%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO614+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 : n001.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 07:18:14 AM UTC 2026
% Result : Theorem 210.89s 33.36s
% Output : CNFRefutation 210.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 35
% Syntax : Number of formulae : 283 ( 148 unt; 0 def)
% Number of atoms : 525 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 393 ( 151 ~; 147 |; 59 &)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-7 aty)
% Number of variables : 467 ( 31 sgn 179 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
fof(ruleD7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('theBenchmark.p',ruleD7) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(ruleD10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('theBenchmark.p',ruleD10) ).
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(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(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('theBenchmark.p',ruleD41) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(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(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(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(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(ruleD69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD69) ).
fof(ruleX7,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( coll(D,A,B)
& coll(C,A,B)
& midp(N,C,D)
& midp(M,A,B) )
=> midp(P,A,Q) ),
file('theBenchmark.p',ruleX7) ).
fof(exemplo6GDDFULL618076,conjecture,
! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
file('theBenchmark.p',exemplo6GDDFULL618076) ).
fof(exemplo6GDDFULL618076_neg,negated_conjecture,
~ ! [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ( circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) )
=> perp(E,K,K,N) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618076]) ).
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]) ).
fof(nnf_95,plain,
? [A,B,C,O,G,E,K,H,N,NWPNT1] :
( ~ perp(E,K,K,N)
& circle(N,K,G,H)
& coll(H,O,G)
& perp(H,A,O,G)
& coll(K,A,B)
& perp(K,E,A,B)
& circle(O,A,E,NWPNT1)
& coll(E,O,G)
& midp(G,C,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618076_neg]) ).
fof(sk_exemplo6GDDFULL618076_neg,plain,
( ~ perp(sK4,sK5,sK5,sK6)
& circle(sK6,sK5,sK7,sK10)
& coll(sK10,sK0,sK7)
& perp(sK10,sK1,sK0,sK7)
& coll(sK5,sK1,sK2)
& perp(sK5,sK4,sK1,sK2)
& circle(sK0,sK1,sK4,sK9)
& coll(sK4,sK0,sK7)
& midp(sK7,sK3,sK2)
& circle(sK0,sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK7,sK4,sK9,sK5,sK10,sK6]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3),skolemize(O,sK0),skolemize(G,sK7),skolemize(E,sK4),skolemize(K,sK5),skolemize(H,sK10),skolemize(N,sK6),skolemize(NWPNT1,sK9)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
cnf(c_144,negated_conjecture,
( perp(sK1,sK2,sK2,sK3)
| ~ coll(sK0,sK1,sK3) ),
inference(resolve,[status(thm)],[c_109,c_101]) ).
cnf(c_187,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]) ).
cnf(c_192,negated_conjecture,
~ perp(sK4,sK5,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
cnf(c_195,negated_conjecture,
coll(sK5,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
cnf(c_196,negated_conjecture,
perp(sK5,sK4,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
cnf(c_197,negated_conjecture,
coll(sK4,sK0,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
cnf(c_198,negated_conjecture,
midp(sK7,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618076_neg]) ).
fof(nnf_83,plain,
! [A,B,C,D,M,N,Q] :
? [P] :
( midp(P,A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(fof_nnf,[status(thm)],[ruleX7]) ).
fof(sk_ruleX7,plain,
! [A,B,C,D,M,N,Q] :
( midp(sK8(A,B,C,D,M,N,Q),A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(P,sK8(A,B,C,D,M,N,Q))],[nnf_83]) ).
cnf(c_215,plain,
( midp(sK8(B,C,E,F,A,D,V6),B,V6)
| ~ coll(F,B,C)
| ~ coll(E,B,C)
| ~ midp(D,E,F)
| ~ midp(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX7]) ).
cnf(c_234,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_235,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_236,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_237,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_239,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_240,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_246,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_247,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_248,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_253,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_255,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_256,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_258,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_259,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_275,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_276,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_282,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_283,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_284,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_285,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_286,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_287,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_288,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_289,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_290,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_291,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_293,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_294,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_295,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_296,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_297,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_312,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_187]) ).
cnf(c_330,plain,
( midp(sK8(B,C,B,C,A,A,D),B,D)
| ~ coll(C,B,C)
| ~ coll(B,B,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_215]) ).
