%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO638+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 : n007.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 07:18:17 AM UTC 2026
% Result : Theorem 98.10s 13.58s
% Output : CNFRefutation 98.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 198 ( 94 unt; 0 def)
% Number of atoms : 382 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 290 ( 106 ~; 102 |; 52 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 385 ( 42 sgn 144 !; 11 ?)
% 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(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(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(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(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
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(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(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(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD69) ).
fof(exemplo6GDDFULL81109104,conjecture,
! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) )
=> perp(C,H,D,H) ),
file('theBenchmark.p',exemplo6GDDFULL81109104) ).
fof(exemplo6GDDFULL81109104_neg,negated_conjecture,
~ ! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) )
=> perp(C,H,D,H) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL81109104]) ).
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_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
cnf(c_172,plain,
( ~ cong(A,B,A,C)
| ~ cong(A,B,A,D)
| perp(B,D,D,C)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_101,c_97]) ).
fof(nnf_95,plain,
? [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ~ perp(C,H,D,H)
& coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL81109104_neg]) ).
fof(sk_exemplo6GDDFULL81109104_neg,plain,
( ~ perp(sK0,sK1,sK2,sK1)
& coll(sK1,sK3,sK4)
& perp(sK1,sK10,sK3,sK4)
& midp(sK10,sK0,sK2)
& coll(sK0,sK8,sK2)
& para(sK3,sK2,sK0,sK4)
& perp(sK5,sK8,sK8,sK2)
& circle(sK5,sK3,sK8,sK9)
& circle(sK5,sK3,sK6,sK7)
& midp(sK5,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK3,sK4,sK6,sK7,sK8,sK9,sK2,sK0,sK10,sK1]),skolemize(A,sK3),skolemize(B,sK4),skolemize(E,sK5),skolemize(G,sK8),skolemize(D,sK2),skolemize(C,sK0),skolemize(F,sK10),skolemize(H,sK1),skolemize(NWPNT1,sK6),skolemize(NWPNT2,sK7),skolemize(NWPNT3,sK9)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ perp(sK0,sK1,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109104_neg]) ).
cnf(c_178,negated_conjecture,
coll(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109104_neg]) ).
cnf(c_184,negated_conjecture,
midp(sK5,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109104_neg]) ).
cnf(c_220,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_221,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_222,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_225,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_233,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_234,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_240,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_241,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_242,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_244,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_245,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_266,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_268,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_269,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_270,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_271,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_272,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_273,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_274,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_275,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_276,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_279,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_280,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_281,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_282,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_283,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_298,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_172]) ).
cnf(c_328,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_329,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_241]) ).
cnf(c_330,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,D,D,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_241]) ).
cnf(c_332,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_268]) ).
cnf(c_333,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_272]) ).
cnf(c_337,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_345,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_329]) ).
cnf(c_346,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_333]) ).
cnf(c_579,plain,
coll(sK5,sK3,sK4),
inference(resolve,[status(thm)],[c_220,c_184]) ).
cnf(c_581,plain,
cong(sK5,sK3,sK5,sK4),
inference(resolve,[status(thm)],[c_221,c_184]) ).
cnf(c_617,plain,
( para(sK5,A,sK4,B)
| ~ midp(A,sK3,B) ),
inference(resolve,[status(thm)],[c_240,c_184]) ).
cnf(c_624,plain,
midp(sK5,sK4,sK3),
inference(resolve,[status(thm)],[c_273,c_184]) ).
cnf(c_656,plain,
coll(sK3,sK1,sK4),
inference(resolve,[status(thm)],[c_282,c_178]) ).
cnf(c_658,plain,
coll(sK1,sK4,sK3),
inference(resolve,[status(thm)],[c_283,c_178]) ).
cnf(c_691,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_337,c_178]) ).
cnf(c_22792,plain,
( ~ cong(sK5,sK3,sK5,sK4)
| perp(sK3,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_579,c_298]) ).
cnf(c_704,plain,
perp(sK3,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_581,c_22792]) ).
cnf(c_705,plain,
coll(sK5,sK4,sK3),
inference(resolve,[status(thm)],[c_579,c_283]) ).
cnf(c_777,plain,
cong(sK5,sK4,sK5,sK3),
inference(resolve,[status(thm)],[c_624,c_221]) ).
cnf(c_887,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_656,c_337]) ).
cnf(c_964,plain,
coll(sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_658,c_337]) ).
cnf(c_1057,plain,
coll(sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_691,c_283]) ).
