%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO576+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 : n011.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 07:18:08 AM UTC 2026
% Result : Theorem 18.81s 3.23s
% Output : CNFRefutation 18.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 27
% Syntax : Number of formulae : 165 ( 71 unt; 0 def)
% Number of atoms : 322 ( 0 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 251 ( 94 ~; 90 |; 39 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 489 ( 77 sgn 164 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ruleD18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('theBenchmark.p',ruleD18) ).
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(ruleD22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('theBenchmark.p',ruleD22) ).
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(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(ruleD48,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,B) ),
file('theBenchmark.p',ruleD48) ).
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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(ruleX14,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX14) ).
fof(exemplo6GDDFULL214038,conjecture,
! [A,B,C,D,O,D1,P,NWPNT1] :
( ( coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(O,A,A,D,C,A,A,P) ),
file('theBenchmark.p',exemplo6GDDFULL214038) ).
fof(exemplo6GDDFULL214038_neg,negated_conjecture,
~ ! [A,B,C,D,O,D1,P,NWPNT1] :
( ( coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(O,A,A,D,C,A,A,P) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214038]) ).
cnf(c_96,plain,
( eqangle(B,E,B,C,D,B,D,C)
| ~ perp(A,B,B,E)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD48]) ).
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_90,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[ruleX14]) ).
fof(sk_ruleX14,plain,
! [A,B,C,D] :
( circle(sK1(A,B,C,D),A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(O,sK1(A,B,C,D))],[nnf_90]) ).
cnf(c_108,plain,
( circle(sK1(A,C,B,D),A,C,B)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(split_conjunct,[status(thm)],[sk_ruleX14]) ).
fof(nnf_95,plain,
? [A,B,C,D,O,D1,P,NWPNT1] :
( ~ eqangle(O,A,A,D,C,A,A,P)
& coll(P,B,C)
& perp(A,C,D1,P)
& coll(D1,A,D)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214038_neg]) ).
fof(sk_exemplo6GDDFULL214038_neg,plain,
( ~ eqangle(sK2,sK3,sK3,sK6,sK5,sK3,sK3,sK7)
& coll(sK7,sK4,sK5)
& perp(sK3,sK5,sK8,sK7)
& coll(sK8,sK3,sK6)
& circle(sK2,sK3,sK8,sK9)
& circle(sK2,sK3,sK4,sK5)
& coll(sK6,sK4,sK5)
& perp(sK6,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK3,sK4,sK5,sK2,sK8,sK9,sK7]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(D,sK6),skolemize(O,sK2),skolemize(D1,sK8),skolemize(P,sK7),skolemize(NWPNT1,sK9)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214038_neg]) ).
cnf(c_130,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_139,plain,
( eqangle(A,E,A,C,B,A,B,C)
| ~ perp(sK1(A,C,B,D),A,A,E)
| ~ cyclic(A,C,B,D)
| ~ perp(A,B,B,C) ),
inference(resolve,[status(thm)],[c_108,c_96]) ).
cnf(c_177,negated_conjecture,
~ eqangle(sK2,sK3,sK3,sK6,sK5,sK3,sK3,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214038_neg]) ).
cnf(c_180,negated_conjecture,
coll(sK8,sK3,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214038_neg]) ).
cnf(c_182,negated_conjecture,
perp(sK6,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214038_neg]) ).
cnf(c_221,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_230,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_231,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_239,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_240,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_242,plain,
( eqangle(C,A,C,B,D,A,D,B)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD41]) ).
cnf(c_243,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_244,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_261,plain,
( eqangle(A,B,C,D,V8,V9,V10,V11)
| ~ eqangle(E,F,V6,V7,V8,V9,V10,V11)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD22]) ).
cnf(c_262,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_264,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_265,plain,
( eqangle(B,A,C,D,E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD18]) ).
cnf(c_266,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_267,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_268,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_269,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_273,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_274,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_275,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_277,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_278,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_279,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_280,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_324,plain,
( perp(B,A,A,B)
| ~ cyclic(A,C,B,B)
| ~ cong(A,B,C,B) ),
inference(factor,[status(thm)],[c_230]) ).
cnf(c_330,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_266]) ).
cnf(c_335,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_409,plain,
( para(sK6,sK3,A,B)
| ~ perp(sK4,sK5,A,B) ),
inference(resolve,[status(thm)],[c_273,c_182]) ).
cnf(c_415,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_273,c_130]) ).
cnf(c_417,plain,
perp(sK4,sK5,sK6,sK3),
inference(resolve,[status(thm)],[c_274,c_182]) ).
