%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO574+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 : n013.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 07:18:08 AM UTC 2026
% Result : Theorem 30.59s 4.95s
% Output : CNFRefutation 30.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 38
% Syntax : Number of formulae : 318 ( 147 unt; 0 def)
% Number of atoms : 607 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 488 ( 199 ~; 195 |; 55 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 759 ( 133 sgn 209 !; 12 ?)
% 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(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(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(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(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(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(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(ruleD54,axiom,
! [A,B,C,D] :
( ( para(A,B,C,D)
& cyclic(A,B,C,D) )
=> eqangle(A,D,C,D,C,D,C,B) ),
file('theBenchmark.p',ruleD54) ).
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(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(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
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(exemplo6GDDFULL214036,conjecture,
! [A,B,C,O,D,E,H,O1] :
( ( circle(O1,A,H,B)
& coll(H,B,E)
& coll(H,C,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) )
=> eqangle(O1,A,A,B,B,A,A,O) ),
file('theBenchmark.p',exemplo6GDDFULL214036) ).
fof(exemplo6GDDFULL214036_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,H,O1] :
( ( circle(O1,A,H,B)
& coll(H,B,E)
& coll(H,C,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) )
=> eqangle(O1,A,A,B,B,A,A,O) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214036]) ).
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_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]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
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(sK1(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(O,sK1(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK1(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,E,H,O1] :
( ~ eqangle(O1,A,A,B,B,A,A,O)
& circle(O1,A,H,B)
& coll(H,B,E)
& coll(H,C,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214036_neg]) ).
fof(sk_exemplo6GDDFULL214036_neg,plain,
( ~ eqangle(sK2,sK3,sK3,sK5,sK5,sK3,sK3,sK6)
& circle(sK2,sK3,sK4,sK5)
& coll(sK4,sK5,sK9)
& coll(sK4,sK7,sK8)
& coll(sK9,sK3,sK7)
& perp(sK9,sK5,sK3,sK7)
& coll(sK8,sK3,sK5)
& perp(sK8,sK7,sK3,sK5)
& circle(sK6,sK3,sK5,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK3,sK5,sK7,sK8,sK9,sK4,sK2]),skolemize(A,sK3),skolemize(B,sK5),skolemize(C,sK7),skolemize(O,sK6),skolemize(D,sK8),skolemize(E,sK9),skolemize(H,sK4),skolemize(O1,sK2)],[nnf_95]) ).
cnf(c_110,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_116,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_139,plain,
( eqangle(A,E,A,C,B,A,B,C)
| ~ perp(sK1(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]) ).
cnf(c_173,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]) ).
cnf(c_177,negated_conjecture,
~ eqangle(sK2,sK3,sK3,sK5,sK5,sK3,sK3,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_179,negated_conjecture,
coll(sK4,sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_180,negated_conjecture,
coll(sK9,sK3,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_181,negated_conjecture,
perp(sK9,sK5,sK3,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_183,negated_conjecture,
perp(sK8,sK7,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214036_neg]) ).
cnf(c_214,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_222,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_223,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_224,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_231,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_232,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_233,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_234,plain,
( eqangle(A,D,C,D,C,D,C,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD54]) ).
cnf(c_237,plain,
( eqangle(A,B,B,C,B,C,A,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD46]) ).
cnf(c_238,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_240,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_241,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_243,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_244,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_245,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_261,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_262,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_263,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_265,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_267,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_268,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_269,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_270,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_272,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_274,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_275,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_276,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_278,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_279,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_280,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_281,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_282,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_298,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_173]) ).
cnf(c_322,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_224]) ).
cnf(c_325,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_231]) ).
cnf(c_326,plain,
( perp(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_232]) ).
cnf(c_329,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_240]) ).
cnf(c_330,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,E,D,E,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_331,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_267]) ).
cnf(c_336,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_280]) ).
cnf(c_410,plain,
( para(sK8,sK7,A,B)
| ~ perp(sK3,sK5,A,B) ),
inference(resolve,[status(thm)],[c_274,c_183]) ).
cnf(c_411,plain,
( para(sK9,sK5,A,B)
| ~ perp(sK3,sK7,A,B) ),
inference(resolve,[status(thm)],[c_274,c_181]) ).
cnf(c_414,plain,
( para(A,B,sK3,sK5)
| ~ perp(A,B,sK8,sK7) ),
inference(resolve,[status(thm)],[c_274,c_183]) ).
cnf(c_415,plain,
( para(A,B,sK3,sK7)
| ~ perp(A,B,sK9,sK5) ),
inference(resolve,[status(thm)],[c_274,c_181]) ).
cnf(c_417,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_274,c_116]) ).
cnf(c_418,plain,
perp(sK3,sK5,sK8,sK7),
inference(resolve,[status(thm)],[c_275,c_183]) ).
cnf(c_419,plain,
perp(sK3,sK7,sK9,sK5),
inference(resolve,[status(thm)],[c_275,c_181]) ).
cnf(c_421,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_275,c_116]) ).
cnf(c_423,plain,
perp(sK9,sK5,sK7,sK3),
inference(resolve,[status(thm)],[c_276,c_181]) ).
cnf(c_436,plain,
coll(sK7,sK4,sK8),
inference(resolve,[status(thm)],[c_281,c_179]) ).
cnf(c_443,plain,
coll(sK7,sK7,sK9),
inference(resolve,[status(thm)],[c_336,c_180]) ).
cnf(c_454,plain,
coll(sK8,sK8,sK7),
inference(resolve,[status(thm)],[c_436,c_336]) ).
cnf(c_483,plain,
coll(sK7,sK9,sK7),
inference(resolve,[status(thm)],[c_443,c_282]) ).
cnf(c_511,plain,
coll(sK8,sK7,sK8),
inference(resolve,[status(thm)],[c_454,c_282]) ).
cnf(c_556,plain,
coll(sK7,sK7,sK7),
inference(resolve,[status(thm)],[c_483,c_336]) ).
cnf(c_722,plain,
perp(sK3,sK5,sK7,sK8),
inference(resolve,[status(thm)],[c_418,c_276]) ).
cnf(c_736,plain,
perp(sK3,sK7,sK5,sK9),
inference(resolve,[status(thm)],[c_419,c_276]) ).
cnf(c_764,plain,
perp(sK7,sK3,sK9,sK5),
inference(resolve,[status(thm)],[c_423,c_275]) ).
cnf(c_914,plain,
para(sK8,sK7,sK7,sK8),
inference(resolve,[status(thm)],[c_410,c_722]) ).
cnf(c_915,plain,
para(sK8,sK7,sK8,sK7),
inference(resolve,[status(thm)],[c_410,c_418]) ).
cnf(c_916,plain,
para(sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_411,c_736]) ).
cnf(c_922,plain,
para(sK7,sK8,sK8,sK7),
inference(resolve,[status(thm)],[c_914,c_278]) ).
cnf(c_925,plain,
eqangle(sK8,sK7,A,B,sK7,sK8,A,B),
inference(resolve,[status(thm)],[c_914,c_244]) ).
cnf(c_927,plain,
( eqratio(A,sK8,sK8,sK7,A,sK7,sK7,sK8)
| ~ coll(A,sK7,sK8)
| ~ coll(A,sK8,sK7) ),
inference(resolve,[status(thm)],[c_914,c_223]) ).
cnf(c_937,plain,
eqangle(sK8,sK7,A,B,sK8,sK7,A,B),
inference(resolve,[status(thm)],[c_915,c_244]) ).
cnf(c_950,plain,
para(sK5,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_916,c_278]) ).
cnf(c_978,plain,
para(sK7,sK8,sK7,sK8),
inference(resolve,[status(thm)],[c_922,c_279]) ).
cnf(c_994,plain,
para(sK5,sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_950,c_279]) ).
cnf(c_1007,plain,
para(sK3,sK5,sK3,sK5),
inference(resolve,[status(thm)],[c_414,c_418]) ).
cnf(c_1011,plain,
eqangle(sK7,sK8,A,B,sK7,sK8,A,B),
inference(resolve,[status(thm)],[c_978,c_244]) ).
cnf(c_1020,plain,
( midp(A,sK9,sK9)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_994,c_322]) ).
cnf(c_1049,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1007,c_322]) ).
cnf(c_1088,plain,
para(sK7,sK3,sK3,sK7),
inference(resolve,[status(thm)],[c_415,c_764]) ).
cnf(c_1089,plain,
para(sK3,sK7,sK3,sK7),
inference(resolve,[status(thm)],[c_415,c_419]) ).
cnf(c_1094,plain,
para(sK7,sK3,sK7,sK3),
inference(resolve,[status(thm)],[c_1088,c_279]) ).
cnf(c_1110,plain,
eqangle(sK3,sK7,A,B,sK3,sK7,A,B),
inference(resolve,[status(thm)],[c_1089,c_244]) ).
cnf(c_1119,plain,
( midp(A,sK3,sK3)
| ~ midp(A,sK7,sK7) ),
inference(resolve,[status(thm)],[c_1094,c_322]) ).
cnf(c_1122,plain,
eqangle(sK7,sK3,A,B,sK7,sK3,A,B),
inference(resolve,[status(thm)],[c_1094,c_244]) ).
cnf(c_1162,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_421,c_417]) ).
cnf(c_1252,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1162,c_279]) ).
cnf(c_1253,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1162,c_244]) ).
cnf(c_1312,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_1252,c_278]) ).
cnf(c_1344,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1312,c_279]) ).
cnf(c_1371,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_1344,c_244]) ).
cnf(c_3122,plain,
eqangle(A,B,sK8,sK7,A,B,sK7,sK8),
inference(resolve,[status(thm)],[c_925,c_265]) ).
cnf(c_3123,plain,
eqangle(sK8,sK7,sK7,sK8,A,B,A,B),
inference(resolve,[status(thm)],[c_925,c_263]) ).
cnf(c_22766,plain,
( eqratio(sK8,sK8,sK8,sK7,sK8,sK7,sK7,sK8)
| ~ coll(sK8,sK7,sK8) ),
inference(resolve,[status(thm)],[c_927,c_454]) ).
cnf(c_3135,plain,
eqratio(sK8,sK8,sK8,sK7,sK8,sK7,sK7,sK8),
inference(resolve,[status(thm)],[c_511,c_22766]) ).
cnf(c_22767,plain,
( ~ cong(sK8,sK8,sK8,sK7)
| midp(sK7,sK7,sK7)
| ~ coll(sK7,sK7,sK7) ),
inference(resolve,[status(thm)],[c_937,c_298]) ).
cnf(c_3181,plain,
( ~ cong(sK8,sK8,sK8,sK7)
| midp(sK7,sK7,sK7) ),
inference(resolve,[status(thm)],[c_556,c_22767]) ).
cnf(c_3182,plain,
eqangle(A,B,sK8,sK7,A,B,sK8,sK7),
inference(resolve,[status(thm)],[c_937,c_265]) ).
cnf(c_3184,plain,
( cyclic(sK7,A,sK8,sK8)
| ~ coll(sK8,sK8,A) ),
inference(resolve,[status(thm)],[c_937,c_241]) ).
cnf(c_3558,plain,
( cyclic(sK8,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_1011,c_241]) ).
cnf(c_3559,plain,
( cong(sK8,A,sK8,A)
| ~ cyclic(sK8,A,sK7,sK7)
| ~ cyclic(sK8,A,sK7,A)
| ~ cyclic(sK8,A,sK7,sK8) ),
inference(resolve,[status(thm)],[c_1011,c_240]) ).
cnf(c_3566,plain,
( ~ cong(sK7,sK7,sK7,A)
| ~ cong(sK7,sK7,sK7,sK8)
| midp(A,sK8,A)
| ~ coll(A,sK8,A) ),
inference(resolve,[status(thm)],[c_1011,c_173]) ).
cnf(c_4006,plain,
( cyclic(sK7,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1110,c_241]) ).
cnf(c_4007,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK3,sK3)
| ~ cyclic(sK7,A,sK3,A)
| ~ cyclic(sK7,A,sK3,sK7) ),
inference(resolve,[status(thm)],[c_1110,c_240]) ).
cnf(c_4063,plain,
( cyclic(sK3,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_1122,c_241]) ).
cnf(c_4456,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1253,c_241]) ).
cnf(c_4457,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,sK3)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_1253,c_240]) ).
cnf(c_4543,plain,
( cong(sK3,sK2,sK3,sK2)
| ~ cyclic(sK3,sK2,sK2,sK2)
| ~ cyclic(sK3,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_1371,c_330]) ).
cnf(c_4548,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1371,c_241]) ).
cnf(c_4549,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_1371,c_240]) ).
cnf(c_4686,plain,
eqangle(A,B,A,B,sK8,sK7,sK7,sK8),
inference(resolve,[status(thm)],[c_3122,c_263]) ).
cnf(c_4726,plain,
( eqangle(sK8,sK7,sK7,sK8,C,D,E,F)
| ~ eqangle(A,B,A,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_3123,c_262]) ).
cnf(c_4787,plain,
( cong(sK8,sK8,sK8,sK7)
| ~ cong(sK8,sK7,sK7,sK8) ),
inference(resolve,[status(thm)],[c_3135,c_214]) ).
cnf(c_4794,plain,
( cong(sK8,sK7,sK8,sK7)
| ~ cyclic(sK8,sK7,sK8,sK7)
| ~ cyclic(sK8,sK7,sK8,sK8) ),
inference(resolve,[status(thm)],[c_3182,c_329]) ).
cnf(c_4797,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3182,c_245]) ).
cnf(c_22768,plain,
( cyclic(A,sK7,sK8,sK8)
| ~ coll(sK8,sK8,sK7) ),
inference(resolve,[status(thm)],[c_3182,c_241]) ).
cnf(c_4799,plain,
cyclic(A,sK7,sK8,sK8),
inference(resolve,[status(thm)],[c_454,c_22768]) ).
cnf(c_4805,plain,
( ~ cong(sK8,sK8,sK8,sK7)
| ~ cong(sK8,sK8,sK8,A)
| midp(sK7,A,sK7)
| ~ coll(sK7,A,sK7) ),
inference(resolve,[status(thm)],[c_3182,c_173]) ).
cnf(c_4810,plain,
( cong(sK8,sK7,sK8,sK7)
| ~ cyclic(sK8,sK7,sK8,sK7) ),
inference(resolve,[status(thm)],[c_4799,c_4794]) ).
cnf(c_4812,plain,
( midp(A,C,C)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_4797,c_322]) ).
cnf(c_4820,plain,
( midp(C,B,C)
| ~ coll(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_4797,c_238]) ).
cnf(c_4822,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4797,c_222]) ).
cnf(c_5071,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4822,c_336]) ).
cnf(c_5072,plain,
coll(A,B,A),
inference(resolve,[status(thm)],[c_4822,c_281]) ).
cnf(c_5079,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_5071,c_4548]) ).
cnf(c_5081,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_5071,c_4456]) ).
cnf(c_5083,plain,
cyclic(sK3,A,sK7,sK7),
inference(resolve,[status(thm)],[c_5071,c_4063]) ).
cnf(c_5084,plain,
cyclic(sK7,A,sK3,sK3),
inference(resolve,[status(thm)],[c_5071,c_4006]) ).
cnf(c_5088,plain,
cyclic(sK8,A,sK7,sK7),
inference(resolve,[status(thm)],[c_5071,c_3558]) ).
cnf(c_5090,plain,
cyclic(sK7,A,sK8,sK8),
inference(resolve,[status(thm)],[c_5071,c_3184]) ).
cnf(c_5208,plain,
( midp(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_5072,c_4820]) ).
cnf(c_5209,plain,
( ~ cong(sK8,sK8,sK8,sK7)
| ~ cong(sK8,sK8,sK8,A)
| midp(sK7,A,sK7) ),
inference(resolve,[status(thm)],[c_5072,c_4805]) ).
cnf(c_5219,plain,
( ~ cong(sK7,sK7,sK7,A)
| ~ cong(sK7,sK7,sK7,sK8)
| midp(A,sK8,A) ),
inference(resolve,[status(thm)],[c_5072,c_3566]) ).
cnf(c_5238,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_5079,c_4549]) ).
cnf(c_5240,plain,
( cong(sK3,sK2,sK3,sK2)
| ~ cyclic(sK3,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_5079,c_4543]) ).
cnf(c_5244,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_5081,c_4457]) ).
cnf(c_5253,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK3,A)
| ~ cyclic(sK7,A,sK3,sK7) ),
inference(resolve,[status(thm)],[c_5084,c_4007]) ).
cnf(c_5268,plain,
( cong(sK8,A,sK8,A)
| ~ cyclic(sK8,A,sK7,A)
| ~ cyclic(sK8,A,sK7,sK8) ),
inference(resolve,[status(thm)],[c_5088,c_3559]) ).
cnf(c_5732,plain,
cyclic(A,sK8,sK7,sK8),
inference(resolve,[status(thm)],[c_4799,c_269]) ).
cnf(c_5751,plain,
cyclic(A,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_5079,c_331]) ).
cnf(c_5753,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_5079,c_269]) ).
cnf(c_5798,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_5081,c_269]) ).
cnf(c_5800,plain,
( cyclic(A,sK3,B,sK3)
| ~ cyclic(sK2,A,sK3,B) ),
inference(resolve,[status(thm)],[c_5081,c_267]) ).
cnf(c_5831,plain,
cyclic(sK3,sK7,A,sK7),
inference(resolve,[status(thm)],[c_5083,c_269]) ).
cnf(c_5848,plain,
cyclic(sK7,sK3,A,sK3),
inference(resolve,[status(thm)],[c_5084,c_269]) ).
cnf(c_5931,plain,
cyclic(sK8,sK7,A,sK7),
inference(resolve,[status(thm)],[c_5088,c_269]) ).