cnf(c_337,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_338,plain,
( para(B,B,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_240]) ).
cnf(c_344,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_255]) ).
cnf(c_345,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,E,D,E,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_255]) ).
cnf(c_346,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_282]) ).
cnf(c_347,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_286]) ).
cnf(c_351,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_295]) ).
cnf(c_360,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_347]) ).
cnf(c_449,plain,
coll(sK7,sK3,sK2),
inference(resolve,[status(thm)],[c_234,c_198]) ).
cnf(c_450,plain,
cong(sK7,sK3,sK7,sK2),
inference(resolve,[status(thm)],[c_235,c_198]) ).
cnf(c_451,plain,
( para(sK3,A,sK2,B)
| ~ midp(sK7,A,B) ),
inference(resolve,[status(thm)],[c_240,c_198]) ).
cnf(c_463,plain,
midp(sK7,sK2,sK3),
inference(resolve,[status(thm)],[c_287,c_198]) ).
cnf(c_469,plain,
( para(A,B,sK1,sK2)
| ~ perp(A,B,sK5,sK4) ),
inference(resolve,[status(thm)],[c_289,c_196]) ).
cnf(c_474,plain,
perp(sK1,sK2,sK5,sK4),
inference(resolve,[status(thm)],[c_290,c_196]) ).
cnf(c_479,plain,
perp(sK5,sK4,sK2,sK1),
inference(resolve,[status(thm)],[c_291,c_196]) ).
cnf(c_491,plain,
coll(sK1,sK5,sK2),
inference(resolve,[status(thm)],[c_296,c_195]) ).
cnf(c_493,plain,
coll(sK4,sK7,sK0),
inference(resolve,[status(thm)],[c_297,c_197]) ).
cnf(c_494,plain,
coll(sK5,sK2,sK1),
inference(resolve,[status(thm)],[c_297,c_195]) ).
cnf(c_496,plain,
( midp(sK8(sK3,sK2,sK3,sK2,sK7,sK7,A),sK3,A)
| ~ coll(sK2,sK3,sK2)
| ~ coll(sK3,sK3,sK2) ),
inference(resolve,[status(thm)],[c_330,c_198]) ).
cnf(c_503,plain,
coll(sK7,sK7,sK4),
inference(resolve,[status(thm)],[c_351,c_197]) ).
cnf(c_504,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_351,c_195]) ).
cnf(c_506,plain,
coll(sK2,sK2,sK7),
inference(resolve,[status(thm)],[c_449,c_351]) ).
cnf(c_507,plain,
coll(sK7,sK2,sK3),
inference(resolve,[status(thm)],[c_449,c_297]) ).
cnf(c_508,plain,
coll(sK3,sK7,sK2),
inference(resolve,[status(thm)],[c_449,c_296]) ).
cnf(c_518,plain,
( midp(sK8(sK2,sK3,sK2,sK3,sK7,sK7,A),sK2,A)
| ~ coll(sK3,sK2,sK3)
| ~ coll(sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_463,c_330]) ).
cnf(c_539,plain,
coll(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_491,c_351]) ).
cnf(c_549,plain,
( coll(sK0,A,sK4)
| ~ coll(sK4,sK7,A) ),
inference(resolve,[status(thm)],[c_493,c_295]) ).
cnf(c_553,plain,
( coll(sK1,A,sK5)
| ~ coll(sK5,sK2,A) ),
inference(resolve,[status(thm)],[c_494,c_295]) ).
cnf(c_560,plain,
( coll(A,sK4,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_503,c_295]) ).
cnf(c_561,plain,
( coll(sK4,A,sK7)
| ~ coll(sK7,sK7,A) ),
inference(resolve,[status(thm)],[c_503,c_295]) ).
cnf(c_563,plain,
coll(sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_504,c_297]) ).
cnf(c_564,plain,
( coll(A,sK5,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_504,c_295]) ).
cnf(c_574,plain,
coll(sK3,sK3,sK7),
inference(resolve,[status(thm)],[c_507,c_351]) ).
cnf(c_575,plain,
coll(sK2,sK7,sK3),
inference(resolve,[status(thm)],[c_507,c_296]) ).
cnf(c_578,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_508,c_351]) ).