cnf(c_419,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_274,c_130]) ).
cnf(c_432,plain,
coll(sK3,sK8,sK6),
inference(resolve,[status(thm)],[c_280,c_180]) ).
cnf(c_444,plain,
coll(sK6,sK6,sK3),
inference(resolve,[status(thm)],[c_432,c_335]) ).
cnf(c_632,plain,
perp(sK4,sK5,sK3,sK6),
inference(resolve,[status(thm)],[c_417,c_275]) ).
cnf(c_1106,plain,
para(sK6,sK3,sK3,sK6),
inference(resolve,[status(thm)],[c_409,c_632]) ).
cnf(c_1107,plain,
para(sK6,sK3,sK6,sK3),
inference(resolve,[status(thm)],[c_409,c_417]) ).
cnf(c_1174,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_419,c_415]) ).
cnf(c_1257,plain,
para(sK3,sK6,sK6,sK3),
inference(resolve,[status(thm)],[c_1106,c_277]) ).
cnf(c_1260,plain,
eqangle(sK6,sK3,A,B,sK3,sK6,A,B),
inference(resolve,[status(thm)],[c_1106,c_243]) ).
cnf(c_1272,plain,
eqangle(sK6,sK3,A,B,sK6,sK3,A,B),
inference(resolve,[status(thm)],[c_1107,c_243]) ).
cnf(c_1442,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_1174,c_278]) ).
cnf(c_1443,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1174,c_243]) ).
cnf(c_1494,plain,
para(sK3,sK6,sK3,sK6),
inference(resolve,[status(thm)],[c_1257,c_278]) ).
cnf(c_1580,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_1442,c_277]) ).
cnf(c_1595,plain,
eqangle(sK3,sK6,A,B,sK3,sK6,A,B),
inference(resolve,[status(thm)],[c_1494,c_243]) ).
cnf(c_1620,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1580,c_278]) ).
cnf(c_1635,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_1620,c_243]) ).
cnf(c_2524,plain,
eqangle(A,B,sK6,sK3,A,B,sK3,sK6),
inference(resolve,[status(thm)],[c_1260,c_264]) ).
cnf(c_2525,plain,
eqangle(sK6,sK3,sK3,sK6,A,B,A,B),
inference(resolve,[status(thm)],[c_1260,c_262]) ).
cnf(c_2534,plain,
eqangle(A,B,sK6,sK3,A,B,sK6,sK3),
inference(resolve,[status(thm)],[c_1272,c_264]) ).
cnf(c_2536,plain,
( cyclic(sK3,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_1272,c_240]) ).
cnf(c_2613,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1443,c_240]) ).
cnf(c_2614,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,sK3)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_1443,c_239]) ).
cnf(c_2690,plain,
( cyclic(sK6,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1595,c_240]) ).
cnf(c_2691,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,sK3)
| ~ cyclic(sK6,A,sK3,A)
| ~ cyclic(sK6,A,sK3,sK6) ),
inference(resolve,[status(thm)],[c_1595,c_239]) ).
cnf(c_2725,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1635,c_240]) ).
cnf(c_2799,plain,
eqangle(A,B,A,B,sK6,sK3,sK3,sK6),
inference(resolve,[status(thm)],[c_2524,c_262]) ).
cnf(c_2803,plain,
( eqangle(sK6,sK3,sK3,sK6,C,D,E,F)
| ~ eqangle(A,B,A,B,C,D,E,F) ),
inference(resolve,[status(thm)],[c_2525,c_261]) ).
cnf(c_2808,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_2534,c_244]) ).
cnf(c_13949,plain,
( cyclic(A,sK3,sK6,sK6)
| ~ coll(sK6,sK6,sK3) ),
inference(resolve,[status(thm)],[c_2534,c_240]) ).
cnf(c_2810,plain,
cyclic(A,sK3,sK6,sK6),
inference(resolve,[status(thm)],[c_444,c_13949]) ).
cnf(c_2833,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_2808,c_221]) ).
cnf(c_2889,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_2833,c_335]) ).
cnf(c_2897,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_2889,c_2725]) ).
cnf(c_2899,plain,
cyclic(sK6,A,sK3,sK3),
inference(resolve,[status(thm)],[c_2889,c_2690]) ).
cnf(c_2902,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_2889,c_2613]) ).
cnf(c_2906,plain,
cyclic(sK3,A,sK6,sK6),
inference(resolve,[status(thm)],[c_2889,c_2536]) ).
cnf(c_3041,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,A)
| ~ cyclic(sK6,A,sK3,sK6) ),
inference(resolve,[status(thm)],[c_2899,c_2691]) ).