cnf(c_5946,plain,
cong(sK8,sK7,sK8,sK7),
inference(resolve,[status(thm)],[c_5931,c_4810]) ).
cnf(c_5967,plain,
cyclic(sK7,sK8,A,sK8),
inference(resolve,[status(thm)],[c_5090,c_269]) ).
cnf(c_5982,plain,
cyclic(sK8,A,sK7,sK8),
inference(resolve,[status(thm)],[c_5732,c_268]) ).
cnf(c_5998,plain,
( cong(sK8,A,sK8,A)
| ~ cyclic(sK8,A,sK7,A) ),
inference(resolve,[status(thm)],[c_5982,c_5268]) ).
cnf(c_6060,plain,
cyclic(sK2,A,sK2,sK2),
inference(resolve,[status(thm)],[c_5751,c_268]) ).
cnf(c_6073,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_5753,c_270]) ).
cnf(c_6074,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_5753,c_268]) ).
cnf(c_6089,plain,
cong(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_6073,c_5240]) ).
cnf(c_6189,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_5798,c_270]) ).
cnf(c_6190,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_5798,c_268]) ).
cnf(c_6272,plain,
cyclic(sK3,sK7,sK7,A),
inference(resolve,[status(thm)],[c_5831,c_270]) ).
cnf(c_6273,plain,
cyclic(sK7,sK3,A,sK7),
inference(resolve,[status(thm)],[c_5831,c_268]) ).
cnf(c_6305,plain,
cyclic(sK3,sK7,A,sK3),
inference(resolve,[status(thm)],[c_5848,c_268]) ).
cnf(c_6461,plain,
cyclic(sK7,sK8,A,sK7),
inference(resolve,[status(thm)],[c_5931,c_268]) ).
cnf(c_6533,plain,
cong(sK8,sK7,sK7,sK8),
inference(resolve,[status(thm)],[c_5946,c_261]) ).
cnf(c_6549,plain,
cong(sK8,sK8,sK8,sK7),
inference(resolve,[status(thm)],[c_6533,c_4787]) ).
cnf(c_6551,plain,
( ~ cong(sK8,sK8,sK8,A)
| midp(sK7,A,sK7) ),
inference(resolve,[status(thm)],[c_6549,c_5209]) ).
cnf(c_6552,plain,
midp(sK7,sK7,sK7),
inference(resolve,[status(thm)],[c_6549,c_3181]) ).
cnf(c_6555,plain,
midp(sK7,sK3,sK3),
inference(resolve,[status(thm)],[c_6552,c_1119]) ).
cnf(c_6611,plain,
midp(sK7,sK5,sK5),
inference(resolve,[status(thm)],[c_6555,c_1049]) ).
cnf(c_6691,plain,
midp(sK7,sK9,sK9),
inference(resolve,[status(thm)],[c_6611,c_1020]) ).
cnf(c_6798,plain,
cyclic(sK7,sK8,sK8,A),
inference(resolve,[status(thm)],[c_5967,c_270]) ).
cnf(c_6929,plain,
cyclic(sK2,sK2,A,sK2),
inference(resolve,[status(thm)],[c_6060,c_269]) ).
cnf(c_6942,plain,
cyclic(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_6073,c_331]) ).
cnf(c_6943,plain,
cyclic(sK2,sK3,sK2,A),
inference(resolve,[status(thm)],[c_6073,c_268]) ).
cnf(c_22769,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_6073,c_267]) ).
cnf(c_6944,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_6073,c_22769]) ).
cnf(c_6958,plain,
cyclic(sK2,A,sK3,sK2),
inference(resolve,[status(thm)],[c_6074,c_269]) ).
cnf(c_6960,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_6074,c_267]) ).
cnf(c_6974,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A) ),
inference(resolve,[status(thm)],[c_6958,c_5244]) ).
cnf(c_6992,plain,
perp(sK3,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_6089,c_326]) ).
cnf(c_7390,plain,
cyclic(sK3,sK3,A,A),
inference(resolve,[status(thm)],[c_6189,c_331]) ).
cnf(c_22770,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_6189,c_267]) ).
cnf(c_7392,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_6189,c_22770]) ).
cnf(c_7406,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_6190,c_269]) ).
cnf(c_7408,plain,
( cyclic(sK2,A,sK3,B)
| ~ cyclic(sK3,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6190,c_267]) ).
cnf(c_7422,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7406,c_5238]) ).
cnf(c_7559,plain,
cyclic(sK7,sK7,A,A),
inference(resolve,[status(thm)],[c_6272,c_331]) ).
