%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO559+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 : n008.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 07:18:06 AM UTC 2026
% Result : Theorem 11.05s 2.00s
% Output : CNFRefutation 11.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 92 ( 38 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 48 ~; 44 |; 30 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 263 ( 27 sgn 108 !; 12 ?)
% 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(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(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL012019,conjecture,
! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
file('theBenchmark.p',exemplo6GDDFULL012019) ).
fof(exemplo6GDDFULL012019_neg,negated_conjecture,
~ ! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012019]) ).
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,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ~ para(C,D,E,F)
& coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012019_neg]) ).
fof(sk_exemplo6GDDFULL012019_neg,plain,
( ~ para(sK4,sK5,sK7,sK8)
& coll(sK5,sK3,sK8)
& circle(sK1,sK3,sK5,sK6)
& coll(sK7,sK2,sK4)
& circle(sK9,sK2,sK7,sK10)
& circle(sK9,sK2,sK3,sK8)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK9,sK8,sK7,sK10,sK5,sK6]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(O,sK1),skolemize(F,sK8),skolemize(P,sK9),skolemize(E,sK7),skolemize(D,sK5),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK6)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012019_neg]) ).
cnf(c_112,negated_conjecture,
circle(sK1,sK3,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012019_neg]) ).
cnf(c_118,negated_conjecture,
perp(sK0(sK3,sK5,sK6,sK1),sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_112,c_102]) ).
cnf(c_160,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_207,negated_conjecture,
~ para(sK4,sK5,sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012019_neg]) ).
cnf(c_248,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_258,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_266,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_267,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_270,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_271,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_291,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_293,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_294,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_295,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_296,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_300,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_301,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_302,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_305,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_306,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_357,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_293]) ).
cnf(c_362,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_306]) ).
cnf(c_460,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_300,c_160]) ).
cnf(c_463,plain,
( para(A,B,sK3,sK1)
| ~ perp(A,B,sK0(sK3,sK5,sK6,sK1),sK3) ),
inference(resolve,[status(thm)],[c_300,c_118]) ).
cnf(c_464,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_301,c_160]) ).
cnf(c_468,plain,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_302,c_160]) ).
cnf(c_471,plain,
perp(sK0(sK3,sK5,sK6,sK1),sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_302,c_118]) ).
cnf(c_682,plain,
perp(sK1,sK2,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_468,c_301]) ).
cnf(c_724,plain,
perp(sK1,sK3,sK0(sK3,sK5,sK6,sK1),sK3),
inference(resolve,[status(thm)],[c_471,c_301]) ).
cnf(c_870,plain,
para(sK1,sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_460,c_682]) ).
cnf(c_871,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_460,c_464]) ).
cnf(c_878,plain,
para(sK1,sK2,sK1,sK2),
inference(resolve,[status(thm)],[c_870,c_305]) ).
cnf(c_894,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_871,c_270]) ).
cnf(c_934,plain,
para(sK1,sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_463,c_724]) ).
cnf(c_1299,plain,
eqangle(sK1,sK2,A,B,sK1,sK2,A,B),
inference(resolve,[status(thm)],[c_878,c_270]) ).
cnf(c_1327,plain,
para(sK1,sK3,sK1,sK3),
inference(resolve,[status(thm)],[c_934,c_305]) ).
cnf(c_1585,plain,
eqangle(sK1,sK3,A,B,sK1,sK3,A,B),
inference(resolve,[status(thm)],[c_1327,c_270]) ).
cnf(c_3906,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_894,c_291]) ).
cnf(c_3908,plain,
( cyclic(sK1,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_894,c_267]) ).
cnf(c_3909,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,sK2)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_894,c_266]) ).
cnf(c_5936,plain,
( cyclic(sK2,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1299,c_267]) ).
cnf(c_7448,plain,
( cyclic(sK3,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_1585,c_267]) ).
cnf(c_8085,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3906,c_271]) ).
cnf(c_8110,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_8085,c_248]) ).
cnf(c_8321,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_8110,c_362]) ).
cnf(c_8331,plain,
cyclic(sK3,A,sK1,sK1),
inference(resolve,[status(thm)],[c_8321,c_7448]) ).
