%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO581+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 : n016.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 07:18:09 AM UTC 2026
% Result : Theorem 101.79s 14.09s
% Output : CNFRefutation 101.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 42
% Syntax : Number of formulae : 307 ( 138 unt; 0 def)
% Number of atoms : 574 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 450 ( 183 ~; 179 |; 45 &)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 671 ( 91 sgn 208 !; 6 ?)
% 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(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(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(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('theBenchmark.p',ruleD24) ).
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(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(ruleD46,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('theBenchmark.p',ruleD46) ).
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(ruleD50,axiom,
! [A,B,C,O,M] :
( ( midp(M,B,C)
& circle(O,A,B,C) )
=> eqangle(A,B,A,C,O,B,O,M) ),
file('theBenchmark.p',ruleD50) ).
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(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(ruleD73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD73) ).
fof(exemplo6GDDFULL416043,conjecture,
! [A,B,C,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
file('theBenchmark.p',exemplo6GDDFULL416043) ).
fof(exemplo6GDDFULL416043_neg,negated_conjecture,
~ ! [A,B,C,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416043]) ).
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_99,plain,
( eqangle(B,C,B,D,A,C,A,E)
| ~ midp(E,C,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD50]) ).
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_142,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]) ).
cnf(c_144,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| eqangle(D,B,D,C,E,B,E,A)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_99,c_97]) ).
cnf(c_146,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,
? [A,B,C,F,E,P] :
( ~ eqangle(A,C,C,P,P,C,C,B)
& coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416043_neg]) ).
fof(sk_exemplo6GDDFULL416043_neg,plain,
( ~ eqangle(sK0,sK1,sK1,sK2,sK2,sK1,sK1,sK3)
& coll(sK2,sK0,sK4)
& coll(sK2,sK3,sK5)
& cong(sK0,sK5,sK5,sK4)
& eqangle(sK3,sK0,sK0,sK5,sK0,sK5,sK5,sK4)
& perp(sK1,sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK5,sK4,sK2]),skolemize(A,sK0),skolemize(B,sK3),skolemize(C,sK1),skolemize(F,sK4),skolemize(E,sK5),skolemize(P,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ eqangle(sK0,sK1,sK1,sK2,sK2,sK1,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416043_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK2,sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416043_neg]) ).
cnf(c_149,negated_conjecture,
coll(sK2,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416043_neg]) ).
cnf(c_150,negated_conjecture,
cong(sK0,sK5,sK5,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416043_neg]) ).
cnf(c_185,plain,
( para(A,B,C,D)
| ~ para(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD73]) ).
cnf(c_189,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_190,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_191,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
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_200,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_201,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_202,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
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_206,plain,
( eqangle(A,B,B,C,B,C,A,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD46]) ).
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_208,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
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_212,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
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_229,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
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_232,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_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_235,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_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_240,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_241,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_242,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
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_266,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_142]) ).
cnf(c_270,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_146]) ).
cnf(c_291,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_193]) ).
cnf(c_294,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_200]) ).
cnf(c_296,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_208]) ).
cnf(c_297,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_209]) ).
cnf(c_298,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_209]) ).
cnf(c_300,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_236]) ).
cnf(c_301,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_304,plain,
( para(A,B,A,B)
| ~ perp(A,B,A,B) ),
inference(factor,[status(thm)],[c_243]) ).
cnf(c_305,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_249]) ).
cnf(c_313,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_297]) ).
cnf(c_314,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_301]) ).
cnf(c_390,plain,
cong(sK5,sK4,sK0,sK5),
inference(resolve,[status(thm)],[c_229,c_150]) ).
cnf(c_407,plain,
coll(sK0,sK2,sK4),
inference(resolve,[status(thm)],[c_250,c_148]) ).
cnf(c_409,plain,
coll(sK2,sK4,sK0),
inference(resolve,[status(thm)],[c_251,c_148]) ).
cnf(c_422,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_305,c_149]) ).
cnf(c_423,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_305,c_148]) ).
cnf(c_462,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_407,c_305]) ).
cnf(c_476,plain,
coll(sK0,sK4,sK2),
inference(resolve,[status(thm)],[c_407,c_251]) ).
cnf(c_477,plain,
( coll(A,sK4,sK0)
| ~ coll(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_407,c_249]) ).
cnf(c_538,plain,
coll(sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_409,c_305]) ).
cnf(c_552,plain,
coll(sK4,sK2,sK0),
inference(resolve,[status(thm)],[c_409,c_250]) ).
cnf(c_576,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_422,c_305]) ).
cnf(c_615,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_423,c_305]) ).
cnf(c_630,plain,
coll(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_423,c_251]) ).
cnf(c_731,plain,
coll(sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_462,c_305]) ).
cnf(c_770,plain,
coll(sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_476,c_305]) ).
cnf(c_784,plain,
coll(sK4,sK0,sK2),
inference(resolve,[status(thm)],[c_476,c_250]) ).
cnf(c_896,plain,
coll(sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_538,c_251]) ).
cnf(c_903,plain,
( midp(sK0,sK0,sK2)
| ~ cong(sK0,sK0,sK0,sK2) ),
inference(resolve,[status(thm)],[c_538,c_190]) ).
cnf(c_933,plain,
( coll(A,sK0,sK4)
| ~ coll(sK4,sK2,A) ),
inference(resolve,[status(thm)],[c_552,c_249]) ).
cnf(c_971,plain,
( coll(A,sK5,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_576,c_249]) ).
cnf(c_1078,plain,
coll(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_630,c_305]) ).
cnf(c_1289,plain,
coll(sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_731,c_251]) ).
cnf(c_1411,plain,
( midp(sK4,sK0,sK2)
| ~ cong(sK4,sK0,sK4,sK2) ),
inference(resolve,[status(thm)],[c_784,c_190]) ).
cnf(c_1472,plain,
coll(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_896,c_305]) ).
cnf(c_1709,plain,
( midp(sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_1078,c_190]) ).
cnf(c_1900,plain,
coll(sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_1289,c_250]) ).
cnf(c_2107,plain,
( cyclic(A,sK0,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK0,sK0,A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_1472,c_210]) ).
cnf(c_2111,plain,
( midp(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_1472,c_190]) ).
cnf(c_2390,plain,
( midp(sK4,sK0,sK0)
| ~ cong(sK4,sK0,sK4,sK0) ),
inference(resolve,[status(thm)],[c_1900,c_190]) ).
cnf(c_2446,plain,
cong(sK5,sK4,sK5,sK0),
inference(resolve,[status(thm)],[c_390,c_230]) ).
cnf(c_2496,plain,
cyclic(sK4,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2446,c_314]) ).
cnf(c_2515,plain,
( perp(sK4,sK0,sK0,sK0)
| ~ coll(sK5,sK4,sK0) ),
inference(resolve,[status(thm)],[c_2446,c_266]) ).
cnf(c_2556,plain,
cong(sK5,sK0,sK5,sK4),
inference(resolve,[status(thm)],[c_2446,c_229]) ).
cnf(c_2559,plain,
eqangle(sK5,sK4,sK4,sK0,sK4,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_2446,c_206]) ).
cnf(c_2561,plain,
( midp(sK5,sK4,sK0)
| ~ coll(sK5,sK4,sK0) ),
inference(resolve,[status(thm)],[c_2446,c_190]) ).
cnf(c_2696,plain,
cyclic(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2496,c_300]) ).
cnf(c_2704,plain,
cyclic(sK0,sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_2496,c_237]) ).
cnf(c_2730,plain,
cyclic(sK0,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_2556,c_314]) ).
cnf(c_2749,plain,
( perp(sK0,sK4,sK4,sK4)
| ~ coll(sK5,sK0,sK4) ),
inference(resolve,[status(thm)],[c_2556,c_266]) ).
