%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO651+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 : n018.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 07:15:36 AM UTC 2026
% Result : Theorem 126.48s 20.86s
% Output : CNFRefutation 126.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 29
% Syntax : Number of formulae : 219 ( 95 unt; 0 def)
% Number of atoms : 419 ( 0 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 341 ( 141 ~; 137 |; 33 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 430 ( 22 sgn 147 !; 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(ruleD5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ) ).
fof(ruleD6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X2,X3,X4,X5)
& para(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ) ).
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(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(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(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(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(ruleD54,axiom,
! [X0,X1,X2,X3] :
( ( para(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X3) )
=> eqangle(X0,X3,X2,X3,X2,X3,X2,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(exemplo6GDDFULLmoreE02212,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( para(X0,X2,X5,X3)
& perp(X2,X4,X2,X5)
& perp(X1,X2,X8,X4)
& midp(X8,X1,X2)
& perp(X0,X2,X7,X4)
& midp(X7,X0,X2)
& perp(X0,X1,X6,X4)
& midp(X6,X0,X1)
& eqangle(X0,X2,X2,X3,X3,X2,X2,X1)
& coll(X3,X0,X1) )
=> cong(X2,X5,X3,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( para(X0,X2,X5,X3)
& perp(X2,X4,X2,X5)
& perp(X1,X2,X8,X4)
& midp(X8,X1,X2)
& perp(X0,X2,X7,X4)
& midp(X7,X0,X2)
& perp(X0,X1,X6,X4)
& midp(X6,X0,X1)
& eqangle(X0,X2,X2,X3,X3,X2,X2,X1)
& coll(X3,X0,X1) )
=> cong(X2,X5,X3,X1) ),
inference(negate_conjecture,[status(cth)],[exemplo6GDDFULLmoreE02212]) ).
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(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD4]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD5]) ).
cnf(c5,plain,
( para(X4,X5,X2,X3)
| ~ para(X4,X5,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD6]) ).
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(X4,X5,X2,X3)
| ~ perp(X4,X5,X0,X1)
| ~ 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(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(c24,plain,
( cong(X4,X5,X2,X3)
| ~ cong(X4,X5,X0,X1)
| ~ 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(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(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(X1,X4,X3)
| ~ midp(X0,X4,X2)
| ~ coll(X1,X4,X3)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD45]) ).
cnf(c54,plain,
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[ruleD54]) ).
cnf(c63,plain,
( para(X3,X1,X4,X2)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(clausification,[status(esa)],[ruleD63]) ).
cnf(c64,plain,
( midp(X4,X1,X3)
| ~ midp(X4,X0,X2)
| ~ para(X0,X3,X2,X1)
| ~ para(X0,X1,X2,X3) ),
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)
| ~ cong(X0,X1,X0,X2)
| ~ coll(X0,X1,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(sK523,sK524,sK530,sK526),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c117,plain,
para(sK522,sK524,sK527,sK525),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c118,plain,
perp(sK524,sK526,sK524,sK527),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c119,plain,
midp(sK530,sK523,sK524),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c122,plain,
coll(sK525,sK522,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c123,plain,
~ cong(sK524,sK527,sK525,sK523),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ cong(X3,X4,X0,X1)
| cong(X3,X4,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c24]) ).
cnf(d1,plain,
( cong(X0,X1,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[c68,c22]) ).
cnf(d2,plain,
( cong(X0,X1,X2,X3)
| ~ midp(X2,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ midp(sK524,sK527,sK525)
| ~ midp(sK525,sK524,sK523) ),
inference(resolution,[status(thm)],[d2,c123]) ).
cnf(d4,plain,
( ~ midp(sK522,X0,sK527)
| midp(sK524,X0,sK525)
| ~ coll(sK524,X0,sK525) ),
inference(resolution,[status(thm)],[c45,c117]) ).
cnf(d5,plain,
coll(sK525,sK523,sK522),
inference(resolution,[status(thm)],[c122,c0]) ).
cnf(d6,plain,
( ~ coll(sK525,sK523,X0)
| coll(X0,sK522,sK525) ),
inference(resolution,[status(thm)],[c2,d5]) ).
