%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO635+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 : n002.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 07:18:16 AM UTC 2026
% Result : Theorem 27.25s 3.99s
% Output : CNFRefutation 27.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 35
% Syntax : Number of formulae : 278 ( 153 unt; 0 def)
% Number of atoms : 475 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 320 ( 123 ~; 119 |; 42 &)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 461 ( 21 sgn 188 !; 11 ?)
% 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(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('theBenchmark.p',ruleD13) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(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(ruleD20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('theBenchmark.p',ruleD20) ).
fof(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
fof(ruleD22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('theBenchmark.p',ruleD22) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('theBenchmark.p',ruleD24) ).
fof(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(ruleD52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('theBenchmark.p',ruleD52) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('theBenchmark.p',ruleD67) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('theBenchmark.p',ruleD68) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL8110998,conjecture,
! [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) )
=> para(A,B,G,F) ),
file('theBenchmark.p',exemplo6GDDFULL8110998) ).
fof(exemplo6GDDFULL8110998_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) )
=> para(A,B,G,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110998]) ).
cnf(c_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
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_95,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2] :
( ~ para(A,B,G,F)
& coll(G,C,E)
& circle(D,C,G,NWPNT2)
& eqangle(A,C,C,E,F,C,C,B)
& circle(D,A,F,NWPNT1)
& coll(E,A,B)
& circle(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110998_neg]) ).
fof(sk_exemplo6GDDFULL8110998_neg,plain,
( ~ para(sK2,sK3,sK5,sK7)
& coll(sK5,sK4,sK8)
& circle(sK1,sK4,sK5,sK6)
& eqangle(sK2,sK4,sK4,sK8,sK7,sK4,sK4,sK3)
& circle(sK1,sK2,sK7,sK9)
& coll(sK8,sK2,sK3)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK8,sK7,sK9,sK5,sK6]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(D,sK1),skolemize(E,sK8),skolemize(F,sK7),skolemize(G,sK5),skolemize(NWPNT1,sK9),skolemize(NWPNT2,sK6)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_111,negated_conjecture,
circle(sK1,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_117,negated_conjecture,
perp(sK0(sK4,sK5,sK6,sK1),sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_144,negated_conjecture,
( perp(sK2,sK3,sK3,sK4)
| ~ coll(sK1,sK2,sK4) ),
inference(resolve,[status(thm)],[c_109,c_101]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_192,negated_conjecture,
~ para(sK2,sK3,sK5,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_193,negated_conjecture,
coll(sK5,sK4,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_194,negated_conjecture,
eqangle(sK2,sK4,sK4,sK8,sK7,sK4,sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_195,negated_conjecture,
coll(sK8,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110998_neg]) ).
cnf(c_232,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_233,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_234,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_236,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_243,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_244,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_247,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_250,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_252,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_253,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_256,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_257,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_272,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_273,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_274,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_275,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_276,plain,
( eqangle(E,F,V6,V7,A,B,C,D)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD20]) ).
cnf(c_277,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_279,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_280,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_281,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_282,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_283,plain,
( cyclic(B,C,D,E)
| ~ cong(A,B,A,E)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD13]) ).
cnf(c_284,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_286,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_287,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_288,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_290,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_291,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_292,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_293,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_294,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_334,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_236]) ).
cnf(c_337,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_243]) ).
cnf(c_338,plain,
( perp(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_244]) ).
cnf(c_343,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_344,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_283]) ).
cnf(c_347,plain,
( para(A,B,A,B)
| ~ perp(A,B,A,B) ),
inference(factor,[status(thm)],[c_286]) ).
cnf(c_348,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_292]) ).
cnf(c_357,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_344]) ).
cnf(c_424,plain,
( eqangle(sK2,sK4,sK4,sK8,A,B,C,D)
| ~ eqangle(sK7,sK4,sK4,sK3,A,B,C,D) ),
inference(resolve,[status(thm)],[c_274,c_194]) ).
cnf(c_426,plain,
eqangle(sK2,sK4,sK7,sK4,sK4,sK8,sK4,sK3),
inference(resolve,[status(thm)],[c_275,c_194]) ).
cnf(c_427,plain,
eqangle(sK7,sK4,sK4,sK3,sK2,sK4,sK4,sK8),
inference(resolve,[status(thm)],[c_276,c_194]) ).
cnf(c_433,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_286,c_145]) ).
cnf(c_435,plain,
( para(A,B,sK4,sK1)
| ~ perp(A,B,sK0(sK4,sK5,sK6,sK1),sK4) ),
inference(resolve,[status(thm)],[c_286,c_117]) ).
cnf(c_436,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_287,c_145]) ).
cnf(c_438,plain,
perp(sK4,sK1,sK0(sK4,sK5,sK6,sK1),sK4),
inference(resolve,[status(thm)],[c_287,c_117]) ).
cnf(c_446,plain,
coll(sK2,sK8,sK3),
inference(resolve,[status(thm)],[c_293,c_195]) ).
cnf(c_447,plain,
coll(sK4,sK5,sK8),
inference(resolve,[status(thm)],[c_293,c_193]) ).
cnf(c_448,plain,
coll(sK8,sK3,sK2),
inference(resolve,[status(thm)],[c_294,c_195]) ).
cnf(c_449,plain,
coll(sK5,sK8,sK4),
inference(resolve,[status(thm)],[c_294,c_193]) ).
cnf(c_450,plain,
coll(sK3,sK3,sK8),
inference(resolve,[status(thm)],[c_348,c_195]) ).
cnf(c_451,plain,
coll(sK8,sK8,sK5),
inference(resolve,[status(thm)],[c_348,c_193]) ).
cnf(c_452,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_446,c_348]) ).
cnf(c_453,plain,
coll(sK2,sK3,sK8),
inference(resolve,[status(thm)],[c_446,c_294]) ).
cnf(c_456,plain,
coll(sK8,sK8,sK4),
inference(resolve,[status(thm)],[c_447,c_348]) ).
cnf(c_460,plain,
coll(sK2,sK2,sK8),
inference(resolve,[status(thm)],[c_448,c_348]) ).
cnf(c_466,plain,
( coll(A,sK4,sK5)
| ~ coll(sK5,sK8,A) ),
inference(resolve,[status(thm)],[c_449,c_292]) ).
cnf(c_467,plain,
( coll(sK4,A,sK5)
| ~ coll(sK5,sK8,A) ),
inference(resolve,[status(thm)],[c_449,c_292]) ).
cnf(c_468,plain,
coll(sK8,sK8,sK3),
inference(resolve,[status(thm)],[c_450,c_348]) ).
cnf(c_474,plain,
( coll(A,sK5,sK8)
| ~ coll(sK8,sK8,A) ),
inference(resolve,[status(thm)],[c_451,c_292]) ).
cnf(c_475,plain,
( coll(sK5,A,sK8)
| ~ coll(sK8,sK8,A) ),
inference(resolve,[status(thm)],[c_451,c_292]) ).
cnf(c_477,plain,
coll(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_452,c_294]) ).
cnf(c_480,plain,
coll(sK8,sK8,sK2),
inference(resolve,[status(thm)],[c_453,c_348]) ).
cnf(c_487,plain,
( coll(sK4,A,sK8)
| ~ coll(sK8,sK8,A) ),
inference(resolve,[status(thm)],[c_456,c_292]) ).
cnf(c_493,plain,
( coll(A,sK8,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_460,c_292]) ).
cnf(c_502,plain,
coll(sK8,sK3,sK8),
inference(resolve,[status(thm)],[c_468,c_294]) ).
cnf(c_519,plain,
coll(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_477,c_293]) ).
cnf(c_546,plain,
coll(sK3,sK8,sK8),
inference(resolve,[status(thm)],[c_502,c_293]) ).
cnf(c_594,plain,
coll(sK2,sK5,sK8),
inference(resolve,[status(thm)],[c_474,c_480]) ).
cnf(c_595,plain,
coll(sK3,sK5,sK8),
inference(resolve,[status(thm)],[c_474,c_468]) ).
cnf(c_597,plain,
coll(sK5,sK2,sK8),
inference(resolve,[status(thm)],[c_594,c_293]) ).
cnf(c_601,plain,
coll(sK5,sK3,sK8),
inference(resolve,[status(thm)],[c_595,c_293]) ).
cnf(c_610,plain,
coll(sK5,sK8,sK2),
inference(resolve,[status(thm)],[c_597,c_294]) ).
