%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO589+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 : n017.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 07:18:10 AM UTC 2026
% Result : Theorem 2.79s 0.84s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 79 ( 30 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 43 ~; 39 |; 26 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 238 ( 28 sgn 96 !; 8 ?)
% 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(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(exemplo6GDDFULL416051,conjecture,
! [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ( coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> para(B,E,A,C) ),
file('theBenchmark.p',exemplo6GDDFULL416051) ).
fof(exemplo6GDDFULL416051_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ( coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> para(B,E,A,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416051]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,E,NWPNT1,NWPNT2] :
( ~ para(B,E,A,C)
& coll(E,D,O)
& circle(O,D,E,NWPNT2)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416051_neg]) ).
fof(sk_exemplo6GDDFULL416051_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK1,sK4,sK5)
& circle(sK5,sK4,sK1,sK7)
& circle(sK5,sK2,sK4,sK6)
& perp(sK2,sK3,sK0,sK4)
& circle(sK5,sK2,sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK2,sK0,sK3,sK4,sK6,sK1,sK7]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK3),skolemize(O,sK5),skolemize(D,sK4),skolemize(E,sK1),skolemize(NWPNT1,sK6),skolemize(NWPNT2,sK7)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416051_neg]) ).
cnf(c_194,negated_conjecture,
perp(sK2,sK3,sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416051_neg]) ).
cnf(c_233,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_243,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_251,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_252,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_255,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_256,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_276,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_278,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_279,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_280,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_281,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_285,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_286,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_287,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_289,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_290,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_291,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_347,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_291]) ).
cnf(c_431,plain,
( para(sK2,sK3,A,B)
| ~ perp(sK0,sK4,A,B) ),
inference(resolve,[status(thm)],[c_285,c_194]) ).
cnf(c_439,plain,
perp(sK0,sK4,sK2,sK3),
inference(resolve,[status(thm)],[c_286,c_194]) ).
cnf(c_551,plain,
perp(sK0,sK4,sK3,sK2),
inference(resolve,[status(thm)],[c_439,c_287]) ).
cnf(c_674,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_431,c_551]) ).
cnf(c_675,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_431,c_439]) ).
cnf(c_680,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_674,c_289]) ).
cnf(c_695,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_675,c_255]) ).
cnf(c_734,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_680,c_290]) ).
cnf(c_749,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_734,c_255]) ).
cnf(c_768,plain,
eqangle(A,B,sK2,sK3,A,B,sK2,sK3),
inference(resolve,[status(thm)],[c_695,c_276]) ).
cnf(c_770,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_695,c_252]) ).
cnf(c_771,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,sK2)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_695,c_251]) ).
cnf(c_791,plain,
( cyclic(sK2,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_749,c_252]) ).
cnf(c_810,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_768,c_256]) ).
cnf(c_835,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_810,c_233]) ).
cnf(c_858,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_835,c_347]) ).
cnf(c_866,plain,
cyclic(sK2,A,sK3,sK3),
inference(resolve,[status(thm)],[c_858,c_791]) ).
cnf(c_867,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_858,c_770]) ).
cnf(c_894,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A)
| ~ cyclic(sK3,A,sK2,sK3) ),
inference(resolve,[status(thm)],[c_867,c_771]) ).
cnf(c_954,plain,
cyclic(sK2,sK3,A,sK3),
inference(resolve,[status(thm)],[c_866,c_280]) ).
cnf(c_972,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_867,c_280]) ).
cnf(c_1115,plain,
cyclic(sK2,sK3,sK3,A),
inference(resolve,[status(thm)],[c_954,c_281]) ).
cnf(c_1116,plain,
cyclic(sK3,sK2,A,sK3),
inference(resolve,[status(thm)],[c_954,c_279]) ).
cnf(c_1211,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_972,c_279]) ).
cnf(c_1401,plain,
cyclic(sK3,sK2,sK3,A),
inference(resolve,[status(thm)],[c_1115,c_279]) ).
cnf(c_1416,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_1116,c_280]) ).
cnf(c_1432,plain,
( cong(sK3,A,sK3,A)
| ~ cyclic(sK3,A,sK2,A) ),
inference(resolve,[status(thm)],[c_1416,c_894]) ).
cnf(c_1552,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_1211,c_278]) ).
cnf(c_2211,plain,
( cyclic(sK2,sK3,A,B)
| ~ cyclic(sK3,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_1401,c_278]) ).
cnf(c_1633,plain,
cyclic(sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_1401,c_2211]) ).
cnf(c_1647,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_1633,c_1552]) ).
cnf(c_1651,plain,
cong(sK3,A,sK3,A),
inference(resolve,[status(thm)],[c_1647,c_1432]) ).
cnf(c_2212,plain,
( perp(sK3,sK3,A,B)
| ~ cong(sK3,A,sK3,A) ),
inference(resolve,[status(thm)],[c_1651,c_243]) ).
cnf(c_1952,plain,
perp(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_1651,c_2212]) ).
cnf(c_2208,plain,
perp(A,B,sK3,sK3),
inference(resolve,[status(thm)],[c_1952,c_286]) ).
cnf(c_2213,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK3,sK3) ),
inference(resolve,[status(thm)],[c_1952,c_285]) ).
cnf(c_2209,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_2208,c_2213]) ).
cnf(c_2210,plain,
$false,
inference(resolve,[status(thm)],[c_2209,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO589+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 13:38:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2399890 was started by sandbox2 on n017,
% 0.11/0.37 % Fri Sep 25 13:38:47 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.41
% 0.11/0.41 % From the command line: assign(max_seconds, 300).
% 2.79/0.84
% 2.79/0.84 % given #500 (T,wt=10): 1580 perp(c2,c1,c2,c3). [resolve(1234,a,286,a)].
% 2.79/0.84
% 2.79/0.84 % SZS status Theorem for theBenchmark
% 2.79/0.84
% 2.79/0.84 % Proof 1 at 0.30 (+ 0.11) seconds.
% 2.79/0.84 % Length of proof is 73.
% 2.79/0.84 % Level of proof is 19.
% 2.79/0.84 % Maximum clause weight is 34.000.
% 2.79/0.84 % Given clauses 527.
% 2.79/0.84
% 2.79/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------