%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO634+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : 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 01:21:42 PM UTC 2026
% Result : Theorem 83.70s 12.42s
% Output : CNFRefutation 83.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of formulae : 229 ( 33 unt; 0 def)
% Number of atoms : 585 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 615 ( 259 ~; 253 |; 74 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 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 : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 799 ( 0 sgn 775 !; 24 ?; 245 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD4) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD7) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> perp(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD10) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD17) ).
fof(f18,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD18) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
fof(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD22) ).
fof(f24,axiom,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
=> cong(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD24) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD41) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( coll(X2,X3,X1)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
& cyclic(X0,X1,X2,X5)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD43) ).
fof(f53,axiom,
! [X0,X1,X2,X3] :
( ( midp(X3,X0,X2)
& perp(X0,X1,X1,X2) )
=> cong(X0,X3,X1,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD53) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD56) ).
fof(f65,axiom,
! [X0,X1,X2,X3,X4] :
( ( para(X0,X3,X1,X2)
& para(X0,X2,X1,X3)
& midp(X4,X0,X1) )
=> midp(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD64) ).
fof(f68,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD67) ).
fof(f69,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD68) ).
fof(f75,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( perp(X4,X5,X6,X7)
& eqangle(X0,X1,X2,X3,X4,X5,X6,X7) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD74) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( coll(X9,X0,X1)
& perp(X9,X6,X0,X1)
& coll(X8,X1,X2)
& perp(X8,X6,X1,X2)
& coll(X7,X0,X6)
& coll(X7,X1,X2)
& circle(X3,X0,X6,X11)
& eqangle(X6,X0,X0,X1,X2,X0,X0,X4)
& coll(X5,X0,X4)
& circle(X3,X0,X5,X10)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> perp(X8,X9,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110997) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( coll(X9,X0,X1)
& perp(X9,X6,X0,X1)
& coll(X8,X1,X2)
& perp(X8,X6,X1,X2)
& coll(X7,X0,X6)
& coll(X7,X1,X2)
& circle(X3,X0,X6,X11)
& eqangle(X6,X0,X0,X1,X2,X0,X0,X4)
& coll(X5,X0,X4)
& circle(X3,X0,X5,X10)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2) )
=> perp(X8,X9,X5,X0) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,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(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f110,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(f111,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(flattening,[],[f110]) ).
fof(f120,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(f121,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f18]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(ennf_transformation,[],[f19]) ).
fof(f124,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X1,X2,X3)
| cong(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f148,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(f149,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(f150,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f153,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(f154,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,[],[f153]) ).
fof(f155,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(f156,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,[],[f155]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(ennf_transformation,[],[f53]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(flattening,[],[f174]) ).
fof(f180,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(f181,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f180]) ).
fof(f193,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(f194,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,[],[f193]) ).
fof(f198,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(ennf_transformation,[],[f68]) ).
fof(f199,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(flattening,[],[f198]) ).
fof(f200,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f75]) ).
fof(f211,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f210]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( coll(X9,X0,X1)
& perp(X9,X6,X0,X1)
& coll(X8,X1,X2)
& perp(X8,X6,X1,X2)
& coll(X7,X0,X6)
& coll(X7,X1,X2)
& circle(X3,X0,X6,X11)
& eqangle(X6,X0,X0,X1,X2,X0,X0,X4)
& coll(X5,X0,X4)
& circle(X3,X0,X5,X10)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2)
& ~ perp(X8,X9,X5,X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( coll(X9,X0,X1)
& perp(X9,X6,X0,X1)
& coll(X8,X1,X2)
& perp(X8,X6,X1,X2)
& coll(X7,X0,X6)
& coll(X7,X1,X2)
& circle(X3,X0,X6,X11)
& eqangle(X6,X0,X0,X1,X2,X0,X0,X4)
& coll(X5,X0,X4)
& circle(X3,X0,X5,X10)
& midp(X4,X2,X1)
& circle(X3,X0,X1,X2)
& ~ perp(X8,X9,X5,X0) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( coll(sK29,sK20,sK21)
& perp(sK29,sK26,sK20,sK21)
& coll(sK28,sK21,sK22)
& perp(sK28,sK26,sK21,sK22)
& coll(sK27,sK20,sK26)
& coll(sK27,sK21,sK22)
& circle(sK23,sK20,sK26,sK31)
& eqangle(sK26,sK20,sK20,sK21,sK22,sK20,sK20,sK24)
& coll(sK25,sK20,sK24)
& circle(sK23,sK20,sK25,sK30)
& midp(sK24,sK22,sK21)
& circle(sK23,sK20,sK21,sK22)
& ~ perp(sK28,sK29,sK25,sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26),skolemize(X7,sK27),skolemize(X8,sK28),skolemize(X9,sK29),skolemize(X10,sK30),skolemize(X11,sK31)],[f250]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f279,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,[],[f109]) ).