cnf(c_2795,plain,
( midp(sK5,sK0,sK4)
| ~ coll(sK5,sK0,sK4) ),
inference(resolve,[status(thm)],[c_2556,c_190]) ).
cnf(c_2937,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_2696,c_313]) ).
cnf(c_2945,plain,
eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2696,c_212]) ).
cnf(c_2968,plain,
cong(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2945,c_2937]) ).
cnf(c_2970,plain,
midp(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2968,c_2111]) ).
cnf(c_2972,plain,
para(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2970,c_296]) ).
cnf(c_2983,plain,
( para(A,sK0,B,sK0)
| ~ midp(A,sK0,B) ),
inference(resolve,[status(thm)],[c_2970,c_208]) ).
cnf(c_2986,plain,
( cong(sK0,sK0,A,sK0)
| ~ perp(sK0,A,A,sK0) ),
inference(resolve,[status(thm)],[c_2970,c_204]) ).
cnf(c_2987,plain,
( cong(A,sK0,A,sK0)
| ~ perp(A,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_2970,c_202]) ).
cnf(c_3048,plain,
cyclic(sK0,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_2704,c_238]) ).
cnf(c_3076,plain,
cyclic(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_2730,c_300]) ).
cnf(c_3084,plain,
cyclic(sK4,sK0,sK4,sK4),
inference(resolve,[status(thm)],[c_2730,c_237]) ).
cnf(c_3200,plain,
( perp(A,sK0,sK0,sK0)
| ~ cyclic(sK0,sK0,A,sK0)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_2968,c_200]) ).
cnf(c_3263,plain,
eqangle(sK0,sK0,A,B,sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_2972,c_213]) ).
cnf(c_3274,plain,
cyclic(sK0,sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_3048,c_239]) ).
cnf(c_3301,plain,
( cong(sK4,sK4,sK4,sK4)
| ~ eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_3076,c_313]) ).
cnf(c_3309,plain,
eqangle(sK4,sK4,sK4,sK4,sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_3076,c_212]) ).
cnf(c_3332,plain,
cong(sK4,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_3309,c_3301]) ).
cnf(c_3334,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_3332,c_1709]) ).
cnf(c_3412,plain,
cyclic(sK4,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_3084,c_238]) ).
cnf(c_3482,plain,
( cyclic(sK0,sK0,sK4,A)
| ~ cyclic(sK0,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_3274,c_236]) ).
cnf(c_3641,plain,
cyclic(sK4,sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_3412,c_239]) ).
cnf(c_3738,plain,
cyclic(sK4,sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_3641,c_300]) ).
cnf(c_3814,plain,
( perp(sK0,sK4,sK4,sK0)
| ~ cong(sK4,sK0,sK4,sK0) ),
inference(resolve,[status(thm)],[c_3738,c_294]) ).
cnf(c_3945,plain,
coll(sK0,sK5,sK2),
inference(resolve,[status(thm)],[c_971,c_770]) ).
cnf(c_3946,plain,
coll(sK4,sK5,sK2),
inference(resolve,[status(thm)],[c_971,c_615]) ).
cnf(c_3960,plain,
coll(sK0,sK2,sK5),
inference(resolve,[status(thm)],[c_3945,c_251]) ).
cnf(c_3998,plain,
coll(sK4,sK2,sK5),
inference(resolve,[status(thm)],[c_3946,c_251]) ).
cnf(c_4024,plain,
coll(sK5,sK4,sK0),
inference(resolve,[status(thm)],[c_3960,c_477]) ).
cnf(c_4064,plain,
midp(sK5,sK4,sK0),
inference(resolve,[status(thm)],[c_4024,c_2561]) ).
cnf(c_4065,plain,
perp(sK4,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_4024,c_2515]) ).
cnf(c_4122,plain,
coll(sK5,sK0,sK4),
inference(resolve,[status(thm)],[c_3998,c_933]) ).
