(c_4127,plain,
! [X0: $i,X1: $i] :
( para(sK21(sK0,sK1,sK2,sK6),sK0,X0,X1)
| ~ perp(sK6,sK0,X0,X1)
| ~ perp(sK21(sK0,sK1,sK2,sK6),sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_4132,plain,
( para(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK0)
| ~ perp(sK6,sK0,sK0,sK0)
| ~ perp(sK21(sK0,sK1,sK2,sK6),sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_4127]) ).
tcf(c_4301,plain,
! [X0: $i] :
( coll(sK0,X0,sK0)
| ~ coll(sK0,sK4,X0) ),
inference(superposition,[status(thm)],[c_3692,c_111]) ).
tcf(c_4306,plain,
( coll(sK0,sK0,sK0)
| ~ coll(sK0,sK4,sK0) ),
inference(instantiation,[status(thm)],[c_4301]) ).
tcf(c_5076,plain,
! [X0: $i] :
( perp(X0,sK4,sK2,sK0)
| ~ perp(sK2,sK0,X0,sK4) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_5077,plain,
( perp(sK0,sK4,sK2,sK0)
| ~ perp(sK2,sK0,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_5076]) ).
tcf(c_5078,plain,
! [X0: $i] :
( perp(X0,sK5,sK1,sK0)
| ~ perp(sK1,sK0,X0,sK5) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_5079,plain,
( perp(sK0,sK5,sK1,sK0)
| ~ perp(sK1,sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_5078]) ).
tcf(c_5105,plain,
! [X0: $i,X1: $i] :
( perp(sK0,sK6,X0,X1)
| ~ perp(X0,X1,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_5106,plain,
( perp(sK0,sK6,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_5105]) ).
tcf(c_5167,plain,
! [X0: $i] :
( perp(X0,sK4,sK0,sK2)
| ~ perp(X0,sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_5168,plain,
( perp(sK0,sK4,sK0,sK2)
| ~ perp(sK0,sK4,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_5167]) ).
tcf(c_5169,plain,
! [X0: $i] :
( perp(sK0,X0,X0,sK2)
| ~ perp(sK0,X0,sK2,X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_5170,plain,
( perp(sK0,sK0,sK0,sK2)
| ~ perp(sK0,sK0,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_5169]) ).
tcf(c_5171,plain,
! [X0: $i] :
( perp(X0,sK5,sK0,sK1)
| ~ perp(X0,sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_5172,plain,
( perp(sK0,sK5,sK0,sK1)
| ~ perp(sK0,sK5,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_5171]) ).
tcf(c_5173,plain,
! [X0: $i] :
( perp(sK0,X0,X0,sK1)
| ~ perp(sK0,X0,sK1,X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_5174,plain,
( perp(sK0,sK0,sK0,sK1)
| ~ perp(sK0,sK0,sK1,sK0) ),
inference(instantiation,[status(thm)],[c_5173]) ).
tcf(c_5717,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(sK6,X1,sK6,X2)
| ~ midp(X0,X1,X2)
| ~ perp(sK6,X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_5718,plain,
( cong(sK6,sK0,sK6,sK0)
| ~ midp(sK0,sK0,sK0)
| ~ perp(sK6,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_5717]) ).
tcf(c_5866,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X1,sK4)
| ~ cong(X0,sK4,X1,sK4)
| ~ cong(X0,X1,X1,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_5867,plain,
( perp(sK0,sK0,sK0,sK4)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK4,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_5866]) ).
tcf(c_5868,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X1,sK5)
| ~ cong(X0,sK5,X1,sK5)
| ~ cong(X0,X1,X1,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_5869,plain,
( perp(sK0,sK0,sK0,sK5)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_5868]) ).
tcf(c_5941,plain,
! [X0: $i,X1: $i] :
( perp(sK6,sK3,sK4,sK5)
| ~ para(sK6,sK3,X0,X1)
| ~ perp(X0,X1,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_5942,plain,
( perp(sK6,sK3,sK4,sK5)
| ~ para(sK6,sK3,sK0,sK0)
| ~ perp(sK0,sK0,sK4,sK5) ),
inference(instantiation,[status(thm)],[c_5941]) ).
