%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO562+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:18:07 AM UTC 2026
% Result : Theorem 32.56s 4.55s
% Output : CNFRefutation 32.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of formulae : 272 ( 116 unt; 0 def)
% Number of atoms : 549 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 455 ( 178 ~; 174 |; 63 &)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 714 ( 111 sgn 223 !; 15 ?)
% 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(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(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(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(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(exemplo6GDDFULL214023,conjecture,
! [A,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) )
=> eqangle(A,G,G,C,C,D,D,E) ),
file('theBenchmark.p',exemplo6GDDFULL214023) ).
fof(exemplo6GDDFULL214023_neg,negated_conjecture,
~ ! [A,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) )
=> eqangle(A,G,G,C,C,D,D,E) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214023]) ).
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,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ~ eqangle(A,G,G,C,C,D,D,E)
& coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214023_neg]) ).
fof(sk_exemplo6GDDFULL214023_neg,plain,
( ~ eqangle(sK3,sK6,sK6,sK4,sK4,sK5,sK5,sK7)
& coll(sK6,sK4,sK7)
& coll(sK6,sK3,sK9)
& coll(sK12,sK4,sK5)
& coll(sK12,sK3,sK9)
& circle(sK2,sK3,sK7,sK11)
& coll(sK8,sK3,sK9)
& coll(sK8,sK4,sK2)
& circle(sK2,sK3,sK9,sK10)
& perp(sK4,sK2,sK3,sK9)
& circle(sK2,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK9,sK10,sK8,sK7,sK11,sK12,sK6]),skolemize(A,sK3),skolemize(C,sK4),skolemize(D,sK5),skolemize(O,sK2),skolemize(B,sK9),skolemize(M,sK8),skolemize(E,sK7),skolemize(F,sK12),skolemize(G,sK6),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK11)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214023_neg]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_154,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_188,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_192,negated_conjecture,
~ eqangle(sK3,sK6,sK6,sK4,sK4,sK5,sK5,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214023_neg]) ).
cnf(c_198,negated_conjecture,
coll(sK8,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214023_neg]) ).
cnf(c_199,negated_conjecture,
perp(sK4,sK2,sK3,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214023_neg]) ).
cnf(c_230,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_238,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_239,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_240,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_247,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_248,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_249,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_251,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_253,plain,
( eqangle(A,B,B,C,B,C,A,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD46]) ).
cnf(c_254,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_256,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_257,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_259,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_260,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_261,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_277,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_278,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_279,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_281,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_282,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_283,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_284,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_285,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_286,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_288,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_290,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_291,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_292,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_294,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_295,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_296,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_297,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_298,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_314,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_188]) ).
cnf(c_338,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_341,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_247]) ).
cnf(c_345,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_256]) ).
cnf(c_347,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_283]) ).
cnf(c_352,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_296]) ).
cnf(c_436,plain,
( para(sK4,sK2,A,B)
| ~ perp(sK3,sK9,A,B) ),
inference(resolve,[status(thm)],[c_290,c_199]) ).
cnf(c_440,plain,
( para(A,B,sK3,sK9)
| ~ perp(A,B,sK4,sK2) ),
inference(resolve,[status(thm)],[c_290,c_199]) ).
cnf(c_441,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_290,c_145]) ).
cnf(c_444,plain,
perp(sK3,sK9,sK4,sK2),
inference(resolve,[status(thm)],[c_291,c_199]) ).
cnf(c_445,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_291,c_145]) ).
cnf(c_464,plain,
coll(sK4,sK8,sK2),
inference(resolve,[status(thm)],[c_297,c_198]) ).
cnf(c_476,plain,
coll(sK2,sK2,sK8),
inference(resolve,[status(thm)],[c_352,c_198]) ).
cnf(c_482,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_464,c_352]) ).
cnf(c_529,plain,
coll(sK2,sK8,sK2),
inference(resolve,[status(thm)],[c_476,c_298]) ).
cnf(c_552,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_482,c_352]) ).
cnf(c_633,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_529,c_352]) ).
cnf(c_686,plain,
coll(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_552,c_298]) ).
cnf(c_914,plain,
perp(sK3,sK9,sK2,sK4),
inference(resolve,[status(thm)],[c_444,c_292]) ).
cnf(c_1132,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_436,c_914]) ).
cnf(c_1133,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_436,c_444]) ).