cnf(c_3050,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_2902,c_2614]) ).
cnf(c_3246,plain,
cyclic(A,sK6,sK3,sK6),
inference(resolve,[status(thm)],[c_2810,c_268]) ).
cnf(c_3267,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_2897,c_268]) ).
cnf(c_3301,plain,
cyclic(sK6,sK3,A,sK3),
inference(resolve,[status(thm)],[c_2899,c_268]) ).
cnf(c_3420,plain,
cyclic(sK3,sK6,A,sK6),
inference(resolve,[status(thm)],[c_2906,c_268]) ).
cnf(c_3451,plain,
cyclic(sK6,A,sK3,sK6),
inference(resolve,[status(thm)],[c_3246,c_267]) ).
cnf(c_3454,plain,
eqangle(sK3,A,sK3,sK6,sK6,A,sK6,sK6),
inference(resolve,[status(thm)],[c_3246,c_242]) ).
cnf(c_3467,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK3,A) ),
inference(resolve,[status(thm)],[c_3451,c_3041]) ).
cnf(c_3531,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_3267,c_269]) ).
cnf(c_3532,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_3267,c_267]) ).
cnf(c_3625,plain,
cyclic(sK6,sK3,sK3,A),
inference(resolve,[status(thm)],[c_3301,c_269]) ).
cnf(c_3626,plain,
cyclic(sK3,sK6,A,sK3),
inference(resolve,[status(thm)],[c_3301,c_267]) ).
cnf(c_3953,plain,
cyclic(sK3,sK6,sK6,A),
inference(resolve,[status(thm)],[c_3420,c_269]) ).
cnf(c_4093,plain,
cyclic(sK2,sK2,A,A),
inference(resolve,[status(thm)],[c_3531,c_330]) ).
cnf(c_13950,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_3531,c_266]) ).
cnf(c_4095,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_3531,c_13950]) ).
cnf(c_4109,plain,
cyclic(sK2,A,sK3,sK2),
inference(resolve,[status(thm)],[c_3532,c_268]) ).
cnf(c_4125,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A) ),
inference(resolve,[status(thm)],[c_4109,c_3050]) ).
cnf(c_13951,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK6,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_3625,c_266]) ).
cnf(c_4505,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_3625,c_13951]) ).
cnf(c_4521,plain,
( cyclic(sK6,A,sK3,B)
| ~ cyclic(sK3,sK6,A,B) ),
inference(resolve,[status(thm)],[c_3626,c_266]) ).
cnf(c_5324,plain,
cyclic(sK6,sK6,A,A),
inference(resolve,[status(thm)],[c_3953,c_330]) ).
cnf(c_13952,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK3,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_3953,c_266]) ).
cnf(c_5326,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_3953,c_13952]) ).
cnf(c_13953,plain,
( cyclic(sK2,A,B,A)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_4093,c_266]) ).
cnf(c_5424,plain,
cyclic(sK2,A,B,A),
inference(resolve,[status(thm)],[c_4095,c_13953]) ).
cnf(c_5437,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_5424,c_4125]) ).
cnf(c_13954,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_4505,c_266]) ).
cnf(c_5882,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_4505,c_13954]) ).
cnf(c_5894,plain,
cyclic(sK6,A,sK3,B),
inference(resolve,[status(thm)],[c_5882,c_4521]) ).
cnf(c_5972,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_5894,c_3467]) ).
cnf(c_13955,plain,
( perp(A,sK6,sK6,A)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_5324,c_324]) ).
cnf(c_6758,plain,
perp(A,sK6,sK6,A),
inference(resolve,[status(thm)],[c_5972,c_13955]) ).
cnf(c_13956,plain,
( perp(A,sK6,sK6,B)
| ~ cong(sK6,B,sK6,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_5326,c_230]) ).
cnf(c_13957,plain,
( perp(B,sK6,sK6,A)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_5972,c_13956]) ).
cnf(c_6793,plain,
perp(A,sK6,sK6,B),
inference(resolve,[status(thm)],[c_5972,c_13957]) ).
cnf(c_13958,plain,
( eqangle(sK6,C,sK6,sK6,A,sK6,A,sK6)
| ~ perp(sK1(sK6,sK6,A,B),sK6,sK6,C)
| ~ perp(sK6,A,A,sK6) ),
inference(resolve,[status(thm)],[c_5326,c_139]) ).
cnf(c_6801,plain,
( eqangle(sK6,B,sK6,sK6,A,sK6,A,sK6)
| ~ perp(sK6,A,A,sK6) ),
inference(resolve,[status(thm)],[c_6793,c_13958]) ).
