%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO591+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:18:10 AM UTC 2026
% Result : Theorem 38.82s 6.11s
% Output : CNFRefutation 38.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 30
% Syntax : Number of formulae : 189 ( 81 unt; 0 def)
% Number of atoms : 375 ( 0 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 300 ( 114 ~; 110 |; 45 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 405 ( 44 sgn 145 !; 9 ?)
% 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(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('theBenchmark.p',ruleD7) ).
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(ruleD10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('theBenchmark.p',ruleD10) ).
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(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(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('theBenchmark.p',ruleD19) ).
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(ruleD44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('theBenchmark.p',ruleD44) ).
fof(ruleD48,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,B) ),
file('theBenchmark.p',ruleD48) ).
fof(ruleD52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('theBenchmark.p',ruleD52) ).
fof(ruleD55,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('theBenchmark.p',ruleD55) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('theBenchmark.p',ruleD67) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('theBenchmark.p',ruleD68) ).
fof(exemplo6GDDFULL416053,conjecture,
! [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) )
=> cong(O,E,O,D) ),
file('theBenchmark.p',exemplo6GDDFULL416053) ).
fof(exemplo6GDDFULL416053_neg,negated_conjecture,
~ ! [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) )
=> cong(O,E,O,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416053]) ).
cnf(c_96,plain,
( eqangle(B,E,B,C,D,B,D,C)
| ~ perp(A,B,B,E)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD48]) ).
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_176,plain,
( ~ cong(A,B,A,E)
| ~ cong(A,B,A,D)
| eqangle(B,C,B,D,E,B,E,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_96,c_97]) ).
fof(nnf_95,plain,
? [O,A,B,C,E,D,NWPNT1,NWPNT2,NWPNT3] :
( ~ cong(O,E,O,D)
& coll(D,C,E)
& perp(O,C,C,E)
& coll(C,A,B)
& perp(O,A,A,D)
& perp(O,B,B,E)
& circle(O,A,B,NWPNT3)
& circle(O,A,NWPNT1,NWPNT2) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416053_neg]) ).
fof(sk_exemplo6GDDFULL416053_neg,plain,
( ~ cong(sK0,sK1,sK0,sK2)
& coll(sK2,sK3,sK1)
& perp(sK0,sK3,sK3,sK1)
& coll(sK3,sK4,sK5)
& perp(sK0,sK4,sK4,sK2)
& perp(sK0,sK5,sK5,sK1)
& circle(sK0,sK4,sK5,sK8)
& circle(sK0,sK4,sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK6,sK7,sK5,sK8,sK1,sK2,sK3]),skolemize(O,sK0),skolemize(A,sK4),skolemize(B,sK5),skolemize(C,sK3),skolemize(E,sK1),skolemize(D,sK2),skolemize(NWPNT1,sK6),skolemize(NWPNT2,sK7),skolemize(NWPNT3,sK8)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ cong(sK0,sK1,sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416053_neg]) ).
cnf(c_178,negated_conjecture,
coll(sK2,sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416053_neg]) ).
cnf(c_180,negated_conjecture,
coll(sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416053_neg]) ).
cnf(c_182,negated_conjecture,
perp(sK0,sK5,sK5,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416053_neg]) ).
cnf(c_219,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_220,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_221,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_223,plain,
( midp(A,D,E)
| ~ para(B,E,C,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD64]) ).
cnf(c_230,plain,
( perp(B,A,A,D)
| ~ cyclic(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD57]) ).
cnf(c_231,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_232,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_234,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_238,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_239,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_240,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_242,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_243,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_264,plain,
( eqangle(C,D,A,B,V6,V7,E,F)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD19]) ).
cnf(c_266,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_267,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_268,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_269,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_272,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_273,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_274,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_275,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_277,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_278,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_279,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_280,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_281,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_300,plain,
( ~ cong(A,B,A,D)
| eqangle(B,C,B,D,D,B,D,D)
| ~ perp(A,B,B,C) ),
inference(factor,[status(thm)],[c_176]) ).
cnf(c_321,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_223]) ).
cnf(c_324,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_230]) ).
cnf(c_326,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_238]) ).
cnf(c_327,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_239]) ).
cnf(c_329,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,E,D,E,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_330,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_266]) ).
cnf(c_335,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_343,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_327]) ).
cnf(c_584,plain,
( para(sK0,sK5,A,B)
| ~ perp(sK5,sK1,A,B) ),
inference(resolve,[status(thm)],[c_273,c_182]) ).
cnf(c_594,plain,
perp(sK5,sK1,sK0,sK5),
inference(resolve,[status(thm)],[c_274,c_182]) ).
cnf(c_605,plain,
( coll(sK1,A,sK2)
| ~ coll(sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_279,c_178]) ).
cnf(c_607,plain,
( coll(A,sK1,sK2)
| ~ coll(sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_279,c_178]) ).
cnf(c_611,plain,
coll(sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_281,c_178]) ).
cnf(c_624,plain,
coll(sK5,sK5,sK3),
inference(resolve,[status(thm)],[c_335,c_180]) ).
cnf(c_740,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_611,c_335]) ).
cnf(c_778,plain,
coll(sK3,sK3,sK5),
inference(resolve,[status(thm)],[c_624,c_335]) ).
cnf(c_1099,plain,
( coll(A,sK2,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_740,c_279]) ).
cnf(c_2648,plain,
perp(sK5,sK1,sK5,sK0),
inference(resolve,[status(thm)],[c_594,c_275]) ).
cnf(c_3051,plain,
coll(sK5,sK2,sK3),
inference(resolve,[status(thm)],[c_1099,c_778]) ).
cnf(c_3104,plain,
coll(sK2,sK5,sK3),
inference(resolve,[status(thm)],[c_3051,c_280]) ).
cnf(c_3258,plain,
coll(sK2,sK3,sK5),
inference(resolve,[status(thm)],[c_3104,c_281]) ).
cnf(c_3618,plain,
coll(sK5,sK1,sK2),
inference(resolve,[status(thm)],[c_3258,c_607]) ).
cnf(c_3619,plain,
coll(sK1,sK5,sK2),
inference(resolve,[status(thm)],[c_3258,c_605]) ).
cnf(c_4051,plain,
coll(sK5,sK2,sK1),
inference(resolve,[status(thm)],[c_3618,c_281]) ).
cnf(c_4088,plain,
coll(sK1,sK2,sK5),
inference(resolve,[status(thm)],[c_3619,c_281]) ).
cnf(c_4502,plain,
coll(sK1,sK1,sK5),
inference(resolve,[status(thm)],[c_4051,c_335]) ).
cnf(c_4540,plain,
coll(sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_4088,c_335]) ).
cnf(c_4973,plain,
coll(sK1,sK5,sK1),
inference(resolve,[status(thm)],[c_4502,c_281]) ).
cnf(c_5047,plain,
coll(sK5,sK1,sK5),
inference(resolve,[status(thm)],[c_4540,c_281]) ).
cnf(c_5049,plain,
( coll(sK1,A,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_4540,c_279]) ).
cnf(c_5496,plain,
( coll(A,sK1,sK1)
| ~ coll(sK1,sK5,A) ),
inference(resolve,[status(thm)],[c_4973,c_279]) ).
cnf(c_5538,plain,
coll(sK1,sK5,sK5),
inference(resolve,[status(thm)],[c_5047,c_280]) ).
cnf(c_5786,plain,
( midp(sK1,sK5,sK5)
| ~ cong(sK1,sK5,sK1,sK5) ),
inference(resolve,[status(thm)],[c_5538,c_220]) ).
cnf(c_7927,plain,
para(sK0,sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_584,c_2648]) ).
cnf(c_7928,plain,
para(sK0,sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_584,c_594]) ).
cnf(c_7933,plain,
para(sK5,sK0,sK0,sK5),
inference(resolve,[status(thm)],[c_7927,c_277]) ).
