%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO570+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 : n008.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 16.00s 2.49s
% Output : CNFRefutation 16.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 38
% Syntax : Number of formulae : 304 ( 138 unt; 0 def)
% Number of atoms : 589 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 479 ( 194 ~; 190 |; 56 &)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 745 ( 134 sgn 211 !; 13 ?)
% 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(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(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(exemplo6GDDFULL214032,conjecture,
! [B,C,R,O,S,A,M,N,NWPNT1] :
( ( coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) )
=> eqangle(B,A,A,M,N,A,A,C) ),
file('theBenchmark.p',exemplo6GDDFULL214032) ).
fof(exemplo6GDDFULL214032_neg,negated_conjecture,
~ ! [B,C,R,O,S,A,M,N,NWPNT1] :
( ( coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) )
=> eqangle(B,A,A,M,N,A,A,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214032]) ).
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,
? [B,C,R,O,S,A,M,N,NWPNT1] :
( ~ eqangle(B,A,A,M,N,A,A,C)
& coll(N,B,C)
& perp(N,A,B,C)
& coll(M,R,S)
& perp(M,A,R,S)
& coll(A,C,S)
& coll(A,B,R)
& circle(O,B,S,NWPNT1)
& circle(O,B,C,R) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214032_neg]) ).
fof(sk_exemplo6GDDFULL214032_neg,plain,
( ~ eqangle(sK3,sK6,sK6,sK7,sK8,sK6,sK6,sK4)
& coll(sK8,sK3,sK4)
& perp(sK8,sK6,sK3,sK4)
& coll(sK7,sK5,sK9)
& perp(sK7,sK6,sK5,sK9)
& coll(sK6,sK4,sK9)
& coll(sK6,sK3,sK5)
& circle(sK2,sK3,sK9,sK10)
& circle(sK2,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK9,sK10,sK6,sK7,sK8]),skolemize(B,sK3),skolemize(C,sK4),skolemize(R,sK5),skolemize(O,sK2),skolemize(S,sK9),skolemize(A,sK6),skolemize(M,sK7),skolemize(N,sK8),skolemize(NWPNT1,sK10)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214032_neg]) ).
cnf(c_130,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_109,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(sK3,sK6,sK6,sK7,sK8,sK6,sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214032_neg]) ).
cnf(c_179,negated_conjecture,
perp(sK8,sK6,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214032_neg]) ).
cnf(c_181,negated_conjecture,
perp(sK7,sK6,sK5,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214032_neg]) ).
cnf(c_183,negated_conjecture,
coll(sK6,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214032_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_235,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
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_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_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_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(sK7,sK6,A,B)
| ~ perp(sK5,sK9,A,B) ),
inference(resolve,[status(thm)],[c_274,c_181]) ).
cnf(c_411,plain,
( para(sK8,sK6,A,B)
| ~ perp(sK3,sK4,A,B) ),
inference(resolve,[status(thm)],[c_274,c_179]) ).
cnf(c_416,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_274,c_130]) ).
cnf(c_418,plain,
perp(sK5,sK9,sK7,sK6),
inference(resolve,[status(thm)],[c_275,c_181]) ).
cnf(c_419,plain,
perp(sK3,sK4,sK8,sK6),
inference(resolve,[status(thm)],[c_275,c_179]) ).
cnf(c_420,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_275,c_130]) ).
cnf(c_442,plain,
coll(sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_336,c_183]) ).
cnf(c_478,plain,
coll(sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_442,c_336]) ).
cnf(c_546,plain,
coll(sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_478,c_282]) ).
cnf(c_630,plain,
coll(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_546,c_336]) ).
cnf(c_724,plain,
perp(sK5,sK9,sK6,sK7),
inference(resolve,[status(thm)],[c_418,c_276]) ).
cnf(c_738,plain,
perp(sK3,sK4,sK6,sK8),
inference(resolve,[status(thm)],[c_419,c_276]) ).
cnf(c_916,plain,
para(sK7,sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_410,c_724]) ).
cnf(c_917,plain,
para(sK7,sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_410,c_418]) ).
cnf(c_918,plain,
para(sK8,sK6,sK6,sK8),
inference(resolve,[status(thm)],[c_411,c_738]) ).
cnf(c_924,plain,
para(sK6,sK7,sK7,sK6),
inference(resolve,[status(thm)],[c_916,c_278]) ).
cnf(c_927,plain,
eqangle(sK7,sK6,A,B,sK6,sK7,A,B),
inference(resolve,[status(thm)],[c_916,c_244]) ).
cnf(c_929,plain,
( eqratio(A,sK7,sK7,sK6,A,sK6,sK6,sK7)
| ~ coll(A,sK6,sK7)
| ~ coll(A,sK7,sK6) ),
inference(resolve,[status(thm)],[c_916,c_223]) ).
cnf(c_939,plain,
eqangle(sK7,sK6,A,B,sK7,sK6,A,B),
inference(resolve,[status(thm)],[c_917,c_244]) ).
cnf(c_942,plain,
coll(sK7,sK6,sK6),
inference(resolve,[status(thm)],[c_917,c_222]) ).
cnf(c_949,plain,
coll(sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_942,c_336]) ).
cnf(c_957,plain,
coll(sK7,sK7,sK6),
inference(resolve,[status(thm)],[c_949,c_336]) ).
cnf(c_962,plain,
coll(sK7,sK6,sK7),
inference(resolve,[status(thm)],[c_957,c_282]) ).
cnf(c_976,plain,
para(sK6,sK8,sK8,sK6),
inference(resolve,[status(thm)],[c_918,c_278]) ).
cnf(c_1028,plain,
para(sK6,sK7,sK6,sK7),
inference(resolve,[status(thm)],[c_924,c_279]) ).
cnf(c_1057,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_420,c_416]) ).
cnf(c_1120,plain,
para(sK6,sK8,sK6,sK8),
inference(resolve,[status(thm)],[c_976,c_279]) ).
cnf(c_1161,plain,
( midp(A,sK7,sK7)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_1028,c_322]) ).
cnf(c_1164,plain,
eqangle(sK6,sK7,A,B,sK6,sK7,A,B),
inference(resolve,[status(thm)],[c_1028,c_244]) ).
cnf(c_1217,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1057,c_279]) ).
cnf(c_1218,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1057,c_244]) ).
cnf(c_1268,plain,
eqangle(sK6,sK8,A,B,sK6,sK8,A,B),
inference(resolve,[status(thm)],[c_1120,c_244]) ).
cnf(c_1308,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_1217,c_278]) ).
cnf(c_1324,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1308,c_279]) ).
cnf(c_1339,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_1324,c_244]) ).
cnf(c_2978,plain,
eqangle(A,B,sK7,sK6,A,B,sK6,sK7),
inference(resolve,[status(thm)],[c_927,c_265]) ).
cnf(c_2979,plain,
eqangle(sK7,sK6,sK6,sK7,A,B,A,B),
inference(resolve,[status(thm)],[c_927,c_263]) ).
cnf(c_20129,plain,
( eqratio(sK7,sK7,sK7,sK6,sK7,sK6,sK6,sK7)
| ~ coll(sK7,sK6,sK7) ),
inference(resolve,[status(thm)],[c_929,c_957]) ).
cnf(c_2991,plain,
eqratio(sK7,sK7,sK7,sK6,sK7,sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_962,c_20129]) ).
cnf(c_20130,plain,
( ~ cong(sK7,sK7,sK7,sK6)
| midp(sK6,sK6,sK6)
| ~ coll(sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_939,c_298]) ).
cnf(c_3056,plain,
( ~ cong(sK7,sK7,sK7,sK6)
| midp(sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_630,c_20130]) ).
cnf(c_3057,plain,
eqangle(A,B,sK7,sK6,A,B,sK7,sK6),
inference(resolve,[status(thm)],[c_939,c_265]) ).
cnf(c_3059,plain,
( cyclic(sK6,A,sK7,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_939,c_241]) ).