cnf(c_1169,plain,
para(sK3,sK9,sK3,sK9),
inference(resolve,[status(thm)],[c_440,c_444]) ).
cnf(c_1180,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1132,c_294]) ).
cnf(c_1185,plain,
( eqratio(A,sK4,sK4,sK2,A,sK2,sK2,sK4)
| ~ coll(A,sK2,sK4)
| ~ coll(A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1132,c_239]) ).
cnf(c_1195,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1133,c_260]) ).
cnf(c_1221,plain,
( midp(A,sK9,sK9)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1169,c_338]) ).
cnf(c_1237,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_1180,c_295]) ).
cnf(c_1279,plain,
eqangle(sK2,sK4,A,B,sK2,sK4,A,B),
inference(resolve,[status(thm)],[c_1237,c_260]) ).
cnf(c_1288,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_445,c_441]) ).
cnf(c_1326,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1288,c_295]) ).
cnf(c_1327,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1288,c_260]) ).
cnf(c_3450,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_1326,c_294]) ).
cnf(c_3466,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_3450,c_295]) ).
cnf(c_3478,plain,
( midp(A,sK3,sK3)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3466,c_338]) ).
cnf(c_3481,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_3466,c_260]) ).
cnf(c_17927,plain,
( eqratio(sK4,sK4,sK4,sK2,sK4,sK2,sK2,sK4)
| ~ coll(sK4,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1185,c_686]) ).
cnf(c_4082,plain,
eqratio(sK4,sK4,sK4,sK2,sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_552,c_17927]) ).
cnf(c_17928,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1195,c_314]) ).
cnf(c_4141,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_633,c_17928]) ).
cnf(c_4142,plain,
eqangle(A,B,sK4,sK2,A,B,sK4,sK2),
inference(resolve,[status(thm)],[c_1195,c_281]) ).
cnf(c_4144,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1195,c_257]) ).
cnf(c_4145,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,sK4)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1195,c_256]) ).
cnf(c_4624,plain,
( cyclic(sK4,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1279,c_257]) ).
cnf(c_4625,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,sK2)
| ~ cyclic(sK4,A,sK2,A)
| ~ cyclic(sK4,A,sK2,sK4) ),
inference(resolve,[status(thm)],[c_1279,c_256]) ).
cnf(c_4632,plain,
( ~ cong(sK2,sK2,sK2,A)
| ~ cong(sK2,sK2,sK2,sK4)
| midp(A,sK4,A)
| ~ coll(A,sK4,A) ),
inference(resolve,[status(thm)],[c_1279,c_188]) ).
cnf(c_4850,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1327,c_257]) ).
cnf(c_6643,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_3481,c_257]) ).
cnf(c_6644,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_3481,c_256]) ).
cnf(c_6758,plain,
( cong(sK4,sK4,sK4,sK2)
| ~ cong(sK4,sK2,sK2,sK4) ),
inference(resolve,[status(thm)],[c_4082,c_230]) ).
cnf(c_6791,plain,
( cong(sK4,sK2,sK4,sK2)
| ~ cyclic(sK4,sK2,sK4,sK2)
| ~ cyclic(sK4,sK2,sK4,sK4) ),
inference(resolve,[status(thm)],[c_4142,c_345]) ).
cnf(c_6794,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_4142,c_261]) ).
cnf(c_17929,plain,
( cyclic(A,sK2,sK4,sK4)
| ~ coll(sK4,sK4,sK2) ),
inference(resolve,[status(thm)],[c_4142,c_257]) ).
cnf(c_6796,plain,
cyclic(A,sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_552,c_17929]) ).
cnf(c_6802,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| ~ cong(sK4,sK4,sK4,A)
| midp(sK2,A,sK2)
| ~ coll(sK2,A,sK2) ),
inference(resolve,[status(thm)],[c_4142,c_188]) ).
cnf(c_6807,plain,
( cong(sK4,sK2,sK4,sK2)
| ~ cyclic(sK4,sK2,sK4,sK2) ),
inference(resolve,[status(thm)],[c_6796,c_6791]) ).
cnf(c_6809,plain,
( midp(A,C,C)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_6794,c_338]) ).
cnf(c_6817,plain,
( midp(C,B,C)
| ~ coll(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_6794,c_254]) ).
cnf(c_6819,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_6794,c_238]) ).
