%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO621+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 : n004.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 01:21:40 PM UTC 2026
% Result : Theorem 32.56s 12.55s
% Output : CNFRefutation 32.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 251 ( 27 unt; 0 def)
% Number of atoms : 680 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 776 ( 347 ~; 341 |; 59 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 705 ( 0 sgn 687 !; 18 ?; 221 :)
% 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(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD5) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD6) ).
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(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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD21) ).
fof(f25,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cong(X2,X3,X4,X5)
& cong(X0,X1,X2,X3) )
=> cong(X0,X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD25) ).
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(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(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(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( coll(X8,X0,X2)
& coll(X8,X4,X7)
& coll(X7,X0,X1)
& perp(X4,X6,X4,X7)
& circle(X6,X3,X4,X5)
& midp(X5,X0,X2)
& midp(X4,X2,X1)
& midp(X3,X1,X0) )
=> cyclic(X1,X7,X2,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110984) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( coll(X8,X0,X2)
& coll(X8,X4,X7)
& coll(X7,X0,X1)
& perp(X4,X6,X4,X7)
& circle(X6,X3,X4,X5)
& midp(X5,X0,X2)
& midp(X4,X2,X1)
& midp(X3,X1,X0) )
=> cyclic(X1,X7,X2,X8) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( coll(X8,X0,X2)
& coll(X8,X4,X7)
& coll(X7,X0,X1)
& perp(X4,X6,X4,X7)
& circle(X6,X3,X4,X5)
& midp(X5,X0,X2)
& midp(X4,X2,X1)
& midp(X3,X1,X0)
& ~ cyclic(X1,X7,X2,X8) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( coll(X8,X0,X2)
& coll(X8,X4,X7)
& coll(X7,X0,X1)
& perp(X4,X6,X4,X7)
& circle(X6,X3,X4,X5)
& midp(X5,X0,X2)
& midp(X4,X2,X1)
& midp(X3,X1,X0)
& ~ cyclic(X1,X7,X2,X8) ),
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(f123,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
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(f142,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f142]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(flattening,[],[f144]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f10]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f157,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(f158,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,[],[f157]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(flattening,[],[f159]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(flattening,[],[f161]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f187,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(f188,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,[],[f187]) ).
fof(f189,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(f190,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,[],[f189]) ).
fof(f194,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(f195,plain,
! [X0,X1,X2,X3,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(flattening,[],[f194]) ).
fof(f199,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(f200,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,[],[f199]) ).
fof(f203,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(f205,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f6]) ).
fof(f206,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3)
| cong(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f25]) ).
fof(f211,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3)
| cong(X0,X1,X4,X5) ),
inference(flattening,[],[f210]) ).
fof(f216,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(f220,plain,
( coll(sK8,sK0,sK2)
& coll(sK8,sK4,sK7)
& coll(sK7,sK0,sK1)
& perp(sK4,sK6,sK4,sK7)
& circle(sK6,sK3,sK4,sK5)
& midp(sK5,sK0,sK2)
& midp(sK4,sK2,sK1)
& midp(sK3,sK1,sK0)
& ~ cyclic(sK1,sK7,sK2,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8)],[f99]) ).
fof(f240,plain,
coll(sK8,sK4,sK7),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
coll(sK7,sK0,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f242,plain,
perp(sK4,sK6,sK4,sK7),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
midp(sK4,sK2,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f247,plain,
~ cyclic(sK1,sK7,sK2,sK8),
inference(cnf_transformation,[],[f220]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f270,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f273,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(f274,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f143]) ).
fof(f285,plain,
! [X2,X3,X0,X1] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f149]) ).
fof(f288,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f151]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f156]) ).
fof(f295,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,[],[f158]) ).
fof(f296,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f160]) ).
fof(f297,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f312,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,[],[f188]) ).