cnf(c_3060,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,sK7)
| ~ cyclic(sK6,A,sK7,A)
| ~ cyclic(sK6,A,sK7,sK6) ),
inference(resolve,[status(thm)],[c_939,c_240]) ).
cnf(c_3835,plain,
( cyclic(sK7,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1164,c_241]) ).
cnf(c_3836,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK6,sK6)
| ~ cyclic(sK7,A,sK6,A)
| ~ cyclic(sK7,A,sK6,sK7) ),
inference(resolve,[status(thm)],[c_1164,c_240]) ).
cnf(c_3843,plain,
( ~ cong(sK6,sK6,sK6,A)
| ~ cong(sK6,sK6,sK6,sK7)
| midp(A,sK7,A)
| ~ coll(A,sK7,A) ),
inference(resolve,[status(thm)],[c_1164,c_173]) ).
cnf(c_4096,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1218,c_241]) ).
cnf(c_4097,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_1218,c_240]) ).
cnf(c_4327,plain,
( cyclic(sK8,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1268,c_241]) ).
cnf(c_4388,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1339,c_241]) ).
cnf(c_4389,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_1339,c_240]) ).
cnf(c_4474,plain,
eqangle(A,B,A,B,sK7,sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_2978,c_263]) ).
cnf(c_4478,plain,
( eqangle(sK7,sK6,sK6,sK7,C,D,E,F)
| ~ eqangle(A,B,A,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_2979,c_262]) ).
cnf(c_4519,plain,
( cong(sK7,sK7,sK7,sK6)
| ~ cong(sK7,sK6,sK6,sK7) ),
inference(resolve,[status(thm)],[c_2991,c_214]) ).
cnf(c_4558,plain,
( cong(sK7,sK6,sK7,sK6)
| ~ cyclic(sK7,sK6,sK7,sK6)
| ~ cyclic(sK7,sK6,sK7,sK7) ),
inference(resolve,[status(thm)],[c_3057,c_329]) ).
cnf(c_4561,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3057,c_245]) ).
cnf(c_20131,plain,
( cyclic(A,sK6,sK7,sK7)
| ~ coll(sK7,sK7,sK6) ),
inference(resolve,[status(thm)],[c_3057,c_241]) ).
cnf(c_4563,plain,
cyclic(A,sK6,sK7,sK7),
inference(resolve,[status(thm)],[c_957,c_20131]) ).
cnf(c_4569,plain,
( ~ cong(sK7,sK7,sK7,sK6)
| ~ cong(sK7,sK7,sK7,A)
| midp(sK6,A,sK6)
| ~ coll(sK6,A,sK6) ),
inference(resolve,[status(thm)],[c_3057,c_173]) ).
cnf(c_4574,plain,
( cong(sK7,sK6,sK7,sK6)
| ~ cyclic(sK7,sK6,sK7,sK6) ),
inference(resolve,[status(thm)],[c_4563,c_4558]) ).
cnf(c_4576,plain,
( midp(A,C,C)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_4561,c_322]) ).
cnf(c_4584,plain,
( midp(C,B,C)
| ~ coll(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_4561,c_238]) ).
cnf(c_4586,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4561,c_222]) ).
cnf(c_4786,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4586,c_336]) ).
cnf(c_4787,plain,
coll(A,B,A),
inference(resolve,[status(thm)],[c_4586,c_281]) ).
cnf(c_4794,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_4786,c_4388]) ).
cnf(c_4796,plain,
cyclic(sK8,A,sK6,sK6),
inference(resolve,[status(thm)],[c_4786,c_4327]) ).
cnf(c_4797,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_4786,c_4096]) ).
cnf(c_4799,plain,
cyclic(sK7,A,sK6,sK6),
inference(resolve,[status(thm)],[c_4786,c_3835]) ).
cnf(c_4811,plain,
cyclic(sK6,A,sK7,sK7),
inference(resolve,[status(thm)],[c_4786,c_3059]) ).
cnf(c_4925,plain,
( midp(C,B,C)
| ~ midp(A,B,A) ),
inference(resolve,[status(thm)],[c_4787,c_4584]) ).
