%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO606+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:12 AM UTC 2026
% Result : Theorem 13.55s 2.54s
% Output : CNFRefutation 13.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of formulae : 185 ( 88 unt; 0 def)
% Number of atoms : 367 ( 0 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 279 ( 97 ~; 93 |; 61 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 19 ( 19 usr; 18 con; 0-4 aty)
% Number of variables : 488 ( 70 sgn 168 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
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(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(ruleD52,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('theBenchmark.p',ruleD52) ).
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(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(ruleD74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('theBenchmark.p',ruleD74) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL618068,conjecture,
! [A,B,P,D,E,I,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ( coll(G,F,B)
& circle(B,F,G,NWPNT01)
& circle(B,P,F,NWPNT9)
& coll(F,D,I)
& circle(B,P,I,NWPNT8)
& circle(A,P,I,NWPNT7)
& coll(E,D,A)
& circle(A,D,E,NWPNT6)
& circle(A,P,D,NWPNT5)
& circle(B,P,NWPNT3,NWPNT4)
& circle(A,P,NWPNT1,NWPNT2)
& perp(P,A,P,B) )
=> perp(G,F,D,E) ),
file('theBenchmark.p',exemplo6GDDFULL618068) ).
fof(exemplo6GDDFULL618068_neg,negated_conjecture,
~ ! [A,B,P,D,E,I,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ( coll(G,F,B)
& circle(B,F,G,NWPNT01)
& circle(B,P,F,NWPNT9)
& coll(F,D,I)
& circle(B,P,I,NWPNT8)
& circle(A,P,I,NWPNT7)
& coll(E,D,A)
& circle(A,D,E,NWPNT6)
& circle(A,P,D,NWPNT5)
& circle(B,P,NWPNT3,NWPNT4)
& circle(A,P,NWPNT1,NWPNT2)
& perp(P,A,P,B) )
=> perp(G,F,D,E) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618068]) ).
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,P,D,E,I,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01] :
( ~ perp(G,F,D,E)
& coll(G,F,B)
& circle(B,F,G,NWPNT01)
& circle(B,P,F,NWPNT9)
& coll(F,D,I)
& circle(B,P,I,NWPNT8)
& circle(A,P,I,NWPNT7)
& coll(E,D,A)
& circle(A,D,E,NWPNT6)
& circle(A,P,D,NWPNT5)
& circle(B,P,NWPNT3,NWPNT4)
& circle(A,P,NWPNT1,NWPNT2)
& perp(P,A,P,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618068_neg]) ).
fof(sk_exemplo6GDDFULL618068_neg,plain,
( ~ perp(sK7,sK6,sK2,sK3)
& coll(sK7,sK6,sK5)
& circle(sK5,sK6,sK7,sK8)
& circle(sK5,sK9,sK6,sK18)
& coll(sK6,sK2,sK15)
& circle(sK5,sK9,sK15,sK17)
& circle(sK1,sK9,sK15,sK16)
& coll(sK3,sK2,sK1)
& circle(sK1,sK2,sK3,sK4)
& circle(sK1,sK9,sK2,sK14)
& circle(sK5,sK9,sK12,sK13)
& circle(sK1,sK9,sK10,sK11)
& perp(sK9,sK1,sK9,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK1,sK5,sK10,sK11,sK12,sK13,sK2,sK14,sK3,sK4,sK15,sK16,sK17,sK6,sK18,sK7,sK8]),skolemize(A,sK1),skolemize(B,sK5),skolemize(P,sK9),skolemize(D,sK2),skolemize(E,sK3),skolemize(I,sK15),skolemize(F,sK6),skolemize(G,sK7),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK11),skolemize(NWPNT3,sK12),skolemize(NWPNT4,sK13),skolemize(NWPNT5,sK14),skolemize(NWPNT6,sK4),skolemize(NWPNT7,sK16),skolemize(NWPNT8,sK17),skolemize(NWPNT9,sK18),skolemize(NWPNT01,sK8)],[nnf_95]) ).
cnf(c_112,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618068_neg]) ).
cnf(c_116,negated_conjecture,
circle(sK5,sK6,sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618068_neg]) ).
cnf(c_122,negated_conjecture,
perp(sK0(sK6,sK7,sK8,sK5),sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_116,c_102]) ).
cnf(c_178,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_112,c_102]) ).
cnf(c_267,negated_conjecture,
~ perp(sK7,sK6,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618068_neg]) ).
