%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO636+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 : n026.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 07:18:16 AM UTC 2026
% Result : Theorem 14.80s 2.35s
% Output : CNFRefutation 14.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 32
% Syntax : Number of formulae : 193 ( 80 unt; 0 def)
% Number of atoms : 393 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 330 ( 130 ~; 126 |; 41 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-5 aty)
% Number of variables : 545 ( 92 sgn 179 !; 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(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(ruleD20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('theBenchmark.p',ruleD20) ).
fof(ruleD22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('theBenchmark.p',ruleD22) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD39) ).
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(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(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(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(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(ruleD65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('theBenchmark.p',ruleD65) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('theBenchmark.p',ruleD75) ).
fof(ruleX13,axiom,
! [A,B,C,D,M] :
? [O] :
( ( midp(M,A,B)
& para(A,B,C,D)
& cyclic(A,B,C,D) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX13) ).
fof(exemplo6GDDFULL8110999,conjecture,
! [A,B,C,M,N,Q,P] :
( ( coll(P,A,C)
& perp(P,M,A,C)
& coll(Q,A,B)
& perp(Q,M,A,B)
& eqangle(C,A,A,N,M,A,A,B) )
=> perp(A,N,P,Q) ),
file('theBenchmark.p',exemplo6GDDFULL8110999) ).
fof(exemplo6GDDFULL8110999_neg,negated_conjecture,
~ ! [A,B,C,M,N,Q,P] :
( ( coll(P,A,C)
& perp(P,M,A,C)
& coll(Q,A,B)
& perp(Q,M,A,B)
& eqangle(C,A,A,N,M,A,A,B) )
=> perp(A,N,P,Q) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110999]) ).
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]) ).
cnf(c_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
fof(nnf_89,plain,
! [A,B,C,D,M] :
? [O] :
( circle(O,A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[ruleX13]) ).
fof(sk_ruleX13,plain,
! [A,B,C,D,M] :
( circle(sK0(A,B,C,D,M),A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(O,sK0(A,B,C,D,M))],[nnf_89]) ).
cnf(c_107,plain,
( circle(sK0(A,B,C,D,E),A,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX13]) ).
cnf(c_127,plain,
( perp(A,B,B,C)
| ~ coll(sK0(A,B,C,D,E),A,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_107,c_101]) ).
cnf(c_143,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]) ).
fof(nnf_95,plain,
? [A,B,C,M,N,Q,P] :
( ~ perp(A,N,P,Q)
& coll(P,A,C)
& perp(P,M,A,C)
& coll(Q,A,B)
& perp(Q,M,A,B)
& eqangle(C,A,A,N,M,A,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110999_neg]) ).
fof(sk_exemplo6GDDFULL8110999_neg,plain,
( ~ perp(sK1,sK2,sK3,sK4)
& coll(sK3,sK1,sK7)
& perp(sK3,sK5,sK1,sK7)
& coll(sK4,sK1,sK6)
& perp(sK4,sK5,sK1,sK6)
& eqangle(sK7,sK1,sK1,sK2,sK5,sK1,sK1,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK1,sK2,sK5,sK6,sK4,sK3]),skolemize(A,sK1),skolemize(B,sK6),skolemize(C,sK7),skolemize(M,sK5),skolemize(N,sK2),skolemize(Q,sK4),skolemize(P,sK3)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ perp(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110999_neg]) ).
cnf(c_151,negated_conjecture,
perp(sK4,sK5,sK1,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110999_neg]) ).
cnf(c_152,negated_conjecture,
eqangle(sK7,sK1,sK1,sK2,sK5,sK1,sK1,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110999_neg]) ).
cnf(c_183,plain,
( cong(A,B,C,D)
| ~ cong(E,F,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD75]) ).
cnf(c_191,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_192,plain,
( eqratio(E,A,A,C,E,B,B,D)
| ~ coll(E,B,D)
| ~ coll(E,A,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD65]) ).
cnf(c_193,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_201,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_204,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_207,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_209,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_210,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_213,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_214,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_230,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_231,plain,
( eqangle(A,B,C,D,V8,V9,V10,V11)
| ~ eqangle(E,F,V6,V7,V8,V9,V10,V11)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD22]) ).
