%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO636+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 : n011.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 07:15:34 AM UTC 2026
% Result : Theorem 38.76s 13.11s
% Output : CNFRefutation 38.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 28
% Syntax : Number of formulae : 108 ( 22 unt; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 221 ( 87 ~; 84 |; 21 &)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 402 ( 32 sgn 139 !; 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(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(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(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(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(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(exemplo6GDDFULL8110999,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( coll(X6,X0,X2)
& perp(X6,X3,X0,X2)
& coll(X5,X0,X1)
& perp(X5,X3,X0,X1)
& eqangle(X2,X0,X0,X4,X3,X0,X0,X1) )
=> perp(X0,X4,X6,X5) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( coll(X6,X0,X2)
& perp(X6,X3,X0,X2)
& coll(X5,X0,X1)
& perp(X5,X3,X0,X1)
& eqangle(X2,X0,X0,X4,X3,X0,X0,X1) )
=> perp(X0,X4,X6,X5) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL8110999]) ).
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(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(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(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(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(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(c116,plain,
perp(sK528,sK525,sK522,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c118,plain,
~ perp(sK522,sK526,sK528,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( cong(X0,X1,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c22]) ).
cnf(d1,plain,
( ~ cong(X3,X4,X0,X1)
| cong(X3,X4,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c24]) ).
cnf(d2,plain,
( ~ midp(X1,X3,X0)
| cong(X1,X3,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ cong(X0,X3,X2,X3)
| perp(X0,X2,X3,X1)
| ~ midp(X2,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c56]) ).
cnf(d4,plain,
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[c46,c38]) ).
cnf(d5,plain,
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[d4,c68]) ).
cnf(d6,plain,
( ~ midp(X2,X0,X0)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[d5,c64]) ).
cnf(d7,plain,
perp(sK522,sK524,sK528,sK525),
inference(resolution,[status(thm)],[c116,c7]) ).
cnf(d8,plain,
( ~ perp(X0,X1,sK528,sK525)
| para(X0,X1,sK522,sK524) ),
inference(resolution,[status(thm)],[c116,c8]) ).
cnf(d9,plain,
para(sK522,sK524,sK522,sK524),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d11,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d10,c38]) ).
cnf(d12,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d12,c66]) ).
cnf(d14,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d15,d16]) ).
cnf(d18,plain,
( ~ cong(X0,X1,X0,X2)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d17,c67]) ).
cnf(d19,plain,
( eqangle(X0,X2,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c17]) ).
cnf(d20,plain,
( eqangle(X3,X0,X3,X1,X0,X2,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d19,c19]) ).
cnf(d21,plain,
( ~ cyclic(X0,X1,X2,X1)
| ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d20,c43]) ).
cnf(d22,plain,
( ~ para(X0,X2,X0,X2)
| cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[c42,c39]) ).
cnf(d23,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d12,d22]) ).
cnf(d24,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d17,d23]) ).
cnf(d25,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d24,c14]) ).
cnf(d26,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d25,c15]) ).
cnf(d27,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d26,c13]) ).
cnf(d28,plain,
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d27,d21]) ).
cnf(d29,plain,
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d25,d28]) ).
cnf(d30,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d26,d29]) ).
cnf(d31,plain,
midp(X0,X1,X1),
inference(resolution,[status(thm)],[d30,d18]) ).
cnf(d32,plain,
( ~ midp(X0,X0,X1)
| midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
( ~ midp(X2,X1,X2)
| midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[d12,c45]) ).
cnf(d34,plain,
( midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[d17,d33]) ).
cnf(d35,plain,
midp(X0,X1,X0),
inference(resolution,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
midp(X0,X0,X1),
inference(resolution,[status(thm)],[d35,c10]) ).
cnf(d37,plain,
( midp(X2,X1,X0)
| ~ para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( cong(X0,X2,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c23]) ).
cnf(d39,plain,
( eqangle(X1,X2,X0,X2,X0,X1,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[c46,c19]) ).
cnf(d40,plain,
( para(X0,X1,X0,X0)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[d39,c38]) ).
cnf(d41,plain,
( ~ midp(X0,X1,X0)
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
para(X0,X1,X0,X0),
inference(resolution,[status(thm)],[d35,d41]) ).
cnf(d43,plain,
midp(X0,X1,X2),
inference(resolution,[status(thm)],[d42,d37]) ).
cnf(d44,plain,
( ~ cong(X0,X2,X1,X2)
| ~ midp(X0,X3,X1)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d43,d3]) ).
cnf(d45,plain,
( cong(X1,X3,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d43,d2]) ).
cnf(d46,plain,
cong(X0,X1,X2,X3),
inference(resolution,[status(thm)],[d43,d45]) ).
cnf(d47,plain,
( ~ midp(X0,X3,X1)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
~ midp(sK522,sK527,sK526),
inference(resolution,[status(thm)],[d47,c118]) ).
cnf(d49,plain,
$false,
inference(resolution,[status(thm)],[d43,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO636+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
% 0.11/0.57 % Computer : n011.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Fri Sep 25 13:46:14 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.76/13.11 % SZS status Theorem for theBenchmark.p
% 38.76/13.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------