cnf(c_8340,plain,
cyclic(sK2,A,sK1,sK1),
inference(resolve,[status(thm)],[c_8321,c_5936]) ).
cnf(c_8342,plain,
cyclic(sK1,A,sK2,sK2),
inference(resolve,[status(thm)],[c_8321,c_3908]) ).
cnf(c_8535,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A)
| ~ cyclic(sK1,A,sK2,sK1) ),
inference(resolve,[status(thm)],[c_8342,c_3909]) ).
cnf(c_8948,plain,
cyclic(sK3,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8331,c_295]) ).
cnf(c_8998,plain,
cyclic(sK2,sK1,A,sK1),
inference(resolve,[status(thm)],[c_8340,c_295]) ).
cnf(c_9162,plain,
cyclic(sK3,sK1,sK1,A),
inference(resolve,[status(thm)],[c_8948,c_296]) ).
cnf(c_9305,plain,
cyclic(sK1,sK2,A,sK1),
inference(resolve,[status(thm)],[c_8998,c_294]) ).
cnf(c_9716,plain,
cyclic(sK1,sK1,A,A),
inference(resolve,[status(thm)],[c_9162,c_357]) ).
cnf(c_13254,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK3,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_9162,c_293]) ).
cnf(c_9718,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_9162,c_13254]) ).
cnf(c_10300,plain,
cyclic(sK1,A,sK2,sK1),
inference(resolve,[status(thm)],[c_9305,c_295]) ).
cnf(c_10316,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK2,A) ),
inference(resolve,[status(thm)],[c_10300,c_8535]) ).
cnf(c_13255,plain,
( cyclic(sK1,A,B,A)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_9716,c_293]) ).
cnf(c_10788,plain,
cyclic(sK1,A,B,A),
inference(resolve,[status(thm)],[c_9718,c_13255]) ).
cnf(c_10801,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_10788,c_10316]) ).
cnf(c_13256,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_10801,c_258]) ).
cnf(c_11936,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_10801,c_13256]) ).
cnf(c_13251,plain,
perp(A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_11936,c_301]) ).
cnf(c_13257,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_11936,c_300]) ).
cnf(c_13252,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_13251,c_13257]) ).
cnf(c_13253,plain,
$false,
inference(resolve,[status(thm)],[c_13252,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO559+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:42:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1181391 was started by sandbox2 on n008,
% 0.08/0.36 % Fri Sep 25 13:42:42 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.40
% 0.08/0.40 % From the command line: assign(max_seconds, 300).
% 11.05/2.00
% 11.05/2.00 % given #500 (T,wt=10): 870 para(c4,c1,c1,c4). [resolve(460,a,682,a)].
% 11.05/2.00
% 11.05/2.00 % given #1000 (W,wt=13): 950 -coll(c3,c4,A) | coll(c1,A,c3). [resolve(925,a,306,a)].
% 11.05/2.00
% 11.05/2.00 % given #1500 (T,wt=13): 1447 -coll(c8,c4,A) | coll(c5,A,c8). [resolve(1412,a,306,a)].
% 11.05/2.00
% 11.05/2.00 % given #2000 (A,wt=33): 1438 perp(f17(f12(c2,c8,c10,c4),c4,c2,c2,c8),f12(c2,c8,c10,c4),c2,c8). [resolve(1406,a,391,a)].
% 11.05/2.00
% 11.05/2.00 % given #2500 (T,wt=13): 4269 -coll(c6,c3,A) | coll(A,c2,c6). [resolve(4205,a,306,b)].
% 11.05/2.00
% 11.05/2.00 % given #3000 (A,wt=36): 1957 para(f12(c1,c2,c5,c6),f11(c6,f12(c1,c2,c5,c6),c1,c1),f12(c1,c7,c9,c6),c1). [resolve(708,a,655,a)].
% 11.05/2.00
% 11.05/2.00 % SZS status Theorem for theBenchmark
% 11.05/2.00
% 11.05/2.00 % Proof 1 at 1.18 (+ 0.39) seconds.
% 11.05/2.00 % Length of proof is 83.
% 11.05/2.00 % Level of proof is 19.
% 11.05/2.00 % Maximum clause weight is 34.000.
% 11.05/2.00 % Given clauses 3266.
% 11.05/2.00
% 11.05/2.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
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