%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO624+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 07:18:15 AM UTC 2026
% Result : Theorem 217.66s 40.05s
% Output : CNFRefutation 217.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 32
% Syntax : Number of formulae : 357 ( 204 unt; 0 def)
% Number of atoms : 611 ( 0 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 411 ( 157 ~; 153 |; 68 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 430 ( 28 sgn 157 !; 10 ?)
% 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(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(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(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(ruleD25,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('theBenchmark.p',ruleD25) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('theBenchmark.p',ruleD44) ).
fof(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
fof(ruleD55,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('theBenchmark.p',ruleD55) ).
fof(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(ruleD63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('theBenchmark.p',ruleD63) ).
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(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(exemplo6GDDFULL8110988,conjecture,
! [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ( coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) )
=> cyclic(O,P,Q,P1) ),
file('theBenchmark.p',exemplo6GDDFULL8110988) ).
fof(exemplo6GDDFULL8110988_neg,negated_conjecture,
~ ! [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ( coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) )
=> cyclic(O,P,Q,P1) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110988]) ).
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_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
cnf(c_142,plain,
( ~ cong(A,B,A,C)
| ~ cong(A,B,A,D)
| perp(B,D,D,C)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_101,c_97]) ).
fof(nnf_95,plain,
? [O,X,L,A,Y,B,P,Q,Q1,P1] :
( ~ cyclic(O,P,Q,P1)
& coll(P1,L,B)
& coll(P1,O,X)
& coll(Q1,O,Y)
& coll(Q1,L,A)
& cong(L,B,L,Q)
& coll(L,B,Q)
& cong(L,A,L,P)
& coll(L,A,P)
& coll(B,O,Y)
& perp(B,L,O,Y)
& coll(A,O,X)
& perp(A,L,O,X) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110988_neg]) ).
fof(sk_exemplo6GDDFULL8110988_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& coll(sK3,sK4,sK5)
& coll(sK3,sK0,sK6)
& coll(sK7,sK0,sK9)
& coll(sK7,sK4,sK8)
& cong(sK4,sK5,sK4,sK2)
& coll(sK4,sK5,sK2)
& cong(sK4,sK8,sK4,sK1)
& coll(sK4,sK8,sK1)
& coll(sK5,sK0,sK9)
& perp(sK5,sK4,sK0,sK9)
& coll(sK8,sK0,sK6)
& perp(sK8,sK4,sK0,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK4,sK0,sK6,sK5,sK9,sK1,sK2,sK7,sK3]),skolemize(O,sK0),skolemize(X,sK6),skolemize(L,sK4),skolemize(A,sK8),skolemize(Y,sK9),skolemize(B,sK5),skolemize(P,sK1),skolemize(Q,sK2),skolemize(Q1,sK7),skolemize(P1,sK3)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_149,negated_conjecture,
coll(sK3,sK0,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_151,negated_conjecture,
coll(sK7,sK4,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_152,negated_conjecture,
cong(sK4,sK5,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_153,negated_conjecture,
coll(sK4,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_154,negated_conjecture,
cong(sK4,sK8,sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_155,negated_conjecture,
coll(sK4,sK8,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_158,negated_conjecture,
coll(sK8,sK0,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110988_neg]) ).
cnf(c_196,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_197,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_200,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_201,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_207,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_209,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_214,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_215,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_216,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_217,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_219,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_220,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_235,plain,
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD25]) ).
cnf(c_236,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_237,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_241,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_243,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_244,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_245,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_246,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_247,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_248,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_250,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_252,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_254,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_255,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_256,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_257,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_258,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_273,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_142]) ).
cnf(c_298,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_200]) ).
cnf(c_301,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_207]) ).
cnf(c_303,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_215]) ).
cnf(c_304,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,E,D,E,D)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_216]) ).
cnf(c_307,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_243]) ).
cnf(c_308,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_247]) ).
cnf(c_311,plain,
( para(A,B,A,B)
| ~ perp(A,B,A,B) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_312,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_256]) ).
cnf(c_320,plain,
( cong(A,B,D,D)
| ~ eqangle(C,A,C,B,D,D,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_304]) ).
cnf(c_321,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_308]) ).
cnf(c_51266,negated_conjecture,
( midp(sK4,sK8,sK1)
| ~ coll(sK4,sK8,sK1) ),
inference(resolve,[status(thm)],[c_197,c_154]) ).
cnf(c_676,negated_conjecture,
midp(sK4,sK8,sK1),
inference(resolve,[status(thm)],[c_155,c_51266]) ).
cnf(c_51267,negated_conjecture,
( midp(sK4,sK5,sK2)
| ~ coll(sK4,sK5,sK2) ),
inference(resolve,[status(thm)],[c_197,c_152]) ).
cnf(c_677,negated_conjecture,
midp(sK4,sK5,sK2),
inference(resolve,[status(thm)],[c_153,c_51267]) ).
cnf(c_720,plain,
( cong(sK4,sK8,A,B)
| ~ cong(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_235,c_154]) ).
cnf(c_721,plain,
( cong(sK4,sK5,A,B)
| ~ cong(sK4,sK2,A,B) ),
inference(resolve,[status(thm)],[c_235,c_152]) ).
cnf(c_724,plain,
cong(sK4,sK1,sK4,sK8),
inference(resolve,[status(thm)],[c_236,c_154]) ).