cnf(c_7957,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_7928,c_321]) ).
cnf(c_7960,plain,
eqangle(sK0,sK5,A,B,sK0,sK5,A,B),
inference(resolve,[status(thm)],[c_7928,c_243]) ).
cnf(c_7963,plain,
coll(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_7928,c_221]) ).
cnf(c_7989,plain,
coll(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_7963,c_335]) ).
cnf(c_8033,plain,
coll(sK1,sK0,sK5),
inference(resolve,[status(thm)],[c_7989,c_5049]) ).
cnf(c_8043,plain,
coll(sK0,sK0,sK5),
inference(resolve,[status(thm)],[c_7989,c_335]) ).
cnf(c_8135,plain,
coll(sK1,sK5,sK0),
inference(resolve,[status(thm)],[c_8033,c_281]) ).
cnf(c_8472,plain,
coll(sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_8043,c_281]) ).
cnf(c_8475,plain,
( cyclic(A,sK5,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK5,sK0,A,sK0,sK5) ),
inference(resolve,[status(thm)],[c_8043,c_240]) ).
cnf(c_8499,plain,
coll(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_8135,c_5496]) ).
cnf(c_8897,plain,
coll(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_8472,c_335]) ).
cnf(c_8911,plain,
coll(sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_8472,c_280]) ).
cnf(c_9046,plain,
( midp(sK0,sK1,sK1)
| ~ cong(sK0,sK1,sK0,sK1) ),
inference(resolve,[status(thm)],[c_8499,c_220]) ).
cnf(c_10999,plain,
( midp(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_8897,c_220]) ).
cnf(c_11039,plain,
( midp(sK5,sK0,sK0)
| ~ cong(sK5,sK0,sK5,sK0) ),
inference(resolve,[status(thm)],[c_8911,c_220]) ).
cnf(c_11951,plain,
para(sK5,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_7933,c_278]) ).
cnf(c_11975,plain,
( midp(A,sK0,sK0)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_11951,c_321]) ).
cnf(c_12025,plain,
( cong(sK5,sK0,sK5,sK0)
| ~ cyclic(sK5,sK0,sK0,sK0)
| ~ cyclic(sK5,sK0,sK0,sK5) ),
inference(resolve,[status(thm)],[c_7960,c_329]) ).
cnf(c_12028,plain,
eqangle(A,B,sK0,sK5,A,B,sK0,sK5),
inference(resolve,[status(thm)],[c_7960,c_264]) ).
cnf(c_12031,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK0,sK0)
| ~ cyclic(sK5,A,sK0,A)
| ~ cyclic(sK5,A,sK0,sK5) ),
inference(resolve,[status(thm)],[c_7960,c_239]) ).
cnf(c_12039,plain,
cyclic(A,sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_12028,c_8475]) ).
cnf(c_12042,plain,
cyclic(sK5,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12039,c_330]) ).
cnf(c_12050,plain,
cyclic(A,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_12039,c_268]) ).
cnf(c_12051,plain,
cyclic(sK5,A,sK0,sK0),
inference(resolve,[status(thm)],[c_12039,c_267]) ).
cnf(c_12078,plain,
( cong(sK5,sK0,sK5,sK0)
| ~ cyclic(sK5,sK0,sK0,sK5) ),
inference(resolve,[status(thm)],[c_12051,c_12025]) ).
cnf(c_12089,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK0,A)
| ~ cyclic(sK5,A,sK0,sK5) ),
inference(resolve,[status(thm)],[c_12051,c_12031]) ).
cnf(c_12091,plain,
cyclic(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12042,c_330]) ).
cnf(c_12130,plain,
cyclic(A,sK0,sK0,sK5),
inference(resolve,[status(thm)],[c_12050,c_269]) ).
cnf(c_12131,plain,
cyclic(sK0,A,sK5,sK0),
inference(resolve,[status(thm)],[c_12050,c_267]) ).
cnf(c_12159,plain,
cong(sK5,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_12130,c_12078]) ).
