%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO659+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:15:38 AM UTC 2026
% Result : Theorem 91.38s 41.93s
% Output : CNFRefutation 91.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 38
% Syntax : Number of formulae : 221 ( 58 unt; 0 def)
% Number of atoms : 523 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 516 ( 214 ~; 212 |; 51 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-5 aty)
% Number of variables : 727 ( 75 sgn 210 !; 1 ?)
% 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(ruleD4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ) ).
fof(ruleD5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ) ).
fof(ruleD6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ) ).
fof(ruleD7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ) ).
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(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(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(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(ruleD54,axiom,
! [X0,X1,X2,X3] :
( ( para(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X3) )
=> eqangle(X0,X3,X2,X3,X2,X3,X2,X1) ) ).
fof(ruleD55,axiom,
! [X0,X1,X2,X3] :
( ( perp(X3,X2,X0,X1)
& midp(X2,X0,X1) )
=> cong(X3,X0,X3,X1) ) ).
fof(ruleD56,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X0,X1,X2,X3) ) ).
fof(ruleD64,axiom,
! [X0,X1,X2,X3,X4] :
( ( para(X0,X3,X1,X2)
& para(X0,X2,X1,X3)
& midp(X4,X0,X1) )
=> midp(X4,X2,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(ruleD73,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) ) ).
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(ruleX9,axiom,
! [X0,X1,X2,X3,X4] :
? [X5] :
( ( perp(X0,X1,X1,X4)
& cong(X4,X2,X4,X3) )
=> ( cong(X1,X2,X1,X5)
& para(X5,X2,X0,X1)
& cong(X4,X2,X4,X5) ) ) ).
fof(exemplo6GDDFULLmoreE02317,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( circle(X5,X0,X7,X12)
& coll(X0,X3,X7)
& circle(X5,X1,X6,X11)
& coll(X1,X4,X6)
& perp(X2,X1,X10,X5)
& midp(X10,X2,X1)
& perp(X0,X1,X9,X5)
& midp(X9,X0,X1)
& perp(X0,X2,X8,X5)
& midp(X8,X0,X2)
& coll(X4,X0,X2)
& perp(X4,X1,X0,X2)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> para(X3,X4,X6,X7) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( circle(X5,X0,X7,X12)
& coll(X0,X3,X7)
& circle(X5,X1,X6,X11)
& coll(X1,X4,X6)
& perp(X2,X1,X10,X5)
& midp(X10,X2,X1)
& perp(X0,X1,X9,X5)
& midp(X9,X0,X1)
& perp(X0,X2,X8,X5)
& midp(X8,X0,X2)
& coll(X4,X0,X2)
& perp(X4,X1,X0,X2)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> para(X3,X4,X6,X7) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULLmoreE02317]) ).
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(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD4]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD5]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD6]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD7]) ).
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(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(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(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(c54,plain,
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ para(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD54]) ).
cnf(c55,plain,
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD55]) ).
cnf(c56,plain,
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(clausification,[status(esa)],[ruleD56]) ).
cnf(c64,plain,
( midp(X0,X3,X4)
| ~ para(X1,X4,X2,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD64]) ).
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(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD73]) ).
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(c93,plain,
( para(sK468(X3,X4,X1,X2,X0),X1,X3,X4)
| ~ perp(X3,X4,X4,X0)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleX9]) ).
cnf(c113,plain,
perp(sK525,sK522,sK523,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
midp(sK530,sK522,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
midp(sK531,sK522,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c120,plain,
perp(sK522,sK523,sK531,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c121,plain,
midp(sK532,sK524,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c127,plain,
~ para(sK525,sK526,sK528,sK529),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c19]) ).
cnf(d1,plain,
( para(X2,X3,X4,X5)
| ~ para(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d0,c73]) ).
cnf(d2,plain,
( cong(sK522,sK531,sK522,sK527)
| ~ midp(sK523,sK531,sK527) ),
inference(resolution,[status(thm)],[c120,c55]) ).
cnf(d3,plain,
( ~ perp(X0,X1,X1,sK522)
| para(sK468(X0,X1,sK531,sK527,sK522),sK531,X0,X1)
| ~ midp(sK523,sK531,sK527) ),
inference(resolution,[status(thm)],[d2,c93]) ).
cnf(d4,plain,
( ~ para(sK468(X0,X1,sK531,sK527,sK522),sK531,X2,X3)
| para(X0,X1,X2,X3)
| ~ midp(sK523,sK531,sK527)
| ~ perp(X0,X1,X1,sK522) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ midp(X0,sK522,X1)
| para(X0,sK531,X1,sK523) ),
inference(resolution,[status(thm)],[c44,c119]) ).
