%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO646+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:18:18 AM UTC 2026
% Result : Theorem 13.28s 13.95s
% Output : CNFRefutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 27
% Syntax : Number of formulae : 187 ( 88 unt; 0 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 283 ( 102 ~; 98 |; 55 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 14 con; 0-0 aty)
% Number of variables : 360 ( 30 sgn 140 !; 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(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleD12) ).
fof(ruleD13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('theBenchmark.p',ruleD13) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('theBenchmark.p',ruleD19) ).
fof(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(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(exemplo6GDDFULLmoreE0133,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ( circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,B,H) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0133) ).
fof(exemplo6GDDFULLmoreE0133_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ( circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,B,H) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0133]) ).
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_217,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,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ~ para(E,F,B,H)
& circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0133_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0133_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& circle(sK6,sK9,sK3,sK13)
& coll(sK9,sK4,sK3)
& midp(sK4,sK0,sK1)
& circle(sK6,sK2,sK1,sK12)
& coll(sK1,sK5,sK0)
& circle(sK6,sK2,sK0,sK11)
& perp(sK6,sK9,sK9,sK5)
& circle(sK6,sK2,sK9,sK10)
& perp(sK6,sK2,sK2,sK5)
& circle(sK6,sK2,sK7,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK2,sK7,sK8,sK5,sK9,sK10,sK0,sK11,sK1,sK12,sK4,sK3,sK13]),skolemize(A,sK6),skolemize(B,sK2),skolemize(C,sK9),skolemize(D,sK5),skolemize(E,sK0),skolemize(F,sK1),skolemize(G,sK4),skolemize(H,sK3),skolemize(NWPNT1,sK7),skolemize(NWPNT2,sK8),skolemize(NWPNT3,sK10),skolemize(NWPNT4,sK11),skolemize(NWPNT5,sK12),skolemize(NWPNT6,sK13)],[nnf_95]) ).
cnf(c_222,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0133_neg]) ).
cnf(c_224,negated_conjecture,
midp(sK4,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0133_neg]) ).
cnf(c_225,negated_conjecture,
coll(sK1,sK5,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0133_neg]) ).
cnf(c_263,plain,
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD69]) ).
cnf(c_264,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_265,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_268,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_276,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_277,plain,
( cong(D,B,D,C)
| ~ perp(D,A,B,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD55]) ).
cnf(c_283,plain,
( para(A,D,C,E)
| ~ midp(D,B,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD44]) ).
cnf(c_284,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_285,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_287,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_288,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_309,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_311,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_312,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_313,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_314,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_315,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_316,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_318,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_322,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_323,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_324,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_325,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_326,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_341,plain,
( ~ cong(A,B,A,C)
| perp(B,C,C,C)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_217]) ).
cnf(c_371,plain,
( para(A,A,C,C)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_283]) ).
cnf(c_372,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_284]) ).
cnf(c_373,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_284]) ).
cnf(c_375,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_311]) ).
cnf(c_376,plain,
( cyclic(B,C,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_315]) ).
cnf(c_380,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_324]) ).
cnf(c_388,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_372]) ).
cnf(c_389,plain,
( cyclic(B,C,C,C)
| ~ cong(A,B,A,C) ),
inference(factor,[status(thm)],[c_376]) ).
cnf(c_698,plain,
coll(sK4,sK0,sK1),
inference(resolve,[status(thm)],[c_263,c_224]) ).
cnf(c_699,plain,
cong(sK4,sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_264,c_224]) ).
cnf(c_729,plain,
( para(sK4,A,sK1,B)
| ~ midp(A,sK0,B) ),
inference(resolve,[status(thm)],[c_283,c_224]) ).
cnf(c_733,plain,
midp(sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_316,c_224]) ).
cnf(c_796,plain,
coll(sK0,sK0,sK1),
inference(resolve,[status(thm)],[c_380,c_225]) ).
cnf(c_799,plain,
coll(sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_698,c_380]) ).
cnf(c_21241,plain,
( ~ cong(sK4,sK0,sK4,sK1)
| perp(sK0,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_698,c_341]) ).
cnf(c_811,plain,
perp(sK0,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_699,c_21241]) ).
cnf(c_812,plain,
coll(sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_698,c_326]) ).
cnf(c_851,plain,
cong(sK4,sK1,sK4,sK0),
inference(resolve,[status(thm)],[c_733,c_264]) ).
cnf(c_1030,plain,
coll(sK1,sK1,sK0),
inference(resolve,[status(thm)],[c_796,c_380]) ).
cnf(c_1044,plain,
coll(sK0,sK1,sK0),
inference(resolve,[status(thm)],[c_796,c_326]) ).
cnf(c_1123,plain,
coll(sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_799,c_326]) ).
cnf(c_1147,plain,
coll(sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_812,c_380]) ).
