%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO582+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 : n009.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 01:21:32 PM UTC 2026
% Result : Theorem 22.38s 4.03s
% Output : CNFRefutation 22.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 25
% Syntax : Number of formulae : 268 ( 56 unt; 0 def)
% Number of atoms : 660 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 703 ( 311 ~; 305 |; 61 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 11 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 670 ( 0 sgn 645 !; 25 ?; 218 :)
% 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(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(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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
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(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(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(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(f86,axiom,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ( perp(X1,X3,X0,X2)
& perp(X0,X3,X1,X2) )
=> ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX10) ).
fof(f91,axiom,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ( coll(X1,X3,X4)
& perp(X0,X2,X2,X1) )
=> ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX15) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( coll(X6,X0,X1)
& perp(X2,X4,X2,X6)
& coll(X5,X2,X4)
& perp(X0,X1,X0,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2) )
=> para(X4,X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416044) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( coll(X6,X0,X1)
& perp(X2,X4,X2,X6)
& coll(X5,X2,X4)
& perp(X0,X1,X0,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2) )
=> para(X4,X1,X5,X6) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( coll(X6,X0,X1)
& perp(X2,X4,X2,X6)
& coll(X5,X2,X4)
& perp(X0,X1,X0,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2)
& ~ para(X4,X1,X5,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( coll(X6,X0,X1)
& perp(X2,X4,X2,X6)
& coll(X5,X2,X4)
& perp(X0,X1,X0,X5)
& circle(X3,X0,X4,X7)
& circle(X3,X0,X1,X2)
& ~ para(X4,X1,X5,X6) ),
inference(flattening,[],[f98]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(X5,X0,X3,X4)
& coll(X5,X3,X4) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
? [X4,X5] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,X5,X2,X0)
& coll(X5,X2,X0)
& perp(X0,X4,X2,X1)
& coll(X4,X2,X1) ) ),
inference(flattening,[],[f106]) ).
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(f136,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(f137,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,[],[f136]) ).
fof(f142,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(f143,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,[],[f142]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(flattening,[],[f146]) ).
fof(f148,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(f152,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(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f152]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f162,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(f163,plain,
! [X0,X1,X2,X3] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(flattening,[],[f162]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(flattening,[],[f164]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f196,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f198,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(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,
( coll(sK6,sK0,sK1)
& perp(sK2,sK4,sK2,sK6)
& coll(sK5,sK2,sK4)
& perp(sK0,sK1,sK0,sK5)
& circle(sK3,sK0,sK4,sK7)
& circle(sK3,sK0,sK1,sK2)
& ~ para(sK4,sK1,sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f99]) ).
fof(f223,plain,
! [X0,X1,X2,X3,X4] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| ( perp(sK10(X0,X1,X2,X3,X4),X0,X3,X4)
& coll(sK10(X0,X1,X2,X3,X4),X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X5,sK10(X0,X1,X2,X3,X4))],[f105]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| ( perp(X1,sK12(X0,X1,X2,X3),X2,X0)
& coll(sK12(X0,X1,X2,X3),X2,X0)
& perp(X0,sK11(X0,X1,X2,X3),X2,X1)
& coll(sK11(X0,X1,X2,X3),X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1,X2,X3)),skolemize(X5,sK12(X0,X1,X2,X3))],[f107]) ).
fof(f239,plain,
coll(sK6,sK0,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f240,plain,
perp(sK2,sK4,sK2,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f241,plain,
coll(sK5,sK2,sK4),
inference(cnf_transformation,[],[f220]) ).
fof(f242,plain,
perp(sK0,sK1,sK0,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
~ para(sK4,sK1,sK5,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f250,plain,
! [X2,X3,X0,X1,X4] :
( ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1)
| perp(sK10(X0,X1,X2,X3,X4),X0,X3,X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2)
| coll(sK11(X0,X1,X2,X3),X2,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f271,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(f272,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f273,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f281,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,[],[f137]) ).
fof(f284,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,[],[f143]) ).
fof(f286,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1)
| para(X3,X4,X1,X2) ),
inference(cnf_transformation,[],[f147]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f148]) ).