cnf(c_7000,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_6819,c_352]) ).
cnf(c_7001,plain,
coll(A,B,A),
inference(resolve,[status(thm)],[c_6819,c_297]) ).
cnf(c_7008,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_7000,c_6643]) ).
cnf(c_7017,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_7000,c_4850]) ).
cnf(c_7034,plain,
cyclic(sK4,A,sK2,sK2),
inference(resolve,[status(thm)],[c_7000,c_4624]) ).
cnf(c_7037,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_7000,c_4144]) ).
cnf(c_7183,plain,
( midp(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_7001,c_6817]) ).
cnf(c_7184,plain,
( ~ cong(sK4,sK4,sK4,sK2)
| ~ cong(sK4,sK4,sK4,A)
| midp(sK2,A,sK2) ),
inference(resolve,[status(thm)],[c_7001,c_6802]) ).
cnf(c_7193,plain,
( ~ cong(sK2,sK2,sK2,A)
| ~ cong(sK2,sK2,sK2,sK4)
| midp(A,sK4,A) ),
inference(resolve,[status(thm)],[c_7001,c_4632]) ).
cnf(c_7203,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_7008,c_6644]) ).
cnf(c_7209,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,A)
| ~ cyclic(sK4,A,sK2,sK4) ),
inference(resolve,[status(thm)],[c_7034,c_4625]) ).
cnf(c_7218,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_7037,c_4145]) ).
cnf(c_7616,plain,
cyclic(A,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_6796,c_285]) ).
cnf(c_7634,plain,
cyclic(A,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_7008,c_347]) ).
cnf(c_7636,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_7008,c_285]) ).
cnf(c_7653,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_7017,c_285]) ).
cnf(c_7655,plain,
( cyclic(A,sK3,B,sK3)
| ~ cyclic(sK2,A,sK3,B) ),
inference(resolve,[status(thm)],[c_7017,c_283]) ).
cnf(c_7656,plain,
( cyclic(A,sK3,sK3,B)
| ~ cyclic(sK2,A,sK3,B) ),
inference(resolve,[status(thm)],[c_7017,c_283]) ).
cnf(c_7685,plain,
cyclic(sK4,sK2,A,sK2),
inference(resolve,[status(thm)],[c_7034,c_285]) ).
cnf(c_7700,plain,
cong(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_7685,c_6807]) ).
cnf(c_7736,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_7037,c_285]) ).
cnf(c_7794,plain,
cyclic(sK4,A,sK2,sK4),
inference(resolve,[status(thm)],[c_7616,c_284]) ).
cnf(c_7810,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7794,c_7209]) ).
cnf(c_7861,plain,
cyclic(sK2,A,sK2,sK2),
inference(resolve,[status(thm)],[c_7634,c_284]) ).
cnf(c_7874,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_7636,c_286]) ).
cnf(c_7875,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_7636,c_284]) ).
cnf(c_7921,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_7653,c_286]) ).
cnf(c_7922,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_7653,c_284]) ).
cnf(c_7952,plain,
cyclic(sK2,sK4,A,sK2),
inference(resolve,[status(thm)],[c_7685,c_284]) ).
cnf(c_8014,plain,
cong(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_7700,c_277]) ).
cnf(c_8030,plain,
cong(sK4,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_8014,c_6758]) ).
cnf(c_8032,plain,
( ~ cong(sK4,sK4,sK4,A)
| midp(sK2,A,sK2) ),
inference(resolve,[status(thm)],[c_8030,c_7184]) ).
cnf(c_8033,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_8030,c_4141]) ).
cnf(c_8034,plain,
midp(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_8033,c_3478]) ).
cnf(c_8066,plain,
midp(sK2,sK9,sK9),
inference(resolve,[status(thm)],[c_8034,c_1221]) ).
cnf(c_8212,plain,
cyclic(sK2,sK4,sK4,A),
inference(resolve,[status(thm)],[c_7736,c_286]) ).
cnf(c_8406,plain,
cyclic(sK2,sK2,A,sK2),
inference(resolve,[status(thm)],[c_7861,c_285]) ).
cnf(c_8419,plain,
cyclic(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_7874,c_347]) ).
cnf(c_8420,plain,
cyclic(sK2,sK3,sK2,A),
inference(resolve,[status(thm)],[c_7874,c_284]) ).
cnf(c_17930,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_7874,c_283]) ).