cnf(d6,plain,
( para(X0,sK531,X2,X3)
| ~ para(X1,sK523,X2,X3)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( cong(sK525,sK523,sK525,sK524)
| ~ midp(sK522,sK523,sK524) ),
inference(resolution,[status(thm)],[c113,c55]) ).
cnf(d8,plain,
( ~ perp(X0,X1,X1,sK525)
| para(sK468(X0,X1,sK523,sK524,sK525),sK523,X0,X1)
| ~ midp(sK522,sK523,sK524) ),
inference(resolution,[status(thm)],[d7,c93]) ).
cnf(d9,plain,
( ~ midp(X2,sK522,sK468(X0,X1,sK523,sK524,sK525))
| para(X2,sK531,X0,X1)
| ~ midp(sK522,sK523,sK524)
| ~ perp(X0,X1,X1,sK525) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[c46,c38]) ).
cnf(d11,plain,
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[d10,c68]) ).
cnf(d12,plain,
( ~ midp(X2,X0,X0)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d11,c64]) ).
cnf(d13,plain,
( eqangle(X3,X0,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c19]) ).
cnf(d14,plain,
( eqangle(X0,X3,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d13,c17]) ).
cnf(d15,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)],[d14,c43]) ).
cnf(d16,plain,
( eqangle(X4,X5,X2,X3,X4,X5,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d17,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d16,c42]) ).
cnf(d18,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d19,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d18,c38]) ).
cnf(d20,plain,
perp(sK523,sK524,sK525,sK522),
inference(resolution,[status(thm)],[c113,c7]) ).
cnf(d21,plain,
( ~ perp(X0,X1,sK525,sK522)
| para(X0,X1,sK523,sK524) ),
inference(resolution,[status(thm)],[c113,c8]) ).
cnf(d22,plain,
para(sK523,sK524,sK523,sK524),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d23,c66]) ).
cnf(d25,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
( cyclic(X2,X1,X0,X0)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d26,d17]) ).
cnf(d28,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d23,d27]) ).
cnf(d29,plain,
( ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d28,d15]) ).
cnf(d30,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d28,c14]) ).
cnf(d31,plain,
( ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d30,c15]) ).
cnf(d33,plain,
( ~ cyclic(X0,X1,X0,X2)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d30,c13]) ).
cnf(d35,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d34,c15]) ).
cnf(d36,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( midp(X0,X1,X1)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[d36,c67]) ).
cnf(d38,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d26,c2]) ).
cnf(d39,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d26,d38]) ).
cnf(d40,plain,
midp(X0,X1,X1),
inference(resolution,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
( ~ midp(X0,X0,X1)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d40,d12]) ).
cnf(d42,plain,
( para(X0,X1,X0,X0)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d43,plain,
( ~ midp(X0,X0,X1)
| midp(X2,X1,X0)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
( ~ circle(X2,X0,X0,X1)
| midp(X1,X0,X1)
| ~ coll(X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[d14,c51]) ).
cnf(d45,plain,
( ~ cyclic(X1,X0,X2,X1)
| ~ circle(X2,X1,X1,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d25,d44]) ).
cnf(d46,plain,
( ~ circle(X2,X1,X1,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d32,d45]) ).
cnf(d47,plain,
( circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c11]) ).
cnf(d48,plain,
( circle(X0,X1,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,d47]) ).
cnf(d49,plain,
( midp(X2,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d48,d46]) ).
cnf(d50,plain,
( ~ midp(X0,sK522,X1)
| para(X0,sK530,X1,sK524) ),
inference(resolution,[status(thm)],[c44,c117]) ).
cnf(d51,plain,
( para(X0,sK530,sK524,X1)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d50,c3]) ).
cnf(d52,plain,
( ~ midp(X0,X2,sK524)
| midp(sK530,X2,X1)
| ~ coll(sK530,X2,X1)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d51,c45]) ).
cnf(d53,plain,
( midp(sK530,X1,X2)
| ~ midp(X0,sK522,X2)
| ~ midp(X0,X1,sK524) ),
inference(resolution,[status(thm)],[d39,d52]) ).
cnf(d54,plain,
( midp(sK530,X0,sK523)
| ~ midp(sK531,X0,sK524) ),
inference(resolution,[status(thm)],[d53,c119]) ).
cnf(d55,plain,
( para(X0,sK531,sK523,X1)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d56,plain,
( ~ midp(X0,X2,sK523)
| midp(sK531,X2,X1)
| ~ coll(sK531,X2,X1)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d55,c45]) ).
cnf(d57,plain,
( midp(sK531,X1,X2)
| ~ midp(X0,sK522,X2)
| ~ midp(X0,X1,sK523) ),
inference(resolution,[status(thm)],[d39,d56]) ).
cnf(d58,plain,
midp(sK532,sK523,sK524),
inference(resolution,[status(thm)],[c10,c121]) ).
cnf(d59,plain,
midp(sK531,sK523,sK522),
inference(resolution,[status(thm)],[c10,c119]) ).
cnf(d60,plain,
( ~ midp(X0,sK523,X1)
| para(X0,sK531,X1,sK522) ),
inference(resolution,[status(thm)],[c44,d59]) ).
cnf(d61,plain,
( ~ midp(X0,X2,X1)
| midp(sK531,X2,sK522)
| ~ coll(sK531,X2,sK522)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d60,c45]) ).
cnf(d62,plain,
( midp(sK531,X0,sK522)
| ~ midp(sK532,X0,sK524)
| ~ coll(sK531,X0,sK522) ),
inference(resolution,[status(thm)],[d61,d58]) ).
cnf(d63,plain,
( ~ midp(sK532,X0,sK524)
| midp(sK531,X0,sK522) ),
inference(resolution,[status(thm)],[d39,d62]) ).
cnf(d64,plain,
midp(sK531,sK524,sK522),
inference(resolution,[status(thm)],[d63,d40]) ).
cnf(d65,plain,
midp(sK531,sK522,sK524),
inference(resolution,[status(thm)],[d64,c10]) ).
cnf(d66,plain,
( midp(sK531,X0,sK524)
| ~ midp(sK531,X0,sK523) ),
inference(resolution,[status(thm)],[d65,d57]) ).
cnf(d67,plain,
( para(X0,sK531,sK522,X1)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d60,c3]) ).
cnf(d68,plain,
( ~ midp(X0,X2,sK522)
| midp(sK531,X2,X1)
| ~ coll(sK531,X2,X1)
| ~ midp(X0,sK523,X1) ),
inference(resolution,[status(thm)],[d67,c45]) ).
cnf(d69,plain,
( midp(sK531,X1,X2)
| ~ midp(X0,sK523,X2)
| ~ midp(X0,X1,sK522) ),
inference(resolution,[status(thm)],[d39,d68]) ).
cnf(d70,plain,
( midp(sK531,X1,sK523)
| ~ midp(X0,X1,sK522) ),
inference(resolution,[status(thm)],[d69,d40]) ).
cnf(d71,plain,
( para(X1,sK524,X0,sK530)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d50,c4]) ).
cnf(d72,plain,
( ~ midp(X1,X2,X0)
| midp(sK524,X2,sK530)
| ~ coll(sK524,X2,sK530)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d71,c45]) ).
cnf(d73,plain,
( midp(sK524,X1,sK530)
| ~ midp(X2,sK522,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d39,d72]) ).
cnf(d74,plain,
( midp(sK524,X0,sK530)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d73,d40]) ).
cnf(d75,plain,
midp(sK524,X0,sK530),
inference(resolution,[status(thm)],[d74,d40]) ).
cnf(d76,plain,
midp(sK524,sK530,X0),
inference(resolution,[status(thm)],[d75,c10]) ).
cnf(d77,plain,
midp(sK531,sK530,sK523),
inference(resolution,[status(thm)],[d76,d70]) ).
cnf(d78,plain,
midp(sK531,sK530,sK524),
inference(resolution,[status(thm)],[d77,d66]) ).
cnf(d79,plain,
midp(sK530,sK530,sK523),
inference(resolution,[status(thm)],[d78,d54]) ).
cnf(d80,plain,
( ~ midp(X0,X2,X0)
| midp(X0,X2,X1)
| ~ coll(X0,X2,X1)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d11,c45]) ).
cnf(d81,plain,
( ~ midp(X0,X0,X2)
| ~ midp(X0,X1,X0)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d39,d80]) ).
cnf(d82,plain,
( ~ midp(sK530,X0,sK530)
| midp(sK530,X0,sK523) ),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
midp(sK530,X0,sK530),
inference(resolution,[status(thm)],[d49,d75]) ).
cnf(d84,plain,
midp(sK530,X0,sK523),
inference(resolution,[status(thm)],[d83,d82]) ).