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,[],[f190]) ).
fof(f316,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f195]) ).
fof(f320,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,[],[f200]) ).
fof(f322,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f203]) ).
fof(f324,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f206]) ).
fof(f325,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f326,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f208]) ).
fof(f328,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3)
| cong(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f211]) ).
fof(f332,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,[],[f216]) ).
tcf(c_49,negated_conjecture,
~ cyclic(sK1,sK7,sK2,sK8),
inference(cnf_transformation,[],[f247]) ).
tcf(c_51,negated_conjecture,
midp(sK4,sK2,sK1),
inference(cnf_transformation,[],[f245]) ).
tcf(c_54,negated_conjecture,
perp(sK4,sK6,sK4,sK7),
inference(cnf_transformation,[],[f242]) ).
tcf(c_55,negated_conjecture,
coll(sK7,sK0,sK1),
inference(cnf_transformation,[],[f241]) ).
tcf(c_56,negated_conjecture,
coll(sK8,sK4,sK7),
inference(cnf_transformation,[],[f240]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_83,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,[],[f273]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_95,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,[],[f285]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( perp(X4,X5,X2,X3)
| ~ para(X4,X5,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_105,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,[],[f295]) ).
tcf(c_106,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,[],[f296]) ).
tcf(c_107,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,[],[f297]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_122,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,[],[f312]) ).
tcf(c_123,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_126,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,[],[f316]) ).
tcf(c_130,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,[],[f320]) ).
tcf(c_132,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,[],[f322]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_142,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,[],[f332]) ).
tcf(c_148,plain,
( coll(sK4,sK4,sK4)
| ~ para(sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_151,plain,
( eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4)
| ~ para(sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_132]) ).
tcf(c_155,plain,
( midp(sK4,sK4,sK4)
| ~ coll(sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_159,plain,
( perp(sK4,sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_163,plain,
( cyclic(sK4,sK4,sK4,sK4)
| ~ coll(sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_197,plain,
( cong(sK4,sK4,sK4,sK4)
| ~ cyclic(sK4,sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_2043,plain,
( coll(sK4,sK2,sK1)
| ~ midp(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_2049,plain,
( coll(sK8,sK7,sK4)
| ~ coll(sK8,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_2052,plain,
( midp(sK4,sK1,sK2)
| ~ midp(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_2055,plain,
( cong(sK4,sK2,sK4,sK1)
| ~ midp(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2057,plain,
( perp(sK4,sK7,sK4,sK6)
| ~ perp(sK4,sK6,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_2076,plain,
! [X0: $i,X1: $i] :
( para(X0,sK4,X1,sK1)
| ~ midp(sK4,sK2,sK1)
| ~ midp(X0,sK2,X1) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_2244,plain,
! [X0: $i] :
( coll(sK1,X0,sK4)
| ~ coll(sK4,sK2,sK1)
| ~ coll(sK4,sK2,X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2247,plain,
( coll(sK1,sK4,sK4)
| ~ coll(sK4,sK2,sK4)
| ~ coll(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_2244]) ).
tcf(c_2359,plain,
( coll(sK7,sK8,sK4)
| ~ coll(sK8,sK7,sK4) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2429,plain,
( cong(sK4,sK1,sK4,sK2)
| ~ midp(sK4,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2438,plain,
! [X0: $i,X1: $i] :
( midp(X0,sK1,X1)
| ~ midp(sK4,sK1,sK2)
| ~ coll(X0,sK1,X1)
| ~ para(sK4,X0,sK2,X1) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2439,plain,
( midp(sK4,sK1,sK4)
| ~ coll(sK4,sK1,sK4)
| ~ midp(sK4,sK1,sK2)
| ~ para(sK4,sK4,sK2,sK4) ),
inference(instantiation,[status(thm)],[c_2438]) ).
tcf(c_2528,plain,
! [X0: $i,X1: $i] :
( para(sK4,sK7,X0,X1)
| ~ perp(sK4,sK7,sK4,sK6)
| ~ perp(sK4,sK6,X0,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2660,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,sK2,X1,X2)
| ~ cong(X0,sK2,X0,sK1)
| ~ cong(X0,sK1,X1,X2) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_2671,plain,
( para(sK4,sK4,sK1,sK1)
| ~ midp(sK4,sK2,sK1) ),
inference(instantiation,[status(thm)],[c_2076]) ).
tcf(c_2686,plain,
coll(sK4,sK2,sK1),
inference(superposition,[status(thm)],[c_51,c_79]) ).