cnf(c_21242,plain,
( ~ cong(sK4,sK1,sK4,sK0)
| perp(sK1,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_812,c_341]) ).
cnf(c_1159,plain,
perp(sK1,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_851,c_21242]) ).
cnf(c_1530,plain,
coll(sK1,sK0,sK1),
inference(resolve,[status(thm)],[c_1030,c_326]) ).
cnf(c_1556,plain,
coll(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_1044,c_380]) ).
cnf(c_1569,plain,
coll(sK1,sK0,sK0),
inference(resolve,[status(thm)],[c_1044,c_325]) ).
cnf(c_1721,plain,
coll(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_1123,c_380]) ).
cnf(c_1780,plain,
coll(sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_1147,c_326]) ).
cnf(c_2285,plain,
coll(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_1530,c_325]) ).
cnf(c_2338,plain,
( midp(sK0,sK0,sK0)
| ~ cong(sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_1556,c_265]) ).
cnf(c_2378,plain,
( midp(sK1,sK0,sK0)
| ~ cong(sK1,sK0,sK1,sK0) ),
inference(resolve,[status(thm)],[c_1569,c_265]) ).
cnf(c_2579,plain,
( cyclic(A,sK1,sK1,sK1)
| ~ eqangle(sK1,A,sK1,sK1,sK1,A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_1721,c_285]) ).
cnf(c_2583,plain,
( midp(sK1,sK1,sK1)
| ~ cong(sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_1721,c_265]) ).
cnf(c_2690,plain,
( ~ cong(sK0,sK4,sK0,sK0)
| perp(sK4,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_1780,c_341]) ).
cnf(c_2691,plain,
coll(sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_1780,c_325]) ).
cnf(c_3179,plain,
( midp(sK0,sK1,sK1)
| ~ cong(sK0,sK1,sK0,sK1) ),
inference(resolve,[status(thm)],[c_2285,c_265]) ).
cnf(c_3379,plain,
( midp(sK4,sK0,sK0)
| ~ cong(sK4,sK0,sK4,sK0) ),
inference(resolve,[status(thm)],[c_2691,c_265]) ).
cnf(c_3595,plain,
cyclic(sK0,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_699,c_389]) ).
cnf(c_3839,plain,
( para(sK0,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_811,c_318]) ).
cnf(c_3842,plain,
( cong(sK0,sK1,sK0,sK1)
| ~ midp(sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_811,c_277]) ).
cnf(c_3934,plain,
cyclic(sK1,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_851,c_389]) ).
cnf(c_4049,plain,
( cong(sK1,sK0,sK1,sK0)
| ~ midp(sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_1159,c_277]) ).
cnf(c_4082,plain,
cyclic(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3595,c_375]) ).
cnf(c_4232,plain,
cyclic(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_3934,c_375]) ).
cnf(c_4279,plain,
( cong(sK1,sK1,sK1,sK1)
| ~ eqangle(sK1,sK1,sK1,sK1,sK1,sK1,sK1,sK1) ),
inference(resolve,[status(thm)],[c_4082,c_388]) ).
cnf(c_4287,plain,
eqangle(sK1,sK1,sK1,sK1,sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4082,c_287]) ).
cnf(c_4310,plain,
cong(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4287,c_4279]) ).
cnf(c_4312,plain,
midp(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4310,c_2583]) ).
cnf(c_4313,plain,
cong(sK0,sK1,sK0,sK1),
inference(resolve,[status(thm)],[c_4312,c_3842]) ).
cnf(c_4317,plain,
midp(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_4313,c_3179]) ).
cnf(c_4329,plain,
para(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_4312,c_371]) ).
cnf(c_4629,plain,
( cong(sK0,sK0,sK0,sK0)
| ~ eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_4232,c_388]) ).
cnf(c_4637,plain,
eqangle(sK0,sK0,sK0,sK0,sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_4232,c_287]) ).
cnf(c_4660,plain,
cong(sK0,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_4637,c_4629]) ).
cnf(c_4662,plain,
midp(sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_4660,c_2338]) ).
cnf(c_4663,plain,
cong(sK1,sK0,sK1,sK0),
inference(resolve,[status(thm)],[c_4662,c_4049]) ).
cnf(c_4667,plain,
midp(sK1,sK0,sK0),
inference(resolve,[status(thm)],[c_4663,c_2378]) ).
cnf(c_5127,plain,
eqangle(sK1,sK1,A,B,sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_4329,c_288]) ).
cnf(c_12627,plain,
para(sK4,sK1,sK1,sK0),
inference(resolve,[status(thm)],[c_729,c_4667]) ).
cnf(c_12628,plain,
para(sK4,sK0,sK1,sK0),
inference(resolve,[status(thm)],[c_729,c_4662]) ).
