%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO631+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 : n006.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 07:15:33 AM UTC 2026
% Result : Theorem 31.04s 39.39s
% Output : CNFRefutation 31.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 38
% Syntax : Number of formulae : 175 ( 42 unt; 0 def)
% Number of atoms : 417 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 402 ( 160 ~; 157 |; 46 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 630 ( 50 sgn 215 !; 0 ?)
% 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(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(ruleD12,axiom,
! [X0,X1,X2,X3] :
( ( cong(X3,X0,X3,X2)
& cong(X3,X0,X3,X1) )
=> circle(X3,X0,X1,X2) ) ).
fof(ruleD13,axiom,
! [X0,X1,X2,X3,X4] :
( ( cong(X4,X0,X4,X3)
& cong(X4,X0,X4,X2)
& cong(X4,X0,X4,X1) )
=> cyclic(X0,X1,X2,X3) ) ).
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(ruleD29,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqratio(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqratio(X0,X1,X4,X5,X2,X3,X6,X7) ) ).
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(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(ruleD53,axiom,
! [X0,X1,X2,X3] :
( ( coll(X3,X0,X2)
& circle(X3,X0,X1,X2) )
=> perp(X0,X1,X1,X2) ) ).
fof(ruleD55,axiom,
! [X0,X1,X2,X3] :
( ( perp(X3,X2,X0,X1)
& midp(X2,X0,X1) )
=> cong(X3,X0,X3,X1) ) ).
fof(ruleD63,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X2,X3)
& midp(X4,X0,X1) )
=> para(X0,X2,X1,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(ruleD70,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( midp(X5,X2,X3)
& midp(X4,X0,X1) )
=> eqratio(X4,X0,X0,X1,X5,X2,X2,X3) ) ).
fof(ruleD75,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( cong(X4,X5,X6,X7)
& eqratio(X0,X1,X2,X3,X4,X5,X6,X7) )
=> cong(X0,X1,X2,X3) ) ).
fof(exemplo6GDDFULL8110994,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( coll(X10,X8,X9)
& coll(X10,X6,X7)
& coll(X9,X2,X4)
& perp(X9,X5,X2,X4)
& coll(X8,X1,X2)
& perp(X8,X5,X1,X2)
& coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X0,X4)
& perp(X6,X5,X0,X4)
& circle(X3,X0,X5,X12)
& circle(X3,X0,X4,X11)
& circle(X3,X0,X1,X2) )
=> cyclic(X5,X7,X10,X8) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( coll(X10,X8,X9)
& coll(X10,X6,X7)
& coll(X9,X2,X4)
& perp(X9,X5,X2,X4)
& coll(X8,X1,X2)
& perp(X8,X5,X1,X2)
& coll(X7,X0,X1)
& perp(X7,X5,X0,X1)
& coll(X6,X0,X4)
& perp(X6,X5,X0,X4)
& circle(X3,X0,X5,X12)
& circle(X3,X0,X4,X11)
& circle(X3,X0,X1,X2) )
=> cyclic(X5,X7,X10,X8) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL8110994]) ).
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(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(c11,plain,
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD12]) ).
cnf(c12,plain,
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD13]) ).
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(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD29]) ).
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(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(c53,plain,
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD53]) ).
cnf(c55,plain,
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD55]) ).
cnf(c63,plain,
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD63]) ).
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(c70,plain,
( eqratio(X0,X1,X1,X2,X3,X4,X4,X5)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD70]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(clausification,[status(esa)],[ruleD75]) ).
cnf(c113,plain,
circle(sK525,sK522,sK523,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c118,plain,
perp(sK529,sK527,sK522,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c120,plain,
perp(sK530,sK527,sK523,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c126,plain,
~ cyclic(sK527,sK529,sK532,sK530),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( cyclic(X1,X3,X4,X2)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c12]) ).
cnf(d1,plain,
perp(sK522,sK523,sK529,sK527),
inference(resolution,[status(thm)],[c118,c7]) ).
cnf(d2,plain,
( cong(sK522,sK529,sK522,sK527)
| ~ midp(sK523,sK529,sK527) ),
inference(resolution,[status(thm)],[d1,c55]) ).
cnf(d3,plain,
( cong(sK522,sK527,sK522,sK529)
| ~ midp(sK523,sK529,sK527) ),
inference(resolution,[status(thm)],[d2,c23]) ).
cnf(d4,plain,
( cyclic(sK527,sK529,X1,X0)
| ~ cong(sK522,sK527,sK522,X1)
| ~ midp(sK522,sK527,X0)
| ~ midp(sK523,sK529,sK527) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( eqangle(X2,X0,X3,X0,X2,X1,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c20]) ).
cnf(d6,plain,
( eqangle(X0,X2,X3,X0,X2,X1,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,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)],[d6,c43]) ).
cnf(d8,plain,
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c19]) ).
cnf(d9,plain,
( eqangle(X3,X2,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d8,c17]) ).
cnf(d10,plain,
( cyclic(X1,X2,X0,X0)
| ~ coll(X0,X0,X2)
| ~ para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[d9,c42]) ).
cnf(d11,plain,
perp(sK530,sK527,sK524,sK523),
inference(resolution,[status(thm)],[c120,c6]) ).
cnf(d12,plain,
perp(sK524,sK523,sK530,sK527),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
( ~ perp(X0,X1,sK530,sK527)
| para(X0,X1,sK524,sK523) ),
inference(resolution,[status(thm)],[d11,c8]) ).
cnf(d14,plain,
para(sK524,sK523,sK524,sK523),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d16,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d15,c38]) ).
cnf(d17,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d17,c66]) ).
cnf(d19,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
( cyclic(X1,X2,X0,X0)
| ~ para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[d17,c3]) ).
cnf(d23,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d23,c14]) ).
cnf(d25,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d24,c15]) ).
cnf(d26,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d25,c13]) ).
cnf(d27,plain,
( ~ cyclic(X0,X0,X0,X0)
| ~ cyclic(X0,X0,X0,X1)
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[d26,d7]) ).
cnf(d28,plain,
( ~ cyclic(X0,X0,X0,X1)
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[d25,d27]) ).
cnf(d29,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d24,c13]) ).
cnf(d30,plain,
cong(X0,X0,X1,X1),
inference(resolution,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
( midp(X0,X0,X0)
| ~ coll(X0,X0,X0) ),
inference(resolution,[status(thm)],[d30,c67]) ).
cnf(d32,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d33,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d20,d32]) ).
cnf(d34,plain,
midp(X0,X0,X0),
inference(resolution,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
( ~ midp(X0,X1,X2)
| para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d34,c63]) ).
cnf(d36,plain,
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[c46,c38]) ).
cnf(d37,plain,
( cong(X0,X2,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c23]) ).
cnf(d38,plain,
( para(X0,X0,X0,X1)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( ~ midp(X2,X0,X0)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d38,c64]) ).
cnf(d40,plain,
( eqangle(X3,X0,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c19]) ).
cnf(d41,plain,
( eqangle(X0,X3,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d40,c17]) ).
cnf(d42,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)],[d41,c43]) ).
cnf(d43,plain,
( ~ cyclic(X0,X1,X0,X0)
| ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d26,d42]) ).
cnf(d44,plain,
( ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d23,d43]) ).
cnf(d45,plain,
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d24,d44]) ).
cnf(d46,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d25,d45]) ).
cnf(d47,plain,
( ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,c67]) ).
cnf(d48,plain,
midp(X0,X1,X1),
inference(resolution,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
( ~ midp(X0,X1,X0)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d48,d39]) ).
cnf(d50,plain,
( ~ midp(X2,X1,X2)
| ~ midp(X2,X1,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d49,d35]) ).
cnf(d51,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(d52,plain,
( ~ cyclic(X3,X4,X2,X5)
| eqangle(X0,X1,X2,X4,X5,X3,X5,X4)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d51,c40]) ).
cnf(d53,plain,
( ~ circle(X3,X0,X1,X2)
| midp(X2,X1,X2)
| ~ coll(X2,X1,X2)
| ~ cyclic(X1,X2,X0,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d52,c51]) ).
cnf(d54,plain,
( ~ cyclic(X1,X2,X0,X3)
| ~ circle(X3,X0,X1,X2)
| midp(X2,X1,X2)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d19,d53]) ).
cnf(d55,plain,
( ~ cyclic(X1,X0,X3,X2)
| ~ circle(X2,X3,X1,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d17,d54]) ).
cnf(d56,plain,
( ~ circle(X2,X1,X1,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d55,d26]) ).
cnf(d57,plain,
( circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c11]) ).
cnf(d58,plain,
( circle(X0,X1,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d46,d57]) ).
cnf(d59,plain,
( midp(X2,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
( eqratio(X3,X4,X0,X1,X4,X5,X1,X2)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c70,c28]) ).
cnf(d61,plain,
( ~ cong(X1,X2,X4,X5)
| cong(X0,X1,X3,X4)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d60,c75]) ).
cnf(d62,plain,
( perp(sK522,sK523,sK523,sK524)
| ~ coll(sK525,sK522,sK524) ),
inference(resolution,[status(thm)],[c113,c53]) ).
cnf(d63,plain,
( cong(sK522,sK523,sK522,sK524)
| ~ midp(sK523,sK523,sK524)
| ~ coll(sK525,sK522,sK524) ),
inference(resolution,[status(thm)],[d62,c55]) ).
cnf(d64,plain,
( cong(X1,sK522,X0,sK522)
| ~ midp(X1,sK522,sK523)
| ~ midp(X0,sK522,sK524)
| ~ midp(sK523,sK523,sK524)
| ~ coll(sK525,sK522,sK524) ),
inference(resolution,[status(thm)],[d63,d61]) ).
cnf(d65,plain,
( cong(X0,sK522,X1,sK522)
| ~ midp(sK523,sK523,sK524)
| ~ midp(X1,sK522,sK524)
| ~ midp(X0,sK522,sK523) ),
inference(resolution,[status(thm)],[d33,d64]) ).
cnf(d66,plain,
perp(sK523,sK524,sK530,sK527),
inference(resolution,[status(thm)],[c120,c7]) ).
cnf(d67,plain,
( ~ perp(X0,X1,sK530,sK527)
| para(X0,X1,sK523,sK524) ),
inference(resolution,[status(thm)],[c120,c8]) ).
cnf(d68,plain,
para(sK523,sK524,sK523,sK524),
inference(resolution,[status(thm)],[d67,d66]) ).
cnf(d69,plain,
( ~ midp(sK523,X0,sK523)
| midp(sK524,X0,sK524)
| ~ coll(sK524,X0,sK524) ),
inference(resolution,[status(thm)],[d68,c45]) ).
cnf(d70,plain,
( midp(sK524,X0,sK524)
| ~ midp(sK523,X0,sK523) ),
inference(resolution,[status(thm)],[d19,d69]) ).
cnf(d71,plain,
( ~ perp(X0,X1,sK529,sK527)
| para(X0,X1,sK522,sK523) ),
inference(resolution,[status(thm)],[c118,c8]) ).
cnf(d72,plain,
para(sK522,sK523,sK522,sK523),
inference(resolution,[status(thm)],[d71,d1]) ).
cnf(d73,plain,
( ~ midp(sK522,X0,sK522)
| midp(sK523,X0,sK523)
| ~ coll(sK523,X0,sK523) ),
inference(resolution,[status(thm)],[d72,c45]) ).
cnf(d74,plain,
( midp(sK523,X0,sK523)
| ~ midp(sK522,X0,sK522) ),
inference(resolution,[status(thm)],[d19,d73]) ).
cnf(d75,plain,
midp(sK523,sK522,sK523),
inference(resolution,[status(thm)],[d34,d74]) ).
cnf(d76,plain,
midp(sK524,sK522,sK524),
inference(resolution,[status(thm)],[d75,d70]) ).
cnf(d77,plain,
midp(X0,sK522,sK524),
inference(resolution,[status(thm)],[d50,d76]) ).
cnf(d78,plain,
( cong(X0,sK522,X1,sK522)
| ~ midp(sK523,sK523,sK524)
| ~ midp(X0,sK522,sK523) ),
inference(resolution,[status(thm)],[d77,d65]) ).
cnf(d79,plain,
midp(sK524,sK523,sK524),
inference(resolution,[status(thm)],[d34,d70]) ).
cnf(d80,plain,
midp(X0,sK523,sK524),
inference(resolution,[status(thm)],[d50,d79]) ).
cnf(d81,plain,
( cong(X0,sK522,X1,sK522)
| ~ midp(X0,sK522,sK523) ),
inference(resolution,[status(thm)],[d80,d78]) ).
cnf(d82,plain,
midp(X0,sK522,sK523),
inference(resolution,[status(thm)],[d50,d75]) ).
cnf(d83,plain,
cong(X0,sK522,X1,sK522),
inference(resolution,[status(thm)],[d82,d81]) ).
cnf(d84,plain,
cong(X0,sK522,sK522,X1),
inference(resolution,[status(thm)],[d83,c22]) ).
cnf(d85,plain,
cong(sK522,X0,X1,sK522),
inference(resolution,[status(thm)],[d84,c23]) ).
cnf(d86,plain,
cong(sK522,X0,sK522,X1),
inference(resolution,[status(thm)],[d85,c22]) ).
cnf(d87,plain,
midp(sK522,X0,X1),
inference(resolution,[status(thm)],[d86,d47]) ).
cnf(d88,plain,
midp(X0,X1,X0),
inference(resolution,[status(thm)],[d87,d59]) ).
cnf(d89,plain,
midp(X0,X1,X2),
inference(resolution,[status(thm)],[d88,d50]) ).
cnf(d90,plain,
( cyclic(sK527,sK529,X0,X1)
| ~ cong(sK522,sK527,sK522,X0)
| ~ midp(sK523,sK529,sK527) ),
inference(resolution,[status(thm)],[d89,d4]) ).
cnf(d91,plain,
cong(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d89,c68]) ).
cnf(d92,plain,
( cyclic(sK527,sK529,X0,X1)
| ~ midp(sK523,sK529,sK527) ),
inference(resolution,[status(thm)],[d91,d90]) ).
cnf(d93,plain,
~ midp(sK523,sK529,sK527),
inference(resolution,[status(thm)],[d92,c126]) ).
cnf(d94,plain,
$false,
inference(resolution,[status(thm)],[d89,d93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n006.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Fri Sep 25 13:45:40 UTC 2026
% 0.08/0.39 % CPUTime :
% 0.08/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.04/39.39 % SZS status Theorem for theBenchmark.p
% 31.04/39.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------