%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO626+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 07:18:15 AM UTC 2026
% Result : Theorem 12.31s 7.18s
% Output : CNFRefutation 12.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 205 ( 96 unt; 0 def)
% Number of atoms : 408 ( 0 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 321 ( 118 ~; 114 |; 58 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 462 ( 55 sgn 168 !; 14 ?)
% 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(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleD12) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('theBenchmark.p',ruleD19) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD39) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(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(ruleD51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('theBenchmark.p',ruleD51) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('theBenchmark.p',ruleD65) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('theBenchmark.p',ruleD75) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL8110990,conjecture,
! [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(C1,C,B1,B) ),
file('theBenchmark.p',exemplo6GDDFULL8110990) ).
fof(exemplo6GDDFULL8110990_neg,negated_conjecture,
~ ! [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(C1,C,B1,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110990]) ).
cnf(c_97,plain,
( circle(A,B,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD12]) ).
cnf(c_100,plain,
( midp(E,C,D)
| ~ eqangle(B,C,B,D,A,C,A,E)
| ~ coll(E,C,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD51]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ~ para(C1,C,B1,B)
& coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110990_neg]) ).
fof(sk_exemplo6GDDFULL8110990_neg,plain,
( ~ para(sK6,sK4,sK8,sK3)
& coll(sK8,sK5,sK10)
& circle(sK1,sK5,sK8,sK12)
& coll(sK6,sK5,sK9)
& circle(sK1,sK5,sK6,sK7)
& coll(sK10,sK2,sK4)
& perp(sK10,sK5,sK2,sK4)
& coll(sK9,sK2,sK3)
& perp(sK9,sK5,sK2,sK3)
& circle(sK1,sK2,sK5,sK11)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK11,sK9,sK10,sK6,sK7,sK8,sK12]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(O,sK1),skolemize(D,sK5),skolemize(G,sK9),skolemize(F,sK10),skolemize(C1,sK6),skolemize(B1,sK8),skolemize(NWPNT1,sK11),skolemize(NWPNT2,sK7),skolemize(NWPNT3,sK12)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_111,negated_conjecture,
circle(sK1,sK5,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_132,negated_conjecture,
perp(sK0(sK5,sK6,sK7,sK1),sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_160,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_203,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| midp(A,B,C)
| ~ eqangle(D,B,D,C,E,B,E,A)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
cnf(c_207,negated_conjecture,
~ para(sK6,sK4,sK8,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_209,negated_conjecture,
coll(sK6,sK5,sK9),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_211,negated_conjecture,
perp(sK10,sK5,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_213,negated_conjecture,
perp(sK9,sK5,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110990_neg]) ).
cnf(c_244,plain,
( cong(A,B,C,D)
| ~ cong(E,F,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD75]) ).
cnf(c_252,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_253,plain,
( eqratio(E,A,A,C,E,B,B,D)
| ~ coll(E,B,D)
| ~ coll(E,A,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD65]) ).
cnf(c_254,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_261,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_262,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_269,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_270,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_271,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_274,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_275,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_291,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_295,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_297,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_298,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_299,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_300,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_303,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_304,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_305,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_306,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_308,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_309,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_310,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_311,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_312,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_328,plain,
( ~ cong(D,C,D,B)
| midp(A,B,B)
| ~ eqangle(C,B,C,B,D,B,D,A)
| ~ coll(A,B,B) ),
inference(factor,[status(thm)],[c_203]) ).
cnf(c_352,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_254]) ).
cnf(c_357,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_269]) ).
cnf(c_359,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_270]) ).
cnf(c_361,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_297]) ).
cnf(c_366,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_310]) ).
cnf(c_482,plain,
( para(sK9,sK5,A,B)
| ~ perp(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_304,c_213]) ).
cnf(c_489,plain,
( para(A,B,sK2,sK4)
| ~ perp(A,B,sK10,sK5) ),
inference(resolve,[status(thm)],[c_304,c_211]) ).
cnf(c_490,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_304,c_160]) ).