tcf(c_6021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK2,X3,sK0,X2)
| ~ perp(sK2,X3,X0,X1)
| ~ perp(X0,X1,sK0,X2) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_6022,plain,
( para(sK2,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK2,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6021]) ).
tcf(c_6023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK1,X3,sK0,X2)
| ~ perp(sK1,X3,X0,X1)
| ~ perp(X0,X1,sK0,X2) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_6024,plain,
( para(sK1,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6023]) ).
tcf(c_6035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK1,X3,sK2,X2)
| ~ perp(sK1,X3,X0,X1)
| ~ perp(X0,X1,sK2,X2) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_6036,plain,
( para(sK1,sK0,sK2,sK0)
| ~ perp(sK0,sK0,sK2,sK0)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6035]) ).
tcf(c_6116,plain,
! [X0: $i,X1: $i] :
( circle(X0,X1,sK1,sK2)
| ~ cong(X0,X1,X0,sK1)
| ~ cong(X0,X1,X0,sK2) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_6117,plain,
( circle(sK0,sK0,sK1,sK2)
| ~ cong(sK0,sK0,sK0,sK1)
| ~ cong(sK0,sK0,sK0,sK2) ),
inference(instantiation,[status(thm)],[c_6116]) ).
tcf(c_6162,plain,
! [X0: $i,X1: $i] :
( para(X0,X1,sK21(sK0,sK1,sK2,sK6),sK0)
| ~ para(sK21(sK0,sK1,sK2,sK6),sK0,X0,X1) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_6163,plain,
( para(sK0,sK0,sK21(sK0,sK1,sK2,sK6),sK0)
| ~ para(sK21(sK0,sK1,sK2,sK6),sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6162]) ).
tcf(c_6658,plain,
! [X0: $i] :
( perp(X0,sK0,sK2,X0)
| ~ perp(sK2,X0,X0,sK0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_6659,plain,
( perp(sK0,sK0,sK2,sK0)
| ~ perp(sK2,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6658]) ).
tcf(c_6660,plain,
! [X0: $i] :
( perp(X0,sK0,sK1,X0)
| ~ perp(sK1,X0,X0,sK0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_6661,plain,
( perp(sK0,sK0,sK1,sK0)
| ~ perp(sK1,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_6660]) ).
tcf(c_9136,plain,
! [X0: $i,X1: $i] :
( eqangle(sK0,sK0,X0,X1,sK2,sK2,X0,X1)
| ~ para(sK0,sK0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_9137,plain,
( eqangle(sK0,sK0,sK0,sK0,sK2,sK2,sK0,sK0)
| ~ para(sK0,sK0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_9136]) ).
tcf(c_12786,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,sK4,sK5)
| ~ cong(X0,sK5,X1,sK5)
| ~ cong(X0,sK4,X1,sK4) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_12787,plain,
( perp(sK0,sK0,sK4,sK5)
| ~ cong(sK0,sK5,sK0,sK5)
| ~ cong(sK0,sK4,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_12786]) ).
tcf(c_13346,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(sK2,sK0,X2,sK4)
| ~ para(sK2,sK0,X0,X1)
| ~ perp(X0,X1,X2,sK4) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_13347,plain,
( perp(sK2,sK0,sK0,sK4)
| ~ para(sK2,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_13346]) ).
tcf(c_13356,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(sK1,sK0,X2,sK5)
| ~ para(sK1,sK0,X0,X1)
| ~ perp(X0,X1,X2,sK5) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_13357,plain,
( perp(sK1,sK0,sK0,sK5)
| ~ para(sK1,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_13356]) ).
tcf(c_15224,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_103]) ).
tcf(c_15225,plain,
( eqangle(sK0,sK0,sK0,sK1,sK2,sK0,sK2,sK1)
| ~ circle(sK0,sK0,sK1,sK2)
| ~ perp(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_15224]) ).
tcf(c_15256,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK6,sK3,X1,X2)
| ~ midp(sK3,X0,X2)
| ~ midp(sK6,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_15257,plain,
( para(sK6,sK3,sK0,sK0)
| ~ midp(sK3,sK0,sK0)
| ~ midp(sK6,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_15256]) ).