cnf(c_271,negated_conjecture,
perp(sK9,sK1,sK9,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618068_neg]) ).
cnf(c_303,plain,
( perp(A,B,C,D)
| ~ perp(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD74]) ).
cnf(c_309,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_310,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_312,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_319,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_320,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_323,plain,
( cong(A,D,B,D)
| ~ midp(D,A,C)
| ~ perp(A,B,B,C) ),
inference(clausify,[status(thm)],[ruleD52]) ).
cnf(c_328,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_329,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_332,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_333,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_348,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_349,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_351,plain,
( eqangle(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_353,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_355,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_356,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_357,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_358,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_362,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_363,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_364,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_366,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_367,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_368,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_413,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_319]) ).
cnf(c_419,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_355]) ).
cnf(c_424,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_368]) ).
cnf(c_611,plain,
( para(sK9,sK1,A,B)
| ~ perp(sK9,sK5,A,B) ),
inference(resolve,[status(thm)],[c_362,c_271]) ).
cnf(c_620,plain,
( para(A,B,sK9,sK5)
| ~ perp(A,B,sK9,sK1) ),
inference(resolve,[status(thm)],[c_362,c_271]) ).
cnf(c_624,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_362,c_178]) ).
cnf(c_628,plain,
( para(A,B,sK6,sK5)
| ~ perp(A,B,sK0(sK6,sK7,sK8,sK5),sK6) ),
inference(resolve,[status(thm)],[c_362,c_122]) ).
cnf(c_629,plain,
perp(sK9,sK5,sK9,sK1),
inference(resolve,[status(thm)],[c_363,c_271]) ).
cnf(c_633,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_363,c_178]) ).
cnf(c_637,plain,
perp(sK6,sK5,sK0(sK6,sK7,sK8,sK5),sK6),
inference(resolve,[status(thm)],[c_363,c_122]) ).
cnf(c_638,plain,
perp(sK9,sK1,sK5,sK9),
inference(resolve,[status(thm)],[c_364,c_271]) ).
cnf(c_923,plain,
perp(sK9,sK5,sK1,sK9),
inference(resolve,[status(thm)],[c_629,c_364]) ).
cnf(c_931,plain,
perp(sK5,sK9,sK9,sK1),
inference(resolve,[status(thm)],[c_638,c_363]) ).
cnf(c_2381,plain,
para(sK9,sK1,sK1,sK9),
inference(resolve,[status(thm)],[c_611,c_923]) ).
cnf(c_2382,plain,
para(sK9,sK1,sK9,sK1),
inference(resolve,[status(thm)],[c_611,c_629]) ).
cnf(c_2484,plain,
para(sK1,sK9,sK9,sK1),
inference(resolve,[status(thm)],[c_2381,c_366]) ).
cnf(c_2487,plain,
eqangle(sK9,sK1,A,B,sK1,sK9,A,B),
inference(resolve,[status(thm)],[c_2381,c_332]) ).
cnf(c_2499,plain,
eqangle(sK9,sK1,A,B,sK9,sK1,A,B),
inference(resolve,[status(thm)],[c_2382,c_332]) ).
cnf(c_2532,plain,
para(sK5,sK9,sK9,sK5),
inference(resolve,[status(thm)],[c_620,c_931]) ).
cnf(c_2533,plain,
para(sK9,sK5,sK9,sK5),
inference(resolve,[status(thm)],[c_620,c_629]) ).
cnf(c_2700,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_633,c_624]) ).
cnf(c_2793,plain,
para(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_637,c_628]) ).
cnf(c_3169,plain,
para(sK1,sK9,sK1,sK9),
inference(resolve,[status(thm)],[c_2484,c_367]) ).
cnf(c_3185,plain,
para(sK5,sK9,sK5,sK9),
inference(resolve,[status(thm)],[c_2532,c_367]) ).
cnf(c_3201,plain,
eqangle(sK9,sK5,A,B,sK9,sK5,A,B),
inference(resolve,[status(thm)],[c_2533,c_332]) ).
cnf(c_3213,plain,
para(sK2,sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_2700,c_367]) ).
cnf(c_3214,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_2700,c_332]) ).
cnf(c_3226,plain,
para(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_2793,c_367]) ).
cnf(c_3239,plain,
eqangle(sK1,sK9,A,B,sK1,sK9,A,B),
inference(resolve,[status(thm)],[c_3169,c_332]) ).