cnf(c_617,plain,
coll(sK5,sK8,sK3),
inference(resolve,[status(thm)],[c_601,c_294]) ).
cnf(c_633,plain,
coll(sK4,sK2,sK5),
inference(resolve,[status(thm)],[c_610,c_467]) ).
cnf(c_644,plain,
coll(sK4,sK3,sK5),
inference(resolve,[status(thm)],[c_617,c_467]) ).
cnf(c_645,plain,
coll(sK3,sK4,sK5),
inference(resolve,[status(thm)],[c_617,c_466]) ).
cnf(c_662,plain,
coll(sK4,sK5,sK2),
inference(resolve,[status(thm)],[c_633,c_294]) ).
cnf(c_676,plain,
coll(sK4,sK5,sK3),
inference(resolve,[status(thm)],[c_644,c_294]) ).
cnf(c_679,plain,
coll(sK3,sK5,sK4),
inference(resolve,[status(thm)],[c_645,c_294]) ).
cnf(c_693,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_662,c_348]) ).
cnf(c_695,plain,
( coll(A,sK2,sK4)
| ~ coll(sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_662,c_292]) ).
cnf(c_708,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_676,c_348]) ).
cnf(c_712,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_679,c_348]) ).
cnf(c_728,plain,
coll(sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_693,c_294]) ).
cnf(c_747,plain,
coll(sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_708,c_294]) ).
cnf(c_784,plain,
coll(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_747,c_293]) ).
cnf(c_812,plain,
eqangle(sK4,sK8,sK4,sK3,sK2,sK4,sK7,sK4),
inference(resolve,[status(thm)],[c_426,c_276]) ).
cnf(c_813,plain,
( eqangle(A,B,C,D,sK4,sK8,sK4,sK3)
| ~ eqangle(A,B,C,D,sK2,sK4,sK7,sK4) ),
inference(resolve,[status(thm)],[c_426,c_274]) ).
cnf(c_818,plain,
eqangle(sK2,sK4,sK4,sK8,sK2,sK4,sK4,sK8),
inference(resolve,[status(thm)],[c_427,c_424]) ).
cnf(c_837,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_436,c_433]) ).
cnf(c_857,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_837,c_291]) ).
cnf(c_858,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_837,c_256]) ).
cnf(c_859,plain,
( midp(sK1,A,sK1)
| ~ coll(sK1,A,sK1)
| ~ midp(sK2,A,sK2) ),
inference(resolve,[status(thm)],[c_837,c_250]) ).
cnf(c_861,plain,
coll(sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_837,c_234]) ).
cnf(c_868,plain,
coll(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_861,c_348]) ).
cnf(c_869,plain,
coll(sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_861,c_293]) ).
cnf(c_880,plain,
coll(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_868,c_348]) ).
cnf(c_882,plain,
( coll(sK2,A,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_868,c_292]) ).
cnf(c_896,plain,
coll(sK1,sK8,sK2),
inference(resolve,[status(thm)],[c_880,c_493]) ).
cnf(c_923,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_438,c_435]) ).
cnf(c_968,plain,
coll(sK1,sK2,sK8),
inference(resolve,[status(thm)],[c_896,c_294]) ).
cnf(c_1034,plain,
coll(sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_968,c_348]) ).
cnf(c_1123,plain,
coll(sK4,sK1,sK8),
inference(resolve,[status(thm)],[c_1034,c_487]) ).
cnf(c_1125,plain,
coll(sK5,sK1,sK8),
inference(resolve,[status(thm)],[c_1034,c_475]) ).
cnf(c_1165,plain,
coll(sK4,sK8,sK1),
inference(resolve,[status(thm)],[c_1123,c_294]) ).
cnf(c_1177,plain,
coll(sK5,sK8,sK1),
inference(resolve,[status(thm)],[c_1125,c_294]) ).
cnf(c_1225,plain,
coll(sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_1165,c_348]) ).
cnf(c_1240,plain,
coll(sK4,sK1,sK5),
inference(resolve,[status(thm)],[c_1177,c_467]) ).
cnf(c_1311,plain,
coll(sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_1225,c_294]) ).
cnf(c_1328,plain,
coll(sK4,sK5,sK1),
inference(resolve,[status(thm)],[c_1240,c_294]) ).
