%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO557+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 : n026.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 9.94s 1.91s
% