%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Sun Sep 27 07:15:35 AM UTC 2026
% Result : Theorem 48.77s 15.96s
% Output : CNFRefutation 48.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 38
% Syntax : Number of formulae : 174 ( 34 unt; 0 def)
% Number of atoms : 423 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 417 ( 168 ~; 166 |; 44 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 715 ( 69 sgn 218 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ) ).
fof(ruleD2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ) ).
fof(ruleD3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ) ).
fof(ruleD5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ) ).
fof(ruleD8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ) ).
fof(ruleD9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ) ).
fof(ruleD11,axiom,
! [X0,X1,X2] :
( midp(X2,X1,X0)
=> midp(X2,X0,X1) ) ).
fof(ruleD12,axiom,
! [X0,X1,X2,X3] :
( ( cong(X3,X0,X3,X2)
& cong(X3,X0,X3,X1) )
=> circle(X3,X0,X1,X2) ) ).
fof(ruleD14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ) ).
fof(ruleD15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ) ).
fof(ruleD16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ) ).
fof(ruleD18,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) ) ).
fof(ruleD19,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) ) ).
fof(ruleD20,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) ) ).
fof(ruleD21,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) ) ).
fof(ruleD22,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) ) ).
fof(ruleD23,axiom,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
=> cong(X0,X1,X3,X2) ) ).
fof(ruleD24,axiom,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
=> cong(X2,X3,X0,X1) ) ).
fof(ruleD25,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cong(X2,X3,X4,X5)
& cong(X0,X1,X2,X3) )
=> cong(X0,X1,X4,X5) ) ).
fof(ruleD39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ) ).
fof(ruleD40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ) ).
fof(ruleD41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ) ).
fof(ruleD42b,axiom,
! [X0,X1,X2,X3] :
( ( coll(X2,X3,X1)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ) ).
fof(ruleD43,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) ) ).
fof(ruleD44,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X0,X2)
& midp(X3,X0,X1) )
=> para(X3,X4,X1,X2) ) ).
fof(ruleD45,axiom,
! [X0,X1,X2,X3,X4] :
( ( coll(X4,X0,X2)
& para(X3,X4,X1,X2)
& midp(X3,X0,X1) )
=> midp(X4,X0,X2) ) ).
fof(ruleD46,axiom,
! [X0,X1,X2] :
( cong(X2,X0,X2,X1)
=> eqangle(X2,X0,X0,X1,X0,X1,X2,X1) ) ).
fof(ruleD49,axiom,
! [X0,X1,X2,X3,X4] :
( ( eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
& circle(X3,X0,X1,X2) )
=> perp(X3,X0,X0,X4) ) ).
fof(ruleD51,axiom,
! [X0,X1,X2,X3,X4] :
( ( eqangle(X0,X1,X0,X2,X3,X1,X3,X4)
& coll(X4,X1,X2)
& circle(X3,X0,X1,X2) )
=> midp(X4,X1,X2) ) ).
fof(ruleD56,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X0,X1,X2,X3) ) ).
fof(ruleD63,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X2,X3)
& midp(X4,X0,X1) )
=> para(X0,X2,X1,X3) ) ).
fof(ruleD66,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ) ).
fof(ruleD67,axiom,
! [X0,X1,X2] :
( ( coll(X0,X1,X2)
& cong(X0,X1,X0,X2) )
=> midp(X0,X1,X2) ) ).
fof(ruleD68,axiom,
! [X0,X1,X2] :
( midp(X0,X1,X2)
=> cong(X0,X1,X0,X2) ) ).
fof(ruleD74,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) ) ).
fof(ruleX11,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ) ).
fof(ruleX14,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( ( cyclic(X0,X1,X2,X3)
& perp(X0,X2,X2,X1) )
=> circle(X4,X0,X1,X2) ) ).