cnf(c_12185,plain,
midp(sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_12159,c_11039]) ).
cnf(c_12189,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_12185,c_7957]) ).
cnf(c_12307,plain,
( cong(A,sK5,A,sK5)
| ~ perp(A,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_12189,c_232]) ).
cnf(c_12311,plain,
cong(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_12189,c_219]) ).
cnf(c_12367,plain,
cyclic(A,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12051,c_330]) ).
cnf(c_12375,plain,
cyclic(sK5,sK0,A,sK0),
inference(resolve,[status(thm)],[c_12051,c_268]) ).
cnf(c_12402,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_12091,c_343]) ).
cnf(c_12410,plain,
eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12091,c_242]) ).
cnf(c_12432,plain,
cong(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12410,c_12402]) ).
cnf(c_12434,plain,
midp(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_12432,c_10999]) ).
cnf(c_12435,plain,
midp(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_12434,c_7957]) ).
cnf(c_12489,plain,
para(sK0,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_12435,c_326]) ).
cnf(c_12556,plain,
cyclic(sK0,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_12130,c_330]) ).
cnf(c_12621,plain,
cyclic(sK0,sK5,A,sK0),
inference(resolve,[status(thm)],[c_12131,c_268]) ).
cnf(c_12918,plain,
( perp(A,sK5,sK5,sK5)
| ~ cyclic(sK5,sK5,A,sK5)
| ~ cong(sK5,A,sK5,A) ),
inference(resolve,[status(thm)],[c_12311,c_230]) ).
cnf(c_12975,plain,
( cong(A,sK0,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_12367,c_343]) ).
cnf(c_12982,plain,
( perp(sK0,A,A,sK0)
| ~ cong(A,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_12367,c_324]) ).
cnf(c_13015,plain,
cyclic(sK5,sK0,sK0,A),
inference(resolve,[status(thm)],[c_12375,c_269]) ).
cnf(c_13079,plain,
( eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ perp(sK0,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_12432,c_300]) ).
cnf(c_13177,plain,
( perp(sK0,sK0,A,B)
| ~ perp(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_12489,c_272]) ).
cnf(c_13351,plain,
cyclic(sK0,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_12556,c_330]) ).
cnf(c_13359,plain,
( cyclic(sK0,sK5,sK5,A)
| ~ cyclic(sK0,sK0,sK5,A) ),
inference(resolve,[status(thm)],[c_12556,c_266]) ).
cnf(c_13420,plain,
( cyclic(sK5,A,sK0,B)
| ~ cyclic(sK0,sK5,A,B) ),
inference(resolve,[status(thm)],[c_12621,c_266]) ).
cnf(c_26075,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK5,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_13015,c_266]) ).
cnf(c_13546,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_13015,c_26075]) ).
cnf(c_13579,plain,
cyclic(sK0,sK5,sK5,A),
inference(resolve,[status(thm)],[c_13546,c_13359]) ).
cnf(c_26076,plain,
( cyclic(sK5,sK5,A,sK5)
| ~ cyclic(sK0,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_13351,c_266]) ).
cnf(c_13744,plain,
cyclic(sK5,sK5,A,sK5),
inference(resolve,[status(thm)],[c_13579,c_26076]) ).
cnf(c_13759,plain,
( perp(A,sK5,sK5,sK5)
| ~ cong(sK5,A,sK5,A) ),
inference(resolve,[status(thm)],[c_13744,c_12918]) ).
cnf(c_26077,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_13546,c_266]) ).
cnf(c_13940,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_13546,c_26077]) ).
cnf(c_13960,plain,
cyclic(sK5,A,sK0,B),
inference(resolve,[status(thm)],[c_13940,c_13420]) ).
cnf(c_26078,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13960,c_12089]) ).
cnf(c_13990,plain,
cong(sK5,A,sK5,A),
inference(resolve,[status(thm)],[c_13960,c_26078]) ).
cnf(c_14009,plain,
perp(A,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_13990,c_13759]) ).