cnf(c_22771,plain,
( cyclic(sK7,sK7,A,B)
| ~ cyclic(sK3,sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_6272,c_267]) ).
cnf(c_7561,plain,
cyclic(sK7,sK7,A,B),
inference(resolve,[status(thm)],[c_6272,c_22771]) ).
cnf(c_7575,plain,
cyclic(sK7,A,sK3,sK7),
inference(resolve,[status(thm)],[c_6273,c_269]) ).
cnf(c_7591,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7575,c_5253]) ).
cnf(c_7763,plain,
( cyclic(sK7,A,sK3,B)
| ~ cyclic(sK3,sK7,A,B) ),
inference(resolve,[status(thm)],[c_6305,c_267]) ).
cnf(c_8225,plain,
( cyclic(sK8,A,sK7,B)
| ~ cyclic(sK7,sK8,A,B) ),
inference(resolve,[status(thm)],[c_6461,c_267]) ).
cnf(c_8837,plain,
cyclic(sK8,sK8,A,A),
inference(resolve,[status(thm)],[c_6798,c_331]) ).
cnf(c_22772,plain,
( cyclic(sK2,A,sK2,B)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6929,c_267]) ).
cnf(c_8910,plain,
cyclic(sK2,A,sK2,B),
inference(resolve,[status(thm)],[c_6944,c_22772]) ).
cnf(c_22773,plain,
( cyclic(sK2,A,B,A)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6942,c_267]) ).
cnf(c_8926,plain,
cyclic(sK2,A,B,A),
inference(resolve,[status(thm)],[c_6944,c_22773]) ).
cnf(c_8939,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_8926,c_6974]) ).
cnf(c_22774,plain,
( cyclic(sK3,sK2,A,B)
| ~ cyclic(sK2,sK3,sK2,A) ),
inference(resolve,[status(thm)],[c_6943,c_267]) ).
cnf(c_8962,plain,
cyclic(sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_8910,c_22774]) ).
cnf(c_8975,plain,
cyclic(sK2,A,sK3,B),
inference(resolve,[status(thm)],[c_8962,c_7408]) ).
cnf(c_8978,plain,
cyclic(A,sK3,B,sK3),
inference(resolve,[status(thm)],[c_8975,c_5800]) ).
cnf(c_22775,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6944,c_267]) ).
cnf(c_8981,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_6944,c_22775]) ).
cnf(c_8993,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_8981,c_6960]) ).
cnf(c_9021,plain,
cong(sK3,A,sK3,A),
inference(resolve,[status(thm)],[c_8993,c_7422]) ).
cnf(c_9058,plain,
( para(sK3,sK3,A,B)
| ~ perp(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6992,c_274]) ).
cnf(c_22776,plain,
( perp(A,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7390,c_325]) ).
cnf(c_9327,plain,
perp(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_9021,c_22776]) ).
cnf(c_22777,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_7392,c_267]) ).
cnf(c_9380,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_7392,c_22777]) ).
cnf(c_9382,plain,
( eqangle(sK3,B,A,B,A,B,A,sK3)
| ~ para(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_7392,c_234]) ).
cnf(c_22778,plain,
( perp(A,sK3,sK3,B)
| ~ cong(sK3,B,sK3,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7392,c_231]) ).
cnf(c_22779,plain,
( perp(B,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_9021,c_22778]) ).
cnf(c_9383,plain,
perp(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_9021,c_22779]) ).
cnf(c_22780,plain,
( eqangle(sK3,C,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK1(sK3,sK3,A,B),sK3,sK3,C)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_7392,c_139]) ).
cnf(c_9391,plain,
( eqangle(sK3,B,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_9383,c_22780]) ).
cnf(c_9394,plain,
cyclic(sK7,A,sK3,B),
inference(resolve,[status(thm)],[c_9380,c_7763]) ).
cnf(c_9493,plain,
cong(sK7,A,sK7,A),
inference(resolve,[status(thm)],[c_9394,c_7591]) ).
cnf(c_22781,plain,
( perp(A,sK7,sK7,A)
| ~ cong(sK7,A,sK7,A) ),
inference(resolve,[status(thm)],[c_7559,c_325]) ).
cnf(c_9634,plain,
perp(A,sK7,sK7,A),
inference(resolve,[status(thm)],[c_9493,c_22781]) ).
cnf(c_22782,plain,
( cyclic(sK7,A,B,C)
| ~ cyclic(sK7,sK7,A,B) ),
inference(resolve,[status(thm)],[c_7561,c_267]) ).