fof(exemplo6GDDFULL81109108,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( coll(X8,X3,X4)
& coll(X8,X0,X5)
& coll(X7,X1,X4)
& coll(X7,X0,X3)
& coll(X6,X0,X5)
& coll(X6,X1,X4)
& circle(X3,X1,X5,X16)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X4,X12)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X9,X10)
& midp(X2,X1,X0) )
=> perp(X7,X8,X0,X5) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( coll(X8,X3,X4)
& coll(X8,X0,X5)
& coll(X7,X1,X4)
& coll(X7,X0,X3)
& coll(X6,X0,X5)
& coll(X6,X1,X4)
& circle(X3,X1,X5,X16)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X4,X12)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X9,X10)
& midp(X2,X1,X0) )
=> perp(X7,X8,X0,X5) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL81109108]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD1]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD2]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD3]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD5]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD8]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD9]) ).
cnf(c10,plain,
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD11]) ).
cnf(c11,plain,
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD12]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD14]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD15]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD16]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD18]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD19]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD20]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD21]) ).
cnf(c21,plain,
( 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(clausification,[status(esa)],[ruleD22]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD23]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD24]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD25]) ).
cnf(c38,plain,
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(clausification,[status(esa)],[ruleD39]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD40]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD41]) ).
cnf(c42,plain,
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(clausification,[status(esa)],[ruleD42b]) ).
cnf(c43,plain,
( ~ eqangle(X2,X0,X2,X1,X5,X4,X5,X3)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD43]) ).
cnf(c44,plain,
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD44]) ).
cnf(c45,plain,
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD45]) ).
cnf(c46,plain,
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD46]) ).
cnf(c49,plain,
( perp(X0,X1,X1,X4)
| ~ eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD49]) ).
cnf(c51,plain,
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD51]) ).
cnf(c56,plain,
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(clausification,[status(esa)],[ruleD56]) ).
cnf(c63,plain,
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD63]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD66]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD67]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD68]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD74]) ).
cnf(c99,plain,
( perp(sK479(X1,X2,X3,X0),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleX11]) ).
cnf(c105,plain,
( circle(sK498(X0,X2,X1,X3),X0,X2,X1)
| ~ cyclic(X0,X2,X1,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(clausification,[status(esa)],[ruleX14]) ).
cnf(c113,plain,
midp(sK524,sK523,sK522),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
circle(sK525,sK523,sK535,sK536),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c126,plain,
~ perp(sK529,sK530,sK522,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c17]) ).
cnf(d1,plain,
( perp(X1,X0,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d0,c74]) ).
cnf(d2,plain,
( ~ para(X1,X2,X1,X1)
| ~ circle(X0,X1,X3,X1)
| perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[c49,c39]) ).
cnf(d3,plain,
( ~ cyclic(X0,X2,X0,X3)
| ~ perp(X0,X0,X0,X2)
| perp(sK498(X0,X2,X0,X3),X0,X0,X1)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d2,c105]) ).
cnf(d4,plain,
( perp(X5,X4,X0,X1)
| ~ para(X4,X5,sK498(X0,X2,X0,X3),X0)
| ~ cyclic(X0,X2,X0,X3)
| ~ perp(X0,X0,X0,X2)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c19]) ).
cnf(d6,plain,
( eqangle(X3,X2,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
( cyclic(X1,X2,X0,X0)
| ~ coll(X0,X0,X2)
| ~ para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[d6,c42]) ).
cnf(d8,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d9,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d8,c38]) ).
cnf(d10,plain,
( perp(X1,X0,sK479(X1,X2,X3,X0),X1)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c99,c7]) ).
cnf(d11,plain,
( ~ perp(X4,X5,sK479(X1,X2,X3,X0),X1)
| para(X4,X5,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c99,c8]) ).
cnf(d12,plain,
( ~ circle(X1,X0,X2,X3)
| ~ circle(X1,X0,X2,X3)
| para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
para(sK523,sK525,sK523,sK525),
inference(resolution,[status(thm)],[d12,c117]) ).
cnf(d14,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d14,c66]) ).
cnf(d16,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
( cyclic(X1,X2,X0,X0)
| ~ para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
( para(X1,X0,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d0,c38]) ).
cnf(d20,plain,
para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[d14,d19]) ).
cnf(d21,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d21,c14]) ).
cnf(d23,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d22,c15]) ).
cnf(d24,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d23,c13]) ).
cnf(d25,plain,
( ~ perp(X2,X2,X2,X3)
| perp(X1,X0,X2,X5)
| ~ para(X2,X5,X2,X2)
| ~ para(X0,X1,sK498(X2,X3,X2,X4),X2) ),
inference(resolution,[status(thm)],[d24,d4]) ).
cnf(d26,plain,
( ~ cong(X0,X2,X0,X2)
| perp(X0,X0,X2,X1)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[c68,c56]) ).
cnf(d27,plain,
( eqangle(X3,X0,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c19]) ).
cnf(d28,plain,
( eqangle(X0,X3,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d27,c17]) ).
cnf(d29,plain,
( ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X0,X1,X0,X0)
| cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[d28,c43]) ).
cnf(d30,plain,
( ~ cyclic(X0,X1,X0,X0)
| ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d22,d29]) ).
cnf(d31,plain,
( ~ cyclic(X0,X1,X0,X0)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d24,d30]) ).
cnf(d32,plain,
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d21,d31]) ).
cnf(d33,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d23,d32]) ).
cnf(d34,plain,
( ~ midp(X0,X2,X2)
| perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d36,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d17,d35]) ).
cnf(d37,plain,
( ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,c67]) ).
cnf(d38,plain,
midp(X0,X1,X1),
inference(resolution,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
perp(X0,X0,X1,X2),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
( perp(X3,X2,X0,X1)
| ~ para(X2,X3,sK498(X0,X4,X0,X5),X0)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d39,d25]) ).
cnf(d41,plain,
( ~ midp(X3,X1,X2)
| para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d38,c63]) ).
cnf(d42,plain,
( ~ circle(X2,X0,X0,X1)
| midp(X1,X0,X1)
| ~ coll(X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[d28,c51]) ).
cnf(d43,plain,
( ~ circle(X2,X1,X1,X0)
| midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[d23,d42]) ).
cnf(d44,plain,
( ~ circle(X2,X1,X1,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d36,d43]) ).
cnf(d45,plain,
( circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c11]) ).
cnf(d46,plain,
( circle(X0,X1,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,d45]) ).
cnf(d47,plain,
( midp(X2,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( ~ midp(X0,sK523,X1)
| para(X0,sK524,X1,sK522) ),
inference(resolution,[status(thm)],[c44,c113]) ).
cnf(d49,plain,
( para(X1,sK522,X0,sK524)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d48,c4]) ).
cnf(d50,plain,
( ~ midp(X1,X2,X0)
| midp(sK522,X2,sK524)
| ~ coll(sK522,X2,sK524)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d49,c45]) ).
cnf(d51,plain,
( midp(sK522,X1,sK524)
| ~ midp(X2,sK523,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,d50]) ).
cnf(d52,plain,
( midp(sK522,X0,sK524)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d51,d38]) ).
cnf(d53,plain,
midp(sK522,X0,sK524),
inference(resolution,[status(thm)],[d52,d38]) ).
cnf(d54,plain,
midp(sK524,X0,sK524),
inference(resolution,[status(thm)],[d53,d47]) ).
cnf(d55,plain,
midp(sK524,sK524,X0),
inference(resolution,[status(thm)],[d54,c10]) ).
cnf(d56,plain,
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[c46,c38]) ).
cnf(d57,plain,
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[d56,c68]) ).
cnf(d58,plain,
( ~ midp(X0,X2,X0)
| midp(X0,X2,X1)
| ~ coll(X0,X2,X1)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d57,c45]) ).
cnf(d59,plain,
( ~ midp(X0,X0,X2)
| ~ midp(X0,X1,X0)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,d58]) ).
cnf(d60,plain,
( ~ midp(sK524,X0,sK524)
| midp(sK524,X0,X1) ),
inference(resolution,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
midp(sK524,X0,X1),
inference(resolution,[status(thm)],[d54,d60]) ).
cnf(d62,plain,
para(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d61,d41]) ).
cnf(d63,plain,
( perp(X1,X0,X2,X5)
| ~ para(X0,X1,sK498(X2,X3,X2,X4),X2) ),
inference(resolution,[status(thm)],[d62,d40]) ).