fof(f290,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,[],[f153]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f157]) ).
fof(f296,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f163]) ).
fof(f297,plain,
! [X2,X3,X0,X1] :
( ~ perp(X3,X2,X0,X1)
| ~ midp(X2,X0,X1)
| cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f299,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f169]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f187]) ).
fof(f317,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f196]) ).
fof(f319,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,[],[f198]) ).
fof(f325,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(f326,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,
~ para(sK4,sK1,sK5,sK6),
inference(cnf_transformation,[],[f245]) ).
tcf(c_52,negated_conjecture,
perp(sK0,sK1,sK0,sK5),
inference(cnf_transformation,[],[f242]) ).
tcf(c_53,negated_conjecture,
coll(sK5,sK2,sK4),
inference(cnf_transformation,[],[f241]) ).
tcf(c_54,negated_conjecture,
perp(sK2,sK4,sK2,sK6),
inference(cnf_transformation,[],[f240]) ).
tcf(c_55,negated_conjecture,
coll(sK6,sK0,sK1),
inference(cnf_transformation,[],[f239]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( perp(sK10(X0,X2,X1,X3,X4),X0,X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(sK11(X0,X2,X3,X1),X3,X2)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( midp(X1,X4,X3)
| ~ midp(X0,X4,X2)
| ~ coll(X1,X4,X3)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_91,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,[],[f281]) ).
tcf(c_94,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,[],[f284]) ).
tcf(c_96,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,[],[f286]) ).
tcf(c_97,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,[],[f287]) ).
tcf(c_100,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,[],[f290]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_106,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,[],[f296]) ).
tcf(c_107,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,[],[f297]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_127,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,[],[f317]) ).
tcf(c_129,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,[],[f319]) ).
tcf(c_135,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,[],[f325]) ).
tcf(c_136,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,[],[f326]) ).
tcf(c_153,plain,
( midp(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_156,plain,
( perp(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_2147,plain,
( coll(sK6,sK1,sK0)
| ~ coll(sK6,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_2148,plain,
( perp(sK0,sK5,sK0,sK1)
| ~ perp(sK0,sK1,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_2176,plain,
( coll(sK11(sK0,sK0,sK5,sK1),sK5,sK0)
| ~ perp(sK0,sK1,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2327,plain,
! [X0: $i] :
( coll(sK0,X0,sK6)
| ~ coll(sK6,sK1,sK0)
| ~ coll(sK6,sK1,X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2346,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK5,X0,X1)
| ~ perp(sK0,sK5,sK0,sK1)
| ~ perp(sK0,sK1,X0,X1) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_2470,plain,
( coll(sK5,sK11(sK0,sK0,sK5,sK1),sK0)
| ~ coll(sK11(sK0,sK0,sK5,sK1),sK5,sK0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2794,plain,
coll(sK0,sK6,sK1),
inference(superposition,[status(thm)],[c_55,c_83]) ).
tcf(c_2806,plain,
coll(sK6,sK1,sK0),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_2811,plain,
coll(sK5,sK4,sK2),
inference(superposition,[status(thm)],[c_53,c_84]) ).
tcf(c_2997,plain,
perp(sK0,sK5,sK0,sK1),
inference(superposition,[status(thm)],[c_52,c_109]) ).
tcf(c_2998,plain,
perp(sK2,sK6,sK2,sK4),
inference(superposition,[status(thm)],[c_54,c_109]) ).
tcf(c_3004,plain,
perp(sK2,sK6,sK2,sK4),
inference(superposition,[status(thm)],[c_54,c_109]) ).
tcf(c_3039,plain,
perp(sK0,sK1,sK5,sK0),
inference(superposition,[status(thm)],[c_52,c_110]) ).
tcf(c_3040,plain,
perp(sK2,sK4,sK6,sK2),
inference(superposition,[status(thm)],[c_54,c_110]) ).
tcf(c_3046,plain,
perp(sK2,sK4,sK6,sK2),
inference(superposition,[status(thm)],[c_54,c_110]) ).
tcf(c_3403,plain,
! [X0: $i] :
( coll(sK1,X0,sK6)
| ~ coll(sK6,sK0,X0) ),
inference(superposition,[status(thm)],[c_55,c_82]) ).