cnf(c_725,plain,
cong(sK4,sK2,sK4,sK5),
inference(resolve,[status(thm)],[c_236,c_152]) ).
cnf(c_754,plain,
( coll(sK8,A,sK7)
| ~ coll(sK7,sK4,A) ),
inference(resolve,[status(thm)],[c_256,c_151]) ).
cnf(c_761,plain,
( coll(A,sK2,sK4)
| ~ coll(sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_256,c_153]) ).
cnf(c_768,plain,
coll(sK8,sK4,sK1),
inference(resolve,[status(thm)],[c_257,c_155]) ).
cnf(c_769,plain,
coll(sK5,sK4,sK2),
inference(resolve,[status(thm)],[c_257,c_153]) ).
cnf(c_770,plain,
coll(sK4,sK7,sK8),
inference(resolve,[status(thm)],[c_257,c_151]) ).
cnf(c_773,plain,
coll(sK4,sK3,sK5),
inference(resolve,[status(thm)],[c_257,c_148]) ).
cnf(c_776,plain,
coll(sK4,sK1,sK8),
inference(resolve,[status(thm)],[c_258,c_155]) ).
cnf(c_777,plain,
coll(sK4,sK2,sK5),
inference(resolve,[status(thm)],[c_258,c_153]) ).
cnf(c_778,plain,
coll(sK7,sK8,sK4),
inference(resolve,[status(thm)],[c_258,c_151]) ).
cnf(c_51268,negated_conjecture,
( ~ cong(sK4,sK5,sK4,sK2)
| perp(sK5,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_273,c_153]) ).
cnf(c_809,negated_conjecture,
perp(sK5,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_152,c_51268]) ).
cnf(c_866,plain,
( cyclic(sK8,sK1,sK1,A)
| ~ cong(sK4,sK8,sK4,A) ),
inference(resolve,[status(thm)],[c_308,c_154]) ).
cnf(c_872,plain,
coll(sK6,sK6,sK8),
inference(resolve,[status(thm)],[c_312,c_158]) ).
cnf(c_874,plain,
coll(sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_312,c_155]) ).
cnf(c_875,plain,
coll(sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_312,c_153]) ).
cnf(c_876,plain,
coll(sK8,sK8,sK7),
inference(resolve,[status(thm)],[c_312,c_151]) ).
cnf(c_878,plain,
coll(sK6,sK6,sK3),
inference(resolve,[status(thm)],[c_312,c_149]) ).
cnf(c_879,plain,
coll(sK5,sK5,sK3),
inference(resolve,[status(thm)],[c_312,c_148]) ).
cnf(c_888,plain,
cyclic(sK8,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_321,c_154]) ).
cnf(c_889,plain,
cyclic(sK5,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_321,c_152]) ).
cnf(c_902,plain,
( para(A,sK4,B,sK1)
| ~ midp(A,sK8,B) ),
inference(resolve,[status(thm)],[c_676,c_215]) ).
cnf(c_904,plain,
( midp(A,sK8,B)
| ~ coll(A,sK8,B)
| ~ para(sK4,A,sK1,B) ),
inference(resolve,[status(thm)],[c_676,c_214]) ).
cnf(c_907,plain,
( para(A,sK8,B,sK1)
| ~ midp(sK4,A,B) ),
inference(resolve,[status(thm)],[c_676,c_201]) ).
cnf(c_909,plain,
( midp(sK4,A,B)
| ~ para(sK8,B,sK1,A)
| ~ para(sK8,A,sK1,B) ),
inference(resolve,[status(thm)],[c_676,c_200]) ).
cnf(c_950,plain,
( para(A,sK4,B,sK2)
| ~ midp(A,sK5,B) ),
inference(resolve,[status(thm)],[c_677,c_215]) ).
cnf(c_951,plain,
( para(sK4,A,sK2,B)
| ~ midp(A,sK5,B) ),
inference(resolve,[status(thm)],[c_677,c_215]) ).
cnf(c_955,plain,
( para(A,sK5,B,sK2)
| ~ midp(sK4,A,B) ),
inference(resolve,[status(thm)],[c_677,c_201]) ).
cnf(c_956,plain,
( para(sK5,A,sK2,B)
| ~ midp(sK4,A,B) ),
inference(resolve,[status(thm)],[c_677,c_201]) ).
cnf(c_957,plain,
( midp(sK4,A,B)
| ~ para(sK5,B,sK2,A)
| ~ para(sK5,A,sK2,B) ),
inference(resolve,[status(thm)],[c_677,c_200]) ).
cnf(c_1062,plain,
coll(sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_768,c_312]) ).
cnf(c_1076,plain,
coll(sK8,sK1,sK4),
inference(resolve,[status(thm)],[c_768,c_258]) ).
cnf(c_1100,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_769,c_312]) ).
cnf(c_1114,plain,
coll(sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_769,c_258]) ).
cnf(c_1115,plain,
( coll(A,sK2,sK5)
| ~ coll(sK5,sK4,A) ),
inference(resolve,[status(thm)],[c_769,c_256]) ).
cnf(c_1138,plain,
coll(sK8,sK8,sK4),
inference(resolve,[status(thm)],[c_770,c_312]) ).
cnf(c_1153,plain,
( coll(A,sK8,sK4)
| ~ coll(sK4,sK7,A) ),
inference(resolve,[status(thm)],[c_770,c_256]) ).