cnf(c_9666,plain,
cyclic(sK7,A,B,C),
inference(resolve,[status(thm)],[c_7561,c_22782]) ).
cnf(c_9678,plain,
cyclic(sK8,A,sK7,B),
inference(resolve,[status(thm)],[c_9666,c_8225]) ).
cnf(c_9733,plain,
cong(sK8,A,sK8,A),
inference(resolve,[status(thm)],[c_9678,c_5998]) ).
cnf(c_22783,plain,
( perp(A,sK8,sK8,A)
| ~ cong(sK8,A,sK8,A) ),
inference(resolve,[status(thm)],[c_8837,c_325]) ).
cnf(c_10686,plain,
perp(A,sK8,sK8,A),
inference(resolve,[status(thm)],[c_9733,c_22783]) ).
cnf(c_22784,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_8939,c_232]) ).
cnf(c_10851,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_8939,c_22784]) ).
cnf(c_10866,plain,
para(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_10851,c_9058]) ).
cnf(c_10893,plain,
eqangle(sK3,A,B,A,B,A,B,sK3),
inference(resolve,[status(thm)],[c_10866,c_9382]) ).
cnf(c_11107,plain,
eqangle(A,B,A,sK3,sK3,B,sK3,sK3),
inference(resolve,[status(thm)],[c_8978,c_243]) ).
cnf(c_11635,plain,
perp(sK3,A,A,sK3),
inference(resolve,[status(thm)],[c_9327,c_275]) ).
cnf(c_11648,plain,
eqangle(sK3,A,sK3,sK3,B,sK3,B,sK3),
inference(resolve,[status(thm)],[c_11635,c_9391]) ).
cnf(c_11674,plain,
( cong(B,sK3,B,A)
| ~ midp(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_9383,c_233]) ).
cnf(c_12085,plain,
perp(sK7,A,A,sK7),
inference(resolve,[status(thm)],[c_9634,c_275]) ).
cnf(c_12789,plain,
perp(sK8,A,A,sK8),
inference(resolve,[status(thm)],[c_10686,c_275]) ).
cnf(c_12844,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_10851,c_275]) ).
cnf(c_22785,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_10851,c_274]) ).
cnf(c_12845,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_12844,c_22785]) ).
cnf(c_12861,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_12845,c_244]) ).
cnf(c_13227,plain,
perp(sK7,A,sK7,A),
inference(resolve,[status(thm)],[c_12085,c_276]) ).
cnf(c_13650,plain,
perp(sK8,A,sK8,A),
inference(resolve,[status(thm)],[c_12789,c_276]) ).
cnf(c_14005,plain,
( cong(sK7,sK7,sK7,A)
| ~ midp(A,sK7,A) ),
inference(resolve,[status(thm)],[c_13227,c_233]) ).
cnf(c_14349,plain,
( cong(sK8,sK8,sK8,A)
| ~ midp(A,sK8,A) ),
inference(resolve,[status(thm)],[c_13650,c_233]) ).
cnf(c_14551,plain,
midp(sK7,A,A),
inference(resolve,[status(thm)],[c_4812,c_6691]) ).
cnf(c_14570,plain,
midp(A,sK7,A),
inference(resolve,[status(thm)],[c_5208,c_14551]) ).
cnf(c_14571,plain,
cong(sK7,sK7,sK7,A),
inference(resolve,[status(thm)],[c_14570,c_14005]) ).
cnf(c_22786,plain,
( ~ cong(sK7,sK7,sK7,A)
| midp(A,sK8,A) ),
inference(resolve,[status(thm)],[c_14571,c_5219]) ).
cnf(c_14588,plain,
midp(A,sK8,A),
inference(resolve,[status(thm)],[c_14571,c_22786]) ).
cnf(c_14590,plain,
cong(sK8,sK8,sK8,A),
inference(resolve,[status(thm)],[c_14588,c_14349]) ).
cnf(c_14625,plain,
midp(sK7,A,sK7),
inference(resolve,[status(thm)],[c_14590,c_6551]) ).
cnf(c_14920,plain,
midp(A,B,A),
inference(resolve,[status(thm)],[c_14625,c_5208]) ).
cnf(c_15432,plain,
midp(A,A,B),
inference(resolve,[status(thm)],[c_14920,c_272]) ).
cnf(c_15549,plain,
cong(A,sK3,A,B),
inference(resolve,[status(thm)],[c_15432,c_11674]) ).
cnf(c_17942,plain,
eqangle(A,sK3,sK3,B,sK3,B,A,B),
inference(resolve,[status(thm)],[c_15549,c_237]) ).
