%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO577+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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:09 AM UTC 2026
% Result : Theorem 41.69s 6.53s
% Output : CNFRefutation 41.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 84 ( 32 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 147 ( 46 ~; 42 |; 39 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 255 ( 28 sgn 108 !; 9 ?)
% 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(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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD73) ).
fof(exemplo6GDDFULL214039,conjecture,
! [A,B,C,I,O,M,L1,NWPNT1,NWPNT2] :
( ( circle(O,A,L1,NWPNT2)
& perp(B,I,B,L1)
& coll(M,C,I)
& circle(O,C,M,NWPNT1)
& circle(O,A,B,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> para(M,L1,A,I) ),
file('theBenchmark.p',exemplo6GDDFULL214039) ).
fof(exemplo6GDDFULL214039_neg,negated_conjecture,
~ ! [A,B,C,I,O,M,L1,NWPNT1,NWPNT2] :
( ( circle(O,A,L1,NWPNT2)
& perp(B,I,B,L1)
& coll(M,C,I)
& circle(O,C,M,NWPNT1)
& circle(O,A,B,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> para(M,L1,A,I) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214039]) ).
fof(nnf_95,plain,
? [A,B,C,I,O,M,L1,NWPNT1,NWPNT2] :
( ~ para(M,L1,A,I)
& circle(O,A,L1,NWPNT2)
& perp(B,I,B,L1)
& coll(M,C,I)
& circle(O,C,M,NWPNT1)
& circle(O,A,B,C)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214039_neg]) ).
fof(sk_exemplo6GDDFULL214039_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& circle(sK6,sK2,sK1,sK8)
& perp(sK5,sK3,sK5,sK1)
& coll(sK0,sK4,sK3)
& circle(sK6,sK4,sK0,sK7)
& circle(sK6,sK2,sK5,sK4)
& eqangle(sK3,sK4,sK4,sK2,sK3,sK4,sK4,sK5)
& eqangle(sK3,sK5,sK5,sK4,sK3,sK5,sK5,sK2)
& eqangle(sK3,sK2,sK2,sK5,sK3,sK2,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK5,sK4,sK6,sK0,sK7,sK1,sK8]),skolemize(A,sK2),skolemize(B,sK5),skolemize(C,sK4),skolemize(I,sK3),skolemize(O,sK6),skolemize(M,sK0),skolemize(L1,sK1),skolemize(NWPNT1,sK7),skolemize(NWPNT2,sK8)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214039_neg]) ).
cnf(c_194,negated_conjecture,
coll(sK0,sK4,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214039_neg]) ).
cnf(c_197,negated_conjecture,
eqangle(sK3,sK2,sK2,sK5,sK3,sK2,sK2,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214039_neg]) ).
cnf(c_230,plain,
( para(A,B,C,D)
| ~ para(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD73]) ).
cnf(c_236,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_246,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_254,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_255,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_258,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_259,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_277,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_279,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_281,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_282,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_283,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_284,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_288,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_289,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_294,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_295,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_296,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_350,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_517,plain,
eqangle(sK3,sK2,sK3,sK2,sK2,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_277,c_197]) ).
cnf(c_523,plain,
eqangle(sK2,sK5,sK3,sK2,sK2,sK4,sK3,sK2),
inference(resolve,[status(thm)],[c_279,c_197]) ).
cnf(c_551,plain,
coll(sK4,sK0,sK3),
inference(resolve,[status(thm)],[c_295,c_194]) ).
cnf(c_560,plain,
coll(sK3,sK3,sK4),
inference(resolve,[status(thm)],[c_551,c_350]) ).
cnf(c_675,plain,
coll(sK4,sK4,sK3),
inference(resolve,[status(thm)],[c_560,c_350]) ).
cnf(c_924,plain,
( coll(A,sK3,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_675,c_294]) ).
cnf(c_1755,plain,
( para(sK3,sK2,sK3,sK2)
| ~ para(sK2,sK5,sK2,sK4) ),
inference(resolve,[status(thm)],[c_517,c_230]) ).
cnf(c_1797,plain,
para(sK2,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_523,c_259]) ).