cnf(c_582,plain,
( midp(sK8(sK2,sK3,sK2,sK3,sK7,sK7,A),sK2,A)
| ~ coll(sK3,sK2,sK3) ),
inference(resolve,[status(thm)],[c_578,c_518]) ).
cnf(c_591,plain,
coll(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_539,c_351]) ).
cnf(c_592,plain,
coll(sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_539,c_297]) ).
cnf(c_628,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_563,c_351]) ).
cnf(c_644,plain,
coll(sK7,sK7,sK3),
inference(resolve,[status(thm)],[c_574,c_351]) ).
cnf(c_648,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_575,c_351]) ).
cnf(c_652,plain,
( midp(sK8(sK3,sK2,sK3,sK2,sK7,sK7,A),sK3,A)
| ~ coll(sK2,sK3,sK2) ),
inference(resolve,[status(thm)],[c_648,c_496]) ).
cnf(c_653,plain,
coll(sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_578,c_297]) ).
cnf(c_656,plain,
midp(sK8(sK3,sK2,sK3,sK2,sK7,sK7,A),sK3,A),
inference(resolve,[status(thm)],[c_653,c_652]) ).
cnf(c_756,plain,
coll(sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_648,c_297]) ).
cnf(c_759,plain,
midp(sK8(sK2,sK3,sK2,sK3,sK7,sK7,A),sK2,A),
inference(resolve,[status(thm)],[c_756,c_582]) ).
cnf(c_771,plain,
coll(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_653,c_296]) ).
cnf(c_857,plain,
cyclic(sK3,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_450,c_360]) ).
cnf(c_42149,plain,
( perp(sK3,sK2,sK2,sK2)
| ~ coll(sK7,sK3,sK2) ),
inference(resolve,[status(thm)],[c_450,c_312]) ).
cnf(c_873,plain,
perp(sK3,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_449,c_42149]) ).
cnf(c_940,plain,
perp(sK1,sK2,sK4,sK5),
inference(resolve,[status(thm)],[c_474,c_291]) ).
cnf(c_968,plain,
perp(sK2,sK1,sK5,sK4),
inference(resolve,[status(thm)],[c_479,c_290]) ).
cnf(c_1135,plain,
cyclic(sK2,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_857,c_283]) ).
cnf(c_1138,plain,
eqangle(sK2,sK3,sK2,sK2,sK2,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_857,c_258]) ).
cnf(c_1154,plain,
perp(sK2,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_873,c_290]) ).
cnf(c_1179,plain,
perp(sK4,sK5,sK1,sK2),
inference(resolve,[status(thm)],[c_940,c_290]) ).
cnf(c_1325,plain,
cyclic(sK2,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_1135,c_284]) ).
cnf(c_1345,plain,
perp(sK2,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1154,c_291]) ).
cnf(c_1361,plain,
perp(sK4,sK5,sK2,sK1),
inference(resolve,[status(thm)],[c_1179,c_291]) ).
cnf(c_1469,plain,
cyclic(sK2,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1325,c_285]) ).
cnf(c_1491,plain,
perp(sK2,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_1345,c_290]) ).
cnf(c_1493,plain,
( para(sK2,sK2,A,B)
| ~ perp(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_1345,c_289]) ).
cnf(c_1513,plain,
( para(sK4,sK5,A,B)
| ~ perp(sK2,sK1,A,B) ),
inference(resolve,[status(thm)],[c_1361,c_289]) ).
cnf(c_1581,plain,
cyclic(sK2,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_1469,c_346]) ).
cnf(c_1583,plain,
( cyclic(sK2,sK2,A,sK3)
| ~ cyclic(sK2,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1469,c_282]) ).
cnf(c_1584,plain,
( cyclic(sK2,sK2,sK3,A)
| ~ cyclic(sK2,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1469,c_282]) ).
cnf(c_1608,plain,
( cong(sK2,sK2,sK2,sK2)
| ~ midp(sK3,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1491,c_248]) ).
cnf(c_1674,plain,
cyclic(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1581,c_284]) ).
cnf(c_1676,plain,
( cyclic(sK2,sK3,sK3,A)
| ~ cyclic(sK2,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_1581,c_282]) ).
cnf(c_1737,plain,
cyclic(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_1674,c_285]) ).
cnf(c_1738,plain,
cyclic(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1674,c_283]) ).
cnf(c_1777,plain,
( cyclic(sK3,sK3,A,sK2)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1737,c_282]) ).
cnf(c_1778,plain,
( cyclic(sK3,sK3,sK2,A)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1737,c_282]) ).
cnf(c_1813,plain,
coll(sK3,sK4,sK7),
inference(resolve,[status(thm)],[c_560,c_644]) ).
cnf(c_1817,plain,
coll(sK4,sK3,sK7),
inference(resolve,[status(thm)],[c_1813,c_296]) ).
cnf(c_1832,plain,
coll(sK4,sK7,sK3),
inference(resolve,[status(thm)],[c_1817,c_297]) ).
cnf(c_1858,plain,
coll(sK0,sK3,sK4),
inference(resolve,[status(thm)],[c_1832,c_549]) ).
cnf(c_1905,plain,
coll(sK0,sK4,sK3),
inference(resolve,[status(thm)],[c_1858,c_297]) ).
cnf(c_1961,plain,
( coll(A,sK3,sK0)
| ~ coll(sK0,sK4,A) ),
inference(resolve,[status(thm)],[c_1905,c_295]) ).
cnf(c_2113,plain,
coll(sK3,sK5,sK2),
inference(resolve,[status(thm)],[c_564,c_578]) ).
cnf(c_2114,plain,
coll(sK7,sK5,sK2),
inference(resolve,[status(thm)],[c_564,c_506]) ).
cnf(c_2128,plain,
coll(sK5,sK3,sK2),
inference(resolve,[status(thm)],[c_2113,c_296]) ).
cnf(c_2132,plain,
coll(sK5,sK7,sK2),
inference(resolve,[status(thm)],[c_2114,c_296]) ).
cnf(c_2157,plain,
coll(sK5,sK2,sK3),
inference(resolve,[status(thm)],[c_2128,c_297]) ).
cnf(c_2164,plain,
coll(sK5,sK2,sK7),
inference(resolve,[status(thm)],[c_2132,c_297]) ).
cnf(c_2198,plain,
coll(sK1,sK3,sK5),
inference(resolve,[status(thm)],[c_2157,c_553]) ).
cnf(c_2209,plain,
coll(sK1,sK7,sK5),
inference(resolve,[status(thm)],[c_2164,c_553]) ).
cnf(c_2260,plain,
coll(sK1,sK5,sK3),
inference(resolve,[status(thm)],[c_2198,c_297]) ).
cnf(c_2277,plain,
coll(sK1,sK5,sK7),
inference(resolve,[status(thm)],[c_2209,c_297]) ).
cnf(c_2334,plain,
coll(sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_2260,c_351]) ).
cnf(c_2355,plain,
coll(sK7,sK7,sK1),
inference(resolve,[status(thm)],[c_2277,c_351]) ).
cnf(c_2415,plain,
coll(sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_2334,c_297]) ).
cnf(c_2441,plain,
coll(sK4,sK1,sK7),
inference(resolve,[status(thm)],[c_2355,c_561]) ).
cnf(c_2484,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_451,c_463]) ).
cnf(c_2502,plain,
coll(sK1,sK3,sK3),
inference(resolve,[status(thm)],[c_2415,c_296]) ).
cnf(c_2537,plain,
coll(sK4,sK7,sK1),
inference(resolve,[status(thm)],[c_2441,c_297]) ).
cnf(c_2593,plain,
coll(sK0,sK1,sK4),
inference(resolve,[status(thm)],[c_2537,c_549]) ).
cnf(c_2619,plain,
coll(sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_2593,c_297]) ).
cnf(c_2695,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_2484,c_294]) ).
cnf(c_2815,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_469,c_968]) ).
cnf(c_2816,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_469,c_474]) ).
cnf(c_2819,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_2695,c_337]) ).
cnf(c_2822,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_2695,c_259]) ).
cnf(c_2881,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_2815,c_294]) ).
cnf(c_2886,plain,
( midp(sK1,A,sK2)
| ~ coll(sK1,A,sK2)
| ~ midp(sK2,A,sK1) ),
inference(resolve,[status(thm)],[c_2815,c_253]) ).