fof(f280,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,[],[f111]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f288,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f122]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f290,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f291,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f125]) ).
fof(f292,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[],[f127]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X1,X2,X3)
| cong(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f149]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f313,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,[],[f154]) ).
fof(f314,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,[],[f156]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2)
| cong(X0,X3,X1,X3) ),
inference(cnf_transformation,[],[f173]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f175]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f335,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,[],[f194]) ).
fof(f338,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f199]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f200]) ).
fof(f345,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f211]) ).
fof(f385,plain,
perp(sK29,sK26,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f387,plain,
perp(sK28,sK26,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f388,plain,
coll(sK27,sK20,sK26),
inference(cnf_transformation,[],[f270]) ).
fof(f390,plain,
circle(sK23,sK20,sK26,sK31),
inference(cnf_transformation,[],[f270]) ).
fof(f391,plain,
eqangle(sK26,sK20,sK20,sK21,sK22,sK20,sK20,sK24),
inference(cnf_transformation,[],[f270]) ).
fof(f396,plain,
~ perp(sK28,sK29,sK25,sK20),
inference(cnf_transformation,[],[f270]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_51,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_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_57,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,[],[f279]) ).
tcf(c_58,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,[],[f280]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_87,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,[],[f309]) ).
tcf(c_88,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,[],[f310]) ).
tcf(c_89,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,[],[f311]) ).
tcf(c_91,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,[],[f313]) ).
tcf(c_92,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,[],[f314]) ).
tcf(c_101,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,[],[f323]) ).
tcf(c_102,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,[],[f324]) ).
tcf(c_105,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,[],[f327]) ).
tcf(c_113,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,[],[f335]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_162,negated_conjecture,
~ perp(sK28,sK29,sK25,sK20),
inference(cnf_transformation,[],[f396]) ).
tcf(c_167,negated_conjecture,
eqangle(sK26,sK20,sK20,sK21,sK22,sK20,sK20,sK24),
inference(cnf_transformation,[],[f391]) ).
tcf(c_168,negated_conjecture,
circle(sK23,sK20,sK26,sK31),
inference(cnf_transformation,[],[f390]) ).
tcf(c_170,negated_conjecture,
coll(sK27,sK20,sK26),
inference(cnf_transformation,[],[f388]) ).
tcf(c_171,negated_conjecture,
perp(sK28,sK26,sK21,sK22),
inference(cnf_transformation,[],[f387]) ).
tcf(c_173,negated_conjecture,
perp(sK29,sK26,sK20,sK21),
inference(cnf_transformation,[],[f385]) ).
tcf(c_180,plain,
( midp(sK20,sK20,sK20)
| ~ coll(sK20,sK20,sK20)
| ~ cong(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_183,plain,
( eqangle(sK20,sK20,sK20,sK20,sK20,sK20,sK20,sK20)
| ~ cyclic(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_189,plain,
( perp(sK20,sK20,sK20,sK20)
| ~ cong(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_238,plain,
( cong(sK20,sK20,sK20,sK20)
| ~ cyclic(sK20,sK20,sK20,sK20)
| ~ eqangle(sK20,sK20,sK20,sK20,sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_6788,plain,
coll(sK27,sK26,sK20),
inference(superposition,[status(thm)],[c_170,c_49]) ).
tcf(c_7069,plain,
! [X0: $i] :
( coll(sK20,X0,sK27)
| ~ coll(sK27,sK26,X0) ),
inference(superposition,[status(thm)],[c_6788,c_51]) ).
tcf(c_7334,plain,
coll(sK20,sK20,sK27),
inference(superposition,[status(thm)],[c_6788,c_7069]) ).
tcf(c_7350,plain,
coll(sK20,sK27,sK20),
inference(superposition,[status(thm)],[c_7334,c_49]) ).
tcf(c_7364,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(superposition,[status(thm)],[c_89,c_87]) ).
tcf(c_7365,plain,
( para(sK20,sK20,sK20,sK20)
| ~ cyclic(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_7364]) ).