cnf(c_4162,plain,
midp(sK5,sK0,sK4),
inference(resolve,[status(thm)],[c_4122,c_2795]) ).
cnf(c_4163,plain,
perp(sK0,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_4122,c_2749]) ).
cnf(c_29691,plain,
( cong(sK4,sK0,sK4,sK0)
| ~ midp(sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_4065,c_202]) ).
cnf(c_6871,plain,
cong(sK4,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_2970,c_29691]) ).
cnf(c_6903,plain,
perp(sK0,sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_6871,c_3814]) ).
cnf(c_6905,plain,
midp(sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_6871,c_2390]) ).
cnf(c_29692,plain,
( cong(sK0,sK4,sK0,sK4)
| ~ midp(sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_4163,c_202]) ).
cnf(c_6975,plain,
cong(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_3334,c_29692]) ).
cnf(c_7225,plain,
( eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0)
| ~ perp(sK4,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_6871,c_270]) ).
cnf(c_7322,plain,
perp(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_6903,c_245]) ).
cnf(c_7449,plain,
( perp(sK4,sK0,sK0,A)
| ~ cyclic(sK0,sK0,sK4,A)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_6975,c_200]) ).
cnf(c_7630,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_7322,c_304]) ).
cnf(c_7741,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_7630,c_291]) ).
cnf(c_7861,plain,
( para(sK5,sK4,sK4,sK0)
| ~ para(sK4,sK0,sK5,sK0) ),
inference(resolve,[status(thm)],[c_2559,c_185]) ).
cnf(c_7870,plain,
para(sK4,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_2983,c_6905]) ).
cnf(c_7871,plain,
para(sK5,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_2983,c_4162]) ).
cnf(c_7881,plain,
( midp(A,sK0,sK0)
| ~ midp(A,sK4,sK0) ),
inference(resolve,[status(thm)],[c_7870,c_291]) ).
cnf(c_7925,plain,
para(sK4,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_7871,c_247]) ).
cnf(c_7949,plain,
para(sK5,sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_7925,c_7861]) ).
cnf(c_8043,plain,
para(sK4,sK0,sK5,sK4),
inference(resolve,[status(thm)],[c_7949,c_247]) ).
cnf(c_8192,plain,
para(sK4,sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_8043,c_248]) ).
cnf(c_8319,plain,
para(sK4,sK5,sK4,sK0),
inference(resolve,[status(thm)],[c_8192,c_247]) ).
cnf(c_29693,plain,
( midp(A,sK5,sK0)
| ~ para(sK4,sK5,sK4,sK0)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_8192,c_193]) ).
cnf(c_8326,plain,
( midp(A,sK5,sK0)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_8319,c_29693]) ).
cnf(c_9129,plain,
midp(sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_7881,c_4064]) ).
cnf(c_9132,plain,
midp(sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_9129,c_7741]) ).
cnf(c_11910,plain,
midp(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_8326,c_9132]) ).
cnf(c_11929,plain,
midp(sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_11910,c_241]) ).
cnf(c_11938,plain,
cong(sK5,sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_11910,c_189]) ).
cnf(c_12052,plain,
cong(sK5,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_11929,c_189]) ).
cnf(c_12137,plain,
cyclic(sK5,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_11938,c_314]) ).
cnf(c_12434,plain,
cyclic(sK0,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_12052,c_314]) ).
cnf(c_12684,plain,
cyclic(sK0,sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_12137,c_237]) ).
cnf(c_12756,plain,
cyclic(sK5,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_12434,c_237]) ).
cnf(c_12835,plain,
cyclic(sK0,sK0,sK5,sK0),
inference(resolve,[status(thm)],[c_12684,c_238]) ).
cnf(c_12941,plain,
cyclic(sK5,sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_12756,c_238]) ).
cnf(c_13015,plain,
cyclic(sK0,sK0,sK0,sK5),
inference(resolve,[status(thm)],[c_12835,c_239]) ).
cnf(c_13016,plain,
( cyclic(sK0,sK5,A,sK0)
| ~ cyclic(sK0,sK0,sK5,A) ),
inference(resolve,[status(thm)],[c_12835,c_236]) ).
cnf(c_13066,plain,
cyclic(sK5,sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_12941,c_239]) ).
cnf(c_13086,plain,
cyclic(sK0,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_13015,c_300]) ).
cnf(c_13094,plain,
( cyclic(sK0,sK0,sK5,A)
| ~ cyclic(sK0,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_13015,c_236]) ).
cnf(c_13126,plain,
cyclic(sK5,sK5,sK0,sK0),
inference(resolve,[status(thm)],[c_13066,c_300]) ).
cnf(c_13173,plain,
cyclic(sK0,sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_13086,c_238]) ).
cnf(c_13175,plain,
( cyclic(sK0,sK5,sK5,A)
| ~ cyclic(sK0,sK0,sK5,A) ),
inference(resolve,[status(thm)],[c_13086,c_236]) ).
cnf(c_13207,plain,
( cyclic(sK5,sK0,A,sK0)
| ~ cyclic(sK5,sK5,sK0,A) ),
inference(resolve,[status(thm)],[c_13126,c_236]) ).
cnf(c_13237,plain,
cyclic(sK0,sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_13173,c_239]) ).
cnf(c_13272,plain,
( cyclic(sK5,sK5,sK0,A)
| ~ cyclic(sK0,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_13237,c_236]) ).
cnf(c_13302,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_3263,c_298]) ).
cnf(c_13304,plain,
eqangle(A,B,sK0,sK0,A,B,sK0,sK0),
inference(resolve,[status(thm)],[c_3263,c_234]) ).
cnf(c_13315,plain,
cyclic(A,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_13304,c_2107]) ).
cnf(c_13321,plain,
( cong(A,sK0,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_13315,c_313]) ).
cnf(c_13328,plain,
( perp(sK0,A,A,sK0)
| ~ cong(A,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_13315,c_294]) ).
cnf(c_13329,plain,
cyclic(sK0,A,sK0,sK0),
inference(resolve,[status(thm)],[c_13315,c_237]) ).
cnf(c_13335,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13329,c_13302]) ).
cnf(c_13353,plain,
cyclic(sK0,sK0,A,sK0),
inference(resolve,[status(thm)],[c_13329,c_238]) ).
cnf(c_13357,plain,
( cong(sK0,A,sK0,B)
| ~ eqangle(sK0,sK0,sK0,A,C,sK0,C,B)
| ~ cyclic(sK0,A,sK0,C)
| ~ cyclic(sK0,A,sK0,B) ),
inference(resolve,[status(thm)],[c_13329,c_209]) ).
cnf(c_13360,plain,
( perp(A,sK0,sK0,sK0)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13353,c_3200]) ).
cnf(c_13374,plain,
cyclic(sK0,sK0,sK0,A),
inference(resolve,[status(thm)],[c_13353,c_239]) ).
cnf(c_13385,plain,
cyclic(sK0,sK0,sK5,A),
inference(resolve,[status(thm)],[c_13374,c_13094]) ).
cnf(c_13390,plain,
cyclic(sK0,sK0,sK4,A),
inference(resolve,[status(thm)],[c_13374,c_3482]) ).
cnf(c_13402,plain,
cyclic(sK0,sK5,sK5,A),
inference(resolve,[status(thm)],[c_13385,c_13175]) ).
cnf(c_13407,plain,
cyclic(sK0,sK5,A,sK0),
inference(resolve,[status(thm)],[c_13385,c_13016]) ).
cnf(c_13412,plain,
( perp(sK4,sK0,sK0,A)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13390,c_7449]) ).
cnf(c_13430,plain,
cyclic(sK5,sK5,sK0,A),
inference(resolve,[status(thm)],[c_13402,c_13272]) ).