cnf(d7,plain,
coll(sK523,sK525,sK522),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d8,plain,
coll(sK523,sK522,sK525),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ coll(sK523,sK522,X0)
| coll(X0,sK525,sK523) ),
inference(resolution,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
coll(sK525,sK525,sK523),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
coll(sK525,sK523,sK525),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
coll(sK525,sK522,sK525),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( ~ coll(sK525,sK522,X0)
| coll(X0,sK525,sK525) ),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
coll(sK522,sK522,sK525),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d15,plain,
( ~ coll(sK522,sK522,X0)
| coll(X0,sK525,sK522) ),
inference(resolution,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
para(sK527,sK525,sK522,sK524),
inference(resolution,[status(thm)],[c117,c4]) ).
cnf(d17,plain,
para(sK527,sK525,sK524,sK522),
inference(resolution,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
para(sK524,sK522,sK527,sK525),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
( para(sK524,sK522,X0,X1)
| ~ para(sK527,sK525,X0,X1) ),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
para(sK524,sK522,sK524,sK522),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
coll(sK524,sK522,sK522),
inference(resolution,[status(thm)],[d20,c66]) ).
cnf(d22,plain,
coll(sK522,sK524,sK522),
inference(resolution,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
coll(sK522,sK522,sK524),
inference(resolution,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
coll(sK524,sK525,sK522),
inference(resolution,[status(thm)],[d23,d15]) ).
cnf(d25,plain,
coll(sK525,sK524,sK522),
inference(resolution,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
coll(sK525,sK522,sK524),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
coll(sK524,sK525,sK525),
inference(resolution,[status(thm)],[d26,d13]) ).
cnf(d28,plain,
coll(sK525,sK524,sK525),
inference(resolution,[status(thm)],[d27,c1]) ).
cnf(d29,plain,
coll(sK525,sK525,sK524),
inference(resolution,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
( ~ coll(sK525,sK525,X0)
| coll(X0,sK524,sK525) ),
inference(resolution,[status(thm)],[d29,c2]) ).
cnf(d31,plain,
perp(sK530,sK526,sK523,sK524),
inference(resolution,[status(thm)],[c7,c116]) ).
cnf(d32,plain,
perp(sK530,sK526,sK524,sK523),
inference(resolution,[status(thm)],[d31,c6]) ).
cnf(d33,plain,
perp(sK524,sK523,sK530,sK526),
inference(resolution,[status(thm)],[d32,c7]) ).
cnf(d34,plain,
( ~ perp(X0,X1,sK530,sK526)
| para(X0,X1,sK524,sK523) ),
inference(resolution,[status(thm)],[d32,c8]) ).
cnf(d35,plain,
para(sK524,sK523,sK524,sK523),
inference(resolution,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c18]) ).
cnf(d37,plain,
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d36,c38]) ).
cnf(d38,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[d38,c66]) ).
cnf(d40,plain,
coll(X0,X1,X0),
inference(resolution,[status(thm)],[d39,c1]) ).
cnf(d41,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
coll(X0,sK524,sK525),
inference(resolution,[status(thm)],[d41,d30]) ).
cnf(d43,plain,
coll(sK524,X0,sK525),
inference(resolution,[status(thm)],[d42,c1]) ).
cnf(d44,plain,
( midp(sK524,X0,sK525)
| ~ midp(sK522,X0,sK527) ),
inference(resolution,[status(thm)],[d43,d4]) ).
cnf(d45,plain,
perp(sK524,sK527,sK524,sK526),
inference(resolution,[status(thm)],[c7,c118]) ).
cnf(d46,plain,
( ~ perp(X0,X1,sK524,sK526)
| para(X0,X1,sK524,sK527) ),
inference(resolution,[status(thm)],[c8,c118]) ).
cnf(d47,plain,
para(sK524,sK527,sK524,sK527),
inference(resolution,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
( ~ midp(X0,sK524,sK524)
| midp(X0,sK527,sK527)
| ~ para(sK524,sK527,sK524,sK527) ),
inference(resolution,[status(thm)],[d47,c64]) ).