cnf(c_2898,plain,
( midp(sK2,A,sK2)
| ~ coll(sK2,A,sK2)
| ~ midp(sK1,A,sK1) ),
inference(resolve,[status(thm)],[c_2816,c_253]) ).
cnf(c_2959,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_2881,c_337]) ).
cnf(c_4132,plain,
midp(sK8(sK3,sK2,sK3,sK2,sK7,sK7,A),A,sK3),
inference(resolve,[status(thm)],[c_656,c_287]) ).
cnf(c_4135,plain,
( para(B,sK3,C,A)
| ~ midp(sK8(sK3,sK2,sK3,sK2,sK7,sK7,A),B,C) ),
inference(resolve,[status(thm)],[c_656,c_240]) ).
cnf(c_4782,plain,
para(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_759,c_338]) ).
cnf(c_4828,plain,
eqangle(sK2,sK2,A,B,C,C,A,B),
inference(resolve,[status(thm)],[c_4782,c_259]) ).
cnf(c_5250,plain,
coll(sK1,sK3,sK0),
inference(resolve,[status(thm)],[c_1961,c_2619]) ).
cnf(c_5258,plain,
coll(sK1,sK0,sK3),
inference(resolve,[status(thm)],[c_5250,c_297]) ).
cnf(c_5274,plain,
coll(sK0,sK1,sK3),
inference(resolve,[status(thm)],[c_5258,c_296]) ).
cnf(c_5277,negated_conjecture,
perp(sK1,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_5274,c_144]) ).
cnf(c_5334,plain,
perp(sK1,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_5277,c_291]) ).
cnf(c_5376,plain,
perp(sK3,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_5334,c_290]) ).
cnf(c_5438,plain,
perp(sK3,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_5376,c_291]) ).
cnf(c_5495,plain,
( cong(sK3,sK2,sK3,sK1)
| ~ midp(sK2,sK2,sK1) ),
inference(resolve,[status(thm)],[c_5438,c_248]) ).
cnf(c_42150,plain,
( cong(sK3,sK2,sK3,sK2)
| ~ cyclic(sK3,sK2,sK2,sK2)
| ~ cyclic(sK3,sK2,sK2,sK3) ),
inference(resolve,[status(thm)],[c_1138,c_345]) ).
cnf(c_42151,plain,
( cong(sK3,sK2,sK3,sK2)
| ~ cyclic(sK3,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1738,c_42150]) ).
cnf(c_11747,plain,
cong(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_857,c_42151]) ).
cnf(c_42152,plain,
( midp(sK3,sK2,sK2)
| ~ coll(sK3,sK2,sK2) ),
inference(resolve,[status(thm)],[c_11747,c_236]) ).
cnf(c_11855,plain,
midp(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_771,c_42152]) ).
cnf(c_11886,plain,
cong(sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_11855,c_1608]) ).
cnf(c_11894,plain,
midp(sK3,sK1,sK1),
inference(resolve,[status(thm)],[c_11855,c_2959]) ).
cnf(c_11979,plain,
cong(sK3,sK1,sK3,sK1),
inference(resolve,[status(thm)],[c_11894,c_235]) ).
cnf(c_42153,plain,
( midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_11886,c_236]) ).
cnf(c_12180,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_628,c_42153]) ).
cnf(c_12204,plain,
midp(sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_12180,c_2959]) ).
cnf(c_12599,plain,
cong(sK3,sK1,sK1,sK3),
inference(resolve,[status(thm)],[c_11979,c_276]) ).
cnf(c_13171,plain,
cong(sK1,sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_12599,c_275]) ).
cnf(c_13333,plain,
cong(sK1,sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_13171,c_276]) ).
cnf(c_42154,plain,
( midp(sK1,sK3,sK3)
| ~ coll(sK1,sK3,sK3) ),
inference(resolve,[status(thm)],[c_13333,c_236]) ).
cnf(c_13584,plain,
midp(sK1,sK3,sK3),
inference(resolve,[status(thm)],[c_2502,c_42154]) ).
cnf(c_13620,plain,
midp(sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_13584,c_2819]) ).
cnf(c_13665,plain,
midp(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_13620,c_2959]) ).
cnf(c_26520,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_2822,c_256]) ).
cnf(c_42155,plain,
( midp(sK1,sK1,sK2)
| ~ coll(sK1,sK1,sK2) ),
inference(resolve,[status(thm)],[c_2886,c_12204]) ).