cnf(c_12634,plain,
para(sK1,sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_12627,c_322]) ).
cnf(c_12665,plain,
para(sK4,sK0,sK0,sK1),
inference(resolve,[status(thm)],[c_12628,c_323]) ).
cnf(c_12719,plain,
para(sK1,sK0,sK1,sK4),
inference(resolve,[status(thm)],[c_12634,c_323]) ).
cnf(c_12750,plain,
para(sK0,sK1,sK4,sK0),
inference(resolve,[status(thm)],[c_12665,c_322]) ).
cnf(c_12844,plain,
para(sK1,sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_12719,c_322]) ).
cnf(c_21243,plain,
( midp(A,sK4,sK0)
| ~ para(sK1,sK4,sK1,sK0)
| ~ midp(A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_12719,c_268]) ).
cnf(c_12851,plain,
( midp(A,sK4,sK0)
| ~ midp(A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_12844,c_21243]) ).
cnf(c_12882,plain,
para(sK0,sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_12750,c_323]) ).
cnf(c_13015,plain,
para(sK0,sK4,sK0,sK1),
inference(resolve,[status(thm)],[c_12882,c_322]) ).
cnf(c_21244,plain,
( midp(A,sK4,sK1)
| ~ para(sK0,sK4,sK0,sK1)
| ~ midp(A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_12882,c_268]) ).
cnf(c_13022,plain,
( midp(A,sK4,sK1)
| ~ midp(A,sK0,sK0) ),
inference(resolve,[status(thm)],[c_13015,c_21244]) ).
cnf(c_13123,plain,
midp(sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_12851,c_4317]) ).
cnf(c_13149,plain,
cong(sK0,sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_13123,c_264]) ).
cnf(c_13175,plain,
perp(sK4,sK0,sK0,sK0),
inference(resolve,[status(thm)],[c_13149,c_2690]) ).
cnf(c_21245,plain,
( cong(sK4,sK0,sK4,sK0)
| ~ midp(sK0,sK0,sK0) ),
inference(resolve,[status(thm)],[c_13175,c_277]) ).
cnf(c_13417,plain,
cong(sK4,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_4662,c_21245]) ).
cnf(c_13445,plain,
midp(sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_13417,c_3379]) ).
cnf(c_16745,plain,
midp(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_13022,c_13445]) ).
cnf(c_16774,plain,
midp(sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_16745,c_316]) ).
cnf(c_16783,plain,
cong(sK4,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_16745,c_264]) ).
cnf(c_16891,plain,
cong(sK4,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_16774,c_264]) ).
cnf(c_16960,plain,
cyclic(sK4,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_16783,c_389]) ).
cnf(c_17136,plain,
cyclic(sK1,sK4,sK4,sK4),
inference(resolve,[status(thm)],[c_16891,c_389]) ).
cnf(c_17314,plain,
cyclic(sK1,sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_16960,c_312]) ).
cnf(c_17367,plain,
cyclic(sK4,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_17136,c_312]) ).
cnf(c_17448,plain,
cyclic(sK1,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_17314,c_313]) ).
cnf(c_17532,plain,
cyclic(sK4,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_17367,c_313]) ).
cnf(c_17606,plain,
cyclic(sK1,sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_17448,c_314]) ).
cnf(c_17607,plain,
( cyclic(sK1,sK4,A,sK1)
| ~ cyclic(sK1,sK1,sK4,A) ),
inference(resolve,[status(thm)],[c_17448,c_311]) ).
cnf(c_17646,plain,
cyclic(sK4,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_17532,c_314]) ).
cnf(c_17667,plain,
cyclic(sK1,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_17606,c_375]) ).
cnf(c_17675,plain,
( cyclic(sK1,sK1,sK4,A)
| ~ cyclic(sK1,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_17606,c_311]) ).
cnf(c_17705,plain,
cyclic(sK4,sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_17646,c_375]) ).
cnf(c_17749,plain,
cyclic(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_17667,c_313]) ).
cnf(c_17751,plain,
( cyclic(sK1,sK4,sK4,A)
| ~ cyclic(sK1,sK1,sK4,A) ),
inference(resolve,[status(thm)],[c_17667,c_311]) ).
cnf(c_17783,plain,
( cyclic(sK4,sK1,A,sK1)
| ~ cyclic(sK4,sK4,sK1,A) ),
inference(resolve,[status(thm)],[c_17705,c_311]) ).
cnf(c_17813,plain,
cyclic(sK1,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_17749,c_314]) ).
cnf(c_17848,plain,
( cyclic(sK4,sK4,sK1,A)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_17813,c_311]) ).
cnf(c_18130,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK1,sK1) ),
inference(resolve,[status(thm)],[c_5127,c_373]) ).
cnf(c_18132,plain,
eqangle(A,B,sK1,sK1,A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_5127,c_309]) ).