cnf(c_8421,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_7874,c_17930]) ).
cnf(c_8437,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_7875,c_283]) ).
cnf(c_8649,plain,
cyclic(sK3,sK3,A,A),
inference(resolve,[status(thm)],[c_7921,c_347]) ).
cnf(c_17931,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_7921,c_283]) ).
cnf(c_8651,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_7921,c_17931]) ).
cnf(c_8665,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_7922,c_285]) ).
cnf(c_8667,plain,
( cyclic(sK2,A,sK3,B)
| ~ cyclic(sK3,sK2,A,B) ),
inference(resolve,[status(thm)],[c_7922,c_283]) ).
cnf(c_8681,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A) ),
inference(resolve,[status(thm)],[c_8665,c_7203]) ).
cnf(c_8752,plain,
cyclic(sK2,A,sK4,sK2),
inference(resolve,[status(thm)],[c_7952,c_285]) ).
cnf(c_8754,plain,
( cyclic(sK4,A,sK2,B)
| ~ cyclic(sK2,sK4,A,B) ),
inference(resolve,[status(thm)],[c_7952,c_283]) ).
cnf(c_8768,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A) ),
inference(resolve,[status(thm)],[c_8752,c_7218]) ).
cnf(c_9202,plain,
cyclic(sK4,sK4,A,A),
inference(resolve,[status(thm)],[c_8212,c_347]) ).
cnf(c_17932,plain,
( cyclic(sK2,A,sK2,B)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_8406,c_283]) ).
cnf(c_9314,plain,
cyclic(sK2,A,sK2,B),
inference(resolve,[status(thm)],[c_8421,c_17932]) ).
cnf(c_9329,plain,
( perp(A,sK2,sK2,A)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_8419,c_341]) ).
cnf(c_17933,plain,
( cyclic(sK2,A,B,A)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_8419,c_283]) ).
cnf(c_9330,plain,
cyclic(sK2,A,B,A),
inference(resolve,[status(thm)],[c_8421,c_17933]) ).
cnf(c_9343,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_9330,c_8768]) ).
cnf(c_9344,plain,
perp(A,sK2,sK2,A),
inference(resolve,[status(thm)],[c_9343,c_9329]) ).
cnf(c_17934,plain,
( cyclic(sK3,sK2,A,B)
| ~ cyclic(sK2,sK3,sK2,A) ),
inference(resolve,[status(thm)],[c_8420,c_283]) ).
cnf(c_9379,plain,
cyclic(sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_9314,c_17934]) ).
cnf(c_9392,plain,
cyclic(sK2,A,sK3,B),
inference(resolve,[status(thm)],[c_9379,c_8667]) ).
cnf(c_9394,plain,
cyclic(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_9392,c_7656]) ).
cnf(c_9395,plain,
cyclic(A,sK3,B,sK3),
inference(resolve,[status(thm)],[c_9392,c_7655]) ).
cnf(c_17935,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_8421,c_283]) ).
cnf(c_9398,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_8421,c_17935]) ).
cnf(c_9410,plain,
cyclic(sK4,A,sK2,B),
inference(resolve,[status(thm)],[c_9398,c_8754]) ).
cnf(c_9412,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_9398,c_8437]) ).
cnf(c_9473,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_9410,c_7810]) ).
cnf(c_9475,plain,
cong(sK3,A,sK3,A),
inference(resolve,[status(thm)],[c_9412,c_8681]) ).
cnf(c_17936,plain,
( perp(A,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_8649,c_341]) ).
cnf(c_9659,plain,
perp(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_9475,c_17936]) ).
cnf(c_17937,plain,
( perp(A,sK3,sK3,B)
| ~ cong(sK3,B,sK3,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_8651,c_247]) ).
cnf(c_17938,plain,
( perp(B,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_9475,c_17937]) ).
cnf(c_9694,plain,
perp(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_9475,c_17938]) ).
cnf(c_17939,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_8651,c_154]) ).
cnf(c_9702,plain,
( eqangle(sK3,B,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_9694,c_17939]) ).
cnf(c_17940,plain,
( perp(A,sK4,sK4,A)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_9202,c_341]) ).
cnf(c_10106,plain,
perp(A,sK4,sK4,A),
inference(resolve,[status(thm)],[c_9473,c_17940]) ).
cnf(c_17941,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_9343,c_248]) ).