cnf(c_20141,plain,
( eqangle(E,F,E,F,A,B,C,D)
| ~ eqangle(sK8,sK7,sK7,sK8,A,B,C,D) ),
inference(resolve,[status(thm)],[c_4686,c_262]) ).
cnf(c_21280,plain,
( eqangle(sK3,B,A,B,C,D,E,F)
| ~ eqangle(A,B,A,sK3,C,D,E,F) ),
inference(resolve,[status(thm)],[c_10893,c_262]) ).
cnf(c_21670,plain,
( eqangle(F,A,F,sK3,B,C,D,E)
| ~ eqangle(sK3,A,sK3,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_11107,c_262]) ).
cnf(c_22009,plain,
( eqangle(sK3,F,sK3,sK3,B,C,D,E)
| ~ eqangle(A,sK3,A,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_11648,c_262]) ).
cnf(c_22250,plain,
eqangle(sK8,sK7,sK7,sK8,A,B,C,D),
inference(resolve,[status(thm)],[c_12861,c_4726]) ).
cnf(c_22257,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_22250,c_20141]) ).
cnf(c_22277,plain,
eqangle(sK3,A,sK3,sK3,B,C,D,E),
inference(resolve,[status(thm)],[c_22257,c_22009]) ).
cnf(c_22350,plain,
eqangle(A,B,A,sK3,C,D,E,F),
inference(resolve,[status(thm)],[c_22277,c_21670]) ).
cnf(c_22377,plain,
eqangle(sK3,A,B,A,C,D,E,F),
inference(resolve,[status(thm)],[c_22350,c_21280]) ).
cnf(c_22787,plain,
( eqangle(B,sK3,sK3,A,C,D,E,F)
| ~ eqangle(sK3,A,B,A,C,D,E,F) ),
inference(resolve,[status(thm)],[c_17942,c_262]) ).
cnf(c_22764,plain,
eqangle(A,sK3,sK3,B,C,D,E,F),
inference(resolve,[status(thm)],[c_22377,c_22787]) ).
cnf(c_22765,plain,
$false,
inference(resolve,[status(thm)],[c_22764,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO574+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:42:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 542270 was started by sandbox2 on n013,
% 0.09/0.37 % Fri Sep 25 13:42:06 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 30.59/4.95
% 30.59/4.95 % given #500 (A,wt=13): 501 -coll(c1,c2,A) | coll(c5,A,c1). [resolve(447,a,280,a)].
% 30.59/4.95
% 30.59/4.95 % given #1000 (T,wt=13): 1208 -coll(c1,c4,A) | coll(A,c4,c1). [resolve(1199,a,280,b)].
% 30.59/4.95
% 30.59/4.95 % given #1500 (A,wt=23): 904 -cong(c2,c3,c2,c1) | coll(c1,c3,f4(c3,c1,c2,c6)). [resolve(848,a,207,a)].
% 30.59/4.95
% 30.59/4.95 % given #2000 (W,wt=13): 2390 -coll(c5,c3,A) | coll(A,c4,c5). [resolve(2198,a,280,b)].
% 30.59/4.95
% 30.59/4.95 % given #2500 (T,wt=9): 5140 coll(A,c7,c1). [back_unit_del(1688),unit_del(a,5071)].
% 30.59/4.95
% 30.59/4.95 % given #3000 (W,wt=10): 8981 cyclic(c8,A,B,C). [resolve(6944,a,267,b),unit_del(a,6944)].
% 30.59/4.95
% 30.59/4.95 % given #3500 (T,wt=10): 12194 perp(c5,c2,A,B). [resolve(9734,a,232,b),unit_del(a,9734)].
% 30.59/4.95
% 30.59/4.95 % given #4000 (A,wt=14): 3414 eqratio(c6,c3,c3,c5,c6,c5,c5,c3). [resolve(983,b,1389,a),unit_del(a,1417)].
% 30.59/4.95
% 30.59/4.95 % given #4500 (T,wt=14): 8115 eqangle(c6,c2,c2,c2,c2,c2,c6,c2). [resolve(6445,a,237,a)].
% 30.59/4.95
% 30.59/4.95 % SZS status Theorem for theBenchmark
% 30.59/4.95
% 30.59/4.95 % Proof 1 at 3.09 (+ 1.02) seconds.
% 30.59/4.95 % Length of proof is 289.
% 30.59/4.95 % Level of proof is 29.
% 30.59/4.95 % Maximum clause weight is 38.000.
% 30.59/4.95 % Given clauses 4989.
% 30.59/4.95
% 30.59/4.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------