tcf(c_7530,plain,
perp(sK21,sK22,sK28,sK26),
inference(superposition,[status(thm)],[c_171,c_56]) ).
tcf(c_7531,plain,
perp(sK20,sK21,sK29,sK26),
inference(superposition,[status(thm)],[c_173,c_56]) ).
tcf(c_7549,plain,
perp(sK21,sK22,sK26,sK28),
inference(superposition,[status(thm)],[c_7530,c_55]) ).
tcf(c_7551,plain,
perp(sK20,sK21,sK26,sK29),
inference(superposition,[status(thm)],[c_7531,c_55]) ).
tcf(c_7633,plain,
! [X0: $i] :
( coll(sK20,X0,sK20)
| ~ coll(sK20,sK27,X0) ),
inference(superposition,[status(thm)],[c_7350,c_51]) ).
tcf(c_7643,plain,
( coll(sK20,sK20,sK20)
| ~ coll(sK20,sK27,sK20) ),
inference(instantiation,[status(thm)],[c_7633]) ).
tcf(c_8281,plain,
( perp(sK20,sK26,sK26,sK31)
| ~ coll(sK23,sK20,sK31) ),
inference(superposition,[status(thm)],[c_168,c_102]) ).
tcf(c_8392,plain,
! [X0: $i,X1: $i] :
( para(sK28,sK26,X0,X1)
| ~ perp(sK21,sK22,X0,X1) ),
inference(superposition,[status(thm)],[c_171,c_57]) ).
tcf(c_8393,plain,
! [X0: $i,X1: $i] :
( para(sK29,sK26,X0,X1)
| ~ perp(sK20,sK21,X0,X1) ),
inference(superposition,[status(thm)],[c_173,c_57]) ).
tcf(c_8397,plain,
! [X0: $i,X1: $i] :
( para(sK20,sK21,X0,X1)
| ~ perp(sK29,sK26,X0,X1) ),
inference(superposition,[status(thm)],[c_7531,c_57]) ).
tcf(c_8668,plain,
! [X0: $i,X1: $i] :
( para(sK20,sK26,X0,X1)
| ~ coll(sK23,sK20,sK31)
| ~ perp(sK26,sK31,X0,X1) ),
inference(superposition,[status(thm)],[c_8281,c_57]) ).
tcf(c_8670,plain,
( perp(sK26,sK31,sK20,sK26)
| ~ coll(sK23,sK20,sK31) ),
inference(superposition,[status(thm)],[c_8281,c_56]) ).
tcf(c_8746,plain,
para(sK28,sK26,sK26,sK28),
inference(superposition,[status(thm)],[c_7549,c_8392]) ).
tcf(c_8814,plain,
para(sK29,sK26,sK26,sK29),
inference(superposition,[status(thm)],[c_7551,c_8393]) ).
tcf(c_8852,plain,
para(sK26,sK28,sK28,sK26),
inference(superposition,[status(thm)],[c_8746,c_53]) ).
tcf(c_8873,plain,
para(sK26,sK29,sK29,sK26),
inference(superposition,[status(thm)],[c_8814,c_53]) ).
tcf(c_8903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_66]) ).
tcf(c_9115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_67]) ).
tcf(c_9180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_69]) ).
tcf(c_22900,plain,
para(sK20,sK21,sK20,sK21),
inference(superposition,[status(thm)],[c_173,c_8397]) ).
tcf(c_23113,plain,
eqangle(sK20,sK26,sK20,sK21,sK22,sK20,sK20,sK24),
inference(superposition,[status(thm)],[c_167,c_66]) ).
tcf(c_23179,plain,
eqangle(sK22,sK20,sK20,sK24,sK20,sK26,sK20,sK21),
inference(superposition,[status(thm)],[c_23113,c_68]) ).
tcf(c_23380,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,X0,X0)
| ~ coll(X0,X0,X2)
| ~ para(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_88,c_91]) ).
tcf(c_23489,plain,
! [X0: $i] :
( cyclic(sK21,X0,sK20,sK20)
| ~ coll(sK20,sK20,X0) ),
inference(superposition,[status(thm)],[c_22900,c_23380]) ).
tcf(c_23494,plain,
( cyclic(sK21,sK20,sK20,sK20)
| ~ coll(sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_23489]) ).
tcf(c_23823,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,sK20,sK20,X1)
| ~ coll(sK20,sK20,X0)
| ~ cyclic(sK21,X0,sK20,X1) ),
inference(superposition,[status(thm)],[c_23489,c_65]) ).