cnf(d85,plain,
midp(sK530,sK523,X0),
inference(resolution,[status(thm)],[d84,c10]) ).
cnf(d86,plain,
midp(X0,sK523,X0),
inference(resolution,[status(thm)],[d85,d49]) ).
cnf(d87,plain,
midp(X0,X0,sK523),
inference(resolution,[status(thm)],[d86,c10]) ).
cnf(d88,plain,
midp(X0,sK523,X1),
inference(resolution,[status(thm)],[d87,d43]) ).
cnf(d89,plain,
( ~ midp(X0,sK522,sK468(X1,X2,sK523,sK524,sK525))
| ~ perp(X1,X2,X2,sK525)
| para(X0,sK531,X1,X2) ),
inference(resolution,[status(thm)],[d88,d9]) ).
cnf(d90,plain,
( midp(sK530,X1,sK522)
| ~ midp(X0,X1,sK524) ),
inference(resolution,[status(thm)],[d53,d40]) ).
cnf(d91,plain,
midp(sK530,sK530,sK522),
inference(resolution,[status(thm)],[d76,d90]) ).
cnf(d92,plain,
( ~ midp(sK530,X0,sK530)
| midp(sK530,X0,sK522) ),
inference(resolution,[status(thm)],[d81,d91]) ).
cnf(d93,plain,
midp(sK530,X0,sK522),
inference(resolution,[status(thm)],[d83,d92]) ).
cnf(d94,plain,
midp(sK530,sK522,X0),
inference(resolution,[status(thm)],[d93,c10]) ).
cnf(d95,plain,
midp(X0,sK522,X0),
inference(resolution,[status(thm)],[d94,d49]) ).
cnf(d96,plain,
midp(X0,X0,sK522),
inference(resolution,[status(thm)],[d95,c10]) ).
cnf(d97,plain,
midp(X0,sK522,X1),
inference(resolution,[status(thm)],[d96,d43]) ).
cnf(d98,plain,
( ~ perp(X1,X2,X2,sK525)
| para(X0,sK531,X1,X2) ),
inference(resolution,[status(thm)],[d97,d89]) ).
cnf(d99,plain,
( eqangle(X2,X0,X2,X1,X4,X5,X6,X7)
| ~ eqangle(X3,X0,X3,X1,X4,X5,X6,X7)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c21]) ).
cnf(d100,plain,
( eqangle(X1,X0,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[c46,c17]) ).
cnf(d101,plain,
( eqangle(X3,X0,X3,X2,X1,X2,X0,X2)
| ~ cyclic(X0,X2,X3,X1)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d100,d99]) ).
cnf(d102,plain,
( para(X0,X0,X1,X2)
| ~ cyclic(X0,X2,X0,X1)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d101,c38]) ).
cnf(d103,plain,
( ~ cong(X0,X1,X0,X2)
| para(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,d102]) ).
cnf(d104,plain,
para(X0,X0,X1,X1),
inference(resolution,[status(thm)],[d103,d36]) ).
cnf(d105,plain,
( eqangle(X3,X0,X2,X3,X2,X3,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c54,c17]) ).
cnf(d106,plain,
( eqangle(X3,X0,X3,X2,X2,X2,X2,X1)
| ~ cyclic(X0,X2,X3,X2)
| ~ cyclic(X0,X1,X2,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d105,d99]) ).
cnf(d107,plain,
( perp(X3,X0,X3,X2)
| ~ perp(X2,X2,X2,X1)
| ~ cyclic(X0,X1,X2,X2)
| ~ cyclic(X0,X2,X3,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d106,c74]) ).
cnf(d108,plain,
( ~ cyclic(X0,X2,X3,X2)
| ~ perp(X2,X2,X2,X1)
| perp(X3,X0,X3,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d28,d107]) ).
cnf(d109,plain,
( ~ perp(X2,X2,X2,X1)
| perp(X3,X0,X3,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d30,d108]) ).
cnf(d110,plain,
( ~ cong(X0,X2,X0,X2)
| perp(X0,X0,X2,X1)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[c68,c56]) ).
cnf(d111,plain,
( ~ midp(X0,X2,X2)
| perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,d110]) ).
cnf(d112,plain,
perp(X0,X0,X1,X2),
inference(resolution,[status(thm)],[d40,d111]) ).
cnf(d113,plain,
( perp(X3,X0,X3,X2)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d112,d109]) ).
cnf(d114,plain,
perp(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d113,d104]) ).
cnf(d115,plain,
perp(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d114,c6]) ).
