%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO607+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 : n013.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 07:15:30 AM UTC 2026
% Result : Theorem 1.78s 9.57s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 17 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 142 ( 55 ~; 53 |; 14 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 263 ( 21 sgn 97 !; 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(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(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(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(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(ruleD57,axiom,
! [X0,X1,X2,X3] :
( ( cyclic(X0,X1,X2,X3)
& cong(X0,X3,X1,X3)
& cong(X0,X2,X1,X2) )
=> perp(X2,X0,X0,X3) ) ).
fof(ruleD66,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ) ).
fof(exemplo6GDDFULL618069,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( circle(X5,X1,X3,X2)
& circle(X4,X0,X2,X3)
& perp(X3,X0,X3,X1)
& midp(X2,X1,X0) )
=> perp(X4,X3,X3,X5) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( circle(X5,X1,X3,X2)
& circle(X4,X0,X2,X3)
& perp(X3,X0,X3,X1)
& midp(X2,X1,X0) )
=> perp(X4,X3,X3,X5) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL618069]) ).
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(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(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(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(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(c57,plain,
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(clausification,[status(esa)],[ruleD57]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD66]) ).
cnf(c114,plain,
perp(sK525,sK522,sK525,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
~ perp(sK526,sK525,sK525,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[c43,c40]) ).
cnf(d1,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d2,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d1,c42]) ).
cnf(d3,plain,
perp(sK525,sK522,sK523,sK525),
inference(resolution,[status(thm)],[c6,c114]) ).
cnf(d4,plain,
perp(sK523,sK525,sK525,sK522),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ perp(X0,X1,sK525,sK522)
| para(X0,X1,sK523,sK525) ),
inference(resolution,[status(thm)],[c8,d3]) ).
cnf(d6,plain,
para(sK523,sK525,sK523,sK525),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d1,c38]) ).
cnf(d8,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ cyclic(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X0,X2)
| cong(X0,X1,X0,X1)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d8,c66]) ).
cnf(d12,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d14,c14]) ).
cnf(d16,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d15,c13]) ).
cnf(d17,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d16,c15]) ).
cnf(d18,plain,
( ~ cyclic(X0,X1,X0,X1)
| cong(X0,X1,X0,X1)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
( cong(X0,X1,X0,X1)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d15,d18]) ).
cnf(d20,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d13,c2]) ).
cnf(d21,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d13,d20]) ).
cnf(d22,plain,
cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c20]) ).
cnf(d24,plain,
( cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d23,c42]) ).
cnf(d25,plain,
( cyclic(X2,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d8,d24]) ).
cnf(d26,plain,
( ~ cong(X2,X0,X2,X0)
| ~ cong(X2,X1,X2,X1)
| perp(X0,X2,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d25,c57]) ).
cnf(d27,plain,
( ~ cong(X1,X0,X1,X0)
| ~ cong(X1,X2,X1,X2)
| perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[d21,d26]) ).
cnf(d28,plain,
( ~ cong(X1,X0,X1,X0)
| perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[d22,d27]) ).
cnf(d29,plain,
perp(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,c117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO607+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
% 0.08/0.35 % Computer : n013.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 13:43:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.78/9.57 % SZS status Theorem for theBenchmark.p
% 1.78/9.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------