cnf(c_3251,plain,
eqangle(sK5,sK9,A,B,sK5,sK9,A,B),
inference(resolve,[status(thm)],[c_3185,c_332]) ).
cnf(c_3279,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_3213,c_366]) ).
cnf(c_3295,plain,
para(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_3226,c_366]) ).
cnf(c_3311,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_3279,c_367]) ).
cnf(c_3327,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_3295,c_367]) ).
cnf(c_3342,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_3311,c_332]) ).
cnf(c_3354,plain,
eqangle(sK5,sK6,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_3327,c_332]) ).
cnf(c_7862,plain,
eqangle(A,B,sK9,sK1,A,B,sK1,sK9),
inference(resolve,[status(thm)],[c_2487,c_353]) ).
cnf(c_7872,plain,
eqangle(A,B,sK9,sK1,A,B,sK9,sK1),
inference(resolve,[status(thm)],[c_2499,c_353]) ).
cnf(c_7874,plain,
( cyclic(sK1,A,sK9,sK9)
| ~ coll(sK9,sK9,A) ),
inference(resolve,[status(thm)],[c_2499,c_329]) ).
cnf(c_7875,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK9,sK9)
| ~ cyclic(sK1,A,sK9,A)
| ~ cyclic(sK1,A,sK9,sK1) ),
inference(resolve,[status(thm)],[c_2499,c_328]) ).
cnf(c_7902,plain,
( cyclic(sK5,A,sK9,sK9)
| ~ coll(sK9,sK9,A) ),
inference(resolve,[status(thm)],[c_3201,c_329]) ).
cnf(c_7903,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK9,sK9)
| ~ cyclic(sK5,A,sK9,A)
| ~ cyclic(sK5,A,sK9,sK5) ),
inference(resolve,[status(thm)],[c_3201,c_328]) ).
cnf(c_7916,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_3214,c_329]) ).
cnf(c_7986,plain,
( cyclic(sK9,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3239,c_329]) ).
cnf(c_8000,plain,
( cyclic(sK9,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_3251,c_329]) ).
cnf(c_8073,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_3342,c_329]) ).
cnf(c_8074,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,sK1)
| ~ cyclic(sK2,A,sK1,A)
| ~ cyclic(sK2,A,sK1,sK2) ),
inference(resolve,[status(thm)],[c_3342,c_328]) ).
cnf(c_8087,plain,
( cyclic(sK6,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_3354,c_329]) ).
cnf(c_8379,plain,
eqangle(A,B,A,B,sK9,sK1,sK1,sK9),
inference(resolve,[status(thm)],[c_7862,c_351]) ).
cnf(c_8423,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_7872,c_333]) ).
cnf(c_8451,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_8423,c_310]) ).
cnf(c_8495,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_8451,c_424]) ).
cnf(c_8503,plain,
cyclic(sK6,A,sK5,sK5),
inference(resolve,[status(thm)],[c_8495,c_8087]) ).
cnf(c_8504,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_8495,c_8073]) ).
cnf(c_8505,plain,
cyclic(sK9,A,sK5,sK5),
inference(resolve,[status(thm)],[c_8495,c_8000]) ).
cnf(c_8506,plain,
cyclic(sK9,A,sK1,sK1),
inference(resolve,[status(thm)],[c_8495,c_7986]) ).
cnf(c_8508,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_8495,c_7916]) ).
cnf(c_8509,plain,
cyclic(sK5,A,sK9,sK9),
inference(resolve,[status(thm)],[c_8495,c_7902]) ).
cnf(c_8510,plain,
cyclic(sK1,A,sK9,sK9),
inference(resolve,[status(thm)],[c_8495,c_7874]) ).
cnf(c_8649,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,A)
| ~ cyclic(sK2,A,sK1,sK2) ),
inference(resolve,[status(thm)],[c_8504,c_8074]) ).
cnf(c_8664,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK9,A)
| ~ cyclic(sK5,A,sK9,sK5) ),
inference(resolve,[status(thm)],[c_8509,c_7903]) ).
cnf(c_8670,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK9,A)
| ~ cyclic(sK1,A,sK9,sK1) ),
inference(resolve,[status(thm)],[c_8510,c_7875]) ).
cnf(c_17961,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_8495,c_368]) ).
cnf(c_8729,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_8495,c_17961]) ).
cnf(c_8748,plain,
( midp(A,B,C)
| ~ cong(A,B,A,C) ),
inference(resolve,[status(thm)],[c_8729,c_309]) ).