cnf(c_1375,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_857,c_290]) ).
cnf(c_1392,plain,
( midp(sK1,A,sK1)
| ~ coll(sK1,A,sK1)
| ~ midp(sK4,A,sK4) ),
inference(resolve,[status(thm)],[c_923,c_250]) ).
cnf(c_1404,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_1375,c_291]) ).
cnf(c_1435,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_1404,c_256]) ).
cnf(c_1436,plain,
( midp(sK2,A,sK2)
| ~ coll(sK2,A,sK2)
| ~ midp(sK1,A,sK1) ),
inference(resolve,[status(thm)],[c_1404,c_250]) ).
cnf(c_1472,plain,
coll(sK1,sK2,sK4),
inference(resolve,[status(thm)],[c_695,c_1328]) ).
cnf(c_1473,negated_conjecture,
perp(sK2,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_1472,c_144]) ).
cnf(c_1508,plain,
( cong(sK2,A,sK3,A)
| ~ midp(A,sK2,sK4) ),
inference(resolve,[status(thm)],[c_1473,c_247]) ).
cnf(c_1669,plain,
eqangle(sK4,sK8,sK4,sK3,sK4,sK8,sK4,sK3),
inference(resolve,[status(thm)],[c_813,c_812]) ).
cnf(c_1718,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_818,c_257]) ).
cnf(c_2124,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1718,c_291]) ).
cnf(c_2154,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_2124,c_290]) ).
cnf(c_2169,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_858,c_277]) ).
cnf(c_2170,plain,
eqangle(sK2,sK1,sK2,sK1,A,B,A,B),
inference(resolve,[status(thm)],[c_858,c_275]) ).
cnf(c_2196,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_2154,c_291]) ).
cnf(c_2208,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_2196,c_334]) ).
cnf(c_3429,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1435,c_253]) ).
cnf(c_3430,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,sK1)
| ~ cyclic(sK2,A,sK1,A)
| ~ cyclic(sK2,A,sK1,sK2) ),
inference(resolve,[status(thm)],[c_1435,c_252]) ).
cnf(c_3545,plain,
para(sK4,sK8,sK4,sK8),
inference(resolve,[status(thm)],[c_1669,c_257]) ).
cnf(c_29551,plain,
( cyclic(sK8,sK3,sK4,sK4)
| ~ coll(sK4,sK4,sK3) ),
inference(resolve,[status(thm)],[c_1669,c_253]) ).
cnf(c_3546,plain,
cyclic(sK8,sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_712,c_29551]) ).
cnf(c_29552,plain,
( cong(sK8,sK3,sK8,sK3)
| ~ cyclic(sK8,sK3,sK4,sK4)
| ~ cyclic(sK8,sK3,sK4,sK3)
| ~ cyclic(sK8,sK3,sK4,sK8) ),
inference(resolve,[status(thm)],[c_1669,c_252]) ).
cnf(c_3547,plain,
( cong(sK8,sK3,sK8,sK3)
| ~ cyclic(sK8,sK3,sK4,sK3)
| ~ cyclic(sK8,sK3,sK4,sK8) ),
inference(resolve,[status(thm)],[c_3546,c_29552]) ).
cnf(c_3552,plain,
para(sK4,sK8,sK8,sK4),
inference(resolve,[status(thm)],[c_3545,c_291]) ).
cnf(c_3564,plain,
cyclic(sK8,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_3546,c_281]) ).
cnf(c_3599,plain,
para(sK8,sK4,sK4,sK8),
inference(resolve,[status(thm)],[c_3552,c_290]) ).
cnf(c_3632,plain,
cyclic(sK8,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_3564,c_282]) ).
cnf(c_3633,plain,
cyclic(sK4,sK8,sK3,sK4),
inference(resolve,[status(thm)],[c_3564,c_280]) ).
cnf(c_3680,plain,
para(sK8,sK4,sK8,sK4),
inference(resolve,[status(thm)],[c_3599,c_291]) ).
cnf(c_3761,plain,
cyclic(sK4,sK8,sK4,sK3),
inference(resolve,[status(thm)],[c_3632,c_280]) ).
cnf(c_3782,plain,
cyclic(sK4,sK3,sK8,sK4),
inference(resolve,[status(thm)],[c_3633,c_281]) ).
cnf(c_3844,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK8,sK8) ),
inference(resolve,[status(thm)],[c_3680,c_334]) ).
cnf(c_3919,plain,
cyclic(sK8,sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_3761,c_343]) ).
cnf(c_3920,plain,
cyclic(sK4,sK4,sK8,sK3),
inference(resolve,[status(thm)],[c_3761,c_281]) ).
cnf(c_3942,plain,
cyclic(sK4,sK3,sK4,sK8),
inference(resolve,[status(thm)],[c_3782,c_282]) ).
cnf(c_4080,plain,
cyclic(sK8,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_3919,c_281]) ).
cnf(c_4102,plain,
( cong(sK8,sK3,sK8,sK3)
| ~ cyclic(sK8,sK3,sK4,sK8) ),
inference(resolve,[status(thm)],[c_4080,c_3547]) ).
cnf(c_4103,plain,
cyclic(sK4,sK4,sK3,sK8),
inference(resolve,[status(thm)],[c_3920,c_282]) ).
cnf(c_4125,plain,
cyclic(sK3,sK4,sK8,sK8),
inference(resolve,[status(thm)],[c_3942,c_343]) ).
cnf(c_4364,plain,
cyclic(sK4,sK3,sK8,sK8),
inference(resolve,[status(thm)],[c_4103,c_343]) ).
cnf(c_4387,plain,
cyclic(sK3,sK8,sK4,sK8),
inference(resolve,[status(thm)],[c_4125,c_281]) ).
cnf(c_4657,plain,
cyclic(sK4,sK8,sK3,sK8),
inference(resolve,[status(thm)],[c_4364,c_281]) ).
cnf(c_4678,plain,
cyclic(sK8,sK3,sK4,sK8),
inference(resolve,[status(thm)],[c_4387,c_280]) ).
cnf(c_4699,plain,
cong(sK8,sK3,sK8,sK3),
inference(resolve,[status(thm)],[c_4678,c_4102]) ).
cnf(c_4936,plain,
cyclic(sK4,sK8,sK8,sK3),
inference(resolve,[status(thm)],[c_4657,c_282]) ).
cnf(c_5057,plain,
cong(sK8,sK3,sK3,sK8),
inference(resolve,[status(thm)],[c_4699,c_273]) ).
cnf(c_5343,plain,
cyclic(sK8,sK8,sK3,sK3),
inference(resolve,[status(thm)],[c_4936,c_343]) ).
cnf(c_5451,plain,
cong(sK3,sK8,sK8,sK3),
inference(resolve,[status(thm)],[c_5057,c_272]) ).
cnf(c_29553,plain,
( perp(sK3,sK8,sK8,sK3)
| ~ cong(sK8,sK3,sK8,sK3) ),
inference(resolve,[status(thm)],[c_5343,c_337]) ).
cnf(c_5619,plain,
perp(sK3,sK8,sK8,sK3),
inference(resolve,[status(thm)],[c_4699,c_29553]) ).
cnf(c_5748,plain,
cong(sK3,sK8,sK3,sK8),
inference(resolve,[status(thm)],[c_5451,c_273]) ).
cnf(c_5872,plain,
perp(sK3,sK8,sK3,sK8),
inference(resolve,[status(thm)],[c_5619,c_288]) ).
cnf(c_29554,plain,
( midp(sK3,sK8,sK8)
| ~ coll(sK3,sK8,sK8) ),
inference(resolve,[status(thm)],[c_5748,c_233]) ).
cnf(c_5985,plain,
midp(sK3,sK8,sK8),
inference(resolve,[status(thm)],[c_546,c_29554]) ).
cnf(c_6103,plain,
para(sK3,sK8,sK3,sK8),
inference(resolve,[status(thm)],[c_5872,c_347]) ).
cnf(c_6172,plain,
( midp(A,sK8,sK8)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_6103,c_334]) ).
cnf(c_6266,plain,
midp(sK3,sK4,sK4),
inference(resolve,[status(thm)],[c_3844,c_5985]) ).
cnf(c_6267,plain,
midp(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_6266,c_2208]) ).
cnf(c_6282,plain,
cong(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_6266,c_232]) ).
cnf(c_6408,plain,
cong(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_6267,c_232]) ).