cnf(c_13959,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_5437,c_231]) ).
cnf(c_6948,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_5437,c_13959]) ).
cnf(c_8734,plain,
perp(sK6,A,A,sK6),
inference(resolve,[status(thm)],[c_6758,c_274]) ).
cnf(c_8747,plain,
eqangle(sK6,A,sK6,sK6,B,sK6,B,sK6),
inference(resolve,[status(thm)],[c_8734,c_6801]) ).
cnf(c_8817,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_6948,c_274]) ).
cnf(c_13960,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_6948,c_273]) ).
cnf(c_8818,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_8817,c_13960]) ).
cnf(c_8834,plain,
eqangle(A,B,C,D,E,F,C,D),
inference(resolve,[status(thm)],[c_8818,c_243]) ).
cnf(c_10544,plain,
( eqangle(E,F,E,F,A,B,C,D)
| ~ eqangle(sK6,sK3,sK3,sK6,A,B,C,D) ),
inference(resolve,[status(thm)],[c_2799,c_261]) ).
cnf(c_11744,plain,
eqangle(A,sK3,sK3,sK6,sK6,A,sK6,sK6),
inference(resolve,[status(thm)],[c_3454,c_265]) ).
cnf(c_13323,plain,
( eqangle(sK6,F,sK6,sK6,B,C,D,E)
| ~ eqangle(A,sK6,A,sK6,B,C,D,E) ),
inference(resolve,[status(thm)],[c_8747,c_261]) ).
cnf(c_13361,plain,
eqangle(sK6,sK3,sK3,sK6,A,B,C,D),
inference(resolve,[status(thm)],[c_8834,c_2803]) ).
cnf(c_13368,plain,
eqangle(A,B,A,B,C,D,E,F),
inference(resolve,[status(thm)],[c_13361,c_10544]) ).
cnf(c_13381,plain,
eqangle(sK6,A,sK6,sK6,B,C,D,E),
inference(resolve,[status(thm)],[c_13368,c_13323]) ).
cnf(c_13961,plain,
( eqangle(A,sK3,sK3,sK6,B,C,D,E)
| ~ eqangle(sK6,A,sK6,sK6,B,C,D,E) ),
inference(resolve,[status(thm)],[c_11744,c_261]) ).
cnf(c_13947,plain,
eqangle(A,sK3,sK3,sK6,B,C,D,E),
inference(resolve,[status(thm)],[c_13381,c_13961]) ).
cnf(c_13948,plain,
$false,
inference(resolve,[status(thm)],[c_13947,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO576+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 13:42:43 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 2139288 was started by sandbox2 on n011,
% 0.13/0.39 % Fri Sep 25 13:42:43 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.42
% 0.13/0.42 % From the command line: assign(max_seconds, 300).
% 18.81/3.23
% 18.81/3.23 % given #500 (A,wt=24): 416 -perp(A,B,f12(c1,c6,c8,c5),c1) | para(A,B,c1,c5). [resolve(273,b,116,a)].
% 18.81/3.23
% 18.81/3.23 % given #1000 (T,wt=10): 2167 perp(c1,c2,c2,c3). [back_unit_del(129),unit_del(a,2163)].
% 18.81/3.23
% 18.81/3.23 % given #1500 (A,wt=23): 1176 para(f12(c1,c2,c3,c5),c1,f12(c1,c2,c3,c5),c1). [resolve(419,a,411,a)].
% 18.81/3.23
% 18.81/3.23 % given #2000 (T,wt=10): 5324 cyclic(c4,c4,A,A). [resolve(3953,a,330,a)].
% 18.81/3.23
% 18.81/3.23 % given #2500 (A,wt=28): 1988 coll(f17(f12(c1,c6,c8,c5),c5,c1,c2,c2),c2,c2). [resolve(1971,a,356,a)].
% 18.81/3.23
% 18.81/3.23 % given #3000 (T,wt=14): 6566 eqangle(A,c2,A,c2,c2,c2,c2,c2). [resolve(5149,a,242,a)].
% 18.81/3.23
% 18.81/3.23 % SZS status Theorem for theBenchmark
% 18.81/3.23
% 18.81/3.23 % Proof 1 at 1.99 (+ 0.65) seconds.
% 18.81/3.23 % Length of proof is 145.
% 18.81/3.23 % Level of proof is 24.
% 18.81/3.23 % Maximum clause weight is 38.000.
% 18.81/3.23 % Given clauses 3384.
% 18.81/3.23
% 18.81/3.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------