cnf(c_1250,plain,
coll(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_773,c_312]) ).
cnf(c_1265,plain,
( coll(A,sK5,sK4)
| ~ coll(sK4,sK3,A) ),
inference(resolve,[status(thm)],[c_773,c_256]) ).
cnf(c_1266,plain,
( coll(sK5,A,sK4)
| ~ coll(sK4,sK3,A) ),
inference(resolve,[status(thm)],[c_773,c_256]) ).
cnf(c_51269,plain,
( ~ cong(sK4,sK1,sK4,sK8)
| perp(sK1,sK8,sK8,sK8) ),
inference(resolve,[status(thm)],[c_776,c_273]) ).
cnf(c_1376,plain,
perp(sK1,sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_724,c_51269]) ).
cnf(c_51270,plain,
( ~ cong(sK4,sK2,sK4,sK5)
| perp(sK2,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_777,c_273]) ).
cnf(c_1408,plain,
perp(sK2,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_725,c_51270]) ).
cnf(c_1444,plain,
( coll(sK4,A,sK7)
| ~ coll(sK7,sK8,A) ),
inference(resolve,[status(thm)],[c_778,c_256]) ).
cnf(c_1596,plain,
( coll(A,sK8,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_872,c_256]) ).
cnf(c_1673,plain,
coll(sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_874,c_258]) ).
cnf(c_1712,plain,
coll(sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_875,c_258]) ).
cnf(c_1751,plain,
coll(sK8,sK7,sK8),
inference(resolve,[status(thm)],[c_876,c_258]) ).
cnf(c_1752,plain,
( coll(A,sK7,sK8)
| ~ coll(sK8,sK8,A) ),
inference(resolve,[status(thm)],[c_876,c_256]) ).
cnf(c_1868,plain,
coll(sK5,sK3,sK5),
inference(resolve,[status(thm)],[c_879,c_258]) ).
cnf(c_2146,plain,
coll(sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_1062,c_312]) ).
cnf(c_2167,plain,
( midp(sK1,sK1,sK8)
| ~ cong(sK1,sK1,sK1,sK8) ),
inference(resolve,[status(thm)],[c_1062,c_197]) ).
cnf(c_2185,plain,
coll(sK4,sK4,sK8),
inference(resolve,[status(thm)],[c_1076,c_312]) ).
cnf(c_2223,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1100,c_312]) ).
cnf(c_2244,plain,
( midp(sK2,sK2,sK5)
| ~ cong(sK2,sK2,sK2,sK5) ),
inference(resolve,[status(thm)],[c_1100,c_197]) ).
cnf(c_2262,plain,
coll(sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_1114,c_312]) ).
cnf(c_2314,plain,
coll(sK8,sK4,sK8),
inference(resolve,[status(thm)],[c_1138,c_258]) ).
cnf(c_2466,plain,
coll(sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_1250,c_258]) ).
cnf(c_3253,plain,
coll(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_1673,c_312]) ).
cnf(c_3336,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_1712,c_312]) ).
cnf(c_3419,plain,
coll(sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_1751,c_312]) ).
cnf(c_3660,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_1868,c_312]) ).
cnf(c_4029,plain,
coll(sK8,sK1,sK8),
inference(resolve,[status(thm)],[c_2146,c_258]) ).
cnf(c_4036,plain,
( midp(sK8,sK8,sK1)
| ~ cong(sK8,sK8,sK8,sK1) ),
inference(resolve,[status(thm)],[c_2146,c_197]) ).
cnf(c_4107,plain,
coll(sK4,sK8,sK4),
inference(resolve,[status(thm)],[c_2185,c_258]) ).
cnf(c_4181,plain,
coll(sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_2223,c_258]) ).
cnf(c_4188,plain,
( midp(sK5,sK5,sK2)
| ~ cong(sK5,sK5,sK5,sK2) ),
inference(resolve,[status(thm)],[c_2223,c_197]) ).
cnf(c_4259,plain,
coll(sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_2262,c_258]) ).
cnf(c_4333,plain,
coll(sK4,sK8,sK8),
inference(resolve,[status(thm)],[c_2314,c_257]) ).
cnf(c_4599,plain,
coll(sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_2466,c_257]) ).
cnf(c_5262,plain,
( cyclic(A,sK1,sK1,sK1)
| ~ eqangle(sK1,A,sK1,sK1,sK1,A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_3253,c_217]) ).
cnf(c_5266,plain,
( midp(sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_3253,c_197]) ).
cnf(c_5386,plain,
( midp(sK2,sK2,sK2)
| ~ cong(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_3336,c_197]) ).
cnf(c_5515,plain,
( midp(sK8,sK8,sK8)
| ~ cong(sK8,sK8,sK8,sK8) ),
inference(resolve,[status(thm)],[c_3419,c_197]) ).
cnf(c_5806,plain,
( midp(sK5,sK5,sK5)
| ~ cong(sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_3660,c_197]) ).
cnf(c_6122,plain,
coll(sK1,sK8,sK8),
inference(resolve,[status(thm)],[c_4029,c_257]) ).
cnf(c_6210,plain,
( midp(sK4,sK8,sK4)
| ~ cong(sK4,sK8,sK4,sK4) ),
inference(resolve,[status(thm)],[c_4107,c_197]) ).
cnf(c_6245,plain,
coll(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_4181,c_257]) ).
