%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:18:07 AM UTC 2026
% Result : Theorem 190.30s 25.77s
% Output : CNFRefutation 190.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 136 ( 53 unt; 0 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 259 ( 96 ~; 92 |; 44 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-7 aty)
% Number of variables : 346 ( 21 sgn 146 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleD12) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('theBenchmark.p',ruleD13) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(ruleD51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('theBenchmark.p',ruleD51) ).
fof(ruleD63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('theBenchmark.p',ruleD63) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('theBenchmark.p',ruleD68) ).
fof(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD69) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( coll(D,A,B)
& coll(C,A,B)
& midp(N,C,D)
& midp(M,A,B) )
=> midp(P,A,Q) ),
file('theBenchmark.p',ruleX7) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL214031,conjecture,
! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
file('theBenchmark.p',exemplo6GDDFULL214031) ).
fof(exemplo6GDDFULL214031_neg,negated_conjecture,
~ ! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214031]) ).
cnf(c_97,plain,
( circle(A,B,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD12]) ).
cnf(c_100,plain,
( midp(E,C,D)
| ~ eqangle(B,C,B,D,A,C,A,E)
| ~ coll(E,C,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD51]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_95,plain,
? [A,B,C,O,C1,B1,P,Q] :
( ~ cyclic(Q,B,C,P)
& coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214031_neg]) ).
fof(sk_exemplo6GDDFULL214031_neg,plain,
( ~ cyclic(sK5,sK3,sK4,sK6)
& coll(sK5,sK2,sK3)
& coll(sK5,sK1,sK7)
& coll(sK6,sK2,sK4)
& coll(sK6,sK1,sK8)
& midp(sK7,sK4,sK2)
& midp(sK8,sK3,sK2)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK8,sK7,sK6,sK5]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(O,sK1),skolemize(C1,sK8),skolemize(B1,sK7),skolemize(P,sK6),skolemize(Q,sK5)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214031_neg]) ).
cnf(c_115,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_158,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| midp(A,B,C)
| ~ eqangle(D,B,D,C,E,B,E,A)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
cnf(c_162,negated_conjecture,
~ cyclic(sK5,sK3,sK4,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214031_neg]) ).
cnf(c_165,negated_conjecture,
coll(sK6,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214031_neg]) ).
cnf(c_167,negated_conjecture,
midp(sK7,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214031_neg]) ).
cnf(c_168,negated_conjecture,
midp(sK8,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214031_neg]) ).
fof(nnf_83,plain,
! [A,B,C,D,M,N,Q] :
? [P] :
( midp(P,A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(fof_nnf,[status(thm)],[ruleX7]) ).
fof(sk_ruleX7,plain,
! [A,B,C,D,M,N,Q] :
( midp(sK9(A,B,C,D,M,N,Q),A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(P,sK9(A,B,C,D,M,N,Q))],[nnf_83]) ).
cnf(c_185,plain,
( midp(sK9(B,C,E,F,A,D,V6),B,V6)
| ~ coll(F,B,C)
| ~ coll(E,B,C)
| ~ midp(D,E,F)
| ~ midp(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX7]) ).
cnf(c_204,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_205,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_207,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_210,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_223,plain,
( midp(D,B,E)
| ~ coll(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD45]) ).
cnf(c_225,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,F,D,F,E)
| ~ cyclic(A,B,C,F)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD43]) ).
cnf(c_226,plain,
( cyclic(B,C,A,D)
| ~ coll(A,D,C)
| ~ eqangle(A,B,A,C,D,B,D,C) ),
inference(clausify,[status(thm)],[ruleD42b]) ).
cnf(c_228,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_229,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_252,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_253,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_254,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_255,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_256,plain,
( cyclic(B,C,D,E)
| ~ cong(A,B,A,E)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD13]) ).
cnf(c_257,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_259,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_260,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_264,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_265,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_266,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_267,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_283,plain,
( ~ cong(D,C,D,B)
| midp(A,B,B)
| ~ eqangle(C,B,C,B,D,B,D,A)
| ~ coll(A,B,B) ),
inference(factor,[status(thm)],[c_158]) ).
cnf(c_300,plain,
( midp(sK9(B,C,B,C,A,A,D),B,D)
| ~ coll(C,B,C)
| ~ coll(B,B,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_185]) ).
cnf(c_313,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,E,D,E,D)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_225]) ).