tcf(c_2742,plain,
coll(sK8,sK7,sK4),
inference(superposition,[status(thm)],[c_56,c_86]) ).
tcf(c_2774,plain,
midp(sK4,sK1,sK2),
inference(superposition,[status(thm)],[c_51,c_108]) ).
tcf(c_2825,plain,
coll(sK4,sK1,sK2),
inference(superposition,[status(thm)],[c_2686,c_86]) ).
tcf(c_2826,plain,
coll(sK2,sK4,sK1),
inference(superposition,[status(thm)],[c_2686,c_85]) ).
tcf(c_2924,plain,
coll(sK7,sK8,sK4),
inference(superposition,[status(thm)],[c_2742,c_85]) ).
tcf(c_3008,plain,
! [X0: $i,X1: $i] :
( para(sK4,sK4,X0,X1)
| ~ para(sK4,sK4,sK1,sK1)
| ~ para(sK1,sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_3011,plain,
( para(sK1,sK1,sK4,sK4)
| ~ para(sK4,sK4,sK1,sK1) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_3013,plain,
( para(sK4,sK4,sK4,sK4)
| ~ para(sK4,sK4,sK1,sK1)
| ~ para(sK1,sK1,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_3008]) ).
tcf(c_3058,plain,
coll(sK1,sK4,sK2),
inference(superposition,[status(thm)],[c_2825,c_85]) ).
tcf(c_3067,plain,
! [X0: $i,X1: $i] :
( coll(X0,sK1,X1)
| ~ coll(sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_3068,plain,
( coll(sK4,sK1,sK4)
| ~ coll(sK1,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_3067]) ).
tcf(c_3076,plain,
coll(sK2,sK1,sK4),
inference(superposition,[status(thm)],[c_2826,c_86]) ).
tcf(c_3100,plain,
! [X0: $i,X1: $i] :
( coll(X0,sK2,X1)
| ~ coll(X0,X1,sK2) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_3101,plain,
( coll(sK4,sK2,sK4)
| ~ coll(sK4,sK4,sK2) ),
inference(instantiation,[status(thm)],[c_3100]) ).
tcf(c_3298,plain,
coll(sK1,sK2,sK4),
inference(superposition,[status(thm)],[c_3058,c_86]) ).
tcf(c_3309,plain,
( cong(sK4,sK4,sK4,sK7)
| ~ midp(sK4,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_3451,plain,
! [X0: $i] :
( coll(sK4,X0,sK7)
| ~ coll(sK7,sK8,X0) ),
inference(superposition,[status(thm)],[c_2924,c_84]) ).
tcf(c_3456,plain,
! [X0: $i] :
( coll(sK4,X0,sK2)
| ~ coll(sK2,sK1,X0) ),
inference(superposition,[status(thm)],[c_3076,c_84]) ).
tcf(c_3531,plain,
( coll(sK4,sK4,sK2)
| ~ coll(sK2,sK1,sK4) ),
inference(instantiation,[status(thm)],[c_3456]) ).
tcf(c_3535,plain,
( coll(sK4,sK4,sK7)
| ~ coll(sK7,sK8,sK4) ),
inference(instantiation,[status(thm)],[c_3451]) ).
tcf(c_4008,plain,
! [X0: $i] :
( coll(sK4,X0,sK1)
| ~ coll(sK1,sK2,X0) ),
inference(superposition,[status(thm)],[c_3298,c_84]) ).
tcf(c_4013,plain,
( coll(sK4,sK4,sK1)
| ~ coll(sK1,sK2,sK4) ),
inference(instantiation,[status(thm)],[c_4008]) ).
tcf(c_4363,plain,
! [X0: $i,X1: $i] :
( para(sK2,X0,sK1,X1)
| ~ midp(sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_51,c_106]) ).
tcf(c_4426,plain,
( para(sK4,sK7,sK4,sK7)
| ~ perp(sK4,sK6,sK4,sK7)
| ~ perp(sK4,sK7,sK4,sK6) ),
inference(instantiation,[status(thm)],[c_2528]) ).