cnf(c_4926,plain,
( ~ cong(sK7,sK7,sK7,sK6)
| ~ cong(sK7,sK7,sK7,A)
| midp(sK6,A,sK6) ),
inference(resolve,[status(thm)],[c_4787,c_4569]) ).
cnf(c_4932,plain,
( ~ cong(sK6,sK6,sK6,A)
| ~ cong(sK6,sK6,sK6,sK7)
| midp(A,sK7,A) ),
inference(resolve,[status(thm)],[c_4787,c_3843]) ).
cnf(c_4949,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_4794,c_4389]) ).
cnf(c_4958,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_4797,c_4097]) ).
cnf(c_4964,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK6,A)
| ~ cyclic(sK7,A,sK6,sK7) ),
inference(resolve,[status(thm)],[c_4799,c_3836]) ).
cnf(c_4976,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,A)
| ~ cyclic(sK6,A,sK7,sK6) ),
inference(resolve,[status(thm)],[c_4811,c_3060]) ).
cnf(c_5451,plain,
cyclic(A,sK7,sK6,sK7),
inference(resolve,[status(thm)],[c_4563,c_269]) ).
cnf(c_5469,plain,
cyclic(A,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_4794,c_331]) ).
cnf(c_5471,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_4794,c_269]) ).
cnf(c_5505,plain,
cyclic(sK8,sK6,A,sK6),
inference(resolve,[status(thm)],[c_4796,c_269]) ).
cnf(c_5520,plain,
cyclic(A,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_4797,c_331]) ).
cnf(c_5522,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_4797,c_269]) ).
cnf(c_5525,plain,
( cyclic(A,sK3,sK3,B)
| ~ cyclic(sK2,A,sK3,B) ),
inference(resolve,[status(thm)],[c_4797,c_267]) ).
cnf(c_5564,plain,
cyclic(sK7,sK6,A,sK6),
inference(resolve,[status(thm)],[c_4799,c_269]) ).
cnf(c_5579,plain,
cong(sK7,sK6,sK7,sK6),
inference(resolve,[status(thm)],[c_5564,c_4574]) ).
cnf(c_5632,plain,
cyclic(sK6,sK7,A,sK7),
inference(resolve,[status(thm)],[c_4811,c_269]) ).
cnf(c_5681,plain,
cyclic(sK7,A,sK6,sK7),
inference(resolve,[status(thm)],[c_5451,c_268]) ).
cnf(c_5697,plain,
( cong(sK7,A,sK7,A)
| ~ cyclic(sK7,A,sK6,A) ),
inference(resolve,[status(thm)],[c_5681,c_4964]) ).
cnf(c_5748,plain,
cyclic(sK2,A,sK2,sK2),
inference(resolve,[status(thm)],[c_5469,c_268]) ).
cnf(c_5761,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_5471,c_270]) ).
cnf(c_5762,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_5471,c_268]) ).
cnf(c_5873,plain,
cyclic(sK8,sK6,sK6,A),
inference(resolve,[status(thm)],[c_5505,c_270]) ).
cnf(c_5916,plain,
cyclic(sK3,A,sK3,sK3),
inference(resolve,[status(thm)],[c_5520,c_268]) ).
cnf(c_5929,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_5522,c_270]) ).
cnf(c_5930,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_5522,c_268]) ).
cnf(c_6016,plain,
cyclic(sK6,sK7,A,sK6),
inference(resolve,[status(thm)],[c_5564,c_268]) ).
cnf(c_6078,plain,
cong(sK7,sK6,sK6,sK7),
inference(resolve,[status(thm)],[c_5579,c_261]) ).
cnf(c_6094,plain,
cong(sK7,sK7,sK7,sK6),
inference(resolve,[status(thm)],[c_6078,c_4519]) ).
cnf(c_6096,plain,
( ~ cong(sK7,sK7,sK7,A)
| midp(sK6,A,sK6) ),
inference(resolve,[status(thm)],[c_6094,c_4926]) ).