cnf(c_13469,plain,
cyclic(sK5,sK0,A,sK0),
inference(resolve,[status(thm)],[c_13430,c_13207]) ).
cnf(c_13631,plain,
cyclic(sK0,sK0,A,A),
inference(resolve,[status(thm)],[c_13374,c_300]) ).
cnf(c_29694,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK0,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_13374,c_236]) ).
cnf(c_13634,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_13374,c_29694]) ).
cnf(c_29695,plain,
( cyclic(sK0,sK5,A,B)
| ~ cyclic(sK0,sK0,sK5,A) ),
inference(resolve,[status(thm)],[c_13385,c_236]) ).
cnf(c_13653,plain,
cyclic(sK0,sK5,A,B),
inference(resolve,[status(thm)],[c_13634,c_29695]) ).
cnf(c_29696,plain,
( cyclic(sK5,A,sK0,B)
| ~ cyclic(sK0,sK5,A,B) ),
inference(resolve,[status(thm)],[c_13407,c_236]) ).
cnf(c_13822,plain,
cyclic(sK5,A,sK0,B),
inference(resolve,[status(thm)],[c_13653,c_29696]) ).
cnf(c_29697,plain,
( cyclic(sK5,sK0,A,B)
| ~ cyclic(sK5,sK5,sK0,A) ),
inference(resolve,[status(thm)],[c_13430,c_236]) ).
cnf(c_13880,plain,
cyclic(sK5,sK0,A,B),
inference(resolve,[status(thm)],[c_13822,c_29697]) ).
cnf(c_29698,plain,
( cyclic(sK0,A,sK0,B)
| ~ cyclic(sK5,sK0,A,B) ),
inference(resolve,[status(thm)],[c_13469,c_236]) ).
cnf(c_13975,plain,
cyclic(sK0,A,sK0,B),
inference(resolve,[status(thm)],[c_13880,c_29698]) ).
cnf(c_29699,plain,
( cong(sK0,A,sK0,C)
| ~ eqangle(sK0,sK0,sK0,A,B,sK0,B,C)
| ~ cyclic(sK0,A,sK0,B) ),
inference(resolve,[status(thm)],[c_13975,c_13357]) ).
cnf(c_13981,plain,
( cong(sK0,A,sK0,C)
| ~ eqangle(sK0,sK0,sK0,A,B,sK0,B,C) ),
inference(resolve,[status(thm)],[c_13975,c_29699]) ).
cnf(c_13985,plain,
cong(sK0,A,sK0,A),
inference(resolve,[status(thm)],[c_13975,c_13335]) ).
cnf(c_13988,plain,
perp(sK4,sK0,sK0,A),
inference(resolve,[status(thm)],[c_13985,c_13412]) ).
cnf(c_13991,plain,
perp(A,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_13985,c_13360]) ).
cnf(c_14036,plain,
eqangle(sK0,A,sK0,sK0,sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_13988,c_7225]) ).
cnf(c_14051,plain,
cong(A,sK0,A,sK0),
inference(resolve,[status(thm)],[c_13991,c_2987]) ).
cnf(c_14167,plain,
cong(A,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_14036,c_13321]) ).
cnf(c_14360,plain,
perp(sK0,A,A,sK0),
inference(resolve,[status(thm)],[c_14167,c_13328]) ).
cnf(c_14367,plain,
cong(sK0,sK0,A,sK0),
inference(resolve,[status(thm)],[c_14360,c_2986]) ).
cnf(c_29700,plain,
( cyclic(sK0,A,B,A)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_13631,c_236]) ).
cnf(c_15290,plain,
cyclic(sK0,A,B,A),
inference(resolve,[status(thm)],[c_13634,c_29700]) ).
cnf(c_29701,plain,
( perp(A,sK0,sK0,B)
| ~ cong(sK0,B,sK0,B)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13634,c_200]) ).