cnf(c_9055,plain,
cyclic(sK6,sK5,A,sK5),
inference(resolve,[status(thm)],[c_8503,c_357]) ).
cnf(c_9072,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8504,c_357]) ).
cnf(c_9088,plain,
cyclic(sK9,sK5,A,sK5),
inference(resolve,[status(thm)],[c_8505,c_357]) ).
cnf(c_9104,plain,
cyclic(sK9,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8506,c_357]) ).
cnf(c_9166,plain,
cyclic(sK1,sK2,A,sK2),
inference(resolve,[status(thm)],[c_8508,c_357]) ).
cnf(c_9449,plain,
cyclic(sK6,sK5,sK5,A),
inference(resolve,[status(thm)],[c_9055,c_358]) ).
cnf(c_9496,plain,
cyclic(sK2,sK1,sK1,A),
inference(resolve,[status(thm)],[c_9072,c_358]) ).
cnf(c_9497,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_9072,c_356]) ).
cnf(c_9547,plain,
cyclic(sK5,sK9,A,sK5),
inference(resolve,[status(thm)],[c_9088,c_356]) ).
cnf(c_9578,plain,
cyclic(sK1,sK9,A,sK1),
inference(resolve,[status(thm)],[c_9104,c_356]) ).
cnf(c_9717,plain,
cyclic(sK2,sK1,A,sK2),
inference(resolve,[status(thm)],[c_9166,c_356]) ).
cnf(c_10240,plain,
cyclic(sK5,sK5,A,A),
inference(resolve,[status(thm)],[c_9449,c_419]) ).
cnf(c_17962,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK6,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_9449,c_355]) ).
cnf(c_10242,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_9449,c_17962]) ).
cnf(c_10487,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_9496,c_419]) ).
cnf(c_17963,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK2,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_9496,c_355]) ).
cnf(c_10489,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_9496,c_17963]) ).
cnf(c_10505,plain,
( cyclic(sK2,A,sK1,B)
| ~ cyclic(sK1,sK2,A,B) ),
inference(resolve,[status(thm)],[c_9497,c_355]) ).
cnf(c_10716,plain,
cyclic(sK5,A,sK9,sK5),
inference(resolve,[status(thm)],[c_9547,c_357]) ).
cnf(c_10732,plain,
( cong(sK5,A,sK5,A)
| ~ cyclic(sK5,A,sK9,A) ),
inference(resolve,[status(thm)],[c_10716,c_8664]) ).
cnf(c_10905,plain,
cyclic(sK1,A,sK9,sK1),
inference(resolve,[status(thm)],[c_9578,c_357]) ).
cnf(c_10921,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK9,A) ),
inference(resolve,[status(thm)],[c_10905,c_8670]) ).
cnf(c_11093,plain,
cyclic(sK2,A,sK1,sK2),
inference(resolve,[status(thm)],[c_9717,c_357]) ).
cnf(c_11109,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK1,A) ),
inference(resolve,[status(thm)],[c_11093,c_8649]) ).
cnf(c_17964,plain,
( cyclic(sK5,A,B,A)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_10240,c_355]) ).
cnf(c_11772,plain,
cyclic(sK5,A,B,A),
inference(resolve,[status(thm)],[c_10242,c_17964]) ).
cnf(c_11785,plain,
cong(sK5,A,sK5,A),
inference(resolve,[status(thm)],[c_11772,c_10732]) ).
cnf(c_12083,plain,
( perp(A,sK1,sK1,A)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_10487,c_413]) ).
cnf(c_17965,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_10487,c_355]) ).
cnf(c_12084,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_10489,c_17965]) ).
cnf(c_12097,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_12084,c_10921]) ).
cnf(c_12100,plain,
perp(A,sK1,sK1,A),
inference(resolve,[status(thm)],[c_12097,c_12083]) ).
cnf(c_17966,plain,
( cyclic(sK1,A,B,C)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_10489,c_355]) ).
cnf(c_12171,plain,
cyclic(sK1,A,B,C),
inference(resolve,[status(thm)],[c_10489,c_17966]) ).
cnf(c_12188,plain,
cyclic(sK2,A,sK1,B),
inference(resolve,[status(thm)],[c_12171,c_10505]) ).
cnf(c_12249,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_12188,c_11109]) ).
cnf(c_17967,plain,
( perp(sK5,sK5,A,B)
| ~ cong(sK5,A,sK5,A) ),
inference(resolve,[status(thm)],[c_11785,c_320]) ).