cnf(c_6097,plain,
midp(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_6094,c_3056]) ).
cnf(c_6099,plain,
midp(sK6,sK7,sK7),
inference(resolve,[status(thm)],[c_6097,c_1161]) ).
cnf(c_6316,plain,
cyclic(sK6,sK7,sK7,A),
inference(resolve,[status(thm)],[c_5632,c_270]) ).
cnf(c_6452,plain,
cyclic(sK2,sK2,A,sK2),
inference(resolve,[status(thm)],[c_5748,c_269]) ).
cnf(c_6465,plain,
cyclic(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_5761,c_331]) ).
cnf(c_6466,plain,
cyclic(sK2,sK3,sK2,A),
inference(resolve,[status(thm)],[c_5761,c_268]) ).
cnf(c_20132,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_5761,c_267]) ).
cnf(c_6467,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_5761,c_20132]) ).
cnf(c_6490,plain,
cyclic(sK2,A,sK3,sK2),
inference(resolve,[status(thm)],[c_5762,c_269]) ).
cnf(c_6492,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_5762,c_267]) ).
cnf(c_6506,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A) ),
inference(resolve,[status(thm)],[c_6490,c_4958]) ).
cnf(c_6920,plain,
cyclic(sK6,sK6,A,A),
inference(resolve,[status(thm)],[c_5873,c_331]) ).
cnf(c_20133,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK8,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_5873,c_267]) ).
cnf(c_6922,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_5873,c_20133]) ).
cnf(c_7112,plain,
cyclic(sK3,sK3,A,sK3),
inference(resolve,[status(thm)],[c_5916,c_269]) ).
cnf(c_7125,plain,
cyclic(sK3,sK3,A,A),
inference(resolve,[status(thm)],[c_5929,c_331]) ).
cnf(c_20134,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_5929,c_267]) ).
cnf(c_7127,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_5929,c_20134]) ).
cnf(c_7141,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_5930,c_269]) ).
cnf(c_7143,plain,
( cyclic(sK2,A,sK3,B)
| ~ cyclic(sK3,sK2,A,B) ),
inference(resolve,[status(thm)],[c_5930,c_267]) ).
cnf(c_7157,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7141,c_4949]) ).
cnf(c_7451,plain,
cyclic(sK6,A,sK7,sK6),
inference(resolve,[status(thm)],[c_6016,c_269]) ).
cnf(c_7453,plain,
( cyclic(sK7,A,sK6,B)
| ~ cyclic(sK6,sK7,A,B) ),
inference(resolve,[status(thm)],[c_6016,c_267]) ).
cnf(c_7467,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK7,A) ),
inference(resolve,[status(thm)],[c_7451,c_4976]) ).
cnf(c_7848,plain,
cyclic(sK7,sK7,A,A),
inference(resolve,[status(thm)],[c_6316,c_331]) ).
cnf(c_20135,plain,
( cyclic(sK2,A,sK2,B)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6452,c_267]) ).
cnf(c_7950,plain,
cyclic(sK2,A,sK2,B),
inference(resolve,[status(thm)],[c_6467,c_20135]) ).
cnf(c_20136,plain,
( cyclic(sK2,A,B,A)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6465,c_267]) ).
cnf(c_7966,plain,
cyclic(sK2,A,B,A),
inference(resolve,[status(thm)],[c_6467,c_20136]) ).
cnf(c_7979,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_7966,c_6506]) ).
cnf(c_20137,plain,
( cyclic(sK3,sK2,A,B)
| ~ cyclic(sK2,sK3,sK2,A) ),
inference(resolve,[status(thm)],[c_6466,c_267]) ).
cnf(c_8002,plain,
cyclic(sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_7950,c_20137]) ).
cnf(c_8015,plain,
cyclic(sK2,A,sK3,B),
inference(resolve,[status(thm)],[c_8002,c_7143]) ).
cnf(c_8017,plain,
cyclic(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_8015,c_5525]) ).
cnf(c_20138,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_6467,c_267]) ).
cnf(c_8021,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_6467,c_20138]) ).