tcf(c_3405,plain,
! [X0: $i] :
( coll(sK1,X0,sK0)
| ~ coll(sK0,sK6,X0) ),
inference(superposition,[status(thm)],[c_2794,c_82]) ).
tcf(c_3407,plain,
! [X0: $i] :
( coll(sK0,X0,sK6)
| ~ coll(sK6,sK1,X0) ),
inference(superposition,[status(thm)],[c_2806,c_82]) ).
tcf(c_3452,plain,
! [X0: $i] :
( coll(sK4,X0,sK5)
| ~ coll(sK5,sK2,X0) ),
inference(superposition,[status(thm)],[c_53,c_82]) ).
tcf(c_3456,plain,
! [X0: $i] :
( coll(sK2,X0,sK5)
| ~ coll(sK5,sK4,X0) ),
inference(superposition,[status(thm)],[c_2811,c_82]) ).
tcf(c_3925,plain,
coll(sK2,sK2,sK5),
inference(superposition,[status(thm)],[c_2811,c_3456]) ).
tcf(c_3933,plain,
! [X0: $i] :
( coll(sK5,X0,sK2)
| ~ coll(sK2,sK2,X0) ),
inference(superposition,[status(thm)],[c_3925,c_82]) ).
tcf(c_3956,plain,
coll(sK0,sK0,sK6),
inference(superposition,[status(thm)],[c_2806,c_3407]) ).
tcf(c_3962,plain,
! [X0: $i] :
( coll(sK6,X0,sK0)
| ~ coll(sK0,sK0,X0) ),
inference(superposition,[status(thm)],[c_3956,c_82]) ).
tcf(c_3963,plain,
coll(sK0,sK6,sK0),
inference(superposition,[status(thm)],[c_3956,c_84]) ).
tcf(c_4085,plain,
! [X0: $i] :
( coll(sK0,X0,sK5)
| ~ coll(sK5,sK11(sK0,sK0,sK5,sK1),sK0)
| ~ coll(sK5,sK11(sK0,sK0,sK5,sK1),X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_4088,plain,
( coll(sK0,sK0,sK5)
| ~ coll(sK5,sK11(sK0,sK0,sK5,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_4085]) ).
tcf(c_4331,plain,
! [X0: $i] :
( coll(sK0,X0,sK0)
| ~ coll(sK0,sK6,X0) ),
inference(superposition,[status(thm)],[c_3963,c_82]) ).
tcf(c_4337,plain,
( coll(sK0,sK0,sK0)
| ~ coll(sK0,sK6,sK0) ),
inference(instantiation,[status(thm)],[c_4331]) ).
tcf(c_5097,plain,
( para(sK0,sK5,sK0,sK5)
| ~ perp(sK0,sK5,sK0,sK1)
| ~ perp(sK0,sK1,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_2346]) ).
tcf(c_5289,plain,
! [X0: $i,X1: $i] :
( coll(X1,sK5,sK0)
| ~ coll(sK0,X0,sK5)
| ~ coll(sK0,X0,X1) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_5290,plain,
( coll(sK0,sK5,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_5289]) ).
tcf(c_5373,plain,
( coll(sK0,sK5,sK6)
| ~ coll(sK6,sK1,sK0)
| ~ coll(sK6,sK1,sK5) ),
inference(instantiation,[status(thm)],[c_2327]) ).
tcf(c_5518,plain,
! [X0: $i,X1: $i] :
( para(sK2,sK4,X0,X1)
| ~ perp(sK2,sK6,X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_100]) ).
tcf(c_5522,plain,
! [X0: $i,X1: $i] :
( para(sK0,sK5,X0,X1)
| ~ perp(sK0,sK1,X0,X1) ),
inference(superposition,[status(thm)],[c_2997,c_100]) ).
tcf(c_5523,plain,
! [X0: $i,X1: $i] :
( para(sK2,sK6,X0,X1)
| ~ perp(sK2,sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_2998,c_100]) ).
tcf(c_5617,plain,
! [X0: $i,X1: $i] :
( para(sK2,sK6,X0,X1)
| ~ perp(sK2,sK4,X0,X1) ),
inference(superposition,[status(thm)],[c_3004,c_100]) ).