cnf(d49,plain,
( midp(X0,sK527,sK527)
| ~ midp(X0,sK524,sK524) ),
inference(resolution,[status(thm)],[d47,d48]) ).
cnf(d50,plain,
( para(sK522,sK524,X0,X1)
| ~ para(sK527,sK525,X0,X1) ),
inference(resolution,[status(thm)],[c5,c117]) ).
cnf(d51,plain,
para(sK522,sK524,sK522,sK524),
inference(resolution,[status(thm)],[d50,d16]) ).
cnf(d52,plain,
( ~ midp(X0,sK522,sK522)
| midp(X0,sK524,sK524)
| ~ para(sK522,sK524,sK522,sK524) ),
inference(resolution,[status(thm)],[d51,c64]) ).
cnf(d53,plain,
( midp(X0,sK524,sK524)
| ~ midp(X0,sK522,sK522) ),
inference(resolution,[status(thm)],[d51,d52]) ).
cnf(d54,plain,
( eqangle(X2,X3,X2,X1,X0,X3,X2,X3)
| ~ cyclic(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c54,c19]) ).
cnf(d55,plain,
( ~ cyclic(X2,X1,X0,X2)
| ~ cyclic(X2,X1,X0,X0)
| ~ cyclic(X2,X1,X0,X2)
| cong(X2,X1,X2,X2)
| ~ cyclic(X0,X1,X0,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d54,c43]) ).
cnf(d56,plain,
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c39,c19]) ).
cnf(d57,plain,
( cyclic(X1,X2,X0,X0)
| ~ coll(X0,X0,X2)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d56,c42]) ).
cnf(d58,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[d38,d57]) ).
cnf(d59,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[d41,d58]) ).
cnf(d60,plain,
( ~ cyclic(X0,X1,X0,X2)
| ~ cyclic(X2,X1,X0,X2)
| cong(X2,X1,X2,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[d59,c14]) ).
cnf(d62,plain,
cyclic(X0,X1,X2,X0),
inference(resolution,[status(thm)],[d61,c15]) ).
cnf(d63,plain,
( ~ cyclic(X0,X1,X0,X2)
| cong(X2,X1,X2,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d62,d60]) ).
cnf(d64,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[d62,c13]) ).
cnf(d65,plain,
( cong(X2,X1,X2,X2)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[d64,d63]) ).
cnf(d66,plain,
cong(X0,X0,X0,X0),
inference(resolution,[status(thm)],[d65,d38]) ).
cnf(d67,plain,
( midp(X0,X0,X0)
| ~ coll(X0,X0,X0) ),
inference(resolution,[status(thm)],[d66,c67]) ).
cnf(d68,plain,
( ~ coll(X2,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[d41,c2]) ).
cnf(d69,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[d41,d68]) ).
cnf(d70,plain,
midp(X0,X0,X0),
inference(resolution,[status(thm)],[d69,d67]) ).
cnf(d71,plain,
midp(sK522,sK524,sK524),
inference(resolution,[status(thm)],[d70,d53]) ).
cnf(d72,plain,
midp(sK522,sK527,sK527),
inference(resolution,[status(thm)],[d71,d49]) ).
cnf(d73,plain,
midp(sK524,sK527,sK525),
inference(resolution,[status(thm)],[d72,d44]) ).
cnf(d74,plain,
~ midp(sK525,sK524,sK523),
inference(resolution,[status(thm)],[d73,d3]) ).
cnf(d75,plain,
( ~ perp(X0,X1,sK530,sK526)
| para(X0,X1,sK523,sK524) ),
inference(resolution,[status(thm)],[d31,c8]) ).
cnf(d76,plain,
para(sK524,sK523,sK523,sK524),
inference(resolution,[status(thm)],[d75,d33]) ).
cnf(d77,plain,
( ~ midp(sK524,X0,sK523)
| midp(sK523,X0,sK524)
| ~ coll(sK523,X0,sK524) ),
inference(resolution,[status(thm)],[d76,c45]) ).
cnf(d78,plain,
para(sK523,sK524,sK523,sK524),
inference(resolution,[status(thm)],[d75,c116]) ).
cnf(d79,plain,
coll(sK523,sK524,sK524),
inference(resolution,[status(thm)],[d78,c66]) ).
cnf(d80,plain,
coll(sK524,sK523,sK524),
inference(resolution,[status(thm)],[d79,c1]) ).
cnf(d81,plain,
coll(sK524,sK524,sK523),
inference(resolution,[status(thm)],[d80,c0]) ).
cnf(d82,plain,
( ~ coll(sK524,sK524,X0)
| coll(X0,sK523,sK524) ),
inference(resolution,[status(thm)],[d81,c2]) ).
cnf(d83,plain,
coll(X0,sK523,sK524),
inference(resolution,[status(thm)],[d41,d82]) ).
cnf(d84,plain,
coll(sK523,X0,sK524),
inference(resolution,[status(thm)],[d83,c1]) ).
cnf(d85,plain,
( midp(sK523,X0,sK524)
| ~ midp(sK524,X0,sK523) ),
inference(resolution,[status(thm)],[d84,d77]) ).
cnf(d86,plain,
( ~ midp(X0,sK524,sK524)
| midp(X0,sK523,sK523)
| ~ para(sK524,sK523,sK524,sK523) ),
inference(resolution,[status(thm)],[d35,c64]) ).
cnf(d87,plain,
( midp(X0,sK523,sK523)
| ~ midp(X0,sK524,sK524) ),
inference(resolution,[status(thm)],[d38,d86]) ).
cnf(d88,plain,
midp(sK524,sK523,sK523),
inference(resolution,[status(thm)],[d70,d87]) ).
cnf(d89,plain,
midp(sK523,sK523,sK524),
inference(resolution,[status(thm)],[d88,d85]) ).
cnf(d90,plain,
( ~ midp(sK530,X0,X1)
| para(sK523,X0,sK524,X1) ),
inference(resolution,[status(thm)],[c63,c119]) ).
cnf(d91,plain,
( ~ midp(sK523,X2,sK524)
| midp(X0,X2,X1)
| ~ coll(X0,X2,X1)
| ~ midp(sK530,X0,X1) ),
inference(resolution,[status(thm)],[d90,c45]) ).
cnf(d92,plain,
( ~ midp(sK530,X0,X2)
| ~ midp(sK523,X1,sK524)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d69,d91]) ).
cnf(d93,plain,
para(sK523,sK524,sK524,sK523),
inference(resolution,[status(thm)],[d34,c116]) ).
cnf(d94,plain,
( ~ midp(sK523,X0,sK524)
| midp(sK524,X0,sK523)
| ~ coll(sK524,X0,sK523) ),
inference(resolution,[status(thm)],[d93,c45]) ).
cnf(d95,plain,
coll(sK522,sK525,sK523),
inference(resolution,[status(thm)],[c1,c122]) ).
cnf(d96,plain,
( ~ coll(sK522,sK525,X0)
| coll(X0,sK523,sK522) ),
inference(resolution,[status(thm)],[c2,d95]) ).
cnf(d97,plain,
coll(sK523,sK523,sK522),
inference(resolution,[status(thm)],[d96,d95]) ).
cnf(d98,plain,
coll(sK523,sK522,sK523),
inference(resolution,[status(thm)],[d97,c0]) ).
cnf(d99,plain,
( ~ coll(sK523,sK522,X0)
| coll(X0,sK523,sK523) ),
inference(resolution,[status(thm)],[d98,c2]) ).
cnf(d100,plain,
( ~ coll(sK523,sK525,X0)
| coll(X0,sK522,sK523) ),
inference(resolution,[status(thm)],[c2,d7]) ).
cnf(d101,plain,
coll(sK522,sK522,sK523),
inference(resolution,[status(thm)],[d100,d7]) ).
cnf(d102,plain,
( ~ coll(sK522,sK522,X0)
| coll(X0,sK523,sK522) ),
inference(resolution,[status(thm)],[d101,c2]) ).
cnf(d103,plain,
coll(sK524,sK523,sK522),
inference(resolution,[status(thm)],[d23,d102]) ).
cnf(d104,plain,
coll(sK523,sK524,sK522),
inference(resolution,[status(thm)],[d103,c1]) ).