cnf(c_8033,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_8021,c_6492]) ).
cnf(c_8061,plain,
cong(sK3,A,sK3,A),
inference(resolve,[status(thm)],[c_8033,c_7157]) ).
cnf(c_8351,plain,
( perp(A,sK6,sK6,A)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_6920,c_325]) ).
cnf(c_20139,plain,
( cyclic(sK6,A,B,A)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_6920,c_267]) ).
cnf(c_8352,plain,
cyclic(sK6,A,B,A),
inference(resolve,[status(thm)],[c_6922,c_20139]) ).
cnf(c_8365,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_8352,c_7467]) ).
cnf(c_8366,plain,
perp(A,sK6,sK6,A),
inference(resolve,[status(thm)],[c_8365,c_8351]) ).
cnf(c_20140,plain,
( cyclic(sK6,A,B,C)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_6922,c_267]) ).
cnf(c_8434,plain,
cyclic(sK6,A,B,C),
inference(resolve,[status(thm)],[c_6922,c_20140]) ).
cnf(c_8446,plain,
cyclic(sK7,A,sK6,B),
inference(resolve,[status(thm)],[c_8434,c_7453]) ).
cnf(c_8509,plain,
cong(sK7,A,sK7,A),
inference(resolve,[status(thm)],[c_8446,c_5697]) ).
cnf(c_20141,plain,
( perp(A,sK3,sK3,sK3)
| ~ cong(sK3,sK3,sK3,sK3)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7112,c_231]) ).
cnf(c_20142,plain,
( perp(A,sK3,sK3,sK3)
| ~ cong(sK3,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_8061,c_20141]) ).
cnf(c_8664,plain,
perp(A,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_8061,c_20142]) ).
cnf(c_20143,plain,
( perp(A,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7125,c_325]) ).
cnf(c_8689,plain,
perp(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_8061,c_20143]) ).
cnf(c_20144,plain,
( perp(A,sK3,sK3,B)
| ~ cong(sK3,B,sK3,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_7127,c_231]) ).
cnf(c_20145,plain,
( perp(B,sK3,sK3,A)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_8061,c_20144]) ).
cnf(c_8737,plain,
perp(A,sK3,sK3,B),
inference(resolve,[status(thm)],[c_8061,c_20145]) ).
cnf(c_20146,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_7127,c_139]) ).
cnf(c_8745,plain,
( eqangle(sK3,B,sK3,sK3,A,sK3,A,sK3)
| ~ perp(sK3,A,A,sK3) ),
inference(resolve,[status(thm)],[c_8737,c_20146]) ).
cnf(c_20147,plain,
( perp(A,sK7,sK7,A)
| ~ cong(sK7,A,sK7,A) ),
inference(resolve,[status(thm)],[c_7848,c_325]) ).
cnf(c_9480,plain,
perp(A,sK7,sK7,A),
inference(resolve,[status(thm)],[c_8509,c_20147]) ).
cnf(c_20148,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_7979,c_232]) ).
cnf(c_9688,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_7979,c_20148]) ).
cnf(c_9900,plain,
( eqangle(A,B,sK3,B,sK3,B,sK3,sK3)
| ~ para(A,sK3,sK3,B) ),
inference(resolve,[status(thm)],[c_8017,c_234]) ).
cnf(c_9901,plain,
( perp(sK3,A,A,B)
| ~ cong(A,B,sK3,B)
| ~ cong(A,sK3,sK3,sK3) ),
inference(resolve,[status(thm)],[c_8017,c_231]) ).
cnf(c_20149,plain,
( perp(sK3,sK3,A,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_8061,c_232]) ).
cnf(c_10032,plain,
perp(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_8061,c_20149]) ).
cnf(c_10481,plain,
perp(sK6,A,A,sK6),
inference(resolve,[status(thm)],[c_8366,c_275]) ).
cnf(c_20150,plain,
( para(C,sK3,A,B)
| ~ perp(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_8664,c_274]) ).
cnf(c_10875,plain,
para(A,sK3,B,C),
inference(resolve,[status(thm)],[c_10032,c_20150]) ).