tcf(c_22012,plain,
! [X0: $i,X1: $i] :
( midp(sK6,X0,X1)
| ~ coll(sK6,X0,X1)
| ~ cong(sK6,X0,sK6,X1) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_22013,plain,
( midp(sK6,sK0,sK0)
| ~ coll(sK6,sK0,sK0)
| ~ cong(sK6,sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_22012]) ).
tcf(c_55448,plain,
! [X0: $i,X1: $i] :
( coll(X0,sK6,X1)
| ~ para(X0,sK6,X0,X1) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_55451,plain,
( coll(sK0,sK6,sK0)
| ~ para(sK0,sK6,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_55448]) ).
tcf(c_55551,plain,
! [X0: $i,X1: $i] :
( coll(sK6,X0,X1)
| ~ coll(X0,sK6,X1) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_55552,plain,
( coll(sK6,sK0,sK0)
| ~ coll(sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_55551]) ).
tcf(c_56234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,sK6,X2,X3)
| ~ perp(X2,sK6,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_56235,plain,
( para(sK0,sK6,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK0,sK6,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_56234]) ).
tcf(c_56236,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_56235,c_55552,c_55451,c_22013,c_15257,c_15225,c_13357,c_13347,c_12787,c_9137,c_6661,c_6659,c_6163,c_6117,c_6036,c_6024,c_6022,c_5942,c_5869,c_5867,c_5718,c_5174,c_5172,c_5170,c_5168,c_5106,c_5079,c_5077,c_4306,c_4132,c_3692,c_2441,c_2438,c_2349,c_2337,c_2335,c_2305,c_2292,c_2250,c_2248,c_2217,c_2215,c_2190,c_2170,c_2152,c_2030,c_2029,c_2027,c_2026,c_2025,c_2024,c_2023,c_748,c_732,c_193,c_159,c_155,c_151,c_147,c_49,c_50,c_51,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO542+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.58 % Computer : n013.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Wed Sep 23 12:20:53 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 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
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.14/0.63 % Proving...
% 16.62/4.97 % SZS status Started for theBenchmark.p
% 16.62/4.97 % SZS status Theorem for theBenchmark.p
% 16.62/4.97
% 16.62/4.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.62/4.97
% 16.62/4.97 % ------ iProver source info
% 16.62/4.97
% 16.62/4.97 % git: date: 2026-07-19 20:42:38 +0200
% 16.62/4.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.62/4.97 % git: non_committed_changes: false
% 16.62/4.97
% 16.62/4.97 % ------ Parsing...
% 16.62/4.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.62/4.97
% 16.62/4.97 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 16.62/4.97
% 16.62/4.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 16.62/4.97 % ------ Proving...
% 16.62/4.97 % ------ Problem Properties
% 16.62/4.97
% 16.62/4.97 %
% 16.62/4.97 % clauses 92
% 16.62/4.97 % conjectures 5
% 16.62/4.97 % EPR 59
% 16.62/4.97 % Horn 87
% 16.62/4.97 % unary 5
% 16.62/4.97 % binary 24
% 16.62/4.97 % lits 261
% 16.62/4.97 % lits eq 0
% 16.62/4.97 % fd_pure 0
% 16.62/4.97 % fd_pseudo 0
% 16.62/4.97 % fd_cond 0
% 16.62/4.97 % fd_pseudo_cond 0
% 16.62/4.97 % AC symbols 0
% 16.62/4.97
% 16.62/4.97 % ------ Schedule dynamic 5 is on
% 16.62/4.97
% 16.62/4.97 % ------ no equalities: superposition off
% 16.62/4.97
% 16.62/4.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.62/4.97
% 16.62/4.97
% 16.62/4.97 % ------
% 16.62/4.97 % Current options:
% 16.62/4.97 % ------
% 16.62/4.97
% 16.62/4.97
% 16.62/4.97 %
% 16.62/4.97
% 16.62/4.97 % ------ Proving...
% 16.62/4.97 %
% 16.62/4.97
% 16.62/4.97 % SZS status Theorem for theBenchmark.p
% 16.62/4.97
% 16.62/4.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.62/4.98
% 16.62/4.98
%------------------------------------------------------------------------------