tcf(c_5809,plain,
! [X0: $i,X1: $i] :
( eqangle(sK0,sK5,X0,X1,sK0,sK5,X0,X1)
| ~ para(sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_5812,plain,
( eqangle(sK0,sK5,sK0,sK0,sK0,sK5,sK0,sK0)
| ~ para(sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_5809]) ).
tcf(c_5816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,X2,X3)
| ~ para(sK0,sK5,sK0,sK5)
| ~ eqangle(X0,X1,X2,X3,sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_5817,plain,
( para(sK0,sK0,sK0,sK0)
| ~ para(sK0,sK5,sK0,sK5)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_5816]) ).
tcf(c_6619,plain,
para(sK2,sK4,sK2,sK4),
inference(superposition,[status(thm)],[c_2998,c_5518]) ).
tcf(c_6835,plain,
! [X0: $i] :
( midp(X0,sK4,sK4)
| ~ midp(X0,sK2,sK2)
| ~ para(sK2,sK4,sK2,sK4) ),
inference(superposition,[status(thm)],[c_6619,c_94]) ).
tcf(c_6838,plain,
! [X0: $i] :
( midp(X0,sK4,sK4)
| ~ midp(X0,sK2,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6835,c_6619]) ).
tcf(c_6841,plain,
( midp(sK0,sK4,sK4)
| ~ midp(sK0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_6838]) ).
tcf(c_7386,plain,
! [X0: $i,X1: $i] :
( perp(sK0,sK5,X0,X1)
| ~ perp(X0,X1,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_7387,plain,
( perp(sK0,sK5,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_7386]) ).
tcf(c_7942,plain,
( para(sK4,sK1,sK5,sK6)
| ~ para(sK4,sK1,sK6,sK5) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_8396,plain,
para(sK0,sK5,sK0,sK5),
inference(superposition,[status(thm)],[c_52,c_5522]) ).
tcf(c_8398,plain,
para(sK0,sK5,sK5,sK0),
inference(superposition,[status(thm)],[c_3039,c_5522]) ).
tcf(c_8426,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK0,sK0)
| ~ para(sK0,sK5,sK0,sK5) ),
inference(superposition,[status(thm)],[c_8396,c_94]) ).
tcf(c_8428,plain,
coll(sK0,sK5,sK5),
inference(superposition,[status(thm)],[c_8396,c_79]) ).
tcf(c_8429,plain,
! [X0: $i] :
( midp(X0,sK5,sK5)
| ~ midp(X0,sK0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8426,c_8396]) ).
tcf(c_8432,plain,
( midp(sK0,sK5,sK5)
| ~ midp(sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_8429]) ).
tcf(c_8954,plain,
! [X0: $i] :
( coll(sK5,X0,sK0)
| ~ coll(sK0,sK5,X0) ),
inference(superposition,[status(thm)],[c_8428,c_82]) ).
tcf(c_8959,plain,
( coll(sK5,sK0,sK0)
| ~ coll(sK0,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_8954]) ).
tcf(c_8969,plain,
para(sK5,sK0,sK0,sK5),
inference(superposition,[status(thm)],[c_8398,c_102]) ).
tcf(c_9132,plain,
para(sK2,sK6,sK6,sK2),
inference(superposition,[status(thm)],[c_3040,c_5523]) ).
tcf(c_9142,plain,
para(sK2,sK6,sK6,sK2),
inference(superposition,[status(thm)],[c_3046,c_5617]) ).
tcf(c_9209,plain,
para(sK6,sK2,sK2,sK6),
inference(superposition,[status(thm)],[c_9132,c_102]) ).
tcf(c_9224,plain,
para(sK6,sK2,sK2,sK6),
inference(superposition,[status(thm)],[c_9142,c_102]) ).
tcf(c_11386,plain,
! [X0: $i] :
( midp(sK0,X0,sK5)
| ~ midp(sK5,X0,sK0)
| ~ coll(sK0,X0,sK5) ),
inference(superposition,[status(thm)],[c_8969,c_81]) ).