cnf(c_10891,plain,
eqangle(A,B,sK3,B,sK3,B,sK3,sK3),
inference(resolve,[status(thm)],[c_10875,c_9900]) ).
cnf(c_10906,plain,
perp(sK3,A,A,sK3),
inference(resolve,[status(thm)],[c_8689,c_275]) ).
cnf(c_10908,plain,
( cong(B,A,sK3,A)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_8689,c_235]) ).
cnf(c_10919,plain,
eqangle(sK3,A,sK3,sK3,B,sK3,B,sK3),
inference(resolve,[status(thm)],[c_10906,c_8745]) ).
cnf(c_11448,plain,
perp(sK7,A,A,sK7),
inference(resolve,[status(thm)],[c_9480,c_275]) ).
cnf(c_11526,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_9688,c_275]) ).
cnf(c_20151,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_9688,c_274]) ).
cnf(c_11527,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_11526,c_20151]) ).
cnf(c_11543,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_11527,c_244]) ).
cnf(c_11737,plain,
perp(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_10481,c_276]) ).
cnf(c_12211,plain,
perp(sK7,A,sK7,A),
inference(resolve,[status(thm)],[c_11448,c_276]) ).
cnf(c_12442,plain,
( cong(sK6,sK6,sK6,A)
| ~ midp(A,sK6,A) ),
inference(resolve,[status(thm)],[c_11737,c_233]) ).
cnf(c_12772,plain,
( cong(sK7,sK7,sK7,A)
| ~ midp(A,sK7,A) ),
inference(resolve,[status(thm)],[c_12211,c_233]) ).
cnf(c_12968,plain,
midp(sK6,A,A),
inference(resolve,[status(thm)],[c_4576,c_6099]) ).
cnf(c_12973,plain,
midp(A,sK6,A),
inference(resolve,[status(thm)],[c_4925,c_12968]) ).
cnf(c_12974,plain,
cong(sK6,sK6,sK6,A),
inference(resolve,[status(thm)],[c_12973,c_12442]) ).
cnf(c_20152,plain,
( ~ cong(sK6,sK6,sK6,A)
| midp(A,sK7,A) ),
inference(resolve,[status(thm)],[c_12974,c_4932]) ).
cnf(c_12990,plain,
midp(A,sK7,A),
inference(resolve,[status(thm)],[c_12974,c_20152]) ).
cnf(c_12992,plain,
cong(sK7,sK7,sK7,A),
inference(resolve,[status(thm)],[c_12990,c_12772]) ).
cnf(c_13011,plain,
midp(sK6,A,sK6),
inference(resolve,[status(thm)],[c_12992,c_6096]) ).
cnf(c_13131,plain,
midp(A,B,A),
inference(resolve,[status(thm)],[c_13011,c_4925]) ).
cnf(c_13543,plain,
midp(A,B,B),
inference(resolve,[status(thm)],[c_13131,c_4576]) ).
cnf(c_13549,plain,
midp(A,A,B),
inference(resolve,[status(thm)],[c_13131,c_272]) ).
cnf(c_13604,plain,
cong(A,B,sK3,B),
inference(resolve,[status(thm)],[c_13543,c_10908]) ).
cnf(c_20153,plain,
( perp(sK3,A,A,B)
| ~ cong(A,B,sK3,B) ),
inference(resolve,[status(thm)],[c_13604,c_9901]) ).
cnf(c_13675,plain,
perp(sK3,A,A,B),
inference(resolve,[status(thm)],[c_13604,c_20153]) ).
cnf(c_20154,plain,
( cong(sK3,A,sK3,B)
| ~ midp(A,A,B) ),
inference(resolve,[status(thm)],[c_13675,c_233]) ).
cnf(c_15483,plain,
cong(sK3,A,sK3,B),
inference(resolve,[status(thm)],[c_13549,c_20154]) ).
cnf(c_16174,plain,
eqangle(sK3,A,A,B,A,B,sK3,B),
inference(resolve,[status(thm)],[c_15483,c_237]) ).
