%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO550+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 : n004.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 07:18:05 AM UTC 2026
% Result : Theorem 8.51s 6.62s
% Output : CNFRefutation 8.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 36 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 121 ( 37 ~; 33 |; 34 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 248 ( 31 sgn 100 !; 13 ?)
% 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(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(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(exemplo6GDDFULL012010,conjecture,
! [A,B,C,D,P,E,O1,O,Q,NWPNT1,NWPNT2] :
( ( circle(O,A,Q,NWPNT2)
& circle(O1,C,Q,NWPNT1)
& circle(O,E,B,A)
& circle(O1,C,D,E)
& coll(E,A,D)
& coll(E,B,C)
& coll(P,A,B)
& coll(P,C,D) )
=> cyclic(P,D,Q,A) ),
file('theBenchmark.p',exemplo6GDDFULL012010) ).
fof(exemplo6GDDFULL012010_neg,negated_conjecture,
~ ! [A,B,C,D,P,E,O1,O,Q,NWPNT1,NWPNT2] :
( ( circle(O,A,Q,NWPNT2)
& circle(O1,C,Q,NWPNT1)
& circle(O,E,B,A)
& circle(O1,C,D,E)
& coll(E,A,D)
& coll(E,B,C)
& coll(P,A,B)
& coll(P,C,D) )
=> cyclic(P,D,Q,A) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012010]) ).
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,D,P,E,O1,O,Q,NWPNT1,NWPNT2] :
( ~ cyclic(P,D,Q,A)
& circle(O,A,Q,NWPNT2)
& circle(O1,C,Q,NWPNT1)
& circle(O,E,B,A)
& circle(O1,C,D,E)
& coll(E,A,D)
& coll(E,B,C)
& coll(P,A,B)
& coll(P,C,D) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012010_neg]) ).
fof(sk_exemplo6GDDFULL012010_neg,plain,
( ~ cyclic(sK9,sK3,sK7,sK6)
& circle(sK5,sK6,sK7,sK8)
& circle(sK1,sK2,sK7,sK11)
& circle(sK5,sK4,sK10,sK6)
& circle(sK1,sK2,sK3,sK4)
& coll(sK4,sK6,sK3)
& coll(sK4,sK10,sK2)
& coll(sK9,sK6,sK10)
& coll(sK9,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK2,sK3,sK6,sK10,sK4,sK1,sK5,sK7,sK11,sK8]),skolemize(A,sK6),skolemize(B,sK10),skolemize(C,sK2),skolemize(D,sK3),skolemize(P,sK9),skolemize(E,sK4),skolemize(O1,sK1),skolemize(O,sK5),skolemize(Q,sK7),skolemize(NWPNT1,sK11),skolemize(NWPNT2,sK8)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012010_neg]) ).
cnf(c_112,negated_conjecture,
circle(sK5,sK6,sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012010_neg]) ).
cnf(c_118,negated_conjecture,
perp(sK0(sK6,sK7,sK8,sK5),sK6,sK6,sK5),
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,
~ cyclic(sK9,sK3,sK7,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012010_neg]) ).
cnf(c_250,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_269,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_272,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_273,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_293,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_295,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_296,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_297,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_298,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_302,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_303,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_306,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_307,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_308,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_359,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_295]) ).
cnf(c_364,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_308]) ).
cnf(c_462,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_302,c_160]) ).
cnf(c_465,plain,
( para(A,B,sK6,sK5)
| ~ perp(A,B,sK0(sK6,sK7,sK8,sK5),sK6) ),
inference(resolve,[status(thm)],[c_302,c_118]) ).
cnf(c_466,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_303,c_160]) ).
cnf(c_469,plain,
perp(sK6,sK5,sK0(sK6,sK7,sK8,sK5),sK6),
inference(resolve,[status(thm)],[c_303,c_118]) ).
cnf(c_1112,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_466,c_462]) ).
cnf(c_1149,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1112,c_272]) ).
cnf(c_1209,plain,
para(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_469,c_465]) ).
cnf(c_2280,plain,
para(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_1209,c_307]) ).
cnf(c_2281,plain,
eqangle(sK6,sK5,A,B,sK6,sK5,A,B),
inference(resolve,[status(thm)],[c_1209,c_272]) ).
cnf(c_2376,plain,
para(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_2280,c_306]) ).
cnf(c_2476,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_2376,c_307]) ).
cnf(c_2539,plain,
eqangle(sK5,sK6,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_2476,c_272]) ).
cnf(c_3049,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_1149,c_293]) ).
cnf(c_4480,plain,
( cyclic(sK5,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_2281,c_269]) ).
cnf(c_4617,plain,
( cyclic(sK6,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_2539,c_269]) ).
cnf(c_4669,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3049,c_273]) ).
cnf(c_4694,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4669,c_250]) ).
cnf(c_4760,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4694,c_364]) ).
cnf(c_4768,plain,
cyclic(sK6,A,sK5,sK5),
inference(resolve,[status(thm)],[c_4760,c_4617]) ).
cnf(c_4771,plain,
cyclic(sK5,A,sK6,sK6),
inference(resolve,[status(thm)],[c_4760,c_4480]) ).
cnf(c_5191,plain,
cyclic(A,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_4768,c_359]) ).
cnf(c_5193,plain,
cyclic(sK6,sK5,A,sK5),
inference(resolve,[status(thm)],[c_4768,c_297]) ).
cnf(c_5244,plain,
cyclic(sK5,sK6,A,sK6),
inference(resolve,[status(thm)],[c_4771,c_297]) ).
cnf(c_5401,plain,
cyclic(sK5,A,sK5,sK5),
inference(resolve,[status(thm)],[c_5191,c_296]) ).
cnf(c_5414,plain,
cyclic(sK6,sK5,sK5,A),
inference(resolve,[status(thm)],[c_5193,c_298]) ).
cnf(c_5606,plain,
cyclic(sK6,sK5,A,sK6),
inference(resolve,[status(thm)],[c_5244,c_296]) ).
cnf(c_5866,plain,
cyclic(sK5,sK5,A,sK5),
inference(resolve,[status(thm)],[c_5401,c_297]) ).
cnf(c_5889,plain,
cyclic(sK5,sK6,sK5,A),
inference(resolve,[status(thm)],[c_5414,c_296]) ).
cnf(c_8016,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK6,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_5414,c_295]) ).
cnf(c_5890,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_5414,c_8016]) ).
cnf(c_6405,plain,
( cyclic(sK5,A,B,sK6)
| ~ cyclic(sK6,sK5,A,B) ),
inference(resolve,[status(thm)],[c_5606,c_295]) ).
cnf(c_8017,plain,
( cyclic(sK5,A,sK5,B)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_5866,c_295]) ).
cnf(c_6700,plain,
cyclic(sK5,A,sK5,B),
inference(resolve,[status(thm)],[c_5890,c_8017]) ).
cnf(c_8018,plain,
( cyclic(sK6,sK5,A,B)
| ~ cyclic(sK5,sK6,sK5,A) ),
inference(resolve,[status(thm)],[c_5889,c_295]) ).
cnf(c_6759,plain,
cyclic(sK6,sK5,A,B),
inference(resolve,[status(thm)],[c_6700,c_8018]) ).
cnf(c_6773,plain,
cyclic(sK5,A,B,sK6),
inference(resolve,[status(thm)],[c_6759,c_6405]) ).
cnf(c_8019,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_5890,c_295]) ).
cnf(c_6778,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_5890,c_8019]) ).
cnf(c_8020,plain,
( cyclic(A,B,C,sK6)
| ~ cyclic(sK5,A,B,C) ),
inference(resolve,[status(thm)],[c_6773,c_295]) ).
cnf(c_8014,plain,
cyclic(A,B,C,sK6),
inference(resolve,[status(thm)],[c_6778,c_8020]) ).
cnf(c_8015,plain,
$false,
inference(resolve,[status(thm)],[c_8014,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO550+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n004.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 13:41:28 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.36 % Process 3291024 was started by sandbox2 on n004,
% 0.08/5.36 % Fri Sep 25 13:41:28 2026
% 0.08/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.39
% 0.08/5.39 % From the command line: assign(max_seconds, 300).
% 8.51/6.62
% 8.51/6.62 % given #500 (W,wt=9): 931 coll(c3,c3,c1). [resolve(868,a,364,a)].
% 8.51/6.62
% 8.51/6.62 % given #1000 (T,wt=13): 786 -coll(c4,c2,A) | coll(A,c1,c4). [resolve(773,a,308,b)].
% 8.51/6.62
% 8.51/6.62 % given #1500 (W,wt=13): 1598 -coll(c7,c2,A) | coll(A,c2,c7). [resolve(1504,a,308,b)].
% 8.51/6.62
% 8.51/6.62 % given #2000 (T,wt=13): 2845 -coll(c8,c3,A) | coll(A,c7,c8). [resolve(2835,a,308,b)].
% 8.51/6.62
% 8.51/6.62 % SZS status Theorem for theBenchmark
% 8.51/6.62
% 8.51/6.62 % Proof 1 at 0.94 (+ 0.26) seconds.
% 8.51/6.62 % Length of proof is 74.
% 8.51/6.62 % Level of proof is 18.
% 8.51/6.62 % Maximum clause weight is 24.000.
% 8.51/6.62 % Given clauses 2497.
% 8.51/6.62
% 8.51/6.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------