cnf(c_10325,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_9343,c_17941]) ).
cnf(c_10399,plain,
perp(sK2,A,A,sK2),
inference(resolve,[status(thm)],[c_9344,c_291]) ).
cnf(c_10642,plain,
( perp(sK3,A,A,B)
| ~ cong(A,B,sK3,B)
| ~ cong(A,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_9394,c_247]) ).
cnf(c_10653,plain,
eqangle(A,B,A,sK3,sK3,B,sK3,sK3),
inference(resolve,[status(thm)],[c_9395,c_259]) ).
cnf(c_11013,plain,
perp(sK3,A,A,sK3),
inference(resolve,[status(thm)],[c_9659,c_291]) ).
cnf(c_11015,plain,
( cong(B,A,sK3,A)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_9659,c_251]) ).
cnf(c_11026,plain,
eqangle(sK3,A,sK3,sK3,B,sK3,B,sK3),
inference(resolve,[status(thm)],[c_11013,c_9702]) ).
cnf(c_11282,plain,
perp(sK4,A,A,sK4),
inference(resolve,[status(thm)],[c_10106,c_291]) ).
cnf(c_11356,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_10325,c_291]) ).
cnf(c_17942,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_10325,c_290]) ).
cnf(c_11357,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_11356,c_17942]) ).
cnf(c_11377,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_11357,c_260]) ).
cnf(c_11395,plain,
perp(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_10399,c_292]) ).
cnf(c_11656,plain,
perp(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_11282,c_292]) ).
cnf(c_11692,plain,
( cong(sK2,sK2,sK2,A)
| ~ midp(A,sK2,A) ),
inference(resolve,[status(thm)],[c_11395,c_249]) ).
cnf(c_11844,plain,
( cong(sK4,sK4,sK4,A)
| ~ midp(A,sK4,A) ),
inference(resolve,[status(thm)],[c_11656,c_249]) ).
cnf(c_11891,plain,
midp(sK2,A,A),
inference(resolve,[status(thm)],[c_6809,c_8066]) ).
cnf(c_11896,plain,
midp(A,sK2,A),
inference(resolve,[status(thm)],[c_7183,c_11891]) ).
cnf(c_11897,plain,
cong(sK2,sK2,sK2,A),
inference(resolve,[status(thm)],[c_11896,c_11692]) ).
cnf(c_17943,plain,
( ~ cong(sK2,sK2,sK2,A)
| midp(A,sK4,A) ),
inference(resolve,[status(thm)],[c_11897,c_7193]) ).
cnf(c_11916,plain,
midp(A,sK4,A),
inference(resolve,[status(thm)],[c_11897,c_17943]) ).
cnf(c_11918,plain,
cong(sK4,sK4,sK4,A),
inference(resolve,[status(thm)],[c_11916,c_11844]) ).
cnf(c_11940,plain,
midp(sK2,A,sK2),
inference(resolve,[status(thm)],[c_11918,c_8032]) ).
cnf(c_12077,plain,
midp(A,B,A),
inference(resolve,[status(thm)],[c_11940,c_7183]) ).
cnf(c_12302,plain,
midp(A,B,B),
inference(resolve,[status(thm)],[c_12077,c_6809]) ).
cnf(c_12305,plain,
midp(A,A,B),
inference(resolve,[status(thm)],[c_12077,c_288]) ).
cnf(c_12333,plain,
cong(A,B,sK3,B),
inference(resolve,[status(thm)],[c_12302,c_11015]) ).
cnf(c_17944,plain,
( perp(sK3,A,A,B)
| ~ cong(A,B,sK3,B) ),
inference(resolve,[status(thm)],[c_12333,c_10642]) ).
cnf(c_12383,plain,
perp(sK3,A,A,B),
inference(resolve,[status(thm)],[c_12333,c_17944]) ).
cnf(c_17945,plain,
( cong(sK3,A,sK3,B)
| ~ midp(A,A,B) ),
inference(resolve,[status(thm)],[c_12383,c_249]) ).
cnf(c_13865,plain,
cong(sK3,A,sK3,B),
inference(resolve,[status(thm)],[c_12305,c_17945]) ).
cnf(c_14337,plain,
eqangle(sK3,A,A,B,A,B,sK3,B),
inference(resolve,[status(thm)],[c_13865,c_253]) ).