tcf(c_4492,plain,
! [X0: $i,X1: $i] :
( para(X0,sK4,X1,sK2)
| ~ midp(X0,sK1,X1) ),
inference(superposition,[status(thm)],[c_2774,c_107]) ).
tcf(c_4806,plain,
! [X0: $i,X1: $i] :
( para(sK2,X0,X1,sK1)
| ~ midp(sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_4363,c_136]) ).
tcf(c_4807,plain,
! [X0: $i,X1: $i] :
( para(sK1,X1,sK2,X0)
| ~ midp(sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_4363,c_135]) ).
tcf(c_4842,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X1,sK7)
| ~ cong(X0,sK7,X1,sK7)
| ~ cong(X0,X1,X1,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_4843,plain,
( perp(sK4,sK4,sK4,sK7)
| ~ cong(sK4,sK4,sK4,sK4)
| ~ cong(sK4,sK7,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_4842]) ).
tcf(c_4947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,sK1,X2,X3)
| ~ para(X2,sK1,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_4948,plain,
( perp(sK4,sK1,sK4,sK4)
| ~ para(sK4,sK1,sK4,sK4)
| ~ perp(sK4,sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_4947]) ).
tcf(c_5258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK4,X3,sK2,X2)
| ~ perp(sK4,X3,X0,X1)
| ~ perp(X0,X1,sK2,X2) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_5259,plain,
( para(sK4,sK4,sK2,sK4)
| ~ perp(sK4,sK4,sK4,sK4)
| ~ perp(sK4,sK4,sK2,sK4) ),
inference(instantiation,[status(thm)],[c_5258]) ).
tcf(c_5262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,sK4,sK7)
| ~ perp(X2,X3,sK4,sK7)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_5263,plain,
( para(sK4,sK4,sK4,sK7)
| ~ perp(sK4,sK4,sK4,sK4)
| ~ perp(sK4,sK4,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_5262]) ).
tcf(c_6014,plain,
! [X0: $i] :
( cong(X0,sK2,X0,sK2)
| ~ cong(X0,sK2,X0,sK1)
| ~ cong(X0,sK1,X0,sK2) ),
inference(instantiation,[status(thm)],[c_2660]) ).
tcf(c_6015,plain,
( cong(sK4,sK2,sK4,sK2)
| ~ cong(sK4,sK2,sK4,sK1)
| ~ cong(sK4,sK1,sK4,sK2) ),
inference(instantiation,[status(thm)],[c_6014]) ).
tcf(c_7668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,sK1,X3)
| ~ midp(sK4,X2,X3)
| ~ para(X0,X1,sK2,X2) ),
inference(superposition,[status(thm)],[c_4363,c_134]) ).
tcf(c_9685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,sK1)
| ~ midp(sK4,X2,X3)
| ~ para(X0,X1,sK2,X2) ),
inference(superposition,[status(thm)],[c_4806,c_134]) ).
tcf(c_9697,plain,
( para(sK4,sK4,sK4,sK1)
| ~ midp(sK4,sK4,sK4)
| ~ para(sK4,sK4,sK2,sK4) ),
inference(instantiation,[status(thm)],[c_9685]) ).
tcf(c_9929,plain,
! [X0: $i,X1: $i] :
( midp(sK4,sK4,sK7)
| ~ coll(sK4,sK4,sK7)
| ~ midp(X0,sK4,X1)
| ~ para(X0,sK4,X1,sK7) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_9930,plain,
( midp(sK4,sK4,sK7)
| ~ coll(sK4,sK4,sK7)
| ~ midp(sK4,sK4,sK4)
| ~ para(sK4,sK4,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_9929]) ).
tcf(c_11345,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(sK4,X1,sK2)
| ~ coll(sK4,X1,sK2)
| ~ midp(X0,sK1,X2)
| ~ midp(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_4492,c_83]) ).
tcf(c_11476,plain,
( midp(sK4,sK4,sK2)
| ~ coll(sK4,sK4,sK2)
| ~ midp(sK4,sK4,sK4)
| ~ midp(sK4,sK1,sK4) ),
inference(instantiation,[status(thm)],[c_11345]) ).