cnf(c_492,plain,
( para(A,B,sK5,sK1)
| ~ perp(A,B,sK0(sK5,sK6,sK7,sK1),sK5) ),
inference(resolve,[status(thm)],[c_304,c_132]) ).
cnf(c_494,plain,
perp(sK2,sK3,sK9,sK5),
inference(resolve,[status(thm)],[c_305,c_213]) ).
cnf(c_495,plain,
perp(sK2,sK4,sK10,sK5),
inference(resolve,[status(thm)],[c_305,c_211]) ).
cnf(c_496,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_305,c_160]) ).
cnf(c_498,plain,
perp(sK5,sK1,sK0(sK5,sK6,sK7,sK1),sK5),
inference(resolve,[status(thm)],[c_305,c_132]) ).
cnf(c_501,plain,
perp(sK10,sK5,sK4,sK2),
inference(resolve,[status(thm)],[c_306,c_211]) ).
cnf(c_516,plain,
coll(sK5,sK6,sK9),
inference(resolve,[status(thm)],[c_311,c_209]) ).
cnf(c_520,plain,
coll(sK6,sK9,sK5),
inference(resolve,[status(thm)],[c_312,c_209]) ).
cnf(c_534,plain,
coll(sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_516,c_366]) ).
cnf(c_550,plain,
coll(sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_520,c_366]) ).
cnf(c_591,plain,
coll(sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_534,c_312]) ).
cnf(c_616,plain,
coll(sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_550,c_312]) ).
cnf(c_705,plain,
coll(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_616,c_366]) ).
cnf(c_806,plain,
perp(sK2,sK3,sK5,sK9),
inference(resolve,[status(thm)],[c_494,c_306]) ).
cnf(c_848,plain,
perp(sK4,sK2,sK10,sK5),
inference(resolve,[status(thm)],[c_501,c_305]) ).
cnf(c_1204,plain,
para(sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_482,c_806]) ).
cnf(c_1205,plain,
para(sK9,sK5,sK9,sK5),
inference(resolve,[status(thm)],[c_482,c_494]) ).
cnf(c_1222,plain,
para(sK5,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_1204,c_308]) ).
cnf(c_1227,plain,
( eqratio(A,sK9,sK9,sK5,A,sK5,sK5,sK9)
| ~ coll(A,sK5,sK9)
| ~ coll(A,sK9,sK5) ),
inference(resolve,[status(thm)],[c_1204,c_253]) ).
cnf(c_1237,plain,
eqangle(sK9,sK5,A,B,sK9,sK5,A,B),
inference(resolve,[status(thm)],[c_1205,c_274]) ).
cnf(c_1278,plain,
para(sK5,sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_1222,c_309]) ).
cnf(c_1309,plain,
eqangle(sK5,sK9,A,B,sK5,sK9,A,B),
inference(resolve,[status(thm)],[c_1278,c_274]) ).
cnf(c_1320,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_489,c_848]) ).
cnf(c_1321,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_489,c_495]) ).
cnf(c_1367,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_1320,c_309]) ).
cnf(c_1380,plain,
( midp(A,sK4,sK4)
| ~ midp(A,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1321,c_352]) ).
cnf(c_1383,plain,
eqangle(sK2,sK4,A,B,sK2,sK4,A,B),
inference(resolve,[status(thm)],[c_1321,c_274]) ).
cnf(c_1422,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1367,c_274]) ).
cnf(c_1452,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_496,c_490]) ).
cnf(c_1508,plain,
para(sK5,sK1,sK5,sK1),
inference(resolve,[status(thm)],[c_498,c_492]) ).
cnf(c_2435,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1452,c_309]) ).
cnf(c_2436,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1452,c_274]) ).
cnf(c_3202,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1508,c_352]) ).
cnf(c_3205,plain,
para(sK5,sK1,sK1,sK5),
inference(resolve,[status(thm)],[c_1508,c_309]) ).
cnf(c_3219,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_2435,c_308]) ).
cnf(c_3261,plain,
para(sK1,sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_3205,c_308]) ).
cnf(c_3277,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_3219,c_309]) ).
cnf(c_3339,plain,
para(sK1,sK5,sK1,sK5),
inference(resolve,[status(thm)],[c_3261,c_309]) ).
