%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO624+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 : n016.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 3.12s 11.27s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 16 unt; 0 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 123 ( 40 ~; 38 |; 26 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 292 ( 22 sgn 111 !; 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(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(ruleD66,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ) ).
fof(exemplo6GDDFULL8110988,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( coll(X9,X2,X5)
& coll(X9,X0,X1)
& coll(X8,X0,X4)
& coll(X8,X2,X3)
& cong(X2,X5,X2,X7)
& coll(X2,X5,X7)
& cong(X2,X3,X2,X6)
& coll(X2,X3,X6)
& coll(X5,X0,X4)
& perp(X5,X2,X0,X4)
& coll(X3,X0,X1)
& perp(X3,X2,X0,X1) )
=> cyclic(X0,X6,X7,X9) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( coll(X9,X2,X5)
& coll(X9,X0,X1)
& coll(X8,X0,X4)
& coll(X8,X2,X3)
& cong(X2,X5,X2,X7)
& coll(X2,X5,X7)
& cong(X2,X3,X2,X6)
& coll(X2,X3,X6)
& coll(X5,X0,X4)
& perp(X5,X2,X0,X4)
& coll(X3,X0,X1)
& perp(X3,X2,X0,X1) )
=> cyclic(X0,X6,X7,X9) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULL8110988]) ).
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(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(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[ruleD66]) ).
cnf(c113,plain,
perp(sK525,sK524,sK522,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c125,plain,
~ cyclic(sK522,sK528,sK529,sK531),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( eqangle(X2,X1,X2,X0,X3,X1,X3,X0)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c18]) ).
cnf(d1,plain,
( eqangle(X1,X2,X2,X0,X3,X1,X3,X0)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( eqangle(X3,X0,X3,X1,X2,X0,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c40,c19]) ).
cnf(d3,plain,
( eqangle(X3,X0,X3,X1,X4,X5,X6,X7)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X6,X7)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
( ~ cyclic(X1,X0,X0,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d6,plain,
( eqangle(X4,X5,X2,X3,X4,X5,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d5,c19]) ).
cnf(d7,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d6,c42]) ).
cnf(d8,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d5,c38]) ).
cnf(d9,plain,
perp(sK522,sK523,sK525,sK524),
inference(resolution,[status(thm)],[c113,c7]) ).
cnf(d10,plain,
( ~ perp(X0,X1,sK525,sK524)
| para(X0,X1,sK522,sK523) ),
inference(resolution,[status(thm)],[c113,c8]) ).
cnf(d11,plain,
para(sK522,sK523,sK522,sK523),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d12,c66]) ).
cnf(d15,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d17,c14]) ).
cnf(d19,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[d18,c13]) ).
cnf(d20,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d19,c15]) ).
cnf(d22,plain,
eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( cyclic(X3,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d22,c42]) ).
cnf(d24,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d25,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d16,d24]) ).
cnf(d26,plain,
cyclic(X0,X1,X2,X3),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,c125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO624+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:50:14 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.12/11.27 % SZS status Theorem for theBenchmark.p
% 3.12/11.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------