tcf(c_12383,plain,
! [X0: $i] :
( cyclic(sK1,sK7,sK2,sK8)
| ~ cyclic(X0,sK1,sK7,sK8)
| ~ cyclic(X0,sK1,sK7,sK2) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_12384,plain,
( cyclic(sK1,sK7,sK2,sK8)
| ~ cyclic(sK4,sK1,sK7,sK8)
| ~ cyclic(sK4,sK1,sK7,sK2) ),
inference(instantiation,[status(thm)],[c_12383]) ).
tcf(c_13796,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(sK4,X2,sK1)
| ~ coll(sK4,X2,sK1)
| ~ midp(X0,X2,X1)
| ~ para(X0,sK4,X1,sK1) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_13797,plain,
( midp(sK4,sK4,sK1)
| ~ coll(sK4,sK4,sK1)
| ~ midp(sK4,sK4,sK4)
| ~ para(sK4,sK4,sK4,sK1) ),
inference(instantiation,[status(thm)],[c_13796]) ).
tcf(c_14541,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X2,sK7,sK7)
| ~ midp(X2,X0,X1)
| ~ para(X0,sK7,X1,sK7) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_14542,plain,
( midp(sK4,sK7,sK7)
| ~ midp(sK4,sK4,sK4)
| ~ para(sK4,sK7,sK4,sK7) ),
inference(instantiation,[status(thm)],[c_14541]) ).
tcf(c_18583,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK1,sK7,sK2)
| ~ cong(X0,X1,X0,sK2)
| ~ cong(X0,X1,X0,sK7)
| ~ cong(X0,X1,X0,sK1) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_18584,plain,
( cyclic(sK4,sK1,sK7,sK2)
| ~ cong(sK4,sK4,sK4,sK2)
| ~ cong(sK4,sK4,sK4,sK7)
| ~ cong(sK4,sK4,sK4,sK1) ),
inference(instantiation,[status(thm)],[c_18583]) ).
tcf(c_19430,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK1,X1,sK1,X2)
| ~ midp(sK4,X0,X2)
| ~ midp(sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_4807,c_7668]) ).
tcf(c_19507,plain,
( para(sK1,sK4,sK1,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_19430]) ).
tcf(c_28161,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X0,sK1)
| ~ perp(X0,sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_28162,plain,
( perp(sK4,sK4,sK4,sK1)
| ~ perp(sK4,sK1,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_28161]) ).
tcf(c_28193,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X0,sK2)
| ~ cong(X0,sK2,X1,sK2)
| ~ cong(X0,X0,X1,X0) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_28194,plain,
( perp(sK4,sK4,sK4,sK2)
| ~ cong(sK4,sK4,sK4,sK4)
| ~ cong(sK4,sK2,sK4,sK2) ),
inference(instantiation,[status(thm)],[c_28193]) ).
tcf(c_28240,plain,
coll(sK4,sK2,sK1),
inference(superposition,[status(thm)],[c_51,c_79]) ).
tcf(c_28247,plain,
coll(sK4,sK8,sK7),
inference(superposition,[status(thm)],[c_56,c_85]) ).
tcf(c_28293,plain,
coll(sK4,sK7,sK8),
inference(superposition,[status(thm)],[c_28247,c_86]) ).
tcf(c_28463,plain,
! [X0: $i] :
( coll(sK1,X0,sK7)
| ~ coll(sK7,sK0,X0) ),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_28467,plain,
! [X0: $i] :
( coll(sK1,X0,sK4)
| ~ coll(sK4,sK2,X0) ),
inference(superposition,[status(thm)],[c_28240,c_84]) ).
tcf(c_28606,plain,
coll(sK1,sK1,sK7),
inference(superposition,[status(thm)],[c_55,c_28463]) ).
tcf(c_28905,plain,
coll(sK1,sK1,sK4),
inference(superposition,[status(thm)],[c_28240,c_28467]) ).
tcf(c_28906,plain,
! [X0: $i] :
( coll(sK4,X0,sK1)
| ~ coll(sK1,sK1,X0) ),
inference(superposition,[status(thm)],[c_28905,c_84]) ).