tcf(c_23828,plain,
( cyclic(sK20,sK20,sK20,sK20)
| ~ coll(sK20,sK20,sK20)
| ~ cyclic(sK21,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_23823]) ).
tcf(c_24491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(sK26,sK20,sK20,sK21,X0,X1,X2,X3)
| ~ eqangle(sK22,sK20,sK20,sK24,X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_167,c_70]) ).
tcf(c_24543,plain,
eqangle(sK26,sK20,sK20,sK21,sK20,sK26,sK20,sK21),
inference(superposition,[status(thm)],[c_23179,c_24491]) ).
tcf(c_24558,plain,
eqangle(sK20,sK26,sK20,sK21,sK20,sK26,sK20,sK21),
inference(superposition,[status(thm)],[c_24543,c_66]) ).
tcf(c_24863,plain,
para(sK20,sK26,sK20,sK26),
inference(superposition,[status(thm)],[c_24558,c_87]) ).
tcf(c_27460,plain,
( perp(sK28,sK29,sK25,sK20)
| ~ perp(sK25,sK20,sK28,sK29) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_30990,plain,
! [X0: $i,X1: $i] :
( perp(sK25,sK20,sK28,sK29)
| ~ perp(X0,X1,sK28,sK29)
| ~ para(sK25,sK20,X0,X1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_30991,plain,
( perp(sK25,sK20,sK28,sK29)
| ~ perp(sK20,sK20,sK28,sK29)
| ~ para(sK25,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_30990]) ).
tcf(c_37016,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,sK28,sK29)
| ~ cong(X0,sK29,X1,sK29)
| ~ cong(X0,sK28,X1,sK28) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_37017,plain,
( perp(sK20,sK20,sK28,sK29)
| ~ cong(sK20,sK29,sK20,sK29)
| ~ cong(sK20,sK28,sK20,sK28) ),
inference(instantiation,[status(thm)],[c_37016]) ).
tcf(c_37355,plain,
! [X0: $i,X1: $i] :
( perp(sK25,sK20,X0,X1)
| ~ cong(sK25,X1,sK20,X1)
| ~ cong(sK25,X0,sK20,X0) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_37356,plain,
( perp(sK25,sK20,sK20,sK20)
| ~ cong(sK25,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_37355]) ).
tcf(c_41482,plain,
( para(sK20,sK26,sK20,sK26)
| ~ coll(sK23,sK20,sK31) ),
inference(superposition,[status(thm)],[c_8670,c_8668]) ).
tcf(c_41518,plain,
para(sK20,sK26,sK20,sK26),
inference(global_subsumption_just,[status(thm)],[c_41482,c_24863]) ).
tcf(c_41722,plain,
! [X0: $i] :
( midp(X0,sK26,sK26)
| ~ midp(X0,sK20,sK20)
| ~ para(sK20,sK26,sK20,sK26) ),
inference(superposition,[status(thm)],[c_41518,c_113]) ).
tcf(c_41724,plain,
! [X0: $i] :
( midp(X0,sK26,sK26)
| ~ midp(X0,sK20,sK20) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41722,c_41518]) ).
tcf(c_41727,plain,
( midp(sK20,sK26,sK26)
| ~ midp(sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_41724]) ).
tcf(c_45029,plain,
para(sK26,sK28,sK26,sK28),
inference(superposition,[status(thm)],[c_8852,c_52]) ).
tcf(c_45035,plain,
para(sK26,sK29,sK26,sK29),
inference(superposition,[status(thm)],[c_8873,c_52]) ).
tcf(c_45094,plain,
! [X0: $i] :
( midp(X0,sK28,sK28)
| ~ midp(X0,sK26,sK26)
| ~ para(sK26,sK28,sK26,sK28) ),
inference(superposition,[status(thm)],[c_45029,c_113]) ).
tcf(c_45101,plain,
! [X0: $i] :
( midp(X0,sK28,sK28)
| ~ midp(X0,sK26,sK26) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45094,c_45029]) ).
tcf(c_45102,plain,
( midp(sK20,sK28,sK28)
| ~ midp(sK20,sK26,sK26) ),
inference(instantiation,[status(thm)],[c_45101]) ).
tcf(c_45104,plain,
! [X0: $i] :
( midp(X0,sK29,sK29)
| ~ midp(X0,sK26,sK26)
| ~ para(sK26,sK29,sK26,sK29) ),
inference(superposition,[status(thm)],[c_45035,c_113]) ).