cnf(d105,plain,
coll(sK523,sK522,sK524),
inference(resolution,[status(thm)],[d104,c0]) ).
cnf(d106,plain,
coll(sK524,sK523,sK523),
inference(resolution,[status(thm)],[d105,d99]) ).
cnf(d107,plain,
coll(sK523,sK524,sK523),
inference(resolution,[status(thm)],[d106,c1]) ).
cnf(d108,plain,
coll(sK523,sK523,sK524),
inference(resolution,[status(thm)],[d107,c0]) ).
cnf(d109,plain,
( ~ coll(sK523,sK523,X0)
| coll(X0,sK524,sK523) ),
inference(resolution,[status(thm)],[d108,c2]) ).
cnf(d110,plain,
coll(X0,sK524,sK523),
inference(resolution,[status(thm)],[d41,d109]) ).
cnf(d111,plain,
coll(sK524,X0,sK523),
inference(resolution,[status(thm)],[d110,c1]) ).
cnf(d112,plain,
( ~ midp(sK523,X0,sK524)
| midp(sK524,X0,sK523) ),
inference(resolution,[status(thm)],[d111,d94]) ).
cnf(d113,plain,
( ~ midp(X0,sK523,sK523)
| midp(X0,sK524,sK524)
| ~ para(sK523,sK524,sK523,sK524) ),
inference(resolution,[status(thm)],[d78,c64]) ).
cnf(d114,plain,
( ~ midp(X0,sK523,sK523)
| midp(X0,sK524,sK524) ),
inference(resolution,[status(thm)],[d38,d113]) ).
cnf(d115,plain,
midp(sK523,sK524,sK524),
inference(resolution,[status(thm)],[d70,d114]) ).
cnf(d116,plain,
midp(sK524,sK524,sK523),
inference(resolution,[status(thm)],[d115,d112]) ).
cnf(d117,plain,
perp(sK523,sK524,sK526,sK530),
inference(resolution,[status(thm)],[c6,c116]) ).
cnf(d118,plain,
perp(sK526,sK530,sK523,sK524),
inference(resolution,[status(thm)],[d117,c7]) ).
cnf(d119,plain,
( ~ perp(X0,X1,sK523,sK524)
| para(X0,X1,sK526,sK530) ),
inference(resolution,[status(thm)],[c8,d117]) ).
cnf(d120,plain,
para(sK526,sK530,sK526,sK530),
inference(resolution,[status(thm)],[d119,d118]) ).
cnf(d121,plain,
( ~ midp(sK526,X0,sK526)
| midp(sK530,X0,sK530)
| ~ coll(sK530,X0,sK530) ),
inference(resolution,[status(thm)],[d120,c45]) ).
cnf(d122,plain,
( midp(sK530,X0,sK530)
| ~ midp(sK526,X0,sK526) ),
inference(resolution,[status(thm)],[d40,d121]) ).
cnf(d123,plain,
( ~ perp(X0,X1,sK524,sK527)
| para(X0,X1,sK524,sK526) ),
inference(resolution,[status(thm)],[d45,c8]) ).
cnf(d124,plain,
para(sK524,sK526,sK524,sK526),
inference(resolution,[status(thm)],[d123,c118]) ).
cnf(d125,plain,
( ~ midp(sK524,X0,sK524)
| midp(sK526,X0,sK526)
| ~ coll(sK526,X0,sK526) ),
inference(resolution,[status(thm)],[d124,c45]) ).
cnf(d126,plain,
( midp(sK526,X0,sK526)
| ~ midp(sK524,X0,sK524) ),
inference(resolution,[status(thm)],[d40,d125]) ).
cnf(d127,plain,
perp(sK524,sK526,sK527,sK524),
inference(resolution,[status(thm)],[c6,c118]) ).
cnf(d128,plain,
perp(sK527,sK524,sK524,sK526),
inference(resolution,[status(thm)],[c7,d127]) ).
cnf(d129,plain,
( ~ perp(X0,X1,sK524,sK526)
| para(X0,X1,sK527,sK524) ),
inference(resolution,[status(thm)],[c8,d127]) ).