tcf(c_29331,plain,
coll(sK4,sK7,sK1),
inference(superposition,[status(thm)],[c_28606,c_28906]) ).
tcf(c_29354,plain,
! [X0: $i] :
( coll(sK1,X0,sK4)
| ~ coll(sK4,sK7,X0) ),
inference(superposition,[status(thm)],[c_29331,c_84]) ).
tcf(c_29497,plain,
coll(sK1,sK8,sK4),
inference(superposition,[status(thm)],[c_28293,c_29354]) ).
tcf(c_36579,plain,
! [X0: $i,X1: $i,X2: $i] :
( cyclic(X1,X2,sK1,sK7)
| ~ cong(X0,X1,X0,sK7)
| ~ cong(X0,X1,X0,sK1)
| ~ cong(X0,X1,X0,X2) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_36580,plain,
( cyclic(sK4,sK4,sK1,sK7)
| ~ cong(sK4,sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK7)
| ~ cong(sK4,sK4,sK4,sK1) ),
inference(instantiation,[status(thm)],[c_36579]) ).
tcf(c_47008,plain,
! [X0: $i] :
( cong(X0,sK7,X0,sK7)
| ~ midp(X0,sK7,sK7) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_47009,plain,
( cong(sK4,sK7,sK4,sK7)
| ~ midp(sK4,sK7,sK7) ),
inference(instantiation,[status(thm)],[c_47008]) ).
tcf(c_53924,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(X2,sK1,X0,X1)
| ~ para(X0,X1,X2,sK1) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_53925,plain,
( para(sK4,sK1,sK4,sK4)
| ~ para(sK4,sK4,sK4,sK1) ),
inference(instantiation,[status(thm)],[c_53924]) ).
tcf(c_57169,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,X2,sK2,X1)
| ~ cong(X0,sK2,X2,sK2)
| ~ cong(X0,X1,X2,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_57170,plain,
( perp(sK4,sK4,sK2,sK4)
| ~ cong(sK4,sK4,sK4,sK4)
| ~ cong(sK4,sK2,sK4,sK2) ),
inference(instantiation,[status(thm)],[c_57169]) ).
tcf(c_68384,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X2,X0,sK1)
| ~ midp(X1,X2,sK1)
| ~ perp(X0,X1,X2,sK1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_68385,plain,
( cong(sK4,sK4,sK4,sK1)
| ~ midp(sK4,sK4,sK1)
| ~ perp(sK4,sK4,sK4,sK1) ),
inference(instantiation,[status(thm)],[c_68384]) ).
tcf(c_69165,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X2,X0,sK2)
| ~ midp(X1,X2,sK2)
| ~ perp(X0,X1,X2,sK2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_69166,plain,
( cong(sK4,sK4,sK4,sK2)
| ~ midp(sK4,sK4,sK2)
| ~ perp(sK4,sK4,sK4,sK2) ),
inference(instantiation,[status(thm)],[c_69165]) ).
tcf(c_74165,plain,
! [X0: $i,X1: $i] :
( cyclic(X1,sK1,sK7,sK8)
| ~ cyclic(X0,X1,sK1,sK8)
| ~ cyclic(X0,X1,sK1,sK7) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_74166,plain,
( cyclic(sK4,sK1,sK7,sK8)
| ~ cyclic(sK4,sK4,sK1,sK8)
| ~ cyclic(sK4,sK4,sK1,sK7) ),
inference(instantiation,[status(thm)],[c_74165]) ).
tcf(c_78800,plain,
! [X0: $i,X1: $i] :
( cyclic(X0,X1,sK1,sK8)
| ~ coll(sK1,sK8,X1)
| ~ eqangle(sK1,X0,sK1,X1,sK8,X0,sK8,X1) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_78801,plain,
( cyclic(sK4,sK4,sK1,sK8)
| ~ coll(sK1,sK8,sK4)
| ~ eqangle(sK1,sK4,sK1,sK4,sK8,sK4,sK8,sK4) ),
inference(instantiation,[status(thm)],[c_78800]) ).