cnf(c_1800,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_1797,c_1755]) ).
cnf(c_1814,plain,
coll(sK2,sK5,sK4),
inference(resolve,[status(thm)],[c_1797,c_236]) ).
cnf(c_1832,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1814,c_350]) ).
cnf(c_1874,plain,
coll(sK2,sK3,sK4),
inference(resolve,[status(thm)],[c_1832,c_924]) ).
cnf(c_2084,plain,
coll(sK2,sK4,sK3),
inference(resolve,[status(thm)],[c_1874,c_296]) ).
cnf(c_2458,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_2084,c_350]) ).
cnf(c_3280,plain,
( cyclic(A,sK2,sK3,sK3)
| ~ eqangle(sK3,A,sK3,sK2,sK3,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_2458,c_255]) ).
cnf(c_5153,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_1800,c_258]) ).
cnf(c_17083,plain,
eqangle(A,B,sK3,sK2,A,B,sK3,sK2),
inference(resolve,[status(thm)],[c_5153,c_279]) ).
cnf(c_17086,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_5153,c_254]) ).
cnf(c_17093,plain,
cyclic(A,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_17083,c_3280]) ).
cnf(c_17140,plain,
cyclic(A,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_17093,c_283]) ).
cnf(c_17141,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_17093,c_282]) ).
cnf(c_17150,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A)
| ~ cyclic(sK2,A,sK3,sK2) ),
inference(resolve,[status(thm)],[c_17141,c_17086]) ).
cnf(c_17282,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_17140,c_282]) ).
cnf(c_17303,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_17141,c_283]) ).
cnf(c_17520,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_17282,c_283]) ).
cnf(c_17552,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_17303,c_284]) ).
cnf(c_17791,plain,
( cyclic(sK2,A,sK3,B)
| ~ cyclic(sK3,sK2,A,B) ),
inference(resolve,[status(thm)],[c_17520,c_281]) ).
cnf(c_28609,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK2,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_17552,c_281]) ).
cnf(c_17817,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_17552,c_28609]) ).
cnf(c_28610,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_17817,c_281]) ).
cnf(c_18334,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_17817,c_28610]) ).
cnf(c_18343,plain,
cyclic(sK2,A,sK3,B),
inference(resolve,[status(thm)],[c_18334,c_17791]) ).
cnf(c_28611,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK3,A) ),
inference(resolve,[status(thm)],[c_18343,c_17150]) ).
cnf(c_18354,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_18343,c_28611]) ).
cnf(c_28612,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_18354,c_246]) ).
cnf(c_20787,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_18354,c_28612]) ).
cnf(c_28606,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_20787,c_289]) ).
cnf(c_28613,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_20787,c_288]) ).
cnf(c_28607,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_28606,c_28613]) ).
cnf(c_28608,plain,
$false,
inference(resolve,[status(thm)],[c_28607,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO577+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 13:45:34 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3408537 was started by sandbox on n002,
% 0.19/0.45 % Fri Sep 25 13:45:34 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/0.49
% 0.22/0.49 % From the command line: assign(max_seconds, 300).
% 41.69/6.53
% 41.69/6.53 % given #500 (W,wt=13): 2355 -coll(c3,c3,A) | coll(c2,A,c3). [resolve(1954,a,294,a)].
% 41.69/6.53
% 41.69/6.53 % given #1000 (T,wt=10): 13721 perp(c2,c1,c1,c2). [back_unit_del(12535),unit_del(a,13712)].
% 41.69/6.53
% 41.69/6.53 % given #1500 (T,wt=10): 20304 cyclic(c2,c1,A,A). [resolve(18079,a,345,a)].
% 41.69/6.53
% 41.69/6.53 % SZS status Theorem for theBenchmark
% 41.69/6.53
% 41.69/6.53 % Proof 1 at 4.08 (+ 1.45) seconds.
% 41.69/6.53 % Length of proof is 76.
% 41.69/6.53 % Level of proof is 21.
% 41.69/6.53 % Maximum clause weight is 34.000.
% 41.69/6.53 % Given clauses 1793.
% 41.69/6.53
% 41.69/6.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------