%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO567+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 : n012.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 07:15:24 AM UTC 2026
% Result : Theorem 18.66s 15.06s
% Output : CNFRefutation 18.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 78 ( 20 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 57 ~; 59 |; 15 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 284 ( 33 sgn 92 !; 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(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(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(ruleD17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X3) )
=> cyclic(X1,X2,X3,X4) ) ).
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(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(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(ruleD42a,axiom,
! [X0,X1,X2,X3] :
( ( ~ coll(X2,X3,X0)
& eqangle(X2,X0,X2,X1,X3,X0,X3,X1) )
=> cyclic(X0,X1,X2,X3) ) ).
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(ruleD66,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ) ).
fof(exemplo6GDDFULL214029,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( coll(X5,X0,X2)
& perp(X5,X3,X0,X2)
& coll(X4,X0,X1)
& perp(X4,X3,X0,X1)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> cyclic(X1,X4,X5,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( coll(X5,X0,X2)
& perp(X5,X3,X0,X2)
& coll(X4,X0,X1)
& perp(X4,X3,X0,X1)
& coll(X3,X1,X2)
& perp(X3,X0,X1,X2) )
=> cyclic(X1,X4,X5,X2) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL214029]) ).
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(X3,X2,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(X4,X5,X2,X3)
| ~ perp(X4,X5,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD9]) ).
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(c16,plain,
( cyclic(X1,X2,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD17]) ).
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(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(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(c41,plain,
( cyclic(X2,X3,X0,X1)
| ~ eqangle(X0,X2,X0,X3,X1,X2,X1,X3)
| coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD42a]) ).
cnf(c42,plain,
( cyclic(X3,X2,X0,X1)
| ~ eqangle(X0,X3,X0,X2,X1,X3,X1,X2)
| ~ coll(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD42b]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD66]) ).
cnf(c118,plain,
perp(sK525,sK522,sK523,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
~ cyclic(sK523,sK526,sK527,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ cyclic(X4,X0,X1,X3)
| ~ cyclic(X4,X0,X1,X2)
| cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c13,c16]) ).
cnf(d1,plain,
perp(sK523,sK524,sK525,sK522),
inference(resolution,[status(thm)],[c118,c7]) ).
cnf(d2,plain,
( ~ perp(X0,X1,sK525,sK522)
| para(X0,X1,sK523,sK524) ),
inference(resolution,[status(thm)],[c118,c8]) ).
cnf(d3,plain,
para(sK523,sK524,sK523,sK524),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c20]) ).
cnf(d5,plain,
( cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d4,c42]) ).
cnf(d6,plain,
( cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[c4,d5]) ).
cnf(d7,plain,
( ~ para(X1,X0,X1,X0)
| ~ coll(X1,X2,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,d6]) ).
cnf(d8,plain,
( cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d4,c41]) ).
cnf(d9,plain,
( cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[c4,d8]) ).
cnf(d10,plain,
( ~ para(X1,X0,X1,X0)
| coll(X1,X2,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,d9]) ).
cnf(d11,plain,
( cyclic(X1,X1,X0,X2)
| ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
cyclic(sK524,sK524,sK523,X0),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( cyclic(sK524,sK523,X1,X0)
| ~ cyclic(sK524,sK524,sK523,X0) ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d15,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d14,c42]) ).
cnf(d16,plain,
( cyclic(X2,X1,X0,X0)
| ~ para(X0,X1,X0,X1)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[c1,d15]) ).
cnf(d17,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
( ~ para(X2,X1,X2,X1)
| ~ coll(X2,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[c13,d17]) ).
cnf(d19,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d14,c38]) ).
cnf(d20,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[c4,d19]) ).
cnf(d21,plain,
( cyclic(X4,X3,X2,X2)
| ~ coll(X2,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d21,d3]) ).
cnf(d23,plain,
( ~ coll(X2,X3,X0)
| ~ coll(X2,X3,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[c1,c2]) ).
cnf(d24,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d20,d3]) ).
cnf(d25,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d24,c66]) ).
cnf(d26,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d27,d28]) ).
cnf(d30,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d29,d22]) ).
cnf(d31,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d30,c14]) ).
cnf(d32,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d31,c15]) ).
cnf(d33,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d32,c13]) ).
cnf(d34,plain,
cyclic(X0,X0,X1,X2),
inference(resolution,[status(thm)],[d33,c14]) ).
cnf(d35,plain,
cyclic(sK524,sK523,X0,X1),
inference(resolution,[status(thm)],[d34,d13]) ).
cnf(d36,plain,
cyclic(sK523,sK524,X0,X1),
inference(resolution,[status(thm)],[d35,c15]) ).
cnf(d37,plain,
cyclic(sK523,X0,sK524,X1),
inference(resolution,[status(thm)],[d36,c14]) ).
cnf(d38,plain,
cyclic(sK523,X0,X1,sK524),
inference(resolution,[status(thm)],[d37,c13]) ).
cnf(d39,plain,
$false,
inference(resolution,[status(thm)],[d38,c119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO567+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:42:05 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.66/15.06 % SZS status Theorem for theBenchmark.p
% 18.66/15.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------