cnf(c_29702,plain,
( perp(B,sK0,sK0,A)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13985,c_29701]) ).
cnf(c_15308,plain,
perp(A,sK0,sK0,B),
inference(resolve,[status(thm)],[c_13985,c_29702]) ).
cnf(c_29703,plain,
( perp(sK0,sK0,A,B)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13985,c_201]) ).
cnf(c_15883,plain,
perp(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_13985,c_29703]) ).
cnf(c_15897,plain,
( ~ cong(sK0,A,sK0,C)
| eqangle(A,B,A,A,C,A,C,A)
| ~ perp(sK0,A,A,B) ),
inference(resolve,[status(thm)],[c_13985,c_146]) ).
cnf(c_17551,plain,
( ~ cong(C,sK0,C,B)
| eqangle(sK0,sK0,sK0,B,C,sK0,C,A)
| ~ midp(A,sK0,B) ),
inference(resolve,[status(thm)],[c_14051,c_144]) ).
cnf(c_17642,plain,
cong(sK0,sK0,sK0,A),
inference(resolve,[status(thm)],[c_14367,c_230]) ).
cnf(c_17715,plain,
midp(sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_17642,c_903]) ).
cnf(c_17749,plain,
midp(sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_17715,c_241]) ).
cnf(c_29704,plain,
( cong(A,sK0,A,sK2)
| ~ perp(A,sK0,sK0,sK2) ),
inference(resolve,[status(thm)],[c_17715,c_202]) ).
cnf(c_17752,plain,
cong(A,sK0,A,sK2),
inference(resolve,[status(thm)],[c_15308,c_29704]) ).
cnf(c_17767,plain,
midp(sK4,sK0,sK2),
inference(resolve,[status(thm)],[c_17752,c_1411]) ).
cnf(c_17905,plain,
( midp(sK0,A,B)
| ~ para(sK2,B,sK0,A)
| ~ para(sK2,A,sK0,B) ),
inference(resolve,[status(thm)],[c_17749,c_193]) ).
cnf(c_18000,plain,
( midp(A,sK0,B)
| ~ coll(A,sK0,B)
| ~ para(sK4,A,sK2,B) ),
inference(resolve,[status(thm)],[c_17767,c_207]) ).
cnf(c_19254,plain,
eqangle(A,sK0,A,B,B,sK0,B,B),
inference(resolve,[status(thm)],[c_15290,c_212]) ).
cnf(c_19318,plain,
( cong(B,sK0,B,A)
| ~ midp(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_15308,c_202]) ).
cnf(c_19355,plain,
perp(A,B,sK0,sK0),
inference(resolve,[status(thm)],[c_15883,c_244]) ).
cnf(c_29705,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK0,sK0) ),
inference(resolve,[status(thm)],[c_15883,c_243]) ).
cnf(c_19356,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_19355,c_29705]) ).
cnf(c_29706,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK0,sK0) ),
inference(resolve,[status(thm)],[c_15883,c_242]) ).
cnf(c_19357,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_19356,c_29706]) ).
cnf(c_19372,plain,
( midp(A,sK0,B)
| ~ coll(A,sK0,B) ),
inference(resolve,[status(thm)],[c_19356,c_18000]) ).
cnf(c_29707,plain,
( midp(sK0,B,A)
| ~ para(sK2,A,sK0,B) ),
inference(resolve,[status(thm)],[c_19356,c_17905]) ).
cnf(c_19373,plain,
midp(sK0,A,B),
inference(resolve,[status(thm)],[c_19356,c_29707]) ).
cnf(c_20955,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_19356,c_213]) ).
cnf(c_20959,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_19356,c_191]) ).
cnf(c_21019,plain,
( ~ cong(sK0,A,sK0,C)
| eqangle(A,B,A,A,C,A,C,A) ),
inference(resolve,[status(thm)],[c_19357,c_15897]) ).