cnf(c_6333,plain,
( midp(sK4,sK5,sK4)
| ~ cong(sK4,sK5,sK4,sK4) ),
inference(resolve,[status(thm)],[c_4259,c_197]) ).
cnf(c_6380,plain,
( midp(sK4,sK8,sK8)
| ~ cong(sK4,sK8,sK4,sK8) ),
inference(resolve,[status(thm)],[c_4333,c_197]) ).
cnf(c_6543,plain,
( midp(sK4,sK5,sK5)
| ~ cong(sK4,sK5,sK4,sK5) ),
inference(resolve,[status(thm)],[c_4599,c_197]) ).
cnf(c_7515,plain,
( midp(sK1,sK8,sK8)
| ~ cong(sK1,sK8,sK1,sK8) ),
inference(resolve,[status(thm)],[c_6122,c_197]) ).
cnf(c_7595,plain,
( midp(sK2,sK5,sK5)
| ~ cong(sK2,sK5,sK2,sK5) ),
inference(resolve,[status(thm)],[c_6245,c_197]) ).
cnf(c_7815,plain,
cyclic(sK1,sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_724,c_321]) ).
cnf(c_7925,plain,
cyclic(sK2,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_725,c_321]) ).
cnf(c_8160,plain,
( cong(sK5,sK2,sK5,sK2)
| ~ midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_809,c_209]) ).
cnf(c_8192,plain,
( cong(sK8,sK1,sK1,sK1)
| ~ eqangle(sK1,sK8,sK1,sK1,sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_888,c_320]) ).
cnf(c_8193,plain,
cyclic(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_888,c_307]) ).
cnf(c_8201,plain,
cyclic(sK1,sK8,sK1,sK1),
inference(resolve,[status(thm)],[c_888,c_244]) ).
cnf(c_8226,plain,
( cong(sK5,sK2,sK2,sK2)
| ~ eqangle(sK2,sK5,sK2,sK2,sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_889,c_320]) ).
cnf(c_8227,plain,
cyclic(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_889,c_307]) ).
cnf(c_8235,plain,
cyclic(sK2,sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_889,c_244]) ).
cnf(c_8386,plain,
( cong(sK1,sK8,sK1,sK8)
| ~ midp(sK8,sK8,sK8) ),
inference(resolve,[status(thm)],[c_1376,c_209]) ).
cnf(c_8424,plain,
( cong(sK2,sK5,sK2,sK5)
| ~ midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1408,c_209]) ).
cnf(c_8585,plain,
cyclic(sK8,sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_7815,c_307]) ).
cnf(c_8624,plain,
cyclic(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_7925,c_307]) ).
cnf(c_8632,plain,
cyclic(sK5,sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_7925,c_244]) ).
cnf(c_8762,plain,
( cong(sK1,sK1,sK1,sK1)
| ~ eqangle(sK1,sK1,sK1,sK1,sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_8193,c_320]) ).
cnf(c_8770,plain,
eqangle(sK1,sK1,sK1,sK1,sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_8193,c_219]) ).
cnf(c_8793,plain,
cong(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_8770,c_8762]) ).
cnf(c_8795,plain,
midp(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_8793,c_5266]) ).
cnf(c_8812,plain,
para(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_8795,c_303]) ).
cnf(c_8929,plain,
cyclic(sK1,sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_8201,c_245]) ).
cnf(c_8955,plain,
( cong(sK2,sK2,sK2,sK2)
| ~ eqangle(sK2,sK2,sK2,sK2,sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_8227,c_320]) ).
cnf(c_8963,plain,
eqangle(sK2,sK2,sK2,sK2,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_8227,c_219]) ).
cnf(c_8986,plain,
cong(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_8963,c_8955]) ).
cnf(c_8988,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_8986,c_5386]) ).
cnf(c_8989,plain,
cong(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_8988,c_8160]) ).
cnf(c_9124,plain,
cyclic(sK2,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_8235,c_245]) ).
cnf(c_9268,plain,
( cong(sK8,sK8,sK8,sK8)
| ~ eqangle(sK8,sK8,sK8,sK8,sK8,sK8,sK8,sK8) ),
inference(resolve,[status(thm)],[c_8585,c_320]) ).
cnf(c_9276,plain,
eqangle(sK8,sK8,sK8,sK8,sK8,sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_8585,c_219]) ).
cnf(c_9299,plain,
cong(sK8,sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_9276,c_9268]) ).
cnf(c_9301,plain,
midp(sK8,sK8,sK8),
inference(resolve,[status(thm)],[c_9299,c_5515]) ).
cnf(c_9302,plain,
cong(sK1,sK8,sK1,sK8),
inference(resolve,[status(thm)],[c_9301,c_8386]) ).
cnf(c_9306,plain,
midp(sK1,sK8,sK8),
inference(resolve,[status(thm)],[c_9302,c_7515]) ).
cnf(c_9481,plain,
( cong(sK5,sK5,sK5,sK5)
| ~ eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_8624,c_320]) ).
cnf(c_9489,plain,
eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_8624,c_219]) ).
cnf(c_9512,plain,
cong(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_9489,c_9481]) ).
cnf(c_9514,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_9512,c_5806]) ).
cnf(c_9515,plain,
cong(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_9514,c_8424]) ).
cnf(c_9519,plain,
midp(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_9515,c_7595]) ).