cnf(c_3351,plain,
( midp(A,sK2,sK2)
| ~ midp(A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_3277,c_352]) ).
cnf(c_3354,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_3277,c_274]) ).
cnf(c_3418,plain,
eqangle(sK1,sK5,A,B,sK1,sK5,A,B),
inference(resolve,[status(thm)],[c_3339,c_274]) ).
cnf(c_16445,plain,
( eqratio(sK9,sK9,sK9,sK5,sK9,sK5,sK5,sK9)
| ~ coll(sK9,sK5,sK9) ),
inference(resolve,[status(thm)],[c_1227,c_534]) ).
cnf(c_3942,plain,
eqratio(sK9,sK9,sK9,sK5,sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_591,c_16445]) ).
cnf(c_16446,plain,
( ~ cong(sK9,sK9,sK9,sK5)
| midp(sK5,sK5,sK5)
| ~ coll(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_1237,c_328]) ).
cnf(c_4027,plain,
( ~ cong(sK9,sK9,sK9,sK5)
| midp(sK5,sK5,sK5) ),
inference(resolve,[status(thm)],[c_705,c_16446]) ).
cnf(c_4028,plain,
eqangle(A,B,sK9,sK5,A,B,sK9,sK5),
inference(resolve,[status(thm)],[c_1237,c_295]) ).
cnf(c_4553,plain,
( cyclic(sK9,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1309,c_271]) ).
cnf(c_4989,plain,
( cyclic(sK4,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1383,c_271]) ).
cnf(c_4990,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,sK2)
| ~ cyclic(sK4,A,sK2,A)
| ~ cyclic(sK4,A,sK2,sK4) ),
inference(resolve,[status(thm)],[c_1383,c_270]) ).
cnf(c_5212,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1422,c_271]) ).
cnf(c_5871,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_2436,c_271]) ).
cnf(c_5872,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,sK2)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_2436,c_270]) ).
cnf(c_8588,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3354,c_271]) ).
cnf(c_8625,plain,
( cyclic(sK5,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3418,c_271]) ).
cnf(c_8801,plain,
( cong(sK9,sK9,sK9,sK5)
| ~ cong(sK9,sK5,sK5,sK9) ),
inference(resolve,[status(thm)],[c_3942,c_244]) ).
cnf(c_8853,plain,
( cong(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK9) ),
inference(resolve,[status(thm)],[c_4028,c_359]) ).
cnf(c_8856,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_4028,c_275]) ).
cnf(c_16447,plain,
( cyclic(A,sK5,sK9,sK9)
| ~ coll(sK9,sK9,sK5) ),
inference(resolve,[status(thm)],[c_4028,c_271]) ).
cnf(c_8858,plain,
cyclic(A,sK5,sK9,sK9),
inference(resolve,[status(thm)],[c_534,c_16447]) ).
cnf(c_8869,plain,
( cong(sK9,sK5,sK9,sK5)
| ~ cyclic(sK9,sK5,sK9,sK5) ),
inference(resolve,[status(thm)],[c_8858,c_8853]) ).
cnf(c_8881,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_8856,c_252]) ).
cnf(c_9155,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_8881,c_366]) ).
cnf(c_9163,plain,
cyclic(sK5,A,sK1,sK1),
inference(resolve,[status(thm)],[c_9155,c_8625]) ).
cnf(c_9164,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_9155,c_8588]) ).
cnf(c_9166,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_9155,c_5871]) ).
cnf(c_9183,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_9155,c_5212]) ).
cnf(c_9185,plain,
cyclic(sK4,A,sK2,sK2),
inference(resolve,[status(thm)],[c_9155,c_4989]) ).
cnf(c_9188,plain,
cyclic(sK9,A,sK5,sK5),
inference(resolve,[status(thm)],[c_9155,c_4553]) ).
cnf(c_9375,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_9166,c_5872]) ).
cnf(c_9384,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,A)
| ~ cyclic(sK4,A,sK2,sK4) ),
inference(resolve,[status(thm)],[c_9185,c_4990]) ).