cnf(c_1120,plain,
coll(sK3,sK3,sK5),
inference(resolve,[status(thm)],[c_705,c_337]) ).
cnf(c_22793,plain,
( ~ cong(sK5,sK4,sK5,sK3)
| perp(sK4,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_705,c_298]) ).
cnf(c_1132,plain,
perp(sK4,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_777,c_22793]) ).
cnf(c_1373,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_887,c_337]) ).
cnf(c_1387,plain,
coll(sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_887,c_283]) ).
cnf(c_1538,plain,
coll(sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_964,c_283]) ).
cnf(c_1721,plain,
coll(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_1057,c_337]) ).
cnf(c_1860,plain,
coll(sK3,sK5,sK3),
inference(resolve,[status(thm)],[c_1120,c_283]) ).
cnf(c_2313,plain,
coll(sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_1373,c_283]) ).
cnf(c_2351,plain,
coll(sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_1387,c_282]) ).
cnf(c_2498,plain,
coll(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_1538,c_337]) ).
cnf(c_2735,plain,
( cyclic(A,sK4,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK4,sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1721,c_242]) ).
cnf(c_2739,plain,
( midp(sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1721,c_222]) ).
cnf(c_2930,plain,
( ~ cong(sK3,sK5,sK3,sK3)
| perp(sK5,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1860,c_298]) ).
cnf(c_2931,plain,
coll(sK5,sK3,sK3),
inference(resolve,[status(thm)],[c_1860,c_282]) ).
cnf(c_3325,plain,
coll(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_2313,c_282]) ).
cnf(c_3379,plain,
( midp(sK3,sK4,sK4)
| ~ cong(sK3,sK4,sK3,sK4) ),
inference(resolve,[status(thm)],[c_2351,c_222]) ).
cnf(c_3538,plain,
( midp(sK3,sK3,sK3)
| ~ cong(sK3,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_2498,c_222]) ).
cnf(c_3896,plain,
( midp(sK5,sK3,sK3)
| ~ cong(sK5,sK3,sK5,sK3) ),
inference(resolve,[status(thm)],[c_2931,c_222]) ).
cnf(c_4176,plain,
( midp(sK4,sK3,sK3)
| ~ cong(sK4,sK3,sK4,sK3) ),
inference(resolve,[status(thm)],[c_3325,c_222]) ).
cnf(c_4312,plain,
cyclic(sK3,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_581,c_346]) ).
cnf(c_4794,plain,
( cong(sK3,sK4,sK3,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_704,c_234]) ).
cnf(c_4924,plain,
cyclic(sK4,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_777,c_346]) ).
cnf(c_5208,plain,
( cong(sK4,sK3,sK4,sK3)
| ~ midp(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1132,c_234]) ).
cnf(c_5279,plain,
cyclic(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_4312,c_332]) ).
cnf(c_5570,plain,
cyclic(sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_4924,c_332]) ).
cnf(c_5690,plain,
( cong(sK4,sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_5279,c_345]) ).
cnf(c_5698,plain,
eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5279,c_244]) ).
cnf(c_5721,plain,
cong(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5698,c_5690]) ).
cnf(c_5723,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5721,c_2739]) ).
cnf(c_5724,plain,
cong(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_5723,c_4794]) ).
cnf(c_5728,plain,
midp(sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_5724,c_3379]) ).
cnf(c_5740,plain,
para(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_5723,c_328]) ).
cnf(c_6317,plain,
( cong(sK3,sK3,sK3,sK3)
| ~ eqangle(sK3,sK3,sK3,sK3,sK3,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_5570,c_345]) ).
cnf(c_6325,plain,
eqangle(sK3,sK3,sK3,sK3,sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_5570,c_244]) ).
cnf(c_6348,plain,
cong(sK3,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6325,c_6317]) ).
cnf(c_6350,plain,
midp(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_6348,c_3538]) ).
cnf(c_6351,plain,
cong(sK4,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_6350,c_5208]) ).
cnf(c_6355,plain,
midp(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_6351,c_4176]) ).
cnf(c_7055,plain,
eqangle(sK4,sK4,A,B,sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_5740,c_245]) ).
cnf(c_10669,plain,
para(sK5,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_617,c_6355]) ).
cnf(c_10670,plain,
para(sK5,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_617,c_6350]) ).
cnf(c_10676,plain,
para(sK4,sK3,sK5,sK4),
inference(resolve,[status(thm)],[c_10669,c_279]) ).
cnf(c_10702,plain,
para(sK5,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_10670,c_280]) ).
cnf(c_10748,plain,
para(sK4,sK3,sK4,sK5),
inference(resolve,[status(thm)],[c_10676,c_280]) ).
cnf(c_10775,plain,
para(sK3,sK4,sK5,sK3),
inference(resolve,[status(thm)],[c_10702,c_279]) ).
cnf(c_10846,plain,
para(sK4,sK5,sK4,sK3),
inference(resolve,[status(thm)],[c_10748,c_279]) ).
cnf(c_22794,plain,
( midp(A,sK5,sK3)
| ~ para(sK4,sK5,sK4,sK3)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_10748,c_225]) ).
cnf(c_10853,plain,
( midp(A,sK5,sK3)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_10846,c_22794]) ).
cnf(c_10870,plain,
para(sK3,sK4,sK3,sK5),
inference(resolve,[status(thm)],[c_10775,c_280]) ).
cnf(c_10969,plain,
para(sK3,sK5,sK3,sK4),
inference(resolve,[status(thm)],[c_10870,c_279]) ).
cnf(c_22795,plain,
( midp(A,sK5,sK4)
| ~ para(sK3,sK5,sK3,sK4)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_10870,c_225]) ).
cnf(c_10976,plain,
( midp(A,sK5,sK4)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_10969,c_22795]) ).
cnf(c_11061,plain,
midp(sK3,sK5,sK3),
inference(resolve,[status(thm)],[c_10853,c_5728]) ).
cnf(c_11086,plain,
cong(sK3,sK5,sK3,sK3),
inference(resolve,[status(thm)],[c_11061,c_221]) ).
cnf(c_11113,plain,
perp(sK5,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_11086,c_2930]) ).
cnf(c_22796,plain,
( cong(sK5,sK3,sK5,sK3)
| ~ midp(sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_11113,c_234]) ).
cnf(c_11346,plain,
cong(sK5,sK3,sK5,sK3),
inference(resolve,[status(thm)],[c_6350,c_22796]) ).
cnf(c_11375,plain,
midp(sK5,sK3,sK3),
inference(resolve,[status(thm)],[c_11346,c_3896]) ).
cnf(c_14268,plain,
midp(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_10976,c_11375]) ).
cnf(c_14297,plain,
midp(sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_14268,c_273]) ).
cnf(c_14306,plain,
cong(sK5,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_14268,c_221]) ).
cnf(c_14411,plain,
cong(sK5,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_14297,c_221]) ).
cnf(c_14480,plain,
cyclic(sK5,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_14306,c_346]) ).
cnf(c_14649,plain,
cyclic(sK4,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_14411,c_346]) ).
cnf(c_14825,plain,
cyclic(sK4,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_14480,c_269]) ).
cnf(c_14878,plain,
cyclic(sK5,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_14649,c_269]) ).
cnf(c_14956,plain,
cyclic(sK4,sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_14825,c_270]) ).
cnf(c_15039,plain,
cyclic(sK5,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_14878,c_270]) ).
cnf(c_15109,plain,
cyclic(sK4,sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_14956,c_271]) ).
cnf(c_15110,plain,
( cyclic(sK4,sK5,A,sK4)
| ~ cyclic(sK4,sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_14956,c_268]) ).
cnf(c_15147,plain,
cyclic(sK5,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_15039,c_271]) ).
cnf(c_15167,plain,
cyclic(sK4,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_15109,c_332]) ).
cnf(c_15175,plain,
( cyclic(sK4,sK4,sK5,A)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_15109,c_268]) ).
cnf(c_15203,plain,
cyclic(sK5,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_15147,c_332]) ).
cnf(c_15245,plain,
cyclic(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_15167,c_270]) ).
cnf(c_15247,plain,
( cyclic(sK4,sK5,sK5,A)
| ~ cyclic(sK4,sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_15167,c_268]) ).
cnf(c_15277,plain,
( cyclic(sK5,sK4,A,sK4)
| ~ cyclic(sK5,sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_15203,c_268]) ).
cnf(c_15305,plain,
cyclic(sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_15245,c_271]) ).
cnf(c_15336,plain,
( cyclic(sK5,sK5,sK4,A)
| ~ cyclic(sK4,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_15305,c_268]) ).
cnf(c_19238,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_7055,c_330]) ).
cnf(c_19240,plain,
eqangle(A,B,sK4,sK4,A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_7055,c_266]) ).
cnf(c_19248,plain,
cyclic(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_19240,c_2735]) ).
cnf(c_19262,plain,
cyclic(sK4,A,sK4,sK4),
inference(resolve,[status(thm)],[c_19248,c_269]) ).
cnf(c_19265,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_19262,c_19238]) ).
cnf(c_19283,plain,
cyclic(sK4,sK4,A,sK4),
inference(resolve,[status(thm)],[c_19262,c_270]) ).
cnf(c_19300,plain,
cyclic(sK4,sK4,sK4,A),
inference(resolve,[status(thm)],[c_19283,c_271]) ).
cnf(c_19307,plain,
cyclic(sK4,sK4,sK5,A),
inference(resolve,[status(thm)],[c_19300,c_15175]) ).
cnf(c_19320,plain,
cyclic(sK4,sK5,sK5,A),
inference(resolve,[status(thm)],[c_19307,c_15247]) ).
cnf(c_19325,plain,
cyclic(sK4,sK5,A,sK4),
inference(resolve,[status(thm)],[c_19307,c_15110]) ).
cnf(c_19344,plain,
cyclic(sK5,sK5,sK4,A),
inference(resolve,[status(thm)],[c_19320,c_15336]) ).
cnf(c_19375,plain,
cyclic(sK5,sK4,A,sK4),
inference(resolve,[status(thm)],[c_19344,c_15277]) ).
cnf(c_22797,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK4,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_19300,c_268]) ).
cnf(c_19490,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_19300,c_22797]) ).
cnf(c_22798,plain,
( cyclic(sK4,sK5,A,B)
| ~ cyclic(sK4,sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_19307,c_268]) ).
cnf(c_19507,plain,
cyclic(sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_19490,c_22798]) ).
cnf(c_22799,plain,
( cyclic(sK5,A,sK4,B)
| ~ cyclic(sK4,sK5,A,B) ),
inference(resolve,[status(thm)],[c_19325,c_268]) ).
cnf(c_19636,plain,
cyclic(sK5,A,sK4,B),
inference(resolve,[status(thm)],[c_19507,c_22799]) ).
cnf(c_22800,plain,
( cyclic(sK5,sK4,A,B)
| ~ cyclic(sK5,sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_19344,c_268]) ).
cnf(c_19693,plain,
cyclic(sK5,sK4,A,B),
inference(resolve,[status(thm)],[c_19636,c_22800]) ).
cnf(c_22801,plain,
( cyclic(sK4,A,sK4,B)
| ~ cyclic(sK5,sK4,A,B) ),
inference(resolve,[status(thm)],[c_19375,c_268]) ).
cnf(c_19780,plain,
cyclic(sK4,A,sK4,B),
inference(resolve,[status(thm)],[c_19693,c_22801]) ).
cnf(c_19792,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_19780,c_19265]) ).
cnf(c_22802,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_19792,c_233]) ).
cnf(c_20906,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_19792,c_22802]) ).
cnf(c_22788,plain,
perp(A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_20906,c_276]) ).
cnf(c_22803,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_20906,c_275]) ).
cnf(c_22789,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_22788,c_22803]) ).
cnf(c_22804,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_20906,c_274]) ).
cnf(c_22790,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_22789,c_22804]) ).
cnf(c_22791,plain,
$false,
inference(resolve,[status(thm)],[c_22790,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO638+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 13:44:08 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1136106 was started by sandbox2 on n007,
% 0.18/0.45 % Fri Sep 25 13:44:08 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.49
% 0.18/0.49 % From the command line: assign(max_seconds, 300).
% 98.10/13.58
% 98.10/13.58 % given #500 (T,wt=13): 1018 -coll(c5,c5,A) | coll(A,c6,c5). [resolve(690,a,281,b)].
% 98.10/13.58
% 98.10/13.58 % given #1000 (W,wt=13): 12887 -midp(A,c2,c1) | midp(A,c3,c3). [resolve(12531,a,323,b)].
% 98.10/13.58
% 98.10/13.58 % given #1500 (T,wt=10): 19266 cong(c3,c3,c2,c2). [resolve(19251,a,261,a)].
% 98.10/13.58
% 98.10/13.58 % SZS status Theorem for theBenchmark
% 98.10/13.58
% 98.10/13.58 % Proof 1 at 3.66 (+ 1.25) seconds.
% 98.10/13.58 % Length of proof is 182.
% 98.10/13.58 % Level of proof is 39.
% 98.10/13.58 % Maximum clause weight is 34.000.
% 98.10/13.58 % Given clauses 1736.
% 98.10/13.58
% 98.10/13.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------