%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO608+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 07:18:13 AM UTC 2026
% Result : Theorem 20.80s 8.71s
% Output : CNFRefutation 20.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 33
% Syntax : Number of formulae : 245 ( 117 unt; 0 def)
% Number of atoms : 454 ( 0 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 341 ( 132 ~; 128 |; 47 &)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 436 ( 35 sgn 161 !; 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(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(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(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(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(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(exemplo6GDDFULL618070,conjecture,
! [P,A,B,O,A1,B1,O1,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O1,P,A1,B1)
& circle(O,A,B1,NWPNT4)
& coll(B1,P,B)
& circle(O,A,A1,NWPNT3)
& coll(A1,P,A)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(O,A1,A1,O1) ),
file('theBenchmark.p',exemplo6GDDFULL618070) ).
fof(exemplo6GDDFULL618070_neg,negated_conjecture,
~ ! [P,A,B,O,A1,B1,O1,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O1,P,A1,B1)
& circle(O,A,B1,NWPNT4)
& coll(B1,P,B)
& circle(O,A,A1,NWPNT3)
& coll(A1,P,A)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) )
=> perp(O,A1,A1,O1) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618070]) ).
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_202,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,
? [P,A,B,O,A1,B1,O1,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ~ perp(O,A1,A1,O1)
& circle(O1,P,A1,B1)
& circle(O,A,B1,NWPNT4)
& coll(B1,P,B)
& circle(O,A,A1,NWPNT3)
& coll(A1,P,A)
& circle(O,A,NWPNT1,NWPNT2)
& midp(O,B,A) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618070_neg]) ).
fof(sk_exemplo6GDDFULL618070_neg,plain,
( ~ perp(sK0,sK1,sK1,sK2)
& circle(sK2,sK4,sK1,sK3)
& circle(sK0,sK6,sK3,sK10)
& coll(sK3,sK4,sK5)
& circle(sK0,sK6,sK1,sK9)
& coll(sK1,sK4,sK6)
& circle(sK0,sK6,sK7,sK8)
& midp(sK0,sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK5,sK6,sK7,sK8,sK1,sK4,sK9,sK3,sK10,sK2]),skolemize(P,sK4),skolemize(A,sK6),skolemize(B,sK5),skolemize(O,sK0),skolemize(A1,sK1),skolemize(B1,sK3),skolemize(O1,sK2),skolemize(NWPNT1,sK7),skolemize(NWPNT2,sK8),skolemize(NWPNT3,sK9),skolemize(NWPNT4,sK10)],[nnf_95]) ).
cnf(c_207,negated_conjecture,
~ perp(sK0,sK1,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618070_neg]) ).
cnf(c_208,negated_conjecture,
coll(sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618070_neg]) ).
cnf(c_209,negated_conjecture,
coll(sK1,sK4,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618070_neg]) ).
cnf(c_210,negated_conjecture,
midp(sK0,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618070_neg]) ).
cnf(c_246,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_247,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_248,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_251,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_252,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_258,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_259,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_260,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_266,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_267,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_268,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_270,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_271,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_287,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_288,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_292,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_294,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_295,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_296,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_297,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_298,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_299,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_300,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_301,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_303,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_305,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_306,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_307,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_308,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_309,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_324,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_202]) ).
cnf(c_349,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_251]) ).
cnf(c_350,plain,
( para(B,B,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_252]) ).
cnf(c_352,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_258]) ).
cnf(c_354,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_266]) ).
cnf(c_355,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_267]) ).
cnf(c_356,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_267]) ).
cnf(c_358,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_359,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_298]) ).
cnf(c_362,plain,
( para(A,B,A,B)
| ~ perp(A,B,A,B) ),
inference(factor,[status(thm)],[c_301]) ).
cnf(c_363,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_307]) ).
cnf(c_371,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_355]) ).
cnf(c_372,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_359]) ).
cnf(c_576,plain,
coll(sK0,sK5,sK6),
inference(resolve,[status(thm)],[c_246,c_210]) ).
cnf(c_577,plain,
cong(sK0,sK5,sK0,sK6),
inference(resolve,[status(thm)],[c_247,c_210]) ).
cnf(c_587,plain,
( para(A,sK5,B,sK6)
| ~ midp(sK0,A,B) ),
inference(resolve,[status(thm)],[c_252,c_210]) ).
cnf(c_601,plain,
( para(sK0,A,sK6,B)
| ~ midp(A,sK5,B) ),
inference(resolve,[status(thm)],[c_266,c_210]) ).
cnf(c_605,plain,
midp(sK0,sK6,sK5),
inference(resolve,[status(thm)],[c_299,c_210]) ).
cnf(c_651,plain,
para(sK5,sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_350,c_210]) ).
cnf(c_653,plain,
coll(sK6,sK6,sK1),
inference(resolve,[status(thm)],[c_363,c_209]) ).
cnf(c_654,plain,
coll(sK5,sK5,sK3),
inference(resolve,[status(thm)],[c_363,c_208]) ).
cnf(c_28249,plain,
( ~ cong(sK0,sK5,sK0,sK6)
| perp(sK5,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_576,c_324]) ).
cnf(c_667,plain,
perp(sK5,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_577,c_28249]) ).
cnf(c_668,plain,
coll(sK0,sK6,sK5),
inference(resolve,[status(thm)],[c_576,c_309]) ).
cnf(c_669,plain,
coll(sK5,sK0,sK6),
inference(resolve,[status(thm)],[c_576,c_308]) ).
cnf(c_700,plain,
( para(sK0,A,sK5,B)
| ~ midp(A,sK6,B) ),
inference(resolve,[status(thm)],[c_605,c_266]) ).
cnf(c_707,plain,
cong(sK0,sK6,sK0,sK5),
inference(resolve,[status(thm)],[c_605,c_247]) ).
cnf(c_901,plain,
coll(sK6,sK1,sK6),
inference(resolve,[status(thm)],[c_653,c_309]) ).
cnf(c_902,plain,
( coll(A,sK1,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_653,c_307]) ).
cnf(c_940,plain,
coll(sK5,sK3,sK5),
inference(resolve,[status(thm)],[c_654,c_309]) ).
cnf(c_1003,plain,
coll(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_668,c_363]) ).
cnf(c_28250,plain,
( ~ cong(sK0,sK6,sK0,sK5)
| perp(sK6,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_668,c_324]) ).
cnf(c_1015,plain,
perp(sK6,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_707,c_28250]) ).
cnf(c_1016,plain,
coll(sK6,sK0,sK5),
inference(resolve,[status(thm)],[c_668,c_308]) ).
cnf(c_1035,plain,
coll(sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_669,c_363]) ).
cnf(c_1415,plain,
coll(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_901,c_363]) ).
cnf(c_1500,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_940,c_363]) ).
cnf(c_1637,plain,
coll(sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_1003,c_309]) ).
cnf(c_1661,plain,
coll(sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_1016,c_363]) ).
cnf(c_1713,plain,
coll(sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_1035,c_309]) ).
cnf(c_1720,plain,
( midp(sK6,sK6,sK5)
| ~ cong(sK6,sK6,sK6,sK5) ),
inference(resolve,[status(thm)],[c_1035,c_248]) ).
cnf(c_2232,plain,
( cyclic(A,sK6,sK6,sK6)
| ~ eqangle(sK6,A,sK6,sK6,sK6,A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_1415,c_268]) ).
cnf(c_2236,plain,
( midp(sK6,sK6,sK6)
| ~ cong(sK6,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_1415,c_248]) ).
cnf(c_2361,plain,
( midp(sK5,sK5,sK5)
| ~ cong(sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1500,c_248]) ).
cnf(c_2552,plain,
( ~ cong(sK5,sK0,sK5,sK5)
| perp(sK0,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1637,c_324]) ).
cnf(c_2553,plain,
coll(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_1637,c_308]) ).
cnf(c_2592,plain,
coll(sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_1661,c_309]) ).
cnf(c_2666,plain,
coll(sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_1713,c_308]) ).
cnf(c_3357,plain,
( midp(sK0,sK5,sK5)
| ~ cong(sK0,sK5,sK0,sK5) ),
inference(resolve,[status(thm)],[c_2553,c_248]) ).
cnf(c_3385,plain,
coll(sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_2592,c_308]) ).
cnf(c_3437,plain,
( midp(sK5,sK6,sK6)
| ~ cong(sK5,sK6,sK5,sK6) ),
inference(resolve,[status(thm)],[c_2666,c_248]) ).
cnf(c_3680,plain,
( midp(sK6,sK5,sK5)
| ~ cong(sK6,sK5,sK6,sK5) ),
inference(resolve,[status(thm)],[c_3385,c_248]) ).
cnf(c_3696,plain,
cyclic(sK5,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_577,c_372]) ).
cnf(c_3815,plain,
( perp(sK5,sK5,A,B)
| ~ perp(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_651,c_300]) ).
cnf(c_3874,plain,
( cong(sK5,sK6,sK5,sK6)
| ~ midp(sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_667,c_260]) ).
cnf(c_3966,plain,
cyclic(sK6,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_707,c_372]) ).
cnf(c_4096,plain,
( cong(sK6,sK5,sK6,sK5)
| ~ midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1015,c_260]) ).
cnf(c_4128,plain,
( cong(sK5,sK6,sK6,sK6)
| ~ eqangle(sK6,sK5,sK6,sK6,sK6,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_3696,c_371]) ).
cnf(c_4129,plain,
cyclic(sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_3696,c_358]) ).
cnf(c_4137,plain,
cyclic(sK6,sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_3696,c_295]) ).
cnf(c_4227,plain,
cyclic(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_3966,c_358]) ).
cnf(c_4274,plain,
( cong(sK6,sK6,sK6,sK6)
| ~ eqangle(sK6,sK6,sK6,sK6,sK6,sK6,sK6,sK6) ),
inference(resolve,[status(thm)],[c_4129,c_371]) ).
cnf(c_4282,plain,
eqangle(sK6,sK6,sK6,sK6,sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_4129,c_270]) ).
cnf(c_4305,plain,
cong(sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_4282,c_4274]) ).
cnf(c_4307,plain,
midp(sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_4305,c_2236]) ).
cnf(c_4308,plain,
cong(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_4307,c_3874]) ).
cnf(c_4312,plain,
midp(sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_4308,c_3437]) ).
cnf(c_4324,plain,
para(sK6,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_4307,c_354]) ).
cnf(c_4451,plain,
cyclic(sK6,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_4137,c_296]) ).
cnf(c_4519,plain,
( cong(sK5,sK5,sK5,sK5)
| ~ eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_4227,c_371]) ).
cnf(c_4527,plain,
eqangle(sK5,sK5,sK5,sK5,sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_4227,c_270]) ).
cnf(c_4550,plain,
cong(sK5,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_4527,c_4519]) ).
cnf(c_4552,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_4550,c_2361]) ).
cnf(c_4553,plain,
cong(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_4552,c_4096]) ).
cnf(c_4557,plain,
midp(sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_4553,c_3680]) ).
cnf(c_5022,plain,
eqangle(sK6,sK6,A,B,sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_4324,c_271]) ).
cnf(c_5033,plain,
cyclic(sK6,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_4451,c_297]) ).
cnf(c_5203,plain,
( perp(sK5,sK6,sK6,sK5)
| ~ cyclic(sK6,sK6,sK5,sK5) ),
inference(resolve,[status(thm)],[c_4553,c_352]) ).
cnf(c_5252,plain,
( perp(A,sK6,sK6,sK5)
| ~ cyclic(sK6,sK6,A,sK5)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_4553,c_258]) ).
cnf(c_5418,plain,
cyclic(sK6,sK6,sK5,sK5),
inference(resolve,[status(thm)],[c_5033,c_358]) ).
cnf(c_5426,plain,
( cyclic(sK6,sK6,A,sK5)
| ~ cyclic(sK6,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_5033,c_294]) ).
cnf(c_5451,plain,
perp(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_5418,c_5203]) ).
cnf(c_5620,plain,
perp(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_5451,c_303]) ).
cnf(c_5765,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_5620,c_362]) ).
cnf(c_5901,plain,
( midp(A,sK6,sK6)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_5765,c_349]) ).
cnf(c_5985,plain,
coll(sK5,sK1,sK6),
inference(resolve,[status(thm)],[c_902,c_1035]) ).
cnf(c_6001,plain,
coll(sK1,sK5,sK6),
inference(resolve,[status(thm)],[c_5985,c_308]) ).
cnf(c_6113,plain,
coll(sK1,sK6,sK5),
inference(resolve,[status(thm)],[c_6001,c_309]) ).
cnf(c_6311,plain,
( midp(sK1,sK6,sK5)
| ~ cong(sK1,sK6,sK1,sK5) ),
inference(resolve,[status(thm)],[c_6113,c_248]) ).
cnf(c_12401,plain,
para(sK0,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_601,c_4557]) ).
cnf(c_12402,plain,
para(sK0,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_601,c_4552]) ).
cnf(c_12408,plain,
para(sK6,sK5,sK0,sK6),
inference(resolve,[status(thm)],[c_12401,c_305]) ).
cnf(c_12439,plain,
para(sK0,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_12402,c_306]) ).
cnf(c_12493,plain,
para(sK6,sK5,sK6,sK0),
inference(resolve,[status(thm)],[c_12408,c_306]) ).
cnf(c_12524,plain,
para(sK5,sK6,sK0,sK5),
inference(resolve,[status(thm)],[c_12439,c_305]) ).
cnf(c_12618,plain,
para(sK6,sK0,sK6,sK5),
inference(resolve,[status(thm)],[c_12493,c_305]) ).
cnf(c_28251,plain,
( midp(A,sK0,sK5)
| ~ para(sK6,sK0,sK6,sK5)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_12493,c_251]) ).
cnf(c_12625,plain,
( midp(A,sK0,sK5)
| ~ midp(A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_12618,c_28251]) ).
cnf(c_12656,plain,
para(sK5,sK6,sK5,sK0),
inference(resolve,[status(thm)],[c_12524,c_306]) ).
cnf(c_12789,plain,
para(sK5,sK0,sK5,sK6),
inference(resolve,[status(thm)],[c_12656,c_305]) ).
cnf(c_28252,plain,
( midp(A,sK0,sK6)
| ~ para(sK5,sK0,sK5,sK6)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_12656,c_251]) ).
cnf(c_12796,plain,
( midp(A,sK0,sK6)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_12789,c_28252]) ).
cnf(c_12897,plain,
midp(sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_12625,c_4312]) ).
cnf(c_12923,plain,
cong(sK5,sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_12897,c_247]) ).
cnf(c_12953,plain,
perp(sK0,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_12923,c_2552]) ).
cnf(c_28253,plain,
( cong(sK0,sK5,sK0,sK5)
| ~ midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_12953,c_260]) ).
cnf(c_13209,plain,
cong(sK0,sK5,sK0,sK5),
inference(resolve,[status(thm)],[c_4552,c_28253]) ).
cnf(c_13241,plain,
midp(sK0,sK5,sK5),
inference(resolve,[status(thm)],[c_13209,c_3357]) ).
cnf(c_13244,plain,
midp(sK0,sK6,sK6),
inference(resolve,[status(thm)],[c_13241,c_5901]) ).
cnf(c_13324,plain,
para(sK6,sK5,sK6,sK6),
inference(resolve,[status(thm)],[c_13244,c_587]) ).
cnf(c_14143,plain,
eqangle(sK6,sK5,A,B,sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_13324,c_271]) ).
cnf(c_14161,plain,
cong(sK5,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_14143,c_4128]) ).
cnf(c_14852,plain,
cong(sK6,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_14161,c_287]) ).
cnf(c_15330,plain,
cong(sK6,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_14852,c_288]) ).
cnf(c_15347,plain,
midp(sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_15330,c_1720]) ).
cnf(c_15383,plain,
( cong(A,sK6,A,sK5)
| ~ perp(A,sK6,sK6,sK5) ),
inference(resolve,[status(thm)],[c_15347,c_260]) ).
cnf(c_16774,plain,
midp(sK0,sK0,sK6),
inference(resolve,[status(thm)],[c_12796,c_13241]) ).
cnf(c_16803,plain,
midp(sK0,sK6,sK0),
inference(resolve,[status(thm)],[c_16774,c_299]) ).
cnf(c_16812,plain,
cong(sK0,sK0,sK0,sK6),
inference(resolve,[status(thm)],[c_16774,c_247]) ).
cnf(c_16953,plain,
cong(sK0,sK6,sK0,sK0),
inference(resolve,[status(thm)],[c_16803,c_247]) ).
cnf(c_17031,plain,
cyclic(sK0,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_16812,c_372]) ).
cnf(c_17237,plain,
cyclic(sK6,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_16953,c_372]) ).
cnf(c_17425,plain,
cyclic(sK6,sK0,sK6,sK6),
inference(resolve,[status(thm)],[c_17031,c_295]) ).
cnf(c_17478,plain,
cyclic(sK0,sK6,sK0,sK0),
inference(resolve,[status(thm)],[c_17237,c_295]) ).
cnf(c_17557,plain,
cyclic(sK6,sK6,sK0,sK6),
inference(resolve,[status(thm)],[c_17425,c_296]) ).
cnf(c_17644,plain,
cyclic(sK0,sK0,sK6,sK0),
inference(resolve,[status(thm)],[c_17478,c_296]) ).
cnf(c_17945,plain,
cyclic(sK6,sK6,sK6,sK0),
inference(resolve,[status(thm)],[c_17557,c_297]) ).
cnf(c_17946,plain,
( cyclic(sK6,sK0,A,sK6)
| ~ cyclic(sK6,sK6,sK0,A) ),
inference(resolve,[status(thm)],[c_17557,c_294]) ).
cnf(c_17985,plain,
cyclic(sK0,sK0,sK0,sK6),
inference(resolve,[status(thm)],[c_17644,c_297]) ).
cnf(c_18032,plain,
cyclic(sK6,sK6,sK0,sK0),
inference(resolve,[status(thm)],[c_17945,c_358]) ).
cnf(c_18040,plain,
( cyclic(sK6,sK6,sK0,A)
| ~ cyclic(sK6,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_17945,c_294]) ).
cnf(c_18070,plain,
cyclic(sK0,sK0,sK6,sK6),
inference(resolve,[status(thm)],[c_17985,c_358]) ).
cnf(c_18114,plain,
cyclic(sK6,sK0,sK6,sK0),
inference(resolve,[status(thm)],[c_18032,c_296]) ).
cnf(c_18116,plain,
( cyclic(sK6,sK0,sK0,A)
| ~ cyclic(sK6,sK6,sK0,A) ),
inference(resolve,[status(thm)],[c_18032,c_294]) ).
cnf(c_18174,plain,
( cyclic(sK0,sK6,A,sK6)
| ~ cyclic(sK0,sK0,sK6,A) ),
inference(resolve,[status(thm)],[c_18070,c_294]) ).
cnf(c_18204,plain,
cyclic(sK6,sK0,sK0,sK6),
inference(resolve,[status(thm)],[c_18114,c_297]) ).
cnf(c_18239,plain,
( cyclic(sK0,sK0,sK6,A)
| ~ cyclic(sK6,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_18204,c_294]) ).
cnf(c_18819,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK6,sK6) ),
inference(resolve,[status(thm)],[c_5022,c_356]) ).
cnf(c_18821,plain,
eqangle(A,B,sK6,sK6,A,B,sK6,sK6),
inference(resolve,[status(thm)],[c_5022,c_292]) ).
cnf(c_18832,plain,
cyclic(A,sK6,sK6,sK6),
inference(resolve,[status(thm)],[c_18821,c_2232]) ).
cnf(c_18846,plain,
cyclic(sK6,A,sK6,sK6),
inference(resolve,[status(thm)],[c_18832,c_295]) ).
cnf(c_18852,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_18846,c_18819]) ).
cnf(c_18870,plain,
cyclic(sK6,sK6,A,sK6),
inference(resolve,[status(thm)],[c_18846,c_296]) ).
cnf(c_18891,plain,
cyclic(sK6,sK6,sK6,A),
inference(resolve,[status(thm)],[c_18870,c_297]) ).
cnf(c_18902,plain,
cyclic(sK6,sK6,sK0,A),
inference(resolve,[status(thm)],[c_18891,c_18040]) ).
cnf(c_18908,plain,
cyclic(sK6,sK6,A,sK5),
inference(resolve,[status(thm)],[c_18891,c_5426]) ).
cnf(c_18917,plain,
cyclic(sK6,sK0,sK0,A),
inference(resolve,[status(thm)],[c_18902,c_18116]) ).
cnf(c_18922,plain,
cyclic(sK6,sK0,A,sK6),
inference(resolve,[status(thm)],[c_18902,c_17946]) ).
cnf(c_18939,plain,
( perp(A,sK6,sK6,sK5)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_18908,c_5252]) ).
cnf(c_18943,plain,
cyclic(sK0,sK0,sK6,A),
inference(resolve,[status(thm)],[c_18917,c_18239]) ).
cnf(c_18981,plain,
cyclic(sK0,sK6,A,sK6),
inference(resolve,[status(thm)],[c_18943,c_18174]) ).
cnf(c_28254,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK6,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_18891,c_294]) ).
cnf(c_19134,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_18891,c_28254]) ).
cnf(c_28255,plain,
( cyclic(sK6,sK0,A,B)
| ~ cyclic(sK6,sK6,sK0,A) ),
inference(resolve,[status(thm)],[c_18902,c_294]) ).
cnf(c_19154,plain,
cyclic(sK6,sK0,A,B),
inference(resolve,[status(thm)],[c_19134,c_28255]) ).
cnf(c_28256,plain,
( cyclic(sK0,A,sK6,B)
| ~ cyclic(sK6,sK0,A,B) ),
inference(resolve,[status(thm)],[c_18922,c_294]) ).
cnf(c_19310,plain,
cyclic(sK0,A,sK6,B),
inference(resolve,[status(thm)],[c_19154,c_28256]) ).
cnf(c_28257,plain,
( cyclic(sK0,sK6,A,B)
| ~ cyclic(sK0,sK0,sK6,A) ),
inference(resolve,[status(thm)],[c_18943,c_294]) ).
cnf(c_19371,plain,
cyclic(sK0,sK6,A,B),
inference(resolve,[status(thm)],[c_19310,c_28257]) ).
cnf(c_28258,plain,
( cyclic(sK6,A,sK6,B)
| ~ cyclic(sK0,sK6,A,B) ),
inference(resolve,[status(thm)],[c_18981,c_294]) ).
cnf(c_19471,plain,
cyclic(sK6,A,sK6,B),
inference(resolve,[status(thm)],[c_19371,c_28258]) ).
cnf(c_19481,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_19471,c_18852]) ).
cnf(c_19483,plain,
perp(A,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_19481,c_18939]) ).
cnf(c_19511,plain,
cong(A,sK6,A,sK5),
inference(resolve,[status(thm)],[c_19483,c_15383]) ).
cnf(c_19581,plain,
midp(sK1,sK6,sK5),
inference(resolve,[status(thm)],[c_19511,c_6311]) ).
cnf(c_20203,plain,
para(sK0,sK1,sK5,sK5),
inference(resolve,[status(thm)],[c_19581,c_700]) ).
cnf(c_28259,plain,
( perp(sK6,sK6,A,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_19481,c_259]) ).
cnf(c_22655,plain,
perp(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_19481,c_28259]) ).
cnf(c_22696,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_22655,c_3815]) ).
cnf(c_28260,plain,
( perp(sK0,sK1,A,B)
| ~ perp(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_20203,c_300]) ).
cnf(c_28247,plain,
perp(sK0,sK1,A,B),
inference(resolve,[status(thm)],[c_22696,c_28260]) ).
cnf(c_28248,plain,
$false,
inference(resolve,[status(thm)],[c_28247,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO608+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.65 % Computer : n002.cluster.edu
% 0.16/5.65 % Model : x86_64 x86_64
% 0.16/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.65 % Memory : 8046.5625MB
% 0.16/5.65 % OS : Linux 6.8.0-71-generic
% 0.16/5.65 % CPULimit : 300
% 0.16/5.65 % WCLimit : 300
% 0.16/5.65 % DateTime : Fri Sep 25 13:46:57 UTC 2026
% 0.16/5.66 % CPUTime :
% 0.16/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.66 % Process 3411254 was started by sandbox2 on n002,
% 0.16/5.66 % Fri Sep 25 13:46:57 2026
% 0.16/5.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/5.70
% 0.21/5.70 % From the command line: assign(max_seconds, 300).
% 20.80/8.71
% 20.80/8.71 % given #500 (T,wt=9): 8205 coll(c6,c3,c5). [resolve(8054,a,309,a)].
% 20.80/8.71
% 20.80/8.71 % given #1000 (A,wt=40): 486 -perp(c2,c2,f12(c2,c5,c10,c4),c4) | coll(f11(f12(c2,c5,c10,c4),c2,c4,c2),c4,f12(c2,c5,c10,c4)). [resolve(219,a,146,a)].
% 20.80/8.71
% 20.80/8.71 % given #1500 (T,wt=14): 4491 -midp(A,c2,c3) | cong(c2,A,c2,A). [resolve(4192,a,262,a)].
% 20.80/8.71
% 20.80/8.71 % SZS status Theorem for theBenchmark
% 20.80/8.71
% 20.80/8.71 % Proof 1 at 2.28 (+ 0.65) seconds.
% 20.80/8.71 % Length of proof is 230.
% 20.80/8.71 % Level of proof is 40.
% 20.80/8.71 % Maximum clause weight is 34.000.
% 20.80/8.71 % Given clauses 1811.
% 20.80/8.71
% 20.80/8.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------