cnf(c_17612,plain,
( eqangle(E,F,E,F,A,B,C,D)
| ~ eqangle(sK7,sK6,sK6,sK7,A,B,C,D) ),
inference(resolve,[status(thm)],[c_4474,c_262]) ).
cnf(c_19223,plain,
( eqangle(F,A,sK3,A,B,C,D,E)
| ~ eqangle(sK3,A,sK3,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_10891,c_262]) ).
cnf(c_19239,plain,
( eqangle(sK3,F,sK3,sK3,B,C,D,E)
| ~ eqangle(A,sK3,A,sK3,B,C,D,E) ),
inference(resolve,[status(thm)],[c_10919,c_262]) ).
cnf(c_19448,plain,
eqangle(sK7,sK6,sK6,sK7,A,B,C,D),
inference(resolve,[status(thm)],[c_11543,c_4478]) ).
cnf(c_19455,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_19448,c_17612]) ).
cnf(c_19472,plain,
eqangle(sK3,A,sK3,sK3,B,C,D,E),
inference(resolve,[status(thm)],[c_19455,c_19239]) ).
cnf(c_19534,plain,
eqangle(A,B,sK3,B,C,D,E,F),
inference(resolve,[status(thm)],[c_19472,c_19223]) ).
cnf(c_20155,plain,
( eqangle(sK3,A,A,B,C,D,E,F)
| ~ eqangle(A,B,sK3,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_16174,c_262]) ).
cnf(c_20127,plain,
eqangle(sK3,A,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_19534,c_20155]) ).
cnf(c_20128,plain,
$false,
inference(resolve,[status(thm)],[c_20127,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO570+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:42:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1182420 was started by sandbox on n008,
% 0.10/0.36 % Fri Sep 25 13:42:55 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 16.00/2.49
% 16.00/2.49 % given #500 (A,wt=13): 500 -coll(c1,c3,A) | coll(A,c6,c1). [resolve(447,a,280,b)].
% 16.00/2.49
% 16.00/2.49 % given #1000 (T,wt=9): 2762 coll(c4,c7,c6). [resolve(958,a,1853,a)].
% 16.00/2.49
% 16.00/2.49 % given #1500 (A,wt=15): 904 -perp(c2,c1,A,B) | para(c6,c8,A,B). [resolve(850,a,274,a)].
% 16.00/2.49
% 16.00/2.49 % given #2000 (W,wt=13): 2320 -coll(c2,c4,A) | coll(A,c2,c2). [resolve(2189,a,280,b)].
% 16.00/2.49
% 16.00/2.49 % given #2500 (T,wt=9): 4889 coll(A,c1,c6). [back_unit_del(580),unit_del(a,4786)].
% 16.00/2.49
% 16.00/2.49 % given #3000 (W,wt=10): 8516 perp(c7,c7,A,c6). [back_unit_del(6080),unit_del(a,8509)].
% 16.00/2.49
% 16.00/2.49 % given #3500 (T,wt=10): 12366 cong(A,c2,A,c2). [resolve(11602,a,261,a)].
% 16.00/2.49
% 16.00/2.49 % given #4000 (A,wt=20): 3641 coll(f20(c6,c8,c8,c6,c4,c4),c8,c6). [resolve(1119,b,2806,a),unit_del(a,2811)].
% 16.00/2.49
% 16.00/2.49 % given #4500 (T,wt=14): 10903 eqangle(A,c4,c4,c4,c4,c4,c4,c1). [back_unit_del(5781),unit_del(a,10875)].
% 16.00/2.49
% 16.00/2.49 % SZS status Theorem for theBenchmark
% 16.00/2.49
% 16.00/2.49 % Proof 1 at 1.58 (+ 0.49) seconds.
% 16.00/2.49 % Length of proof is 270.
% 16.00/2.49 % Level of proof is 30.
% 16.00/2.49 % Maximum clause weight is 38.000.
% 16.00/2.49 % Given clauses 4786.
% 16.00/2.49
% 16.00/2.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------