cnf(c_316,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_252]) ).
cnf(c_317,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_256]) ).
cnf(c_321,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_265]) ).
cnf(c_329,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,D,D,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_313]) ).
cnf(c_330,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_317]) ).
cnf(c_372,plain,
coll(sK8,sK3,sK2),
inference(resolve,[status(thm)],[c_204,c_168]) ).
cnf(c_373,plain,
coll(sK7,sK4,sK2),
inference(resolve,[status(thm)],[c_204,c_167]) ).
cnf(c_374,plain,
cong(sK8,sK3,sK8,sK2),
inference(resolve,[status(thm)],[c_205,c_168]) ).
cnf(c_375,plain,
cong(sK7,sK4,sK7,sK2),
inference(resolve,[status(thm)],[c_205,c_167]) ).
cnf(c_387,plain,
midp(sK7,sK2,sK4),
inference(resolve,[status(thm)],[c_257,c_167]) ).
cnf(c_389,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_259,c_115]) ).
cnf(c_390,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_260,c_115]) ).
cnf(c_401,plain,
coll(sK2,sK6,sK4),
inference(resolve,[status(thm)],[c_266,c_165]) ).
cnf(c_426,plain,
coll(sK2,sK2,sK8),
inference(resolve,[status(thm)],[c_372,c_321]) ).
cnf(c_433,plain,
coll(sK4,sK7,sK2),
inference(resolve,[status(thm)],[c_373,c_266]) ).
cnf(c_466,plain,
( midp(sK9(sK2,sK4,sK2,sK4,sK7,sK7,A),sK2,A)
| ~ coll(sK4,sK2,sK4)
| ~ coll(sK2,sK2,sK4) ),
inference(resolve,[status(thm)],[c_387,c_300]) ).
cnf(c_486,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_401,c_321]) ).
cnf(c_535,plain,
coll(sK2,sK8,sK2),
inference(resolve,[status(thm)],[c_426,c_267]) ).
cnf(c_557,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_433,c_321]) ).
cnf(c_561,plain,
( midp(sK9(sK2,sK4,sK2,sK4,sK7,sK7,A),sK2,A)
| ~ coll(sK4,sK2,sK4) ),
inference(resolve,[status(thm)],[c_557,c_466]) ).
cnf(c_572,plain,
coll(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_486,c_267]) ).
cnf(c_575,plain,
midp(sK9(sK2,sK4,sK2,sK4,sK7,sK7,A),sK2,A),
inference(resolve,[status(thm)],[c_572,c_561]) ).
cnf(c_653,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_535,c_321]) ).
cnf(c_940,plain,
cyclic(sK3,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_374,c_330]) ).
cnf(c_1023,plain,
cyclic(sK4,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_375,c_330]) ).
cnf(c_1387,plain,
cyclic(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_940,c_316]) ).
cnf(c_1437,plain,
cyclic(sK2,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_1023,c_253]) ).
cnf(c_1631,plain,
eqangle(sK2,sK2,sK2,sK2,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_1387,c_228]) ).
cnf(c_1686,plain,
cyclic(sK2,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_1437,c_254]) ).
cnf(c_1907,plain,
cyclic(sK2,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_1686,c_255]) ).
cnf(c_2140,plain,
( cyclic(sK2,sK2,A,sK4)
| ~ cyclic(sK2,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1907,c_252]) ).
cnf(c_2286,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_390,c_389]) ).
cnf(c_2446,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_2286,c_229]) ).
cnf(c_2447,plain,
( midp(sK1,A,sK1)
| ~ coll(sK1,A,sK1)
| ~ midp(sK2,A,sK2) ),
inference(resolve,[status(thm)],[c_2286,c_223]) ).
cnf(c_2449,plain,
coll(sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_2286,c_207]) ).
cnf(c_2457,plain,
coll(sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_2449,c_266]) ).
cnf(c_4377,plain,
midp(sK9(sK2,sK4,sK2,sK4,sK7,sK7,A),A,sK2),
inference(resolve,[status(thm)],[c_575,c_257]) ).
cnf(c_4380,plain,
( para(B,sK2,C,A)
| ~ midp(sK9(sK2,sK4,sK2,sK4,sK7,sK7,A),B,C) ),
inference(resolve,[status(thm)],[c_575,c_210]) ).
cnf(c_44194,plain,
( cong(sK2,sK2,sK2,sK2)
| ~ cyclic(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1631,c_329]) ).
cnf(c_24182,plain,
cong(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_1387,c_44194]) ).
cnf(c_44195,plain,
( ~ cong(sK2,sK2,sK2,sK2)
| midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1631,c_283]) ).
cnf(c_44196,plain,
( ~ cong(sK2,sK2,sK2,sK2)
| midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_653,c_44195]) ).
cnf(c_24184,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_24182,c_44196]) ).
cnf(c_35576,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_2446,c_226]) ).
cnf(c_44197,plain,
( midp(sK1,sK2,sK1)
| ~ coll(sK1,sK2,sK1) ),
inference(resolve,[status(thm)],[c_2447,c_24184]) ).
cnf(c_35581,plain,
midp(sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_2457,c_44197]) ).
cnf(c_35656,plain,
midp(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_35581,c_257]) ).
cnf(c_35738,plain,
cong(sK1,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_35656,c_205]) ).
cnf(c_35866,plain,
cyclic(sK1,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_35738,c_330]) ).
cnf(c_36091,plain,
( cyclic(sK2,sK2,sK2,A)
| ~ cyclic(sK1,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_35866,c_252]) ).
cnf(c_42974,plain,
para(A,sK2,sK2,A),
inference(resolve,[status(thm)],[c_4380,c_4377]) ).
cnf(c_42975,plain,
para(A,sK2,A,sK2),
inference(resolve,[status(thm)],[c_42974,c_264]) ).
cnf(c_42980,plain,
coll(A,sK2,sK2),
inference(resolve,[status(thm)],[c_42975,c_207]) ).
cnf(c_42981,plain,
coll(sK2,sK2,A),
inference(resolve,[status(thm)],[c_42980,c_321]) ).
cnf(c_42985,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_42981,c_35576]) ).
cnf(c_43879,plain,
cyclic(sK1,sK2,A,sK2),
inference(resolve,[status(thm)],[c_42985,c_254]) ).
cnf(c_43890,plain,
cyclic(sK1,sK2,sK2,A),
inference(resolve,[status(thm)],[c_43879,c_255]) ).
cnf(c_43894,plain,
cyclic(sK2,sK2,sK2,A),
inference(resolve,[status(thm)],[c_43890,c_36091]) ).
cnf(c_43897,plain,
cyclic(sK2,sK2,A,sK4),
inference(resolve,[status(thm)],[c_43894,c_2140]) ).
cnf(c_44198,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK1,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_43890,c_252]) ).
cnf(c_43982,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_43890,c_44198]) ).
cnf(c_44199,plain,
( cyclic(sK2,A,B,sK4)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_43897,c_252]) ).
cnf(c_43995,plain,
cyclic(sK2,A,B,sK4),
inference(resolve,[status(thm)],[c_43982,c_44199]) ).
cnf(c_44200,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_43982,c_252]) ).
cnf(c_44161,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_43982,c_44200]) ).
cnf(c_44201,plain,
( cyclic(A,B,sK4,C)
| ~ cyclic(sK2,A,B,C) ),
inference(resolve,[status(thm)],[c_43995,c_252]) ).
cnf(c_44192,plain,
cyclic(A,B,sK4,C),
inference(resolve,[status(thm)],[c_44161,c_44201]) ).
cnf(c_44193,plain,
$false,
inference(resolve,[status(thm)],[c_44192,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 13:42:17 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3605833 was started by sandbox on n005,
% 0.18/0.44 % Fri Sep 25 13:42:17 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 190.30/25.77
% 190.30/25.77 % given #500 (A,wt=8): 395 -coll(c8,c1,A) | coll(c2,A,c8). [resolve(265,a,163,a)].
% 190.30/25.77
% 190.30/25.77 % given #1000 (A,wt=13): 610 coll(f17(f12(c1,c2,c3,c4),c4,c1,c4,c8),c4,c8). [resolve(508,a,336,a)].
% 190.30/25.77
% 190.30/25.77 % given #1500 (A,wt=24): 971 -cong(A,c2,A,B) | c5 = A | cong(f13(c2,c1,B,B,A,c5),c5,c5,c2) | -cong(A,c2,A,c1). [resolve(374,a,276,b)].
% 190.30/25.77
% 190.30/25.77 % given #2000 (A,wt=24): 1074 -cong(c6,c3,c6,A) | -cong(B,c3,B,A) | c6 = B | cong(f14(c3,A,c1,A,c6,B),B,B,c3). [resolve(375,a,269,e),flip(c)].
% 190.30/25.77
% 190.30/25.77 % given #2500 (A,wt=18): 1178 -coll(A,c1,c2) | -coll(B,c1,c1) | coll(f20(c1,c1,c2,c2,A,B),c2,c2). [resolve(437,a,287,a)].
% 190.30/25.77
% 190.30/25.77 % given #3000 (A,wt=10): 1282 -perp(c3,c3,A,B) | perp(c6,c6,A,B). [resolve(459,a,258,a)].
% 190.30/25.77
% 190.30/25.77 % given #3500 (A,wt=29): 1385 -cong(A,c1,A,B) | c6 = A | cong(f14(c1,c3,C,B,A,c6),c6,c6,c1) | -cong(A,c1,A,c3) | -cong(A,c1,A,C). [resolve(471,a,152,b)].
% 190.30/25.77
% 190.30/25.77 % given #4000 (A,wt=10): 1516 -perp(c5,c5,A,B) | perp(c2,c2,A,B). [resolve(1165,a,258,a)].
% 190.30/25.77
% 190.30/25.77 % given #4500 (A,wt=10): 1708 -perp(c3,c1,A,B) | para(c1,c1,A,B). [resolve(1456,a,259,a)].
% 190.30/25.77
% 190.30/25.77 % given #5000 (A,wt=18): 1941 -perp(c3,c1,c3,A) | -midp(B,c1,A) | midp(f18(c1,c1,c3,A,B),c1,c3). [resolve(1706,a,173,a)].
% 190.30/25.77
% 190.30/25.77 % given #5500 (A,wt=10): 2126 -perp(c5,c5,A,B) | para(c1,c2,A,B). [resolve(1902,a,259,a)].
% 190.30/25.77
% 190.30/25.77 % given #6000 (A,wt=13): 2340 -perp(c1,c5,c5,c2) | coll(f10(c5,c1,c2,c5),c2,c1). [resolve(2124,a,179,a)].
% 190.30/25.77
% 190.30/25.77 % given #6500 (A,wt=18): 2543 -midp(A,c2,c1) | -coll(f15(c2,c1,c2,c1,A),c2,c2) | perp(c2,c1,c1,c2). [resolve(2393,a,142,a),unit_del(a,1820)].
% 190.30/25.77
% 190.30/25.77 % given #7000 (A,wt=10): 2785 midp(f6(c2,c1,c2,c1,c5,c5),c1,c2). [resolve(414,a,257,a)].
% 190.30/25.77
% 190.30/25.77 % given #7500 (A,wt=16): 3147 midp(f6(c2,c1,c1,c2,f6(c2,c1,c2,c1,c5,c5),c5),c2,c2). [resolve(451,a,414,a)].
% 190.30/25.77
% 190.30/25.77 % given #8000 (A,wt=17): 3393 para(f6(c1,c3,c3,c1,f6(c1,c3,c1,c3,c6,c6),c6),c6,c1,c3). [resolve(462,a,357,a)].
% 190.30/25.77
% 190.30/25.77 % given #8500 (A,wt=15): 3691 eqratio(f6(c1,c3,c1,c3,c6,c6),c1,c1,c3,c6,c1,c1,c3). [resolve(472,a,462,a)].
% 190.30/25.77
% 190.30/25.77 % given #9000 (A,wt=18): 4335 para(f6(c1,A,c1,c2,f7(c1,c3,c1,c3,c6,c6,A),c5),c5,c1,c1). [resolve(575,a,455,a)].
% 190.30/25.77
% 190.30/25.77 % given #9500 (A,wt=16): 4639 -midp(A,c1,B) | para(f7(c1,c2,c1,c2,c5,c5,C),A,C,B). [resolve(593,a,224,a)].
% 190.30/25.77
% 190.30/25.77 % SZS status Theorem for theBenchmark
% 190.30/25.77
% 190.30/25.77 % Proof 1 at 21.08 (+ 3.71) seconds.
% 190.30/25.77 % Length of proof is 121.
% 190.30/25.77 % Level of proof is 19.
% 190.30/25.77 % Maximum clause weight is 29.000.
% 190.30/25.77 % Given clauses 9508.
% 190.30/25.77
% 190.30/25.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------