tcf(c_11388,plain,
para(sK5,sK0,sK5,sK0),
inference(superposition,[status(thm)],[c_8969,c_103]) ).
tcf(c_11403,plain,
( midp(sK0,sK0,sK5)
| ~ midp(sK5,sK0,sK0)
| ~ coll(sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_11386]) ).
tcf(c_12592,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_97,c_136]) ).
tcf(c_12605,plain,
( cyclic(sK0,sK0,sK0,sK0)
| ~ coll(sK0,sK0,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_12592]) ).
tcf(c_12661,plain,
para(sK6,sK2,sK6,sK2),
inference(superposition,[status(thm)],[c_9209,c_103]) ).
tcf(c_12681,plain,
para(sK6,sK2,sK6,sK2),
inference(superposition,[status(thm)],[c_9224,c_103]) ).
tcf(c_12720,plain,
( coll(sK6,sK1,sK5)
| ~ coll(sK1,sK6,sK5) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_12852,plain,
coll(sK5,sK0,sK0),
inference(superposition,[status(thm)],[c_11388,c_79]) ).
tcf(c_12909,plain,
! [X0: $i,X1: $i] :
( eqangle(X0,X1,sK0,sK5,X0,X1,sK0,sK5)
| ~ eqangle(sK0,sK5,X0,X1,sK0,sK5,X0,X1) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_12910,plain,
( eqangle(sK0,sK0,sK0,sK5,sK0,sK0,sK0,sK5)
| ~ eqangle(sK0,sK5,sK0,sK0,sK0,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_12909]) ).
tcf(c_14412,plain,
coll(sK0,sK5,sK0),
inference(superposition,[status(thm)],[c_12852,c_83]) ).
tcf(c_14445,plain,
coll(sK0,sK0,sK5),
inference(superposition,[status(thm)],[c_14412,c_84]) ).
tcf(c_14578,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(sK10(X0,X2,X1,sK5,sK6),X0,sK5,sK6)
| ~ coll(X2,sK5,sK6)
| ~ perp(X0,X1,X1,X2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_14580,plain,
( perp(sK10(sK0,sK0,sK0,sK5,sK6),sK0,sK5,sK6)
| ~ coll(sK0,sK5,sK6)
| ~ perp(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_14578]) ).
tcf(c_14608,plain,
! [X0: $i] :
( midp(X0,sK2,sK2)
| ~ midp(X0,sK6,sK6)
| ~ para(sK6,sK2,sK6,sK2) ),
inference(superposition,[status(thm)],[c_12661,c_94]) ).
tcf(c_14614,plain,
! [X0: $i] :
( midp(X0,sK2,sK2)
| ~ midp(X0,sK6,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14608,c_12661]) ).
tcf(c_14617,plain,
( midp(sK0,sK2,sK2)
| ~ midp(sK0,sK6,sK6) ),
inference(instantiation,[status(thm)],[c_14614]) ).
tcf(c_14625,plain,
coll(sK6,sK2,sK2),
inference(superposition,[status(thm)],[c_12681,c_79]) ).
tcf(c_15494,plain,
coll(sK2,sK6,sK2),
inference(superposition,[status(thm)],[c_14625,c_83]) ).
tcf(c_15629,plain,
coll(sK2,sK2,sK6),
inference(superposition,[status(thm)],[c_15494,c_84]) ).
tcf(c_15746,plain,
coll(sK5,sK6,sK2),
inference(superposition,[status(thm)],[c_15629,c_3933]) ).
tcf(c_15794,plain,
coll(sK6,sK5,sK0),
inference(superposition,[status(thm)],[c_14445,c_3962]) ).
tcf(c_16923,plain,
coll(sK5,sK2,sK6),
inference(superposition,[status(thm)],[c_15746,c_84]) ).
tcf(c_17017,plain,
coll(sK6,sK0,sK5),
inference(superposition,[status(thm)],[c_15794,c_84]) ).
tcf(c_17104,plain,
coll(sK4,sK6,sK5),
inference(superposition,[status(thm)],[c_16923,c_3452]) ).
tcf(c_17583,plain,
coll(sK6,sK4,sK5),
inference(superposition,[status(thm)],[c_17104,c_83]) ).