cnf(d130,plain,
para(sK527,sK524,sK527,sK524),
inference(resolution,[status(thm)],[d129,d128]) ).
cnf(d131,plain,
( ~ midp(sK527,X0,sK527)
| midp(sK524,X0,sK524)
| ~ coll(sK524,X0,sK524) ),
inference(resolution,[status(thm)],[d130,c45]) ).
cnf(d132,plain,
( ~ midp(sK527,X0,sK527)
| midp(sK524,X0,sK524) ),
inference(resolution,[status(thm)],[d40,d131]) ).
cnf(d133,plain,
para(sK522,sK524,sK525,sK527),
inference(resolution,[status(thm)],[c117,c3]) ).
cnf(d134,plain,
para(sK525,sK527,sK522,sK524),
inference(resolution,[status(thm)],[d133,c4]) ).
cnf(d135,plain,
( para(sK525,sK527,X0,X1)
| ~ para(sK522,sK524,X0,X1) ),
inference(resolution,[status(thm)],[d134,c5]) ).
cnf(d136,plain,
para(sK525,sK527,sK525,sK527),
inference(resolution,[status(thm)],[d135,d133]) ).
cnf(d137,plain,
( ~ midp(sK525,X0,sK525)
| midp(sK527,X0,sK527)
| ~ coll(sK527,X0,sK527) ),
inference(resolution,[status(thm)],[d136,c45]) ).
cnf(d138,plain,
( midp(sK527,X0,sK527)
| ~ midp(sK525,X0,sK525) ),
inference(resolution,[status(thm)],[d40,d137]) ).
cnf(d139,plain,
midp(sK527,sK525,sK527),
inference(resolution,[status(thm)],[d70,d138]) ).
cnf(d140,plain,
midp(sK524,sK525,sK524),
inference(resolution,[status(thm)],[d139,d132]) ).
cnf(d141,plain,
midp(sK526,sK525,sK526),
inference(resolution,[status(thm)],[d140,d126]) ).
cnf(d142,plain,
midp(sK530,sK525,sK530),
inference(resolution,[status(thm)],[d141,d122]) ).
cnf(d143,plain,
midp(sK530,sK530,sK525),
inference(resolution,[status(thm)],[d142,c10]) ).
cnf(d144,plain,
midp(sK530,sK524,sK523),
inference(resolution,[status(thm)],[c10,c119]) ).
cnf(d145,plain,
( ~ midp(sK530,X0,X1)
| para(sK524,X0,sK523,X1) ),
inference(resolution,[status(thm)],[c63,d144]) ).
cnf(d146,plain,
( ~ midp(sK524,X2,sK523)
| midp(X0,X2,X1)
| ~ coll(X0,X2,X1)
| ~ midp(sK530,X0,X1) ),
inference(resolution,[status(thm)],[d145,c45]) ).
cnf(d147,plain,
( ~ midp(sK530,X0,X2)
| ~ midp(sK524,X1,sK523)
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[d69,d146]) ).
cnf(d148,plain,
( ~ midp(sK524,X0,sK523)
| midp(sK530,X0,sK525) ),
inference(resolution,[status(thm)],[d147,d143]) ).
cnf(d149,plain,
midp(sK530,sK524,sK525),
inference(resolution,[status(thm)],[d148,d116]) ).
cnf(d150,plain,
midp(sK530,sK525,sK524),
inference(resolution,[status(thm)],[d149,c10]) ).
cnf(d151,plain,
( ~ midp(sK523,X0,sK524)
| midp(sK525,X0,sK524) ),
inference(resolution,[status(thm)],[d150,d92]) ).
cnf(d152,plain,
midp(sK525,sK523,sK524),
inference(resolution,[status(thm)],[d151,d89]) ).
cnf(d153,plain,
midp(sK525,sK524,sK523),
inference(resolution,[status(thm)],[d152,c10]) ).
cnf(d154,plain,
$false,
inference(resolution,[status(thm)],[d153,d74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO651+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 13:48:50 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 126.48/20.86 % SZS status Theorem for theBenchmark.p
% 126.48/20.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------