cnf(c_21169,plain,
cong(A,sK0,A,B),
inference(resolve,[status(thm)],[c_19373,c_19318]) ).
cnf(c_21178,plain,
midp(A,sK0,B),
inference(resolve,[status(thm)],[c_20959,c_19372]) ).
cnf(c_29708,plain,
( ~ cong(B,sK0,B,A)
| eqangle(sK0,sK0,sK0,A,B,sK0,B,C) ),
inference(resolve,[status(thm)],[c_21178,c_17551]) ).
cnf(c_21538,plain,
eqangle(sK0,sK0,sK0,A,B,sK0,B,C),
inference(resolve,[status(thm)],[c_21169,c_29708]) ).
cnf(c_21667,plain,
cong(sK0,A,sK0,B),
inference(resolve,[status(thm)],[c_21538,c_13981]) ).
cnf(c_21812,plain,
eqangle(A,B,A,A,C,A,C,A),
inference(resolve,[status(thm)],[c_21667,c_21019]) ).
cnf(c_26969,plain,
eqangle(sK0,A,A,B,B,sK0,B,B),
inference(resolve,[status(thm)],[c_19254,c_235]) ).
cnf(c_26991,plain,
eqangle(A,B,C,D,A,B,E,F),
inference(resolve,[status(thm)],[c_20955,c_234]) ).
cnf(c_27227,plain,
( eqangle(B,V6,B,B,C,D,E,F)
| ~ eqangle(A,B,A,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_21812,c_231]) ).
cnf(c_29565,plain,
( eqangle(sK0,F,F,A,B,C,D,E)
| ~ eqangle(A,sK0,A,A,B,C,D,E) ),
inference(resolve,[status(thm)],[c_26969,c_231]) ).
cnf(c_29591,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_26991,c_232]) ).
cnf(c_29645,plain,
eqangle(A,B,A,A,C,D,E,F),
inference(resolve,[status(thm)],[c_29591,c_27227]) ).
cnf(c_29689,plain,
eqangle(sK0,A,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_29645,c_29565]) ).
cnf(c_29690,plain,
$false,
inference(resolve,[status(thm)],[c_29689,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO581+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:47:29 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 2510068 was started by sandbox2 on n016,
% 0.17/0.45 % Fri Sep 25 13:47:29 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 101.79/14.09
% 101.79/14.09 % given #500 (T,wt=13): 4001 -coll(c4,c5,A) | coll(c6,A,c4). [resolve(3946,a,249,a)].
% 101.79/14.09
% 101.79/14.09 % given #1000 (T,wt=10): 13839 cyclic(c4,c4,A,B). [resolve(13420,a,236,b),unit_del(a,13752)].
% 101.79/14.09
% 101.79/14.09 % given #1500 (W,wt=10): 25252 cong(A,B,c4,B). [resolve(25075,a,230,a)].
% 101.79/14.09
% 101.79/14.09 % given #2000 (T,wt=14): 21491 eqangle(c4,c5,c4,c5,c5,c5,c5,A). [back_unit_del(10885),unit_del(a,21177)].
% 101.79/14.09
% 101.79/14.09 % given #2500 (T,wt=14): 25864 eqangle(A,B,c4,c5,A,B,c1,c4). [resolve(8667,a,234,a)].
% 101.79/14.09
% 101.79/14.09 % given #3000 (W,wt=14): 26720 eqratio(c2,c1,c2,c6,c1,c2,c2,c6). [resolve(17942,a,227,a)].
% 101.79/14.09
% 101.79/14.09 % SZS status Theorem for theBenchmark
% 101.79/14.09
% 101.79/14.09 % Proof 1 at 4.15 (+ 1.33) seconds.
% 101.79/14.09 % Length of proof is 286.
% 101.79/14.09 % Level of proof is 49.
% 101.79/14.09 % Maximum clause weight is 34.000.
% 101.79/14.09 % Given clauses 3149.
% 101.79/14.09
% 101.79/14.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------