cnf(c_233,plain,
( eqangle(E,F,V6,V7,A,B,C,D)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD20]) ).
cnf(c_234,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_236,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_237,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_238,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_239,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_243,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_244,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_245,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_247,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_248,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_249,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_250,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_251,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_267,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_143]) ).
cnf(c_300,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_236]) ).
cnf(c_305,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_249]) ).
cnf(c_341,plain,
( eqangle(A,B,C,D,sK5,sK1,sK1,sK6)
| ~ eqangle(A,B,C,D,sK7,sK1,sK1,sK2) ),
inference(resolve,[status(thm)],[c_231,c_152]) ).
cnf(c_343,plain,
eqangle(sK5,sK1,sK1,sK6,sK7,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_233,c_152]) ).
cnf(c_346,plain,
( para(sK4,sK5,A,B)
| ~ perp(sK1,sK6,A,B) ),
inference(resolve,[status(thm)],[c_243,c_151]) ).
cnf(c_348,plain,
( para(A,B,sK1,sK6)
| ~ perp(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_243,c_151]) ).
cnf(c_350,plain,
perp(sK1,sK6,sK4,sK5),
inference(resolve,[status(thm)],[c_244,c_151]) ).
cnf(c_352,plain,
perp(sK4,sK5,sK6,sK1),
inference(resolve,[status(thm)],[c_245,c_151]) ).
cnf(c_506,plain,
perp(sK1,sK6,sK5,sK4),
inference(resolve,[status(thm)],[c_350,c_245]) ).
cnf(c_534,plain,
perp(sK6,sK1,sK4,sK5),
inference(resolve,[status(thm)],[c_352,c_244]) ).
cnf(c_705,plain,
eqangle(sK5,sK1,sK1,sK6,sK5,sK1,sK1,sK6),
inference(resolve,[status(thm)],[c_343,c_341]) ).
cnf(c_727,plain,
para(sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_346,c_506]) ).
cnf(c_728,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_346,c_350]) ).
cnf(c_755,plain,
para(sK6,sK1,sK1,sK6),
inference(resolve,[status(thm)],[c_348,c_534]) ).
cnf(c_756,plain,
para(sK1,sK6,sK1,sK6),
inference(resolve,[status(thm)],[c_348,c_350]) ).
cnf(c_953,plain,
para(sK5,sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_727,c_247]) ).
cnf(c_958,plain,
( eqratio(A,sK4,sK4,sK5,A,sK5,sK5,sK4)
| ~ coll(A,sK5,sK4)
| ~ coll(A,sK4,sK5) ),
inference(resolve,[status(thm)],[c_727,c_192]) ).
cnf(c_968,plain,
eqangle(sK4,sK5,A,B,sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_728,c_213]) ).
cnf(c_971,plain,
coll(sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_728,c_191]) ).
cnf(c_978,plain,
coll(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_971,c_305]) ).
cnf(c_979,plain,
coll(sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_971,c_250]) ).
cnf(c_986,plain,
coll(sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_978,c_305]) ).
cnf(c_989,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_979,c_305]) ).
cnf(c_996,plain,
coll(sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_986,c_251]) ).
cnf(c_1213,plain,
para(sK6,sK1,sK6,sK1),
inference(resolve,[status(thm)],[c_755,c_248]) ).
cnf(c_1229,plain,
eqangle(sK1,sK6,A,B,sK1,sK6,A,B),
inference(resolve,[status(thm)],[c_756,c_213]) ).
cnf(c_1271,plain,
para(sK5,sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_953,c_248]) ).
cnf(c_1302,plain,
eqangle(sK6,sK1,A,B,sK6,sK1,A,B),
inference(resolve,[status(thm)],[c_1213,c_213]) ).
cnf(c_1356,plain,
eqangle(sK5,sK4,A,B,sK5,sK4,A,B),
inference(resolve,[status(thm)],[c_1271,c_213]) ).
cnf(c_1468,plain,
para(sK5,sK1,sK5,sK1),
inference(resolve,[status(thm)],[c_705,c_214]) ).
cnf(c_1472,plain,
para(sK5,sK1,sK1,sK5),
inference(resolve,[status(thm)],[c_1468,c_248]) ).
cnf(c_1473,plain,
eqangle(sK5,sK1,A,B,sK5,sK1,A,B),
inference(resolve,[status(thm)],[c_1468,c_213]) ).
cnf(c_1486,plain,
para(sK1,sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_1472,c_247]) ).
cnf(c_1502,plain,
para(sK1,sK5,sK1,sK5),
inference(resolve,[status(thm)],[c_1486,c_248]) ).
cnf(c_1517,plain,
eqangle(sK1,sK5,A,B,sK1,sK5,A,B),
inference(resolve,[status(thm)],[c_1502,c_213]) ).
cnf(c_9448,plain,
( ~ cong(sK4,sK4,sK4,sK5)
| midp(sK5,sK5,sK5)
| ~ coll(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_968,c_267]) ).
cnf(c_1566,plain,
( ~ cong(sK4,sK4,sK4,sK5)
| midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_989,c_9448]) ).
cnf(c_1567,plain,
eqangle(A,B,sK4,sK5,A,B,sK4,sK5),
inference(resolve,[status(thm)],[c_968,c_234]) ).
cnf(c_1611,plain,
( cyclic(sK6,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1229,c_210]) ).
cnf(c_1660,plain,
( cyclic(sK1,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1302,c_210]) ).
cnf(c_1661,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK6,sK6)
| ~ cyclic(sK1,A,sK6,A)
| ~ cyclic(sK1,A,sK6,sK1) ),
inference(resolve,[status(thm)],[c_1302,c_209]) ).
cnf(c_1702,plain,
( cyclic(sK4,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1356,c_210]) ).
cnf(c_1765,plain,
( cyclic(sK1,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1473,c_210]) ).
cnf(c_1793,plain,
( cyclic(sK5,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1517,c_210]) ).
cnf(c_9449,plain,
( eqratio(sK4,sK4,sK4,sK5,sK4,sK5,sK5,sK4)
| ~ coll(sK4,sK5,sK4) ),
inference(resolve,[status(thm)],[c_958,c_986]) ).
cnf(c_2266,plain,
eqratio(sK4,sK4,sK4,sK5,sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_996,c_9449]) ).
cnf(c_2575,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1567,c_214]) ).
cnf(c_9450,plain,
( cyclic(A,sK5,sK4,sK4)
| ~ coll(sK4,sK4,sK5) ),
inference(resolve,[status(thm)],[c_1567,c_210]) ).
cnf(c_2577,plain,
cyclic(A,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_986,c_9450]) ).
cnf(c_9451,plain,
( cong(A,sK5,A,sK5)
| ~ cyclic(A,sK5,sK4,sK4)
| ~ cyclic(A,sK5,sK4,sK5)
| ~ cyclic(A,sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_1567,c_209]) ).
cnf(c_2578,plain,
( cong(A,sK5,A,sK5)
| ~ cyclic(A,sK5,sK4,sK5)
| ~ cyclic(A,sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_2577,c_9451]) ).
cnf(c_2600,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_2575,c_191]) ).
cnf(c_2678,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_2600,c_305]) ).
cnf(c_2710,plain,
cyclic(sK5,A,sK1,sK1),
inference(resolve,[status(thm)],[c_2678,c_1793]) ).
cnf(c_2711,plain,
cyclic(sK1,A,sK5,sK5),
inference(resolve,[status(thm)],[c_2678,c_1765]) ).
cnf(c_2713,plain,
cyclic(sK4,A,sK5,sK5),
inference(resolve,[status(thm)],[c_2678,c_1702]) ).
cnf(c_2715,plain,
cyclic(sK1,A,sK6,sK6),
inference(resolve,[status(thm)],[c_2678,c_1660]) ).
cnf(c_2717,plain,
cyclic(sK6,A,sK1,sK1),
inference(resolve,[status(thm)],[c_2678,c_1611]) ).
cnf(c_2829,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK6,A)
| ~ cyclic(sK1,A,sK6,sK1) ),
inference(resolve,[status(thm)],[c_2715,c_1661]) ).
cnf(c_9452,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_2678,c_249]) ).
cnf(c_2932,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_2678,c_9452]) ).
cnf(c_2937,plain,
( midp(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_2932,c_207]) ).
cnf(c_2944,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_2932,c_127]) ).
cnf(c_2949,plain,
cyclic(A,sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_2577,c_238]) ).
cnf(c_2969,plain,
cyclic(sK5,sK1,A,sK1),
inference(resolve,[status(thm)],[c_2710,c_238]) ).
cnf(c_2986,plain,
cyclic(sK1,sK5,A,sK5),
inference(resolve,[status(thm)],[c_2711,c_238]) ).
cnf(c_3018,plain,
cyclic(sK4,sK5,A,sK5),
inference(resolve,[status(thm)],[c_2713,c_238]) ).
cnf(c_3019,plain,
cyclic(A,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_2713,c_237]) ).
cnf(c_3085,plain,
cyclic(sK6,sK1,A,sK1),
inference(resolve,[status(thm)],[c_2717,c_238]) ).
cnf(c_3135,plain,
cyclic(sK4,A,sK5,sK4),
inference(resolve,[status(thm)],[c_2949,c_237]) ).
cnf(c_3215,plain,
cyclic(sK5,sK1,sK1,A),
inference(resolve,[status(thm)],[c_2969,c_239]) ).
cnf(c_3263,plain,
cyclic(sK1,sK5,sK5,A),
inference(resolve,[status(thm)],[c_2986,c_239]) ).
cnf(c_3325,plain,
cyclic(sK5,sK4,A,sK5),
inference(resolve,[status(thm)],[c_3018,c_237]) ).
cnf(c_3341,plain,
cyclic(A,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_3019,c_238]) ).
cnf(c_3353,plain,
( cong(A,sK5,A,sK5)
| ~ cyclic(A,sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_3341,c_2578]) ).
cnf(c_3528,plain,
cyclic(sK1,sK6,A,sK1),
inference(resolve,[status(thm)],[c_3085,c_237]) ).
cnf(c_3650,plain,
( cyclic(A,sK5,sK4,B)
| ~ cyclic(sK4,A,sK5,B) ),
inference(resolve,[status(thm)],[c_3135,c_236]) ).
cnf(c_3740,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_3215,c_300]) ).
cnf(c_9453,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK5,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3215,c_236]) ).
cnf(c_3742,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_3215,c_9453]) ).
cnf(c_9454,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK1,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_3263,c_236]) ).
cnf(c_3941,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_3263,c_9454]) ).
cnf(c_4182,plain,
( cyclic(sK4,A,sK5,B)
| ~ cyclic(sK5,sK4,A,B) ),
inference(resolve,[status(thm)],[c_3325,c_236]) ).
cnf(c_4662,plain,
cyclic(sK1,A,sK6,sK1),
inference(resolve,[status(thm)],[c_3528,c_238]) ).
cnf(c_4678,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK6,A) ),
inference(resolve,[status(thm)],[c_4662,c_2829]) ).
cnf(c_9455,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_3740,c_236]) ).
cnf(c_4882,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_3742,c_9455]) ).
cnf(c_4895,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_4882,c_4678]) ).
cnf(c_9456,plain,
( cyclic(sK1,A,B,C)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_3742,c_236]) ).
cnf(c_4951,plain,
cyclic(sK1,A,B,C),
inference(resolve,[status(thm)],[c_3742,c_9456]) ).
cnf(c_9457,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_3941,c_236]) ).
cnf(c_5210,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_3941,c_9457]) ).
cnf(c_5222,plain,
cyclic(sK4,A,sK5,B),
inference(resolve,[status(thm)],[c_5210,c_4182]) ).
cnf(c_5306,plain,
cyclic(A,sK5,sK4,B),
inference(resolve,[status(thm)],[c_5222,c_3650]) ).
cnf(c_5312,plain,
cong(A,sK5,A,sK5),
inference(resolve,[status(thm)],[c_5306,c_3353]) ).
cnf(c_9458,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4895,c_201]) ).
cnf(c_6203,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_4895,c_9458]) ).
cnf(c_9459,plain,
( cyclic(A,B,C,D)
| ~ cyclic(sK1,A,B,C) ),
inference(resolve,[status(thm)],[c_4951,c_236]) ).
cnf(c_6631,plain,
cyclic(A,B,C,D),
inference(resolve,[status(thm)],[c_4951,c_9459]) ).
cnf(c_6645,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D) ),
inference(resolve,[status(thm)],[c_6631,c_2944]) ).
cnf(c_7284,plain,
cong(A,sK5,sK5,A),
inference(resolve,[status(thm)],[c_5312,c_230]) ).
cnf(c_7677,plain,
perp(A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_6203,c_244]) ).
cnf(c_9460,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_6203,c_243]) ).
cnf(c_7678,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_7677,c_9460]) ).
cnf(c_7686,plain,
( perp(B,C,C,D)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7678,c_6645]) ).
cnf(c_7691,plain,
( midp(D,B,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7678,c_2937]) ).
cnf(c_9461,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7678,c_193]) ).
cnf(c_7695,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_7678,c_9461]) ).
cnf(c_9462,plain,
( cong(sK4,sK4,sK4,sK5)
| ~ cong(sK4,sK5,sK5,sK4) ),
inference(resolve,[status(thm)],[c_2266,c_183]) ).
cnf(c_8567,plain,
cong(sK4,sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_7284,c_9462]) ).
cnf(c_8571,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_8567,c_1566]) ).
cnf(c_8572,plain,
midp(sK5,A,B),
inference(resolve,[status(thm)],[c_8571,c_7695]) ).
cnf(c_8946,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_8572,c_7691]) ).
cnf(c_9040,plain,
perp(A,B,B,C),
inference(resolve,[status(thm)],[c_8946,c_7686]) ).
cnf(c_9463,plain,
( cong(B,A,D,A)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_9040,c_204]) ).
cnf(c_9161,plain,
cong(A,B,C,B),
inference(resolve,[status(thm)],[c_8946,c_9463]) ).
cnf(c_9464,plain,
( perp(A,C,D,B)
| ~ cong(A,B,C,B) ),
inference(resolve,[status(thm)],[c_9161,c_201]) ).
cnf(c_9446,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_9161,c_9464]) ).
cnf(c_9447,plain,
$false,
inference(resolve,[status(thm)],[c_9446,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO636+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:48:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2665703 was started by sandbox2 on n026,
% 0.08/0.36 % Fri Sep 25 13:48:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 14.80/2.35
% 14.80/2.35 % given #500 (T,wt=9): 1149 coll(c3,c7,c4). [resolve(1116,a,251,a)].
% 14.80/2.35
% 14.80/2.35 % given #1000 (A,wt=24): 626 -perp(c1,c6,c4,c2) | perp(c1,f10(c1,c4,c2,c6),c2,c4). [resolve(562,a,162,b)].
% 14.80/2.35
% 14.80/2.35 % given #1500 (T,wt=13): 2110 -coll(c5,c7,A) | coll(A,c6,c5). [resolve(1955,a,249,b)].
% 14.80/2.35
% 14.80/2.35 % given #2000 (A,wt=33): 1617 coll(c1,A,c2) | eqangle(c1,c2,A,c2,c1,f5(c1,A,c2,c2,c2),A,f5(c1,A,c2,c2,c2)). [resolve(1229,a,174,a)].
% 14.80/2.35
% 14.80/2.35 % SZS status Theorem for theBenchmark
% 14.80/2.35
% 14.80/2.35 % Proof 1 at 1.28 (+ 0.46) seconds.
% 14.80/2.35 % Length of proof is 171.
% 14.80/2.35 % Level of proof is 25.
% 14.80/2.35 % Maximum clause weight is 38.000.
% 14.80/2.35 % Given clauses 2476.
% 14.80/2.35
% 14.80/2.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------