cnf(c_10104,plain,
cyclic(sK5,sK1,A,sK1),
inference(resolve,[status(thm)],[c_9163,c_299]) ).
cnf(c_10120,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_9164,c_299]) ).
cnf(c_10170,plain,
cyclic(sK1,sK2,A,sK2),
inference(resolve,[status(thm)],[c_9166,c_299]) ).
cnf(c_10185,plain,
cyclic(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_9183,c_361]) ).
cnf(c_10187,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_9183,c_299]) ).
cnf(c_10220,plain,
cyclic(sK4,sK2,A,sK2),
inference(resolve,[status(thm)],[c_9185,c_299]) ).
cnf(c_10284,plain,
cyclic(sK9,sK5,A,sK5),
inference(resolve,[status(thm)],[c_9188,c_299]) ).
cnf(c_10299,plain,
cong(sK9,sK5,sK9,sK5),
inference(resolve,[status(thm)],[c_10284,c_8869]) ).
cnf(c_10462,plain,
cyclic(sK5,sK1,sK1,A),
inference(resolve,[status(thm)],[c_10104,c_300]) ).
cnf(c_10522,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_10120,c_298]) ).
cnf(c_10621,plain,
cyclic(sK1,sK2,sK2,A),
inference(resolve,[status(thm)],[c_10170,c_300]) ).
cnf(c_10653,plain,
cyclic(sK4,A,sK4,sK4),
inference(resolve,[status(thm)],[c_10185,c_298]) ).
cnf(c_10667,plain,
cyclic(sK4,sK2,A,sK4),
inference(resolve,[status(thm)],[c_10187,c_298]) ).
cnf(c_10755,plain,
cyclic(sK2,sK4,A,sK2),
inference(resolve,[status(thm)],[c_10220,c_298]) ).
cnf(c_10933,plain,
cong(sK9,sK5,sK5,sK9),
inference(resolve,[status(thm)],[c_10299,c_291]) ).
cnf(c_10949,plain,
cong(sK9,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_10933,c_8801]) ).
cnf(c_10952,plain,
midp(sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_10949,c_4027]) ).
cnf(c_10953,plain,
midp(sK5,sK1,sK1),
inference(resolve,[status(thm)],[c_10952,c_3202]) ).
cnf(c_10970,plain,
midp(sK5,sK2,sK2),
inference(resolve,[status(thm)],[c_10953,c_3351]) ).
cnf(c_10971,plain,
para(sK5,sK5,sK1,sK1),
inference(resolve,[status(thm)],[c_10953,c_357]) ).
cnf(c_11016,plain,
midp(sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_10970,c_1380]) ).
cnf(c_11034,plain,
para(sK5,sK5,sK4,sK4),
inference(resolve,[status(thm)],[c_11016,c_357]) ).
cnf(c_11334,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_10462,c_361]) ).
cnf(c_16448,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK5,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_10462,c_297]) ).
cnf(c_11336,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_10462,c_16448]) ).
cnf(c_11583,plain,
cyclic(sK1,A,sK2,sK1),
inference(resolve,[status(thm)],[c_10522,c_299]) ).
cnf(c_11599,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A) ),
inference(resolve,[status(thm)],[c_11583,c_9375]) ).
cnf(c_16449,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK1,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_10621,c_297]) ).
cnf(c_11859,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_10621,c_16449]) ).
cnf(c_11974,plain,
cyclic(sK4,sK4,A,sK4),
inference(resolve,[status(thm)],[c_10653,c_299]) ).
cnf(c_12003,plain,
cyclic(sK4,A,sK2,sK4),
inference(resolve,[status(thm)],[c_10667,c_299]) ).
cnf(c_12019,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK2,A) ),
inference(resolve,[status(thm)],[c_12003,c_9384]) ).
cnf(c_12393,plain,
( cyclic(sK4,A,sK2,B)
| ~ cyclic(sK2,sK4,A,B) ),
inference(resolve,[status(thm)],[c_10755,c_297]) ).
cnf(c_12755,plain,
( perp(sK5,sK5,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_10971,c_303]) ).