cnf(d116,plain,
perp(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d115,c7]) ).
cnf(d117,plain,
para(X0,sK531,X1,X2),
inference(resolution,[status(thm)],[d116,d98]) ).
cnf(d118,plain,
( ~ midp(sK523,sK531,sK527)
| ~ perp(X0,X1,X1,sK522)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d117,d4]) ).
cnf(d119,plain,
( ~ midp(sK523,sK531,sK527)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d116,d118]) ).
cnf(d120,plain,
( ~ midp(X0,X2,X1)
| midp(sK530,X2,sK524)
| ~ coll(sK530,X2,sK524)
| ~ midp(X0,sK522,X1) ),
inference(resolution,[status(thm)],[d50,c45]) ).
cnf(d121,plain,
( midp(sK530,X0,sK524)
| ~ midp(sK531,X0,sK523)
| ~ coll(sK530,X0,sK524) ),
inference(resolution,[status(thm)],[d120,c119]) ).
cnf(d122,plain,
( ~ midp(sK531,X0,sK523)
| midp(sK530,X0,sK524) ),
inference(resolution,[status(thm)],[d39,d121]) ).
cnf(d123,plain,
midp(sK530,sK530,sK524),
inference(resolution,[status(thm)],[d77,d122]) ).
cnf(d124,plain,
( ~ midp(sK530,X0,sK530)
| midp(sK530,X0,sK524) ),
inference(resolution,[status(thm)],[d81,d123]) ).
cnf(d125,plain,
midp(sK530,X0,sK524),
inference(resolution,[status(thm)],[d83,d124]) ).
cnf(d126,plain,
midp(sK524,X0,sK524),
inference(resolution,[status(thm)],[d125,d49]) ).
cnf(d127,plain,
midp(sK524,sK524,X0),
inference(resolution,[status(thm)],[d126,c10]) ).
cnf(d128,plain,
midp(X0,X1,sK524),
inference(resolution,[status(thm)],[d127,d43]) ).
cnf(d129,plain,
( ~ midp(sK468(X0,X1,sK523,sK524,sK525),X2,X0)
| midp(sK523,X2,X1)
| ~ coll(sK523,X2,X1)
| ~ midp(sK522,sK523,sK524)
| ~ perp(X0,X1,X1,sK525) ),
inference(resolution,[status(thm)],[d8,c45]) ).
cnf(d130,plain,
( midp(sK523,X2,X1)
| ~ midp(sK522,sK523,sK524)
| ~ midp(sK468(X0,X1,sK523,sK524,sK525),X2,X0)
| ~ perp(X0,X1,X1,sK525) ),
inference(resolution,[status(thm)],[d39,d129]) ).
cnf(d131,plain,
( midp(sK523,X2,X1)
| ~ midp(sK468(X0,X1,sK523,sK524,sK525),X2,X0)
| ~ perp(X0,X1,X1,sK525) ),
inference(resolution,[status(thm)],[d88,d130]) ).
cnf(d132,plain,
( midp(sK523,X2,X1)
| ~ midp(sK468(X0,X1,sK523,sK524,sK525),X2,X0) ),
inference(resolution,[status(thm)],[d116,d131]) ).
cnf(d133,plain,
midp(sK523,X0,X1),
inference(resolution,[status(thm)],[d132,d128]) ).
cnf(d134,plain,
midp(X0,X1,X0),
inference(resolution,[status(thm)],[d133,d49]) ).
cnf(d135,plain,
midp(X0,X0,X1),
inference(resolution,[status(thm)],[d134,c10]) ).
cnf(d136,plain,
midp(X0,X1,X2),
inference(resolution,[status(thm)],[d135,d43]) ).
cnf(d137,plain,
para(X0,X1,X2,X3),
inference(resolution,[status(thm)],[d136,d119]) ).
cnf(d138,plain,
$false,
inference(resolution,[status(thm)],[d137,c127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO659+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.45 % Computer : n004.cluster.edu
% 0.16/10.45 % Model : x86_64 x86_64
% 0.16/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.45 % Memory : 8046.5625MB
% 0.16/10.45 % OS : Linux 6.8.0-71-generic
% 0.16/10.45 % CPULimit : 300
% 0.16/10.45 % WCLimit : 300
% 0.16/10.45 % DateTime : Fri Sep 25 13:47:16 UTC 2026
% 0.16/10.45 % CPUTime :
% 0.16/10.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.38/41.93 % SZS status Theorem for theBenchmark.p
% 91.38/41.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------