cnf(c_9663,plain,
cyclic(sK5,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_8632,c_245]) ).
cnf(c_10116,plain,
eqangle(sK1,sK1,A,B,sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_8812,c_220]) ).
cnf(c_10127,plain,
cyclic(sK1,sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_8929,c_246]) ).
cnf(c_10273,plain,
( perp(sK2,sK5,sK5,sK2)
| ~ cyclic(sK5,sK5,sK2,sK2) ),
inference(resolve,[status(thm)],[c_8989,c_301]) ).
cnf(c_10420,plain,
cyclic(sK2,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_9124,c_246]) ).
cnf(c_10642,plain,
( perp(sK8,sK1,sK1,sK8)
| ~ cyclic(sK1,sK1,sK8,sK8) ),
inference(resolve,[status(thm)],[c_9302,c_301]) ).
cnf(c_10983,plain,
( perp(sK5,sK2,sK2,sK5)
| ~ cyclic(sK2,sK2,sK5,sK5) ),
inference(resolve,[status(thm)],[c_9515,c_301]) ).
cnf(c_11142,plain,
cyclic(sK5,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_9663,c_246]) ).
cnf(c_11298,plain,
cyclic(sK1,sK1,sK8,sK8),
inference(resolve,[status(thm)],[c_10127,c_307]) ).
cnf(c_11307,plain,
( cyclic(sK1,sK1,sK8,A)
| ~ cyclic(sK1,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_10127,c_243]) ).
cnf(c_11331,plain,
perp(sK8,sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_11298,c_10642]) ).
cnf(c_11375,plain,
cyclic(sK2,sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_10420,c_307]) ).
cnf(c_11408,plain,
perp(sK5,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_11375,c_10983]) ).
cnf(c_11595,plain,
cyclic(sK5,sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_11142,c_307]) ).
cnf(c_11628,plain,
perp(sK2,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_11595,c_10273]) ).
cnf(c_11737,plain,
perp(sK8,sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_11331,c_252]) ).
cnf(c_11789,plain,
perp(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_11408,c_252]) ).
cnf(c_11912,plain,
perp(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_11628,c_252]) ).
cnf(c_11989,plain,
para(sK8,sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_11737,c_311]) ).
cnf(c_11997,plain,
( cong(sK8,sK8,sK8,sK1)
| ~ midp(sK1,sK8,sK1) ),
inference(resolve,[status(thm)],[c_11737,c_209]) ).
cnf(c_12041,plain,
para(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_11789,c_311]) ).
cnf(c_12049,plain,
( cong(sK5,sK5,sK5,sK2)
| ~ midp(sK2,sK5,sK2) ),
inference(resolve,[status(thm)],[c_11789,c_209]) ).
cnf(c_12147,plain,
para(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_11912,c_311]) ).
cnf(c_12240,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK8,sK8) ),
inference(resolve,[status(thm)],[c_11989,c_298]) ).
cnf(c_12332,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_12041,c_298]) ).
cnf(c_12390,plain,
( midp(A,sK5,sK5)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_12147,c_298]) ).
cnf(c_13868,plain,
coll(sK3,sK8,sK6),
inference(resolve,[status(thm)],[c_1596,c_878]) ).
cnf(c_13882,plain,
coll(sK3,sK6,sK8),
inference(resolve,[status(thm)],[c_13868,c_258]) ).
cnf(c_13907,plain,
coll(sK8,sK8,sK3),
inference(resolve,[status(thm)],[c_13882,c_312]) ).
cnf(c_15126,plain,
coll(sK3,sK7,sK8),
inference(resolve,[status(thm)],[c_1752,c_13907]) ).
cnf(c_15143,plain,
coll(sK7,sK3,sK8),
inference(resolve,[status(thm)],[c_15126,c_257]) ).
cnf(c_15280,plain,
coll(sK7,sK8,sK3),
inference(resolve,[status(thm)],[c_15143,c_258]) ).
cnf(c_15515,plain,
coll(sK4,sK3,sK7),
inference(resolve,[status(thm)],[c_15280,c_1444]) ).
cnf(c_15904,plain,
coll(sK5,sK7,sK4),
inference(resolve,[status(thm)],[c_15515,c_1266]) ).
cnf(c_15905,plain,
coll(sK7,sK5,sK4),
inference(resolve,[status(thm)],[c_15515,c_1265]) ).
cnf(c_16489,plain,
coll(sK5,sK4,sK7),
inference(resolve,[status(thm)],[c_15904,c_258]) ).
cnf(c_16514,plain,
coll(sK7,sK4,sK5),
inference(resolve,[status(thm)],[c_15905,c_258]) ).
cnf(c_17200,plain,
coll(sK4,sK5,sK7),
inference(resolve,[status(thm)],[c_16489,c_257]) ).
cnf(c_17227,plain,
coll(sK4,sK7,sK5),
inference(resolve,[status(thm)],[c_16514,c_257]) ).
cnf(c_18190,plain,
coll(sK7,sK2,sK4),
inference(resolve,[status(thm)],[c_17200,c_761]) ).
cnf(c_18262,plain,
coll(sK5,sK8,sK4),
inference(resolve,[status(thm)],[c_17227,c_1153]) ).
cnf(c_19018,plain,
coll(sK7,sK4,sK2),
inference(resolve,[status(thm)],[c_18190,c_258]) ).