cnf(c_12828,plain,
para(sK4,sK4,sK5,sK5),
inference(resolve,[status(thm)],[c_11034,c_308]) ).
cnf(c_16450,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_11334,c_297]) ).
cnf(c_13188,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_11336,c_16450]) ).
cnf(c_13201,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_13188,c_11599]) ).
cnf(c_16451,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_11859,c_297]) ).
cnf(c_13893,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_11859,c_16451]) ).
cnf(c_13907,plain,
cyclic(sK4,A,sK2,B),
inference(resolve,[status(thm)],[c_13893,c_12393]) ).
cnf(c_13985,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_13907,c_12019]) ).
cnf(c_16452,plain,
( perp(A,sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_11974,c_261]) ).
cnf(c_16453,plain,
( perp(A,sK4,sK4,sK4)
| ~ cong(sK4,sK4,sK4,sK4) ),
inference(resolve,[status(thm)],[c_13985,c_16452]) ).
cnf(c_14052,plain,
perp(A,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_13985,c_16453]) ).
cnf(c_14530,plain,
( perp(sK4,sK4,A,B)
| ~ perp(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_12828,c_303]) ).
cnf(c_16454,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_13201,c_262]) ).
cnf(c_14987,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_13201,c_16454]) ).
cnf(c_15003,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_14987,c_12755]) ).
cnf(c_15031,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_15003,c_14530]) ).
cnf(c_16455,plain,
( para(C,sK4,A,B)
| ~ perp(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_14052,c_304]) ).
cnf(c_16443,plain,
para(A,sK4,B,C),
inference(resolve,[status(thm)],[c_15031,c_16455]) ).
cnf(c_16444,plain,
$false,
inference(resolve,[status(thm)],[c_16443,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO626+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n001.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 13:51:16 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3435242 was started by sandbox2 on n001,
% 0.11/5.38 % Fri Sep 25 13:51:16 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 12.31/7.18
% 12.31/7.18 % given #500 (W,wt=9): 1066 coll(c5,c8,c1). [resolve(1037,a,312,a)].
% 12.31/7.18
% 12.31/7.18 % given #1000 (T,wt=9): 2256 coll(c7,c8,c8). [resolve(2036,a,311,a)].
% 12.31/7.18
% 12.31/7.18 % given #1500 (A,wt=24): 941 -perp(c1,c7,c5,c3) | perp(c5,f10(c5,c1,c3,c7),c3,c1). [resolve(876,a,223,a)].
% 12.31/7.18
% 12.31/7.18 % given #2000 (T,wt=13): 1962 -coll(c8,c5,A) | coll(A,c3,c8). [resolve(1845,a,310,b)].
% 12.31/7.18
% 12.31/7.18 % given #2500 (A,wt=44): 1546 -cong(f12(c1,c2,c3,c4),c4,f12(c1,c2,c3,c4),c1) | coll(f4(c4,c1,f12(c1,c2,c3,c4),c1),f12(c1,c2,c3,c4),c1). [resolve(502,a,236,a)].
% 12.31/7.18
% 12.31/7.18 % given #3000 (T,wt=13): 3681 -coll(c2,c3,A) | coll(A,c8,c2). [resolve(3658,a,310,b)].
% 12.31/7.18
% 12.31/7.18 % given #3500 (A,wt=28): 2982 coll(f17(f12(c5,c9,c12,c4),c4,c5,c6,c5),c6,c5). [resolve(2911,a,399,a)].
% 12.31/7.18
% 12.31/7.18 % given #4000 (W,wt=10): 13172 cyclic(c4,A,c4,B). [resolve(11321,a,297,a),unit_del(a,11336)].
% 12.31/7.18
% 12.31/7.18 % SZS status Theorem for theBenchmark
% 12.31/7.18
% 12.31/7.18 % Proof 1 at 1.40 (+ 0.36) seconds.
% 12.31/7.18 % Length of proof is 189.
% 12.31/7.18 % Level of proof is 23.
% 12.31/7.18 % Maximum clause weight is 34.000.
% 12.31/7.18 % Given clauses 4199.
% 12.31/7.18
% 12.31/7.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------