cnf(c_27067,plain,
midp(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_591,c_42155]) ).
cnf(c_27102,plain,
cong(sK1,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_27067,c_235]) ).
cnf(c_27137,plain,
cyclic(sK1,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_27102,c_360]) ).
cnf(c_27193,plain,
cyclic(sK2,sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_27137,c_283]) ).
cnf(c_27283,plain,
cyclic(sK2,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_27193,c_284]) ).
cnf(c_27398,plain,
cyclic(sK2,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_27283,c_285]) ).
cnf(c_42156,plain,
( midp(sK2,sK1,sK2)
| ~ coll(sK2,sK1,sK2) ),
inference(resolve,[status(thm)],[c_2898,c_13665]) ).
cnf(c_27448,plain,
midp(sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_592,c_42156]) ).
cnf(c_27512,plain,
midp(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_27448,c_287]) ).
cnf(c_27522,plain,
cong(sK3,sK2,sK3,sK1),
inference(resolve,[status(thm)],[c_27512,c_5495]) ).
cnf(c_27668,plain,
cong(sK2,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_27512,c_235]) ).
cnf(c_27895,plain,
cyclic(sK2,sK2,sK3,sK1),
inference(resolve,[status(thm)],[c_27398,c_1584]) ).
cnf(c_27896,plain,
cyclic(sK2,sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_27398,c_1583]) ).
cnf(c_28164,plain,
cong(sK3,sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_27522,c_276]) ).
cnf(c_28285,plain,
cong(sK2,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_27668,c_276]) ).
cnf(c_28419,plain,
cyclic(sK2,sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_27895,c_1676]) ).
cnf(c_28427,plain,
cyclic(sK2,sK1,sK2,sK3),
inference(resolve,[status(thm)],[c_27896,c_284]) ).
cnf(c_28543,plain,
cong(sK1,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_28164,c_275]) ).
cnf(c_28688,plain,
cong(sK1,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_28285,c_275]) ).
cnf(c_28887,plain,
cyclic(sK3,sK3,sK2,sK1),
inference(resolve,[status(thm)],[c_28419,c_1778]) ).
cnf(c_28923,plain,
cyclic(sK1,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_28427,c_283]) ).
cnf(c_29039,plain,
cong(sK1,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_28543,c_276]) ).
cnf(c_42157,plain,
( perp(sK2,sK3,sK3,sK1)
| ~ cong(sK3,sK1,sK3,sK1)
| ~ cong(sK3,sK2,sK3,sK2) ),
inference(resolve,[status(thm)],[c_28887,c_246]) ).
cnf(c_42158,plain,
( perp(sK2,sK3,sK3,sK1)
| ~ cong(sK3,sK1,sK3,sK1) ),
inference(resolve,[status(thm)],[c_11747,c_42157]) ).
cnf(c_29365,plain,
perp(sK2,sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_11979,c_42158]) ).
cnf(c_42159,plain,
( perp(sK2,sK1,sK1,sK3)
| ~ cong(sK1,sK3,sK2,sK3)
| ~ cong(sK1,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_28923,c_246]) ).
cnf(c_42160,plain,
( perp(sK2,sK1,sK1,sK3)
| ~ cong(sK1,sK3,sK2,sK3) ),
inference(resolve,[status(thm)],[c_28688,c_42159]) ).
cnf(c_29521,plain,
perp(sK2,sK1,sK1,sK3),
inference(resolve,[status(thm)],[c_29039,c_42160]) ).
cnf(c_30186,plain,
para(sK2,sK2,sK3,sK1),
inference(resolve,[status(thm)],[c_29365,c_1493]) ).
cnf(c_30346,plain,
para(sK4,sK5,sK1,sK3),
inference(resolve,[status(thm)],[c_29521,c_1513]) ).
cnf(c_30832,plain,
para(sK3,sK1,sK2,sK2),
inference(resolve,[status(thm)],[c_30186,c_293]) ).
cnf(c_31026,plain,
para(sK4,sK5,sK3,sK1),
inference(resolve,[status(thm)],[c_30346,c_294]) ).
cnf(c_31357,plain,
( perp(sK3,sK1,A,B)
| ~ perp(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_30832,c_288]) ).