cnf(c_14061,plain,
cong(A,sK5,A,sK5),
inference(resolve,[status(thm)],[c_14009,c_12307]) ).
cnf(c_14173,plain,
midp(sK1,sK5,sK5),
inference(resolve,[status(thm)],[c_14061,c_5786]) ).
cnf(c_14552,plain,
midp(sK1,sK0,sK0),
inference(resolve,[status(thm)],[c_14173,c_11975]) ).
cnf(c_14803,plain,
( cong(sK0,sK1,A,sK1)
| ~ perp(sK0,A,A,sK0) ),
inference(resolve,[status(thm)],[c_14552,c_234]) ).
cnf(c_26079,plain,
( perp(sK5,sK5,A,B)
| ~ cong(sK5,A,sK5,A) ),
inference(resolve,[status(thm)],[c_13990,c_231]) ).
cnf(c_16754,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_13990,c_26079]) ).
cnf(c_16781,plain,
perp(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_16754,c_13177]) ).
cnf(c_17058,plain,
eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_16781,c_13079]) ).
cnf(c_17061,plain,
cong(A,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_17058,c_12975]) ).
cnf(c_17065,plain,
perp(sK0,A,A,sK0),
inference(resolve,[status(thm)],[c_17061,c_12982]) ).
cnf(c_17077,plain,
cong(sK0,sK1,A,sK1),
inference(resolve,[status(thm)],[c_17065,c_14803]) ).
cnf(c_17091,plain,
midp(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_17077,c_9046]) ).
cnf(c_17210,plain,
( midp(sK0,A,B)
| ~ para(sK1,B,sK1,A)
| ~ para(sK1,A,sK1,B) ),
inference(resolve,[status(thm)],[c_17091,c_223]) ).
cnf(c_21882,plain,
perp(A,B,sK5,sK5),
inference(resolve,[status(thm)],[c_16754,c_274]) ).
cnf(c_26080,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK5,sK5) ),
inference(resolve,[status(thm)],[c_16754,c_273]) ).
cnf(c_21883,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_21882,c_26080]) ).
cnf(c_26081,plain,
( midp(sK0,B,A)
| ~ para(sK1,A,sK1,B) ),
inference(resolve,[status(thm)],[c_21883,c_17210]) ).
cnf(c_22028,plain,
midp(sK0,A,B),
inference(resolve,[status(thm)],[c_21883,c_26081]) ).
cnf(c_26073,plain,
cong(sK0,A,sK0,B),
inference(resolve,[status(thm)],[c_22028,c_219]) ).
cnf(c_26074,plain,
$false,
inference(resolve,[status(thm)],[c_26073,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO591+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n001.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 13:48:55 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3427436 was started by sandbox2 on n001,
% 0.15/0.43 % Fri Sep 25 13:48:55 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 38.82/6.11
% 38.82/6.11 % given #500 (T,wt=13): 2547 -coll(c2,c4,A) | coll(c4,A,c2). [resolve(2061,a,279,a)].
% 38.82/6.11
% 38.82/6.11 % given #1000 (T,wt=14): 7059 eqangle(c9,c2,c3,c9,c2,c6,c3,c2). [resolve(6787,a,264,a)].
% 38.82/6.11
% 38.82/6.11 % given #1500 (A,wt=40): 532 -cong(f12(c2,c7,c8,c1),c2,f12(c2,c7,c8,c1),c1) | coll(c1,c2,f4(c2,c1,f12(c2,c7,c8,c1),c2)). [resolve(206,a,130,a)].
% 38.82/6.11
% 38.82/6.11 % SZS status Theorem for theBenchmark
% 38.82/6.11
% 38.82/6.11 % Proof 1 at 4.15 (+ 1.35) seconds.
% 38.82/6.11 % Length of proof is 179.
% 38.82/6.11 % Level of proof is 27.
% 38.82/6.11 % Maximum clause weight is 34.000.
% 38.82/6.11 % Given clauses 1769.
% 38.82/6.11
% 38.82/6.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------