cnf(c_15856,plain,
eqangle(A,B,sK3,B,A,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_10653,c_279]) ).
cnf(c_15913,plain,
eqangle(A,sK3,sK3,sK3,B,sK3,B,sK3),
inference(resolve,[status(thm)],[c_11026,c_282]) ).
cnf(c_15959,plain,
eqangle(A,B,C,D,A,B,E,F),
inference(resolve,[status(thm)],[c_11377,c_281]) ).
cnf(c_16167,plain,
( eqangle(sK3,A,A,B,C,D,E,F)
| ~ eqangle(A,B,sK3,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_14337,c_278]) ).
cnf(c_17763,plain,
( eqangle(A,F,sK3,F,B,C,D,E)
| ~ eqangle(A,sK3,sK3,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_15856,c_278]) ).
cnf(c_17807,plain,
( eqangle(F,sK3,sK3,sK3,B,C,D,E)
| ~ eqangle(A,sK3,A,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_15913,c_278]) ).
cnf(c_17851,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_15959,c_279]) ).
cnf(c_17856,plain,
eqangle(A,sK3,sK3,sK3,B,C,D,E),
inference(resolve,[status(thm)],[c_17851,c_17807]) ).
cnf(c_17891,plain,
eqangle(A,B,sK3,B,C,D,E,F),
inference(resolve,[status(thm)],[c_17856,c_17763]) ).
cnf(c_17925,plain,
eqangle(sK3,A,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_17891,c_16167]) ).
cnf(c_17926,plain,
$false,
inference(resolve,[status(thm)],[c_17925,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO562+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 13:43:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 290314 was started by sandbox on n003,
% 0.09/0.36 % Fri Sep 25 13:43:38 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 32.56/4.55
% 32.56/4.55 % given #500 (T,wt=9): 1048 coll(c5,c6,c9). [resolve(1023,a,298,a)].
% 32.56/4.55
% 32.56/4.55 % given #1000 (A,wt=33): 694 perp(f17(f12(c1,c2,c3,c4),c4,c1,c2,c4),f12(c1,c2,c3,c4),c2,c4). [resolve(553,a,374,a)].
% 32.56/4.55
% 32.56/4.55 % given #1500 (T,wt=9): 3755 coll(c4,c3,c1). [resolve(3745,a,297,a)].
% 32.56/4.55
% 32.56/4.55 % given #2000 (A,wt=15): 1265 -para(c5,c1,A,B) | para(c1,c5,A,B). [resolve(1209,a,293,a)].
% 32.56/4.55
% 32.56/4.55 % given #2500 (T,wt=13): 3124 -coll(c1,c5,A) | coll(c3,A,c1). [resolve(2803,a,296,a)].
% 32.56/4.55
% 32.56/4.55 % given #3000 (A,wt=33): 1763 perp(f17(f12(c1,c5,c10,c4),c4,c1,c1,c9),f12(c1,c5,c10,c4),c1,c9). [resolve(1671,a,375,a)].
% 32.56/4.55
% 32.56/4.55 % given #3500 (T,wt=10): 9659 perp(A,c1,c1,A). [resolve(8649,a,341,b),unit_del(a,9475)].
% 32.56/4.55
% 32.56/4.55 % given #4000 (A,wt=28): 2448 coll(f17(f12(c1,c5,c10,c4),c4,c1,c6,c9),c6,c9). [resolve(2119,a,378,a)].
% 32.56/4.55
% 32.56/4.55 % given #4500 (T,wt=14): 14593 eqratio(A,B,B,C,c5,c10,c10,c4). [back_unit_del(14472),unit_del(a,14522)].
% 32.56/4.55
% 32.56/4.55 % given #5000 (A,wt=33): 3971 perp(f17(f12(c1,c2,c3,c4),c4,c1,c5,c3),f12(c1,c2,c3,c4),c5,c3). [resolve(3950,a,374,a)].
% 32.56/4.55
% 32.56/4.55 % SZS status Theorem for theBenchmark
% 32.56/4.55
% 32.56/4.55 % Proof 1 at 3.28 (+ 0.83) seconds.
% 32.56/4.55 % Length of proof is 246.
% 32.56/4.55 % Level of proof is 32.
% 32.56/4.55 % Maximum clause weight is 38.000.
% 32.56/4.55 % Given clauses 5315.
% 32.56/4.55
% 32.56/4.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------