cnf(c_18143,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_18132,c_2579]) ).
cnf(c_18157,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_18143,c_312]) ).
cnf(c_18163,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_18157,c_18130]) ).
cnf(c_18181,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_18157,c_313]) ).
cnf(c_18202,plain,
cyclic(sK1,sK1,sK1,A),
inference(resolve,[status(thm)],[c_18181,c_314]) ).
cnf(c_18213,plain,
cyclic(sK1,sK1,sK4,A),
inference(resolve,[status(thm)],[c_18202,c_17675]) ).
cnf(c_18230,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_18213,c_17751]) ).
cnf(c_18235,plain,
cyclic(sK1,sK4,A,sK1),
inference(resolve,[status(thm)],[c_18213,c_17607]) ).
cnf(c_18258,plain,
cyclic(sK4,sK4,sK1,A),
inference(resolve,[status(thm)],[c_18230,c_17848]) ).
cnf(c_18297,plain,
cyclic(sK4,sK1,A,sK1),
inference(resolve,[status(thm)],[c_18258,c_17783]) ).
cnf(c_21246,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK1,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_18202,c_311]) ).
cnf(c_18455,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_18202,c_21246]) ).
cnf(c_21247,plain,
( cyclic(sK1,sK4,A,B)
| ~ cyclic(sK1,sK1,sK4,A) ),
inference(resolve,[status(thm)],[c_18213,c_311]) ).
cnf(c_18474,plain,
cyclic(sK1,sK4,A,B),
inference(resolve,[status(thm)],[c_18455,c_21247]) ).
cnf(c_21248,plain,
( cyclic(sK4,A,sK1,B)
| ~ cyclic(sK1,sK4,A,B) ),
inference(resolve,[status(thm)],[c_18235,c_311]) ).
cnf(c_18630,plain,
cyclic(sK4,A,sK1,B),
inference(resolve,[status(thm)],[c_18474,c_21248]) ).
cnf(c_21249,plain,
( cyclic(sK4,sK1,A,B)
| ~ cyclic(sK4,sK4,sK1,A) ),
inference(resolve,[status(thm)],[c_18258,c_311]) ).
cnf(c_18691,plain,
cyclic(sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_18630,c_21249]) ).
cnf(c_21250,plain,
( cyclic(sK1,A,sK1,B)
| ~ cyclic(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_18297,c_311]) ).
cnf(c_18796,plain,
cyclic(sK1,A,sK1,B),
inference(resolve,[status(thm)],[c_18691,c_21250]) ).
cnf(c_18806,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_18796,c_18163]) ).
cnf(c_21251,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_18806,c_276]) ).
cnf(c_21200,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_18806,c_21251]) ).
cnf(c_21239,plain,
para(sK0,sK1,A,B),
inference(resolve,[status(thm)],[c_21200,c_3839]) ).
cnf(c_21240,plain,
$false,
inference(resolve,[status(thm)],[c_21239,c_222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO646+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/10.35 % Computer : n012.cluster.edu
% 0.04/10.35 % Model : x86_64 x86_64
% 0.04/10.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.35 % Memory : 8046.5625MB
% 0.04/10.35 % OS : Linux 6.8.0-71-generic
% 0.04/10.35 % CPULimit : 300
% 0.04/10.35 % WCLimit : 300
% 0.04/10.35 % DateTime : Fri Sep 25 13:46:31 UTC 2026
% 0.04/10.35 % CPUTime :
% 0.04/10.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/10.36 % Process 2225156 was started by sandbox on n012,
% 0.04/10.36 % Fri Sep 25 13:46:31 2026
% 0.04/10.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/10.37
% 0.04/10.37 % From the command line: assign(max_seconds, 300).
% 13.28/13.95
% 13.28/13.95 % given #500 (W,wt=9): 6924 coll(c3,c3,c4). [resolve(6823,a,380,a)].
% 13.28/13.95
% 13.28/13.95 % given #1000 (T,wt=13): 10087 -coll(c6,c6,A) | coll(A,c8,c6). [resolve(9170,a,324,b)].
% 13.28/13.95
% 13.28/13.95 % given #1500 (W,wt=14): 3829 eqratio(c7,c6,c6,c7,c7,c6,c6,c7). [back_unit_del(2519),unit_del(a,3806)].
% 13.28/13.95
% 13.28/13.95 % SZS status Theorem for theBenchmark
% 13.28/13.95
% 13.28/13.95 % Proof 1 at 1.33 (+ 0.33) seconds.
% 13.28/13.95 % Length of proof is 173.
% 13.28/13.95 % Level of proof is 37.
% 13.28/13.95 % Maximum clause weight is 34.000.
% 13.28/13.95 % Given clauses 1704.
% 13.28/13.95
% 13.28/13.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------