cnf(c_6553,plain,
cong(sK3,sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_6282,c_273]) ).
cnf(c_6812,plain,
cong(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_6408,c_273]) ).
cnf(c_7124,plain,
cong(sK4,sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_6553,c_272]) ).
cnf(c_7326,plain,
cong(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_6812,c_272]) ).
cnf(c_7498,plain,
cong(sK4,sK3,sK4,sK3),
inference(resolve,[status(thm)],[c_7124,c_273]) ).
cnf(c_7602,plain,
cong(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_7326,c_273]) ).
cnf(c_29555,plain,
( midp(sK4,sK3,sK3)
| ~ coll(sK4,sK3,sK3) ),
inference(resolve,[status(thm)],[c_7498,c_233]) ).
cnf(c_7706,plain,
midp(sK4,sK3,sK3),
inference(resolve,[status(thm)],[c_784,c_29555]) ).
cnf(c_29556,plain,
( midp(sK2,sK3,sK3)
| ~ coll(sK2,sK3,sK3) ),
inference(resolve,[status(thm)],[c_7602,c_233]) ).
cnf(c_7843,plain,
midp(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_519,c_29556]) ).
cnf(c_8161,plain,
midp(sK2,sK8,sK8),
inference(resolve,[status(thm)],[c_6172,c_7843]) ).
cnf(c_8162,plain,
midp(sK4,sK8,sK8),
inference(resolve,[status(thm)],[c_6172,c_7706]) ).
cnf(c_8215,plain,
midp(sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_8161,c_3844]) ).
cnf(c_8239,plain,
midp(sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_8162,c_3844]) ).
cnf(c_8458,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_8215,c_2208]) ).
cnf(c_29557,plain,
( midp(sK1,sK2,sK1)
| ~ coll(sK1,sK2,sK1) ),
inference(resolve,[status(thm)],[c_8458,c_859]) ).
cnf(c_8851,plain,
midp(sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_869,c_29557]) ).
cnf(c_9091,plain,
cong(sK1,sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_8851,c_232]) ).
cnf(c_11897,plain,
cyclic(sK2,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_9091,c_357]) ).
cnf(c_12759,plain,
cyclic(sK1,sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_11897,c_280]) ).
cnf(c_13107,plain,
cyclic(sK1,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_12759,c_281]) ).
cnf(c_13324,plain,
cyclic(sK1,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_13107,c_282]) ).
cnf(c_13325,plain,
( cyclic(sK1,sK2,A,sK1)
| ~ cyclic(sK1,sK1,sK2,A) ),
inference(resolve,[status(thm)],[c_13107,c_279]) ).
cnf(c_13453,plain,
cyclic(sK1,sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_13324,c_343]) ).
cnf(c_13675,plain,
( cyclic(sK1,sK2,A,sK2)
| ~ cyclic(sK1,sK1,sK2,A) ),
inference(resolve,[status(thm)],[c_13453,c_279]) ).
cnf(c_29558,plain,
( midp(sK1,sK4,sK1)
| ~ coll(sK1,sK4,sK1) ),
inference(resolve,[status(thm)],[c_1392,c_8239]) ).
cnf(c_14427,plain,
midp(sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_1311,c_29558]) ).
cnf(c_29559,plain,
( midp(sK2,sK4,sK2)
| ~ coll(sK2,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1436,c_14427]) ).
cnf(c_16078,plain,
midp(sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_728,c_29559]) ).
cnf(c_16107,plain,
midp(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_16078,c_284]) ).
cnf(c_16136,plain,
cong(sK2,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_16107,c_1508]) ).
cnf(c_16605,plain,
perp(sK2,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_16136,c_338]) ).
cnf(c_17257,plain,
( para(sK2,sK3,A,B)
| ~ perp(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_16605,c_286]) ).
cnf(c_27514,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_2169,c_257]) ).
cnf(c_27523,plain,
( cyclic(sK1,sK1,sK2,A)
| ~ coll(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_2170,c_253]) ).
cnf(c_27662,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_27514,c_234]) ).
cnf(c_27764,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_27662,c_348]) ).
cnf(c_27796,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_27764,c_3429]) ).
cnf(c_27841,plain,
coll(sK2,A,sK1),
inference(resolve,[status(thm)],[c_27764,c_882]) ).