cnf(c_31429,plain,
( perp(sK4,sK5,A,B)
| ~ perp(sK3,sK1,A,B) ),
inference(resolve,[status(thm)],[c_31026,c_288]) ).
cnf(c_39581,plain,
para(A,sK3,sK3,A),
inference(resolve,[status(thm)],[c_4135,c_4132]) ).
cnf(c_39582,plain,
para(A,sK3,A,sK3),
inference(resolve,[status(thm)],[c_39581,c_294]) ).
cnf(c_39589,plain,
coll(A,sK3,sK3),
inference(resolve,[status(thm)],[c_39582,c_237]) ).
cnf(c_39627,plain,
coll(sK3,sK3,A),
inference(resolve,[status(thm)],[c_39589,c_351]) ).
cnf(c_39633,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_39627,c_26520]) ).
cnf(c_40635,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_39633,c_284]) ).
cnf(c_40710,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_40635,c_285]) ).
cnf(c_40721,plain,
cyclic(sK3,sK3,A,sK2),
inference(resolve,[status(thm)],[c_40710,c_1777]) ).
cnf(c_42161,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_40710,c_282]) ).
cnf(c_41066,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_40710,c_42161]) ).
cnf(c_42162,plain,
( cyclic(sK3,A,B,sK2)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_40721,c_282]) ).
cnf(c_41106,plain,
cyclic(sK3,A,B,sK2),
inference(resolve,[status(thm)],[c_41066,c_42162]) ).
cnf(c_42163,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_41066,c_282]) ).
cnf(c_41599,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_41066,c_42163]) ).
cnf(c_42164,plain,
( cyclic(A,B,C,sK2)
| ~ cyclic(sK3,A,B,C) ),
inference(resolve,[status(thm)],[c_41106,c_282]) ).
cnf(c_41694,plain,
cyclic(A,B,C,sK2),
inference(resolve,[status(thm)],[c_41599,c_42164]) ).
cnf(c_42165,plain,
( cyclic(A,B,sK2,C)
| ~ cyclic(sK3,A,B,C) ),
inference(resolve,[status(thm)],[c_41106,c_282]) ).
cnf(c_41695,plain,
cyclic(A,B,sK2,C),
inference(resolve,[status(thm)],[c_41599,c_42165]) ).
cnf(c_42166,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_4828,c_344]) ).
cnf(c_42167,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_41694,c_42166]) ).
cnf(c_41719,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_41695,c_42167]) ).
cnf(c_42168,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_41719,c_247]) ).
cnf(c_42072,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_41719,c_42168]) ).
cnf(c_42086,plain,
perp(sK3,sK1,A,B),
inference(resolve,[status(thm)],[c_42072,c_31357]) ).
cnf(c_42147,plain,
perp(sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_42086,c_31429]) ).
cnf(c_42148,plain,
$false,
inference(resolve,[status(thm)],[c_42147,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO614+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n001.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Fri Sep 25 13:50:31 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 3432563 was started by sandbox2 on n001,
% 0.17/5.45 % Fri Sep 25 13:50:31 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.49
% 0.17/5.49 % From the command line: assign(max_seconds, 300).
% 210.89/33.36
% 210.89/33.36 % given #500 (A,wt=13): 415 -perp(c4,c1,c8,c5) | coll(f10(c4,c8,c5,c1),c5,c8). [resolve(209,b,194,a)].
% 210.89/33.36
% 210.89/33.36 % given #1000 (A,wt=8): 637 -coll(c5,c8,A) | coll(c5,A,c5). [resolve(567,a,295,a)].
% 210.89/33.36
% 210.89/33.36 % given #1500 (A,wt=23): 877 -cong(A,c3,A,B) | c5 = A | coll(f13(c3,B,B,c2,c5,A),c3,B) | -cong(c5,c3,c5,B). [resolve(450,a,310,a),flip(b)].
% 210.89/33.36
% 210.89/33.36 % given #2000 (A,wt=14): 981 -perp(c2,c6,c7,c1) | perp(c2,f11(c7,c2,c1,c6),c1,c7). [resolve(479,a,206,a)].
% 210.89/33.36
% 210.89/33.36 % given #2500 (A,wt=23): 1086 -cong(c5,c2,c5,A) | -cong(B,c2,B,c3) | c5 = B | coll(f14(c2,c3,c3,A,c5,B),c3,A). [resolve(523,a,304,e),flip(c)].
% 210.89/33.36
% 210.89/33.36 % given #3000 (A,wt=10): 1208 -perp(A,B,c2,c1) | para(A,B,c7,c6). [resolve(968,a,289,b)].
% 210.89/33.36
% 210.89/33.36 % given #3500 (A,wt=9): 1364 -midp(c7,c1,c2) | cong(c6,c1,c6,c2). [resolve(1179,a,248,b)].
% 210.89/33.36
% 210.89/33.36 % given #4000 (A,wt=14): 1520 -perp(c2,c7,c6,c1) | perp(c6,f10(c6,c2,c1,c7),c1,c2). [resolve(1361,a,208,a)].
% 210.89/33.36
% 210.89/33.36 % given #4500 (A,wt=14): 1704 -perp(c2,c5,c5,c3) | perp(c2,f11(c5,c2,c3,c5),c3,c5). [resolve(1613,a,206,a)].
% 210.89/33.36
% 210.89/33.36 % given #5000 (A,wt=13): 2058 coll(f17(f12(c1,c6,c10,c4),c4,c1,c3,c4),c3,c4). [resolve(2012,a,377,a)].
% 210.89/33.36
% 210.89/33.36 % given #5500 (A,wt=18): 2519 perp(f17(f12(c1,c6,c10,c4),c4,c1,c7,c6),f12(c1,c6,c10,c4),c7,c6). [resolve(2425,a,374,a)].
% 210.89/33.36
% 210.89/33.36 % given #6000 (A,wt=24): 2763 -midp(A,c7,c7) | -para(c7,c6,B,A) | -coll(c6,c6,B) | coll(f8(c7,c7,C,c6,c6,B,A),A,B). [resolve(2654,a,213,c)].
% 210.89/33.36
% 210.89/33.36 % given #6500 (A,wt=17): 2911 -coll(A,c6,c6) | -coll(A,c7,c7) | eqratio(A,c6,c6,c6,A,c7,c7,c7). [resolve(2847,a,238,a)].
% 210.89/33.36
% 210.89/33.36 % given #7000 (A,wt=21): 3068 -perp(f12(c1,c6,c10,c4),c4,c1,c1) | coll(f10(f12(c1,c6,c10,c4),c1,c1,c4),c1,c1). [resolve(477,a,209,b)].
% 210.89/33.36
% 210.89/33.36 % given #7500 (A,wt=9): 3320 eqratio(c5,c3,c5,c3,c3,c2,c3,c2). [resolve(500,a,270,a)].
% 210.89/33.36
% 210.89/33.36 % given #8000 (A,wt=18): 3594 perp(f17(f12(c7,c5,c8,c9),c9,c7,c7,c7),f12(c7,c5,c8,c9),c7,c7). [resolve(3590,a,375,a)].
% 210.89/33.36
% 210.89/33.36 % given #8500 (A,wt=18): 3905 perp(f17(f12(c7,c5,c8,c9),c9,c7,c7,c1),f12(c7,c5,c8,c9),c7,c1). [resolve(3866,a,375,a)].
% 210.89/33.36
% 210.89/33.36 % given #9000 (A,wt=18): 4256 perp(f17(f12(c1,c2,c3,c4),c4,c1,c9,c4),f12(c1,c2,c3,c4),c9,c4). [resolve(4185,a,373,a)].
% 210.89/33.36
% 210.89/33.36 % given #9500 (A,wt=16): 4764 eqratio(c5,c2,c2,c3,f7(c2,c3,c2,c3,c5,c5,A),c2,c2,A). [resolve(759,a,525,a)].
% 210.89/33.36
% 210.89/33.36 % SZS status Theorem for theBenchmark
% 210.89/33.36
% 210.89/33.36 % Proof 1 at 23.65 (+ 3.80) seconds.
% 210.89/33.36 % Length of proof is 258.
% 210.89/33.36 % Level of proof is 32.
% 210.89/33.36 % Maximum clause weight is 29.000.
% 210.89/33.36 % Given clauses 9977.
% 210.89/33.36
% 210.89/33.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------