tcf(c_81022,plain,
! [X0: $i,X1: $i] :
( eqangle(sK1,X0,sK1,X1,sK8,X0,sK8,X1)
| ~ eqangle(sK1,X0,sK8,X0,sK1,X1,sK8,X1) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_81023,plain,
( eqangle(sK1,sK4,sK1,sK4,sK8,sK4,sK8,sK4)
| ~ eqangle(sK1,sK4,sK8,sK4,sK1,sK4,sK8,sK4) ),
inference(instantiation,[status(thm)],[c_81022]) ).
tcf(c_87605,plain,
! [X0: $i] :
( eqangle(sK1,X0,sK8,X0,sK1,X0,sK8,X0)
| ~ para(sK1,X0,sK1,X0) ),
inference(instantiation,[status(thm)],[c_132]) ).
tcf(c_87606,plain,
( eqangle(sK1,sK4,sK8,sK4,sK1,sK4,sK8,sK4)
| ~ para(sK1,sK4,sK1,sK4) ),
inference(instantiation,[status(thm)],[c_87605]) ).
tcf(c_87607,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_87606,c_81023,c_78801,c_74166,c_69166,c_68385,c_57170,c_53925,c_47009,c_36580,c_29497,c_28194,c_28162,c_19507,c_18584,c_14542,c_13797,c_12384,c_11476,c_9930,c_9697,c_6015,c_5263,c_5259,c_4948,c_4843,c_4426,c_4013,c_3535,c_3531,c_3309,c_3298,c_3101,c_3076,c_3068,c_3013,c_3011,c_2671,c_2439,c_2429,c_2359,c_2247,c_2057,c_2055,c_2052,c_2049,c_2043,c_197,c_163,c_159,c_155,c_151,c_148,c_49,c_54,c_51,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO621+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n004.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Wed Sep 23 12:34:28 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.63 Running first-order theorem proving
% 0.16/5.63 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
% 0.16/5.65
% 0.16/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.65
% 0.16/5.65 % Detected problem language: tptp
% 0.16/5.66 % Proving...
% 32.56/12.55 % SZS status Started for theBenchmark.p
% 32.56/12.55 % SZS status Theorem for theBenchmark.p
% 32.56/12.55
% 32.56/12.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.56/12.55
% 32.56/12.55 % ------ iProver source info
% 32.56/12.55
% 32.56/12.55 % git: date: 2026-07-19 20:42:38 +0200
% 32.56/12.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.56/12.55 % git: non_committed_changes: false
% 32.56/12.55
% 32.56/12.55 % ------ Parsing...
% 32.56/12.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.56/12.55
% 32.56/12.55 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 32.56/12.55
% 32.56/12.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 32.56/12.55 % ------ Proving...
% 32.56/12.55 % ------ Problem Properties
% 32.56/12.55
% 32.56/12.55 %
% 32.56/12.55 % clauses 96
% 32.56/12.55 % conjectures 9
% 32.56/12.55 % EPR 63
% 32.56/12.55 % Horn 91
% 32.56/12.55 % unary 9
% 32.56/12.55 % binary 24
% 32.56/12.55 % lits 265
% 32.56/12.55 % lits eq 0
% 32.56/12.55 % fd_pure 0
% 32.56/12.55 % fd_pseudo 0
% 32.56/12.55 % fd_cond 0
% 32.56/12.55 % fd_pseudo_cond 0
% 32.56/12.55 % AC symbols 0
% 32.56/12.55
% 32.56/12.55 % ------ Schedule dynamic 5 is on
% 32.56/12.55
% 32.56/12.55 % ------ no equalities: superposition off
% 32.56/12.55
% 32.56/12.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.56/12.55
% 32.56/12.55
% 32.56/12.55 % ------
% 32.56/12.55 % Current options:
% 32.56/12.55 % ------
% 32.56/12.55
% 32.56/12.55
% 32.56/12.55 %
% 32.56/12.55
% 32.56/12.55 % ------ Proving...
% 32.56/12.55 %
% 32.56/12.55
% 32.56/12.55 % SZS status Theorem for theBenchmark.p
% 32.56/12.55
% 32.56/12.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.56/12.55
% 32.56/12.55
%------------------------------------------------------------------------------