tcf(c_45111,plain,
! [X0: $i] :
( midp(X0,sK29,sK29)
| ~ midp(X0,sK26,sK26) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45104,c_45035]) ).
tcf(c_45112,plain,
( midp(sK20,sK29,sK29)
| ~ midp(sK20,sK26,sK26) ),
inference(instantiation,[status(thm)],[c_45111]) ).
tcf(c_49381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( perp(X0,X1,sK25,sK20)
| ~ perp(X2,X3,X4,X5)
| ~ eqangle(X0,X1,sK25,sK20,X2,X3,X4,X5) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_52801,plain,
! [X0: $i] :
( cong(X0,sK28,X0,sK28)
| ~ midp(X0,sK28,sK28) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_52802,plain,
( cong(sK20,sK28,sK20,sK28)
| ~ midp(sK20,sK28,sK28) ),
inference(instantiation,[status(thm)],[c_52801]) ).
tcf(c_52865,plain,
! [X0: $i] :
( cong(X0,sK29,X0,sK29)
| ~ midp(X0,sK29,sK29) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_52866,plain,
( cong(sK20,sK29,sK20,sK29)
| ~ midp(sK20,sK29,sK29) ),
inference(instantiation,[status(thm)],[c_52865]) ).
tcf(c_59709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK25,sK20,X2,X3)
| ~ perp(sK25,sK20,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_59713,plain,
( para(sK25,sK20,sK20,sK20)
| ~ perp(sK20,sK20,sK20,sK20)
| ~ perp(sK25,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_59709]) ).
tcf(c_60977,plain,
! [X0: $i,X1: $i] :
( perp(sK25,X0,sK25,sK20)
| ~ perp(X1,X0,X1,sK20)
| ~ eqangle(sK25,X0,sK25,sK20,X1,X0,X1,sK20) ),
inference(instantiation,[status(thm)],[c_49381]) ).
tcf(c_60979,plain,
( perp(sK25,sK20,sK25,sK20)
| ~ perp(sK20,sK20,sK20,sK20)
| ~ eqangle(sK25,sK20,sK25,sK20,sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_60977]) ).
tcf(c_75663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( perp(X0,X1,sK25,sK20)
| ~ perp(X2,X3,X4,X5)
| ~ eqangle(X0,X1,sK25,sK20,X2,X3,X4,X5) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_77390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK25,sK20,X2,X3)
| ~ eqangle(sK25,sK20,X0,X1,X2,X3,X0,X1) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_78200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X4,X5,sK25,sK20,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_78221,plain,
! [X0: $i,X1: $i] :
( perp(X0,sK25,sK25,sK20)
| ~ perp(X1,X0,X1,sK20)
| ~ eqangle(X0,sK25,sK25,sK20,X1,X0,X1,sK20) ),
inference(instantiation,[status(thm)],[c_75663]) ).
tcf(c_81057,plain,
! [X0: $i] :
( cong(sK25,sK20,X0,sK20)
| ~ cong(X0,sK20,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_81058,plain,
( cong(sK25,sK20,sK20,sK20)
| ~ cong(sK20,sK20,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_81057]) ).
tcf(c_88232,plain,
! [X0: $i,X1: $i] :
( para(sK25,sK20,sK25,sK20)
| ~ eqangle(sK25,sK20,X0,X1,sK25,sK20,X0,X1) ),
inference(instantiation,[status(thm)],[c_77390]) ).
tcf(c_88233,plain,
! [X0: $i,X1: $i] :
( eqangle(sK25,sK20,X0,X1,sK25,sK20,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(instantiation,[status(thm)],[c_9115]) ).
tcf(c_88234,plain,
( para(sK25,sK20,sK25,sK20)
| ~ eqangle(sK25,sK20,sK20,sK20,sK25,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_88232]) ).
tcf(c_88235,plain,
( eqangle(sK25,sK20,sK20,sK20,sK25,sK20,sK20,sK20)
| ~ para(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_88233]) ).
tcf(c_89879,plain,
! [X0: $i] :
( perp(X0,sK25,sK25,sK20)
| ~ perp(sK25,X0,sK25,sK20)
| ~ eqangle(X0,sK25,sK25,sK20,sK25,X0,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_78221]) ).