cnf(c_27905,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,A)
| ~ cyclic(sK2,A,sK1,sK2) ),
inference(resolve,[status(thm)],[c_27796,c_3430]) ).
cnf(c_28072,plain,
cyclic(sK1,sK1,sK2,A),
inference(resolve,[status(thm)],[c_27841,c_27523]) ).
cnf(c_28247,plain,
cyclic(sK1,sK2,A,sK2),
inference(resolve,[status(thm)],[c_28072,c_13675]) ).
cnf(c_28248,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_28072,c_13325]) ).
cnf(c_29560,plain,
( cyclic(sK1,sK2,A,B)
| ~ cyclic(sK1,sK1,sK2,A) ),
inference(resolve,[status(thm)],[c_28072,c_279]) ).
cnf(c_28711,plain,
cyclic(sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_28072,c_29560]) ).
cnf(c_29561,plain,
( cyclic(sK2,A,B,sK2)
| ~ cyclic(sK1,sK2,A,B) ),
inference(resolve,[status(thm)],[c_28247,c_279]) ).
cnf(c_28721,plain,
cyclic(sK2,A,B,sK2),
inference(resolve,[status(thm)],[c_28711,c_29561]) ).
cnf(c_28725,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,A) ),
inference(resolve,[status(thm)],[c_28721,c_27905]) ).
cnf(c_29562,plain,
( cyclic(sK2,A,sK1,B)
| ~ cyclic(sK1,sK2,A,B) ),
inference(resolve,[status(thm)],[c_28248,c_279]) ).
cnf(c_28730,plain,
cyclic(sK2,A,sK1,B),
inference(resolve,[status(thm)],[c_28711,c_29562]) ).
cnf(c_28735,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_28730,c_28725]) ).
cnf(c_29563,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_28735,c_244]) ).
cnf(c_29529,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_28735,c_29563]) ).
cnf(c_29549,plain,
para(sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_29529,c_17257]) ).
cnf(c_29550,plain,
$false,
inference(resolve,[status(thm)],[c_29549,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO635+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n002.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Fri Sep 25 13:48:19 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 3413262 was started by sandbox2 on n002,
% 0.19/0.44 % Fri Sep 25 13:48:19 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 27.25/3.99
% 27.25/3.99 % given #500 (A,wt=14): 428 eqangle(c3,c5,c1,c3,c3,c2,c6,c3). [resolve(277,a,194,a)].
% 27.25/3.99
% 27.25/3.99 % given #1000 (T,wt=13): 1072 -coll(c4,c2,A) | coll(A,c2,c4). [resolve(1005,a,292,b)].
% 27.25/3.99
% 27.25/3.99 % given #1500 (A,wt=33): 1060 perp(f17(f12(c1,c6,c8,c4),c4,c1,c5,c2),f12(c1,c6,c8,c4),c5,c2). [resolve(1003,a,371,a)].
% 27.25/3.99
% 27.25/3.99 % given #2000 (T,wt=10): 11725 perp(c5,c5,c6,c6). [resolve(9049,a,338,a)].
% 27.25/3.99
% 27.25/3.99 % given #2500 (A,wt=18): 1538 coll(f11(c3,c1,c2,c2),c2,c3). [resolve(1504,a,204,b),unit_del(a,1528)].
% 27.25/3.99
% 27.25/3.99 % given #3000 (T,wt=10): 23922 cong(c6,c6,c6,c4). [resolve(23762,a,245,b),unit_del(a,22714)].
% 27.25/3.99
% 27.25/3.99 % given #3500 (A,wt=33): 2238 perp(f17(f12(c3,c7,c9,c4),c4,c3,c6,c2),f12(c3,c7,c9,c4),c6,c2). [resolve(2229,a,372,a)].
% 27.25/3.99
% 27.25/3.99 % SZS status Theorem for theBenchmark
% 27.25/3.99
% 27.25/3.99 % Proof 1 at 2.63 (+ 0.81) seconds.
% 27.25/3.99 % Length of proof is 260.
% 27.25/3.99 % Level of proof is 48.
% 27.25/3.99 % Maximum clause weight is 34.000.
% 27.25/3.99 % Given clauses 3838.
% 27.25/3.99
% 27.25/3.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------