cnf(c_13627,plain,
perp(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_11785,c_17967]) ).
cnf(c_14781,plain,
cong(sK2,A,A,sK2),
inference(resolve,[status(thm)],[c_12249,c_349]) ).
cnf(c_15652,plain,
perp(A,B,sK5,sK5),
inference(resolve,[status(thm)],[c_13627,c_363]) ).
cnf(c_17968,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK5,sK5) ),
inference(resolve,[status(thm)],[c_13627,c_362]) ).
cnf(c_15653,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_15652,c_17968]) ).
cnf(c_17969,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_15653,c_312]) ).
cnf(c_15682,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_15653,c_17969]) ).
cnf(c_15922,plain,
cong(A,sK2,sK2,A),
inference(resolve,[status(thm)],[c_14781,c_348]) ).
cnf(c_16551,plain,
cong(A,sK2,A,sK2),
inference(resolve,[status(thm)],[c_15922,c_349]) ).
cnf(c_17970,plain,
( perp(A,B,A,B)
| ~ perp(sK9,sK1,sK1,sK9) ),
inference(resolve,[status(thm)],[c_8379,c_303]) ).
cnf(c_17367,plain,
perp(A,B,A,B),
inference(resolve,[status(thm)],[c_12100,c_17970]) ).
cnf(c_17370,plain,
perp(A,B,B,A),
inference(resolve,[status(thm)],[c_17367,c_364]) ).
cnf(c_17378,plain,
( cong(B,A,C,A)
| ~ midp(A,B,B) ),
inference(resolve,[status(thm)],[c_17370,c_323]) ).
cnf(c_17451,plain,
midp(A,sK2,sK2),
inference(resolve,[status(thm)],[c_8748,c_16551]) ).
cnf(c_17584,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_17451,c_15682]) ).
cnf(c_17611,plain,
cong(A,B,C,B),
inference(resolve,[status(thm)],[c_17584,c_17378]) ).
cnf(c_17971,plain,
( perp(A,C,D,B)
| ~ cong(A,B,C,B) ),
inference(resolve,[status(thm)],[c_17611,c_320]) ).
cnf(c_17959,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_17611,c_17971]) ).
cnf(c_17960,plain,
$false,
inference(resolve,[status(thm)],[c_17959,c_267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO606+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:46:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 298376 was started by sandbox2 on n003,
% 0.10/0.37 % Fri Sep 25 13:46:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 13.55/2.54
% 13.55/2.54 % given #500 (T,wt=9): 1205 coll(c6,c5,c6). [resolve(1171,a,370,a)].
% 13.55/2.54
% 13.55/2.54 % given #1000 (A,wt=13): 781 -coll(c7,c7,A) | coll(A,c2,c7). [resolve(714,a,368,b)].
% 13.55/2.54
% 13.55/2.54 % given #1500 (W,wt=13): 1657 -coll(c7,c8,A) | coll(c1,A,c7). [resolve(1586,a,368,a)].
% 13.55/2.54
% 13.55/2.54 % given #2000 (T,wt=13): 2599 -coll(c1,c4,A) | coll(A,c3,c1). [resolve(2562,a,368,b)].
% 13.55/2.54
% 13.55/2.54 % given #2500 (W,wt=13): 5327 -coll(c5,c2,A) | coll(c3,A,c5). [resolve(5311,a,368,a)].
% 13.55/2.54
% 13.55/2.54 % given #3000 (T,wt=10): 10082 perp(c8,c18,c8,c7). [resolve(9336,a,364,a)].
% 13.55/2.54
% 13.55/2.54 % given #3500 (A,wt=19): 2385 para(f12(c3,c11,c12,c2),c3,c1,c3). [resolve(613,a,923,a)].
% 13.55/2.54
% 13.55/2.54 % given #4000 (T,wt=14): 8148 eqangle(c3,c6,c1,c3,c16,c6,c16,c3). [resolve(4931,a,353,a)].
% 13.55/2.54
% 13.55/2.54 % SZS status Theorem for theBenchmark
% 13.55/2.54
% 13.55/2.54 % Proof 1 at 1.67 (+ 0.41) seconds.
% 13.55/2.54 % Length of proof is 169.
% 13.55/2.54 % Level of proof is 24.
% 13.55/2.54 % Maximum clause weight is 34.000.
% 13.55/2.54 % Given clauses 4089.
% 13.55/2.54
% 13.55/2.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------