tcf(c_19357,plain,
coll(sK0,sK6,sK5),
inference(superposition,[status(thm)],[c_17017,c_83]) ).
tcf(c_19358,plain,
coll(sK1,sK5,sK6),
inference(superposition,[status(thm)],[c_17017,c_3403]) ).
tcf(c_19752,plain,
coll(sK1,sK6,sK5),
inference(superposition,[status(thm)],[c_19358,c_84]) ).
tcf(c_21199,plain,
coll(sK6,sK5,sK4),
inference(superposition,[status(thm)],[c_17583,c_84]) ).
tcf(c_22871,plain,
coll(sK1,sK5,sK0),
inference(superposition,[status(thm)],[c_19357,c_3405]) ).
tcf(c_26982,plain,
coll(sK1,sK0,sK5),
inference(superposition,[status(thm)],[c_22871,c_84]) ).
tcf(c_27400,plain,
perp(sK0,sK5,sK0,sK1),
inference(superposition,[status(thm)],[c_52,c_109]) ).
tcf(c_27487,plain,
perp(sK0,sK5,sK1,sK0),
inference(superposition,[status(thm)],[c_27400,c_110]) ).
tcf(c_27494,plain,
perp(sK1,sK0,sK0,sK5),
inference(superposition,[status(thm)],[c_27487,c_109]) ).
tcf(c_27886,plain,
( cong(sK1,sK0,sK1,sK5)
| ~ midp(sK0,sK0,sK5) ),
inference(superposition,[status(thm)],[c_27494,c_107]) ).
tcf(c_28323,plain,
( midp(sK1,sK0,sK5)
| ~ midp(sK0,sK0,sK5)
| ~ coll(sK1,sK0,sK5) ),
inference(superposition,[status(thm)],[c_27886,c_78]) ).
tcf(c_33508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( cong(X1,X3,X2,X3)
| ~ cyclic(X1,X3,X0,X3)
| ~ cyclic(X1,X3,X0,X2)
| ~ cyclic(X1,X3,X0,X0)
| ~ para(X0,X1,X0,X2) ),
inference(superposition,[status(thm)],[c_97,c_135]) ).
tcf(c_33598,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,sK0,sK0)
| ~ para(sK0,sK0,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_33508]) ).
tcf(c_33811,plain,
! [X0: $i] :
( coll(sK4,X0,sK6)
| ~ coll(sK6,sK5,X0) ),
inference(superposition,[status(thm)],[c_21199,c_82]) ).
tcf(c_33816,plain,
( coll(sK4,sK0,sK6)
| ~ coll(sK6,sK5,sK0) ),
inference(instantiation,[status(thm)],[c_33811]) ).
tcf(c_41596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(sK0,sK5,X2,X3)
| ~ perp(sK0,sK5,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_41597,plain,
( para(sK0,sK5,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK0)
| ~ perp(sK0,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_41596]) ).
tcf(c_42777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( eqangle(X0,X1,X2,X3,sK0,sK5,sK0,sK5)
| ~ eqangle(X0,X1,sK0,sK5,X2,X3,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_42778,plain,
( eqangle(sK0,sK0,sK0,sK0,sK0,sK5,sK0,sK5)
| ~ eqangle(sK0,sK0,sK0,sK5,sK0,sK0,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_42777]) ).
tcf(c_49583,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_106]) ).
tcf(c_49584,plain,
( perp(sK0,sK0,sK0,sK5)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK5,sK0,sK5) ),
inference(instantiation,[status(thm)],[c_49583]) ).
tcf(c_49585,plain,
! [X0: $i,X1: $i] :
( perp(X0,X1,X1,sK6)
| ~ cong(X0,sK6,X1,sK6)
| ~ cong(X0,X1,X1,X1) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_49586,plain,
( perp(sK0,sK0,sK0,sK6)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK6,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_49585]) ).
tcf(c_49615,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_106]) ).
tcf(c_49616,plain,
( perp(sK0,sK0,sK0,sK4)
| ~ cong(sK0,sK0,sK0,sK0)
| ~ cong(sK0,sK4,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_49615]) ).