tcf(c_89880,plain,
! [X0: $i] :
( eqangle(X0,sK25,sK25,sK20,sK25,X0,sK25,sK20)
| ~ para(sK25,X0,sK25,X0) ),
inference(instantiation,[status(thm)],[c_8903]) ).
tcf(c_89881,plain,
( perp(sK20,sK25,sK25,sK20)
| ~ perp(sK25,sK20,sK25,sK20)
| ~ eqangle(sK20,sK25,sK25,sK20,sK25,sK20,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_89879]) ).
tcf(c_89882,plain,
( eqangle(sK20,sK25,sK25,sK20,sK25,sK20,sK25,sK20)
| ~ para(sK25,sK20,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_89880]) ).
tcf(c_93561,plain,
! [X0: $i,X1: $i] :
( eqangle(sK25,X1,sK25,sK20,X0,X1,X0,sK20)
| ~ eqangle(X0,X1,X0,sK20,sK25,X1,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_78200]) ).
tcf(c_93563,plain,
( eqangle(sK25,sK20,sK25,sK20,sK20,sK20,sK20,sK20)
| ~ eqangle(sK20,sK20,sK20,sK20,sK25,sK20,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_93561]) ).
tcf(c_93608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X2,X3,sK25,sK20,sK25,sK20)
| ~ para(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_9180]) ).
tcf(c_93609,plain,
( eqangle(sK20,sK20,sK20,sK20,sK25,sK20,sK25,sK20)
| ~ para(sK20,sK20,sK20,sK20) ),
inference(instantiation,[status(thm)],[c_93608]) ).
tcf(c_96336,plain,
! [X0: $i,X1: $i] :
( cong(X0,sK20,sK25,sK20)
| ~ midp(sK20,X0,X1)
| ~ perp(X0,sK25,sK25,X1) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_96337,plain,
( cong(sK20,sK20,sK25,sK20)
| ~ midp(sK20,sK20,sK20)
| ~ perp(sK20,sK25,sK25,sK20) ),
inference(instantiation,[status(thm)],[c_96336]) ).
tcf(c_96338,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_96337,c_93609,c_93563,c_89882,c_89881,c_88235,c_88234,c_81058,c_60979,c_59713,c_52866,c_52802,c_45112,c_45102,c_41727,c_37356,c_37017,c_30991,c_27460,c_23828,c_23494,c_7643,c_7365,c_7350,c_238,c_189,c_183,c_180,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO634+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:35:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 83.70/12.42 % SZS status Started for theBenchmark.p
% 83.70/12.42 % SZS status Theorem for theBenchmark.p
% 83.70/12.42
% 83.70/12.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 83.70/12.42
% 83.70/12.42 % ------ iProver source info
% 83.70/12.42
% 83.70/12.42 % git: date: 2026-07-19 20:42:38 +0200
% 83.70/12.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 83.70/12.42 % git: non_committed_changes: false
% 83.70/12.42
% 83.70/12.42 % ------ Parsing...
% 83.70/12.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 83.70/12.42
% 83.70/12.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 83.70/12.42
% 83.70/12.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 83.70/12.42
% 83.70/12.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 83.70/12.42 % ------ Proving...
% 83.70/12.42 % ------ Problem Properties
% 83.70/12.42
% 83.70/12.42 %
% 83.70/12.42 % clauses 125
% 83.70/12.42 % conjectures 13
% 83.70/12.42 % EPR 88
% 83.70/12.42 % Horn 115
% 83.70/12.42 % unary 13
% 83.70/12.42 % binary 37
% 83.70/12.42 % lits 341
% 83.70/12.42 % lits eq 4
% 83.70/12.42 % fd_pure 0
% 83.70/12.42 % fd_pseudo 0
% 83.70/12.42 % fd_cond 0
% 83.70/12.42 % fd_pseudo_cond 4
% 83.70/12.42 % AC symbols 0
% 83.70/12.42
% 83.70/12.42 % ------ Input Options Time Limit: Unbounded
% 83.70/12.42
% 83.70/12.42
% 83.70/12.42 % ------
% 83.70/12.42 % Current options:
% 83.70/12.42 % ------
% 83.70/12.42
% 83.70/12.42
% 83.70/12.42 %
% 83.70/12.42
% 83.70/12.42 % ------ Proving...
% 83.70/12.42 %
% 83.70/12.42
% 83.70/12.42 % SZS status Theorem for theBenchmark.p
% 83.70/12.42
% 83.70/12.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 83.70/12.42
% 83.70/12.42
%------------------------------------------------------------------------------