cnf(d64,plain,
( ~ midp(X0,X3,X2)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d38,c44]) ).
cnf(d65,plain,
( eqangle(X0,X1,X4,X5,X6,X7,X8,X9)
| ~ eqangle(X2,X3,X4,X5,X6,X7,X8,X9)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c21]) ).
cnf(d66,plain,
( eqangle(X1,X2,X0,X2,X0,X1,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[c46,c19]) ).
cnf(d67,plain,
( eqangle(X3,X4,X0,X2,X0,X1,X1,X2)
| ~ para(X3,X4,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
( ~ cyclic(X1,X2,X0,X2)
| ~ cyclic(X1,X2,X0,X0)
| ~ cyclic(X1,X2,X0,X0)
| cong(X1,X2,X0,X2)
| ~ cong(X0,X0,X0,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d67,c43]) ).
cnf(d69,plain,
( ~ cyclic(X1,X2,X0,X0)
| ~ cong(X0,X0,X0,X2)
| cong(X1,X2,X0,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d22,d68]) ).
cnf(d70,plain,
( ~ cong(X0,X0,X0,X2)
| cong(X1,X2,X0,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d21,d69]) ).
cnf(d71,plain,
( ~ cong(X2,X2,X2,X1)
| cong(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[d62,d70]) ).
cnf(d72,plain,
( cong(X0,X2,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c23]) ).
cnf(d73,plain,
( ~ cong(X3,X4,X0,X2)
| cong(X3,X4,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d72,c24]) ).
cnf(d74,plain,
( eqangle(X2,X0,X3,X0,X2,X1,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c20]) ).
cnf(d75,plain,
( eqangle(X0,X2,X3,X0,X2,X1,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d74,c17]) ).
cnf(d76,plain,
( ~ cyclic(X0,X0,X0,X1)
| ~ cyclic(X0,X0,X0,X0)
| ~ cyclic(X0,X0,X0,X1)
| cong(X0,X0,X1,X1)
| ~ cyclic(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d75,c43]) ).
cnf(d77,plain,
cyclic(X0,X0,X1,X2),
inference(resolution,[status(thm)],[d24,c14]) ).
cnf(d78,plain,
( ~ cyclic(X0,X0,X0,X0)
| ~ cyclic(X0,X1,X0,X0)
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
( ~ cyclic(X0,X1,X0,X0)
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[d22,d78]) ).
cnf(d80,plain,
cong(X0,X0,X1,X1),
inference(resolution,[status(thm)],[d24,d79]) ).
cnf(d81,plain,
( cong(X2,X2,X0,X1)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d80,d73]) ).
cnf(d82,plain,
( circle(X0,X2,X3,X1)
| ~ cong(X0,X2,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d72,c11]) ).
cnf(d83,plain,
( circle(X0,X2,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,d82]) ).
cnf(d84,plain,
( midp(X1,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d83,d44]) ).
cnf(d85,plain,
midp(X0,X1,X0),
inference(resolution,[status(thm)],[d61,d84]) ).
cnf(d86,plain,
cong(X0,X0,X1,X2),
inference(resolution,[status(thm)],[d85,d81]) ).
cnf(d87,plain,
cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d86,d71]) ).
cnf(d88,plain,
cong(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d87,c22]) ).
cnf(d89,plain,
cong(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d88,c23]) ).
cnf(d90,plain,
cong(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d89,c22]) ).
cnf(d91,plain,
midp(X0,X1,X2),
inference(resolution,[status(thm)],[d90,d37]) ).
cnf(d92,plain,
para(X0,X1,X2,X3),
inference(resolution,[status(thm)],[d91,d64]) ).
cnf(d93,plain,
perp(X0,X1,X2,X3),
inference(resolution,[status(thm)],[d92,d63]) ).
cnf(d94,plain,
$false,
inference(resolution,[status(thm)],[d93,c126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:48:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.77/15.96 % SZS status Theorem for theBenchmark.p
% 48.77/15.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------