tcf(c_54112,plain,
! [X0: $i] :
( cong(X0,sK5,X0,sK5)
| ~ midp(X0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_54113,plain,
( cong(sK0,sK5,sK0,sK5)
| ~ midp(sK0,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_54112]) ).
tcf(c_58408,plain,
! [X0: $i] :
( para(sK4,sK1,sK6,sK5)
| ~ midp(sK1,X0,sK5)
| ~ midp(sK4,X0,sK6) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_58409,plain,
( para(sK4,sK1,sK6,sK5)
| ~ midp(sK1,sK0,sK5)
| ~ midp(sK4,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_58408]) ).
tcf(c_58478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,X1,sK5,sK6)
| ~ perp(X2,X3,sK5,sK6)
| ~ perp(X0,X1,X2,X3) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_58614,plain,
! [X0: $i,X1: $i,X2: $i] :
( midp(sK4,X2,sK6)
| ~ coll(sK4,X2,sK6)
| ~ midp(X0,X2,X1)
| ~ para(X0,sK4,X1,sK6) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_58615,plain,
( midp(sK4,sK0,sK6)
| ~ midp(sK0,sK0,sK0)
| ~ coll(sK4,sK0,sK6)
| ~ para(sK0,sK4,sK0,sK6) ),
inference(instantiation,[status(thm)],[c_58614]) ).
tcf(c_58763,plain,
! [X0: $i,X1: $i] :
( perp(sK5,sK6,X0,X1)
| ~ perp(X0,X1,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_58978,plain,
! [X0: $i] :
( cong(X0,sK6,X0,sK6)
| ~ midp(X0,sK6,sK6) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_58979,plain,
( cong(sK0,sK6,sK0,sK6)
| ~ midp(sK0,sK6,sK6) ),
inference(instantiation,[status(thm)],[c_58978]) ).
tcf(c_59017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( midp(X3,X1,sK6)
| ~ midp(X3,X0,X2)
| ~ para(X0,sK6,X2,X1)
| ~ para(X0,X1,X2,sK6) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_59410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( para(X0,X1,sK5,sK6)
| ~ perp(sK10(X2,X3,X4,sK5,sK6),X2,sK5,sK6)
| ~ perp(X0,X1,sK10(X2,X3,X4,sK5,sK6),X2) ),
inference(instantiation,[status(thm)],[c_58478]) ).
tcf(c_60413,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(sK5,sK6,sK10(X0,X1,X2,sK5,sK6),X0)
| ~ perp(sK10(X0,X1,X2,sK5,sK6),X0,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_58763]) ).
tcf(c_60414,plain,
( perp(sK5,sK6,sK10(sK0,sK0,sK0,sK5,sK6),sK0)
| ~ perp(sK10(sK0,sK0,sK0,sK5,sK6),sK0,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_60413]) ).
tcf(c_61031,plain,
! [X0: $i] :
( cong(X0,sK4,X0,sK4)
| ~ midp(X0,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_61032,plain,
( cong(sK0,sK4,sK0,sK4)
| ~ midp(sK0,sK4,sK4) ),
inference(instantiation,[status(thm)],[c_61031]) ).
tcf(c_61129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( midp(sK5,X3,X2)
| ~ coll(sK5,X3,X2)
| ~ midp(X0,X3,X1)
| ~ para(X0,sK5,X1,X2) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_61130,plain,
( midp(sK5,sK0,sK0)
| ~ midp(sK0,sK0,sK0)
| ~ coll(sK5,sK0,sK0)
| ~ para(sK0,sK5,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_61129]) ).
tcf(c_61376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X0,sK4,X3,sK6)
| ~ perp(X1,X2,X3,sK6)
| ~ perp(X0,sK4,X1,X2) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_61379,plain,
( para(sK0,sK4,sK0,sK6)
| ~ perp(sK0,sK0,sK0,sK6)
| ~ perp(sK0,sK4,sK0,sK0) ),
inference(instantiation,[status(thm)],[c_61376]) ).