cnf(c_19096,plain,
coll(sK5,sK4,sK8),
inference(resolve,[status(thm)],[c_18262,c_258]) ).
cnf(c_19787,plain,
coll(sK8,sK2,sK7),
inference(resolve,[status(thm)],[c_19018,c_754]) ).
cnf(c_19873,plain,
coll(sK8,sK2,sK5),
inference(resolve,[status(thm)],[c_19096,c_1115]) ).
cnf(c_20546,plain,
coll(sK8,sK7,sK2),
inference(resolve,[status(thm)],[c_19787,c_258]) ).
cnf(c_20640,plain,
coll(sK8,sK5,sK2),
inference(resolve,[status(thm)],[c_19873,c_258]) ).
cnf(c_21393,plain,
coll(sK2,sK2,sK8),
inference(resolve,[status(thm)],[c_20546,c_312]) ).
cnf(c_21501,plain,
coll(sK5,sK8,sK2),
inference(resolve,[status(thm)],[c_20640,c_257]) ).
cnf(c_22044,plain,
coll(sK2,sK8,sK2),
inference(resolve,[status(thm)],[c_21393,c_258]) ).
cnf(c_22190,plain,
( ~ cong(sK5,sK8,sK5,sK2)
| perp(sK8,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_21501,c_273]) ).
cnf(c_22669,plain,
coll(sK8,sK2,sK2),
inference(resolve,[status(thm)],[c_22044,c_257]) ).
cnf(c_23082,plain,
( midp(sK8,sK2,sK2)
| ~ cong(sK8,sK2,sK8,sK2) ),
inference(resolve,[status(thm)],[c_22669,c_197]) ).
cnf(c_28926,plain,
cong(sK4,sK8,sK4,sK8),
inference(resolve,[status(thm)],[c_720,c_724]) ).
cnf(c_28948,plain,
midp(sK4,sK8,sK8),
inference(resolve,[status(thm)],[c_28926,c_6380]) ).
cnf(c_28949,plain,
midp(sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_28948,c_12240]) ).
cnf(c_29065,plain,
cong(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_721,c_725]) ).
cnf(c_29083,plain,
midp(sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_29065,c_6543]) ).
cnf(c_29151,plain,
midp(sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_29083,c_12332]) ).
cnf(c_29787,plain,
para(sK1,sK4,sK8,sK1),
inference(resolve,[status(thm)],[c_902,c_9306]) ).
cnf(c_29804,plain,
para(sK8,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_29787,c_254]) ).
cnf(c_29960,plain,
( midp(sK5,sK8,sK2)
| ~ para(sK4,sK5,sK1,sK2) ),
inference(resolve,[status(thm)],[c_904,c_21501]) ).
cnf(c_30170,plain,
para(sK1,sK8,sK1,sK1),
inference(resolve,[status(thm)],[c_907,c_28949]) ).
cnf(c_30276,plain,
eqangle(sK1,sK8,A,B,sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_30170,c_220]) ).
cnf(c_30283,plain,
cong(sK8,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_30276,c_8192]) ).
cnf(c_30397,plain,
( midp(sK4,sK1,sK4)
| ~ para(sK8,sK4,sK1,sK1) ),
inference(resolve,[status(thm)],[c_909,c_29804]) ).
cnf(c_30399,plain,
( midp(sK4,sK4,sK1)
| ~ para(sK8,sK4,sK1,sK1) ),
inference(resolve,[status(thm)],[c_909,c_29804]) ).
cnf(c_30580,plain,
cong(sK1,sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_30283,c_236]) ).
cnf(c_30909,plain,
cong(sK1,sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_30580,c_237]) ).
cnf(c_30925,plain,
midp(sK1,sK1,sK8),
inference(resolve,[status(thm)],[c_30909,c_2167]) ).
cnf(c_30950,plain,
midp(sK1,sK8,sK1),
inference(resolve,[status(thm)],[c_30925,c_248]) ).
cnf(c_30961,plain,
cong(sK8,sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_30950,c_11997]) ).
cnf(c_30972,plain,
midp(sK8,sK8,sK1),
inference(resolve,[status(thm)],[c_30961,c_4036]) ).
cnf(c_31061,plain,
para(sK8,sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_30972,c_902]) ).
cnf(c_31083,plain,
midp(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_31061,c_30399]) ).
cnf(c_31084,plain,
midp(sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_31061,c_30397]) ).
cnf(c_31136,plain,
cong(sK4,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_31084,c_196]) ).
cnf(c_31698,plain,
cong(sK4,sK8,sK4,sK4),
inference(resolve,[status(thm)],[c_31136,c_720]) ).
cnf(c_31743,plain,
midp(sK4,sK8,sK4),
inference(resolve,[status(thm)],[c_31698,c_6210]) ).
cnf(c_32669,plain,
para(sK4,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_951,c_9519]) ).
cnf(c_33014,plain,
para(sK4,sK5,sK1,sK2),
inference(resolve,[status(thm)],[c_955,c_31083]) ).
cnf(c_33016,plain,
para(sK2,sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_955,c_29151]) ).
cnf(c_33024,plain,
midp(sK5,sK8,sK2),
inference(resolve,[status(thm)],[c_33014,c_29960]) ).
cnf(c_33063,plain,
cong(sK5,sK8,sK5,sK2),
inference(resolve,[status(thm)],[c_33024,c_196]) ).
cnf(c_33076,plain,
perp(sK8,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_33063,c_22190]) ).
cnf(c_33218,plain,
para(sK5,sK8,sK2,sK4),
inference(resolve,[status(thm)],[c_956,c_31743]) ).
cnf(c_33493,plain,
para(sK4,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_32669,c_255]) ).
cnf(c_34045,plain,
eqangle(sK2,sK5,A,B,sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_33016,c_220]) ).
cnf(c_34052,plain,
cong(sK5,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_34045,c_8226]) ).
cnf(c_51271,plain,
( cong(sK8,sK2,sK8,sK2)
| ~ midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_33076,c_209]) ).
cnf(c_34192,plain,
cong(sK8,sK2,sK8,sK2),
inference(resolve,[status(thm)],[c_8988,c_51271]) ).
cnf(c_34206,plain,
midp(sK8,sK2,sK2),
inference(resolve,[status(thm)],[c_34192,c_23082]) ).
cnf(c_34207,plain,
midp(sK8,sK5,sK5),
inference(resolve,[status(thm)],[c_34206,c_12390]) ).
cnf(c_34291,plain,
para(sK4,sK8,sK2,sK5),
inference(resolve,[status(thm)],[c_34207,c_951]) ).
cnf(c_34534,plain,
para(sK5,sK8,sK4,sK2),
inference(resolve,[status(thm)],[c_33218,c_255]) ).
cnf(c_34662,plain,
para(sK5,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_33493,c_254]) ).
cnf(c_34936,plain,
cong(sK2,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_34052,c_236]) ).
cnf(c_34973,plain,
para(sK4,sK8,sK5,sK2),
inference(resolve,[status(thm)],[c_34291,c_255]) ).
cnf(c_35182,plain,
para(sK4,sK2,sK5,sK8),
inference(resolve,[status(thm)],[c_34534,c_254]) ).
cnf(c_35310,plain,
para(sK5,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_34662,c_255]) ).
cnf(c_35502,plain,
cong(sK2,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_34936,c_237]) ).
cnf(c_35519,plain,
midp(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_35502,c_2244]) ).
cnf(c_35558,plain,
midp(sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_35519,c_248]) ).
cnf(c_35569,plain,
cong(sK5,sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_35558,c_12049]) ).
cnf(c_35581,plain,
midp(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_35569,c_4188]) ).
cnf(c_35673,plain,
para(sK5,sK4,sK2,sK2),
inference(resolve,[status(thm)],[c_35581,c_950]) ).
cnf(c_51272,plain,
( midp(A,sK2,sK8)
| ~ para(sK4,sK2,sK5,sK8)
| ~ midp(A,sK4,sK5) ),
inference(resolve,[status(thm)],[c_34973,c_200]) ).
cnf(c_35719,plain,
( midp(A,sK2,sK8)
| ~ midp(A,sK4,sK5) ),
inference(resolve,[status(thm)],[c_35182,c_51272]) ).
cnf(c_51273,plain,
( midp(sK4,sK2,sK4)
| ~ para(sK5,sK4,sK2,sK2) ),
inference(resolve,[status(thm)],[c_35310,c_957]) ).
cnf(c_36216,plain,
midp(sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_35673,c_51273]) ).
cnf(c_36308,plain,
cong(sK4,sK2,sK4,sK4),
inference(resolve,[status(thm)],[c_36216,c_196]) ).
cnf(c_37344,plain,
cong(sK4,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_36308,c_721]) ).
cnf(c_37388,plain,
midp(sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_37344,c_6333]) ).
cnf(c_37420,plain,
midp(sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_37388,c_248]) ).
cnf(c_44201,plain,
midp(sK4,sK2,sK8),
inference(resolve,[status(thm)],[c_35719,c_37420]) ).
cnf(c_44230,plain,
midp(sK4,sK8,sK2),
inference(resolve,[status(thm)],[c_44201,c_248]) ).
cnf(c_44298,plain,
cong(sK4,sK8,sK4,sK2),
inference(resolve,[status(thm)],[c_44230,c_196]) ).
cnf(c_44624,plain,
cyclic(sK8,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_44298,c_866]) ).
cnf(c_45320,plain,
cyclic(sK1,sK8,sK1,sK2),
inference(resolve,[status(thm)],[c_44624,c_244]) ).
cnf(c_46027,plain,
cyclic(sK1,sK1,sK8,sK2),
inference(resolve,[status(thm)],[c_45320,c_245]) ).
cnf(c_46676,plain,
( cyclic(sK1,sK8,A,sK2)
| ~ cyclic(sK1,sK1,sK8,A) ),
inference(resolve,[status(thm)],[c_46027,c_243]) ).
cnf(c_50678,plain,
eqangle(A,B,sK1,sK1,A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_10116,c_241]) ).
cnf(c_50685,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_50678,c_5262]) ).
cnf(c_50688,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_50685,c_244]) ).
cnf(c_50691,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_50688,c_245]) ).
cnf(c_50694,plain,
cyclic(sK1,sK1,sK1,A),
inference(resolve,[status(thm)],[c_50691,c_246]) ).
cnf(c_50698,plain,
cyclic(sK1,sK1,sK8,A),
inference(resolve,[status(thm)],[c_50694,c_11307]) ).
cnf(c_50701,plain,
cyclic(sK1,sK8,A,sK2),
inference(resolve,[status(thm)],[c_50698,c_46676]) ).
cnf(c_51274,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK1,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_50694,c_243]) ).
cnf(c_50804,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_50694,c_51274]) ).
cnf(c_51275,plain,
( cyclic(sK1,sK8,A,B)
| ~ cyclic(sK1,sK1,sK8,A) ),
inference(resolve,[status(thm)],[c_50698,c_243]) ).
cnf(c_50815,plain,
cyclic(sK1,sK8,A,B),
inference(resolve,[status(thm)],[c_50804,c_51275]) ).
cnf(c_51276,plain,
( cyclic(sK8,A,B,sK2)
| ~ cyclic(sK1,sK8,A,B) ),
inference(resolve,[status(thm)],[c_50701,c_243]) ).
cnf(c_50845,plain,
cyclic(sK8,A,B,sK2),
inference(resolve,[status(thm)],[c_50815,c_51276]) ).
cnf(c_51277,plain,
( cyclic(sK1,A,B,C)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_50804,c_243]) ).
cnf(c_51175,plain,
cyclic(sK1,A,B,C),
inference(resolve,[status(thm)],[c_50804,c_51277]) ).
cnf(c_51278,plain,
( cyclic(sK8,A,B,C)
| ~ cyclic(sK1,sK8,A,B) ),
inference(resolve,[status(thm)],[c_50815,c_243]) ).
cnf(c_51215,plain,
cyclic(sK8,A,B,C),
inference(resolve,[status(thm)],[c_51175,c_51278]) ).
cnf(c_51279,plain,
( cyclic(A,B,sK2,C)
| ~ cyclic(sK8,A,B,C) ),
inference(resolve,[status(thm)],[c_50845,c_243]) ).
cnf(c_51264,plain,
cyclic(A,B,sK2,C),
inference(resolve,[status(thm)],[c_51215,c_51279]) ).
cnf(c_51265,plain,
$false,
inference(resolve,[status(thm)],[c_51264,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO624+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 : n003.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 13:46:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 300032 was started by sandbox on n003,
% 0.10/0.37 % Fri Sep 25 13:46:37 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 217.66/40.05
% 217.66/40.05 % given #500 (A,wt=38): 364 -cong(A,c6,A,B) | c3 = A | coll(f14(c6,c8,C,B,A,c3),c8,B) | -cong(A,c6,A,c8) | -cong(A,c6,A,C). [resolve(152,a,138,b)].
% 217.66/40.05
% 217.66/40.05 % given #1000 (T,wt=9): 19422 coll(c6,c3,c5). [resolve(18704,a,1636,a)].
% 217.66/40.05
% 217.66/40.05 % given #1500 (W,wt=13): 2544 -coll(c1,c1,A) | coll(c4,A,c1). [resolve(1288,a,256,a)].
% 217.66/40.05
% 217.66/40.05 % given #2000 (T,wt=9): 26647 coll(c6,c2,c9). [resolve(26643,a,257,a)].
% 217.66/40.05
% 217.66/40.05 % given #2500 (W,wt=13): 19339 -coll(c4,c6,A) | coll(A,c1,c4). [resolve(18523,a,256,b)].
% 217.66/40.05
% 217.66/40.05 % given #3000 (T,wt=13): 22224 -coll(c10,c7,A) | coll(c7,A,c10). [resolve(21550,a,256,a)].
% 217.66/40.05
% 217.66/40.05 % given #3500 (T,wt=10): 30626 para(c7,c6,c4,c6). [resolve(30286,a,254,a)].
% 217.66/40.05
% 217.66/40.05 % given #4000 (A,wt=25): 1051 -perp(A,B,B,c1) | perp(f17(A,c1,B,c6,c5),A,c6,c5). [resolve(767,a,165,b)].
% 217.66/40.05
% 217.66/40.05 % given #4500 (T,wt=10): 41687 cong(c6,c8,c8,c7). [resolve(41535,a,236,a)].
% 217.66/40.05
% 217.66/40.05 % given #5000 (W,wt=10): 42219 para(c3,c6,c3,c7). [resolve(42147,a,255,a)].
% 217.66/40.05
% 217.66/40.05 % given #5500 (T,wt=10): 44502 cong(c7,c4,c8,c7). [resolve(44259,a,237,a)].
% 217.66/40.05
% 217.66/40.05 % given #6000 (W,wt=10): 47886 cong(c6,c8,c7,c6). [resolve(47670,a,237,a)].
% 217.66/40.05
% 217.66/40.05 % given #6500 (T,wt=13): 46600 -midp(A,c8,c7) | midp(A,c6,c6). [resolve(45917,a,298,b)].
% 217.66/40.05
% 217.66/40.05 % given #7000 (T,wt=14): 9547 -midp(c6,A,B) | para(A,c6,B,c6). [resolve(9514,a,201,b)].
% 217.66/40.05
% 217.66/40.05 % SZS status Theorem for theBenchmark
% 217.66/40.05
% 217.66/40.05 % Proof 1 at 5.94 (+ 1.34) seconds.
% 217.66/40.05 % Length of proof is 340.
% 217.66/40.05 % Level of proof is 47.
% 217.66/40.05 % Maximum clause weight is 34.000.
% 217.66/40.05 % Given clauses 7148.
% 217.66/40.05
% 217.66/40.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------