%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO560+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 : n009.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 07:18:06 AM UTC 2026
% Result : Theorem 28.39s 4.04s
% Output : CNFRefutation 28.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 25
% Syntax : Number of formulae : 163 ( 75 unt; 0 def)
% Number of atoms : 318 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 245 ( 90 ~; 86 |; 43 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 460 ( 68 sgn 147 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ruleD18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('theBenchmark.p',ruleD18) ).
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(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
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(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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleX14,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX14) ).
fof(exemplo6GDDFULL012020,conjecture,
! [A,B,C,D,E,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,D) ),
file('theBenchmark.p',exemplo6GDDFULL012020) ).
fof(exemplo6GDDFULL012020_neg,negated_conjecture,
~ ! [A,B,C,D,E,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012020]) ).
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]) ).
fof(nnf_90,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[ruleX14]) ).
fof(sk_ruleX14,plain,
! [A,B,C,D] :
( circle(sK0(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(O,sK0(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK0(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
cnf(c_109,plain,
( eqangle(A,E,A,C,B,A,B,C)
| ~ perp(sK0(A,C,B,D),A,A,E)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_108,c_96]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,H,G] :
( ~ eqangle(E,G,G,H,H,G,G,D)
& coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012020_neg]) ).
fof(sk_exemplo6GDDFULL012020_neg,plain,
( ~ eqangle(sK1,sK2,sK2,sK3,sK3,sK2,sK2,sK4)
& coll(sK2,sK5,sK6)
& perp(sK2,sK3,sK5,sK6)
& coll(sK3,sK6,sK1)
& coll(sK3,sK5,sK4)
& coll(sK1,sK5,sK7)
& perp(sK1,sK6,sK5,sK7)
& coll(sK4,sK6,sK7)
& perp(sK4,sK5,sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK1,sK3,sK2]),skolemize(A,sK5),skolemize(B,sK6),skolemize(C,sK7),skolemize(D,sK4),skolemize(E,sK1),skolemize(H,sK3),skolemize(G,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ eqangle(sK1,sK2,sK2,sK3,sK3,sK2,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012020_neg]) ).
cnf(c_149,negated_conjecture,
perp(sK2,sK3,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012020_neg]) ).
cnf(c_155,negated_conjecture,
perp(sK4,sK5,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012020_neg]) ).
cnf(c_194,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_203,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_204,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_212,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_213,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_215,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_216,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_217,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_234,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_235,plain,
( eqangle(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_237,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_238,plain,
( eqangle(B,A,C,D,E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD18]) ).
cnf(c_239,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_240,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_241,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_242,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_246,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_247,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_248,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_250,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_251,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_252,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_297,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_203]) ).
cnf(c_303,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_308,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_252]) ).
cnf(c_351,plain,
( para(sK4,sK5,A,B)
| ~ perp(sK6,sK7,A,B) ),
inference(resolve,[status(thm)],[c_246,c_155]) ).
cnf(c_353,plain,
( para(sK2,sK3,A,B)
| ~ perp(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_246,c_149]) ).
cnf(c_354,plain,
( para(A,B,sK6,sK7)
| ~ perp(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_246,c_155]) ).
cnf(c_356,plain,
( para(A,B,sK5,sK6)
| ~ perp(A,B,sK2,sK3) ),
inference(resolve,[status(thm)],[c_246,c_149]) ).
cnf(c_357,plain,
perp(sK6,sK7,sK4,sK5),
inference(resolve,[status(thm)],[c_247,c_155]) ).
cnf(c_359,plain,
perp(sK5,sK6,sK2,sK3),
inference(resolve,[status(thm)],[c_247,c_149]) ).
cnf(c_360,plain,
perp(sK4,sK5,sK7,sK6),
inference(resolve,[status(thm)],[c_248,c_155]) ).
cnf(c_362,plain,
perp(sK2,sK3,sK6,sK5),
inference(resolve,[status(thm)],[c_248,c_149]) ).
cnf(c_732,plain,
perp(sK6,sK7,sK5,sK4),
inference(resolve,[status(thm)],[c_357,c_248]) ).
cnf(c_760,plain,
perp(sK5,sK6,sK3,sK2),
inference(resolve,[status(thm)],[c_359,c_248]) ).
cnf(c_774,plain,
perp(sK7,sK6,sK4,sK5),
inference(resolve,[status(thm)],[c_360,c_247]) ).
cnf(c_802,plain,
perp(sK6,sK5,sK2,sK3),
inference(resolve,[status(thm)],[c_362,c_247]) ).
cnf(c_872,plain,
para(sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_351,c_732]) ).
cnf(c_873,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_351,c_357]) ).
cnf(c_966,plain,
eqangle(sK4,sK5,A,B,sK5,sK4,A,B),
inference(resolve,[status(thm)],[c_872,c_216]) ).
cnf(c_978,plain,
eqangle(sK4,sK5,A,B,sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_873,c_216]) ).
cnf(c_987,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_353,c_760]) ).
cnf(c_988,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_353,c_359]) ).
cnf(c_1041,plain,
para(sK7,sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_354,c_774]) ).
cnf(c_1042,plain,
para(sK6,sK7,sK6,sK7),
inference(resolve,[status(thm)],[c_354,c_357]) ).
cnf(c_1106,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_987,c_250]) ).
cnf(c_1121,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_988,c_216]) ).
cnf(c_1142,plain,
para(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_356,c_802]) ).
cnf(c_1158,plain,
para(sK7,sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_1041,c_251]) ).
cnf(c_1174,plain,
eqangle(sK6,sK7,A,B,sK6,sK7,A,B),
inference(resolve,[status(thm)],[c_1042,c_216]) ).
cnf(c_1244,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_1106,c_251]) ).
cnf(c_1260,plain,
para(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_1142,c_251]) ).
cnf(c_1288,plain,
eqangle(sK7,sK6,A,B,sK7,sK6,A,B),
inference(resolve,[status(thm)],[c_1158,c_216]) ).
cnf(c_1354,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1244,c_216]) ).
cnf(c_1366,plain,
eqangle(sK6,sK5,A,B,sK6,sK5,A,B),
inference(resolve,[status(thm)],[c_1260,c_216]) ).
cnf(c_2020,plain,
eqangle(A,B,sK4,sK5,A,B,sK5,sK4),
inference(resolve,[status(thm)],[c_966,c_237]) ).
cnf(c_2021,plain,
eqangle(sK4,sK5,sK5,sK4,A,B,A,B),
inference(resolve,[status(thm)],[c_966,c_235]) ).
cnf(c_2030,plain,
eqangle(A,B,sK4,sK5,A,B,sK4,sK5),
inference(resolve,[status(thm)],[c_978,c_237]) ).
cnf(c_2081,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1121,c_213]) ).
cnf(c_2082,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,sK2)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_1121,c_212]) ).
cnf(c_2102,plain,
( cyclic(sK7,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1174,c_213]) ).
cnf(c_2186,plain,
( cyclic(sK6,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_1288,c_213]) ).
cnf(c_2187,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,sK7)
| ~ cyclic(sK6,A,sK7,A)
| ~ cyclic(sK6,A,sK7,sK6) ),
inference(resolve,[status(thm)],[c_1288,c_212]) ).
cnf(c_2242,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1354,c_213]) ).
cnf(c_2256,plain,
( cyclic(sK5,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1366,c_213]) ).
cnf(c_2273,plain,
eqangle(A,B,A,B,sK4,sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_2020,c_235]) ).
cnf(c_2277,plain,
( eqangle(sK4,sK5,sK5,sK4,C,D,E,F)
| ~ eqangle(A,B,A,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_2021,c_234]) ).
cnf(c_2282,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_2030,c_217]) ).
cnf(c_2307,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_2282,c_194]) ).
cnf(c_2347,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_2307,c_308]) ).
cnf(c_2355,plain,
cyclic(sK5,A,sK6,sK6),
inference(resolve,[status(thm)],[c_2347,c_2256]) ).
cnf(c_2356,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_2347,c_2242]) ).
cnf(c_2359,plain,
cyclic(sK6,A,sK7,sK7),
inference(resolve,[status(thm)],[c_2347,c_2186]) ).
cnf(c_2363,plain,
cyclic(sK7,A,sK6,sK6),
inference(resolve,[status(thm)],[c_2347,c_2102]) ).
cnf(c_2364,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_2347,c_2081]) ).
cnf(c_2490,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,A)
| ~ cyclic(sK6,A,sK7,sK6) ),
inference(resolve,[status(thm)],[c_2359,c_2187]) ).
cnf(c_2505,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_2364,c_2082]) ).
cnf(c_2598,plain,
cyclic(sK5,sK6,A,sK6),
inference(resolve,[status(thm)],[c_2355,c_241]) ).
cnf(c_2615,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_2356,c_241]) ).
cnf(c_2616,plain,
cyclic(A,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_2356,c_240]) ).
cnf(c_2730,plain,
cyclic(sK7,sK6,A,sK6),
inference(resolve,[status(thm)],[c_2363,c_241]) ).
cnf(c_2876,plain,
cyclic(sK5,sK6,sK6,A),
inference(resolve,[status(thm)],[c_2598,c_242]) ).
cnf(c_2923,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_2615,c_242]) ).
cnf(c_2924,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_2615,c_240]) ).
cnf(c_2942,plain,
cyclic(A,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_2616,c_241]) ).
cnf(c_3218,plain,
cyclic(sK6,sK7,A,sK6),
inference(resolve,[status(thm)],[c_2730,c_240]) ).
cnf(c_3475,plain,
cyclic(sK6,sK6,A,A),
inference(resolve,[status(thm)],[c_2876,c_303]) ).
cnf(c_14446,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK5,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_2876,c_239]) ).
cnf(c_3477,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_2876,c_14446]) ).
cnf(c_3672,plain,
cyclic(sK3,sK3,A,A),
inference(resolve,[status(thm)],[c_2923,c_303]) ).
cnf(c_14447,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_2923,c_239]) ).
cnf(c_3674,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_2923,c_14447]) ).
cnf(c_3688,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_2924,c_241]) ).
cnf(c_3704,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A) ),
inference(resolve,[status(thm)],[c_3688,c_2505]) ).
cnf(c_3800,plain,
eqangle(sK2,A,sK2,sK3,sK3,A,sK3,sK3),
inference(resolve,[status(thm)],[c_2942,c_215]) ).
cnf(c_4536,plain,
cyclic(sK6,A,sK7,sK6),
inference(resolve,[status(thm)],[c_3218,c_241]) ).
cnf(c_4552,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,A) ),
inference(resolve,[status(thm)],[c_4536,c_2490]) ).
cnf(c_14448,plain,
( cyclic(sK6,A,B,A)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_3475,c_239]) ).
cnf(c_4857,plain,
cyclic(sK6,A,B,A),
inference(resolve,[status(thm)],[c_3477,c_14448]) ).
cnf(c_4870,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_4857,c_4552]) ).
cnf(c_5124,plain,
( perp(A,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_3672,c_297]) ).
cnf(c_14449,plain,
( cyclic(sK3,A,B,A)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_3672,c_239]) ).
cnf(c_5125,plain,
cyclic(sK3,A,B,A),
inference(resolve,[status(thm)],[c_3674,c_14449]) ).
cnf(c_5138,plain,
cong(sK3,A,sK3,A),
inference(resolve,[status(thm)],[c_5125,c_3704]) ).
cnf(c_5139,plain,
perp(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_5138,c_5124]) ).
cnf(c_14450,plain,
( perp(A,sK3,sK3,B)
| ~ cong(sK3,B,sK3,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_3674,c_203]) ).
cnf(c_14451,plain,
( perp(B,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_5138,c_14450]) ).
cnf(c_5183,plain,
perp(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_5138,c_14451]) ).
cnf(c_14452,plain,
( eqangle(sK3,C,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK0(sK3,sK3,A,B),sK3,sK3,C)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_3674,c_109]) ).
cnf(c_5191,plain,
( eqangle(sK3,B,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_5183,c_14452]) ).
cnf(c_14453,plain,
( perp(sK6,sK6,A,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_4870,c_204]) ).
cnf(c_6370,plain,
perp(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_4870,c_14453]) ).
cnf(c_7102,plain,
perp(sK3,A,A,sK3),
inference(resolve,[status(thm)],[c_5139,c_247]) ).
cnf(c_7116,plain,
eqangle(sK3,A,sK3,sK3,B,sK3,B,sK3),
inference(resolve,[status(thm)],[c_7102,c_5191]) ).
cnf(c_7810,plain,
perp(A,B,sK6,sK6),
inference(resolve,[status(thm)],[c_6370,c_247]) ).
cnf(c_14454,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK6,sK6) ),
inference(resolve,[status(thm)],[c_6370,c_246]) ).
cnf(c_7811,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_7810,c_14454]) ).
cnf(c_7827,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_7811,c_216]) ).
cnf(c_10982,plain,
( eqangle(E,F,E,F,A,B,C,D)
| ~ eqangle(sK4,sK5,sK5,sK4,A,B,C,D) ),
inference(resolve,[status(thm)],[c_2273,c_234]) ).
cnf(c_12696,plain,
eqangle(A,sK2,sK2,sK3,sK3,A,sK3,sK3),
inference(resolve,[status(thm)],[c_3800,c_238]) ).
cnf(c_13578,plain,
( eqangle(sK3,F,sK3,sK3,B,C,D,E)
| ~ eqangle(A,sK3,A,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_7116,c_234]) ).
cnf(c_13854,plain,
eqangle(sK4,sK5,sK5,sK4,A,B,C,D),
inference(resolve,[status(thm)],[c_7827,c_2277]) ).
cnf(c_13861,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_13854,c_10982]) ).
cnf(c_13881,plain,
eqangle(sK3,A,sK3,sK3,B,C,D,E),
inference(resolve,[status(thm)],[c_13861,c_13578]) ).
cnf(c_14455,plain,
( eqangle(A,sK2,sK2,sK3,B,C,D,E)
| ~ eqangle(sK3,A,sK3,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_12696,c_234]) ).
cnf(c_14444,plain,
eqangle(A,sK2,sK2,sK3,B,C,D,E),
inference(resolve,[status(thm)],[c_13881,c_14455]) ).
cnf(c_14445,plain,
$false,
inference(resolve,[status(thm)],[c_14444,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO560+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 13:41:59 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 1717758 was started by sandbox2 on n009,
% 0.08/0.36 % Fri Sep 25 13:41:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 28.39/4.04
% 28.39/4.04 % given #500 (T,wt=4): 1484 coll(c3,c2,c5). [resolve(1441,a,253,a)].
% 28.39/4.04
% 28.39/4.04 % given #1000 (T,wt=8): 1540 -coll(c5,c4,A) | coll(c4,A,c5). [resolve(1470,a,252,a)].
% 28.39/4.04
% 28.39/4.04 % given #1500 (T,wt=4): 2380 coll(A,c6,c3). [back_unit_del(1738),unit_del(a,2347)].
% 28.39/4.04
% 28.39/4.04 % given #2000 (T,wt=5): 5624 cyclic(c4,A,B,c4). [back_unit_del(3353),unit_del(a,5609)].
% 28.39/4.04
% 28.39/4.04 % given #2500 (T,wt=8): 10504 cong(c5,A,f19(c5,c5,A),A). [resolve(10405,a,232,a)].
% 28.39/4.04
% 28.39/4.04 % given #3000 (T,wt=9): 5457 eqangle(c5,c2,c5,A,c2,c2,c2,A). [resolve(4066,a,215,a)].
% 28.39/4.04
% 28.39/4.04 % given #3500 (T,wt=9): 7780 perp(c4,f10(c4,A,A,c4),A,A). [resolve(6208,a,165,b),unit_del(a,7513)].
% 28.39/4.04
% 28.39/4.04 % given #4000 (T,wt=9): 12467 eqangle(c4,c1,c1,c4,c3,c1,c1,c3). [resolve(2232,a,2021,a)].
% 28.39/4.04
% 28.39/4.04 % SZS status Theorem for theBenchmark
% 28.39/4.04
% 28.39/4.04 % Proof 1 at 2.82 (+ 0.79) seconds.
% 28.39/4.04 % Length of proof is 148.
% 28.39/4.04 % Level of proof is 23.
% 28.39/4.04 % Maximum clause weight is 29.000.
% 28.39/4.04 % Given clauses 4106.
% 28.39/4.04
% 28.39/4.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------