tcf(c_62459,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X2,sK4,X0,X1)
| ~ perp(X0,X1,X2,sK4) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_62460,plain,
( perp(sK0,sK4,sK0,sK0)
| ~ perp(sK0,sK0,sK0,sK4) ),
inference(instantiation,[status(thm)],[c_62459]) ).
tcf(c_64096,plain,
! [X0: $i,X1: $i,X2: $i] :
( para(sK5,sK6,sK5,sK6)
| ~ perp(sK5,sK6,sK10(X0,X1,X2,sK5,sK6),X0)
| ~ perp(sK10(X0,X1,X2,sK5,sK6),X0,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_59410]) ).
tcf(c_64097,plain,
( para(sK5,sK6,sK5,sK6)
| ~ perp(sK5,sK6,sK10(sK0,sK0,sK0,sK5,sK6),sK0)
| ~ perp(sK10(sK0,sK0,sK0,sK5,sK6),sK0,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_64096]) ).
tcf(c_66068,plain,
! [X0: $i] :
( midp(X0,sK6,sK6)
| ~ midp(X0,sK5,sK5)
| ~ para(sK5,sK6,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_59017]) ).
tcf(c_66071,plain,
( midp(sK0,sK6,sK6)
| ~ midp(sK0,sK5,sK5)
| ~ para(sK5,sK6,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_66068]) ).
tcf(c_66072,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_66071,c_64097,c_62460,c_61379,c_61130,c_61032,c_60414,c_58979,c_58615,c_58409,c_54113,c_49616,c_49586,c_49584,c_42778,c_41597,c_33816,c_33598,c_28323,c_26982,c_19752,c_15794,c_14617,c_14580,c_12910,c_12720,c_12605,c_11403,c_8959,c_8432,c_7942,c_7387,c_6841,c_5817,c_5812,c_5373,c_5290,c_5097,c_4337,c_4088,c_3963,c_2470,c_2176,c_2148,c_2147,c_156,c_153,c_49,c_52,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO582+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n009.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 12:28:28 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.14/0.63
% 0.14/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.63
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 22.38/4.03 % SZS status Started for theBenchmark.p
% 22.38/4.03 % SZS status Theorem for theBenchmark.p
% 22.38/4.03
% 22.38/4.03 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.38/4.03
% 22.38/4.03 % ------ iProver source info
% 22.38/4.03
% 22.38/4.03 % git: date: 2026-07-19 20:42:38 +0200
% 22.38/4.03 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.38/4.03 % git: non_committed_changes: false
% 22.38/4.03
% 22.38/4.03 % ------ Parsing...
% 22.38/4.03 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.38/4.03
% 22.38/4.03 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.38/4.03
% 22.38/4.03 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 22.38/4.03 % ------ Proving...
% 22.38/4.03 % ------ Problem Properties
% 22.38/4.03
% 22.38/4.03 %
% 22.38/4.03 % clauses 94
% 22.38/4.03 % conjectures 7
% 22.38/4.03 % EPR 61
% 22.38/4.03 % Horn 89
% 22.38/4.03 % unary 7
% 22.38/4.03 % binary 24
% 22.38/4.03 % lits 263
% 22.38/4.03 % lits eq 0
% 22.38/4.03 % fd_pure 0
% 22.38/4.03 % fd_pseudo 0
% 22.38/4.03 % fd_cond 0
% 22.38/4.03 % fd_pseudo_cond 0
% 22.38/4.03 % AC symbols 0
% 22.38/4.03
% 22.38/4.03 % ------ Schedule dynamic 5 is on
% 22.38/4.03
% 22.38/4.03 % ------ no equalities: superposition off
% 22.38/4.03
% 22.38/4.03 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.38/4.03
% 22.38/4.03
% 22.38/4.03 % ------
% 22.38/4.03 % Current options:
% 22.38/4.03 % ------
% 22.38/4.03
% 22.38/4.03
% 22.38/4.03 %
% 22.38/4.03
% 22.38/4.03 % ------ Proving...
% 22.38/4.03 %
% 22.38/4.03
% 22.38/4.03 % SZS status Theorem for theBenchmark.p
% 22.38/4.03
% 22.38/4.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.38/4.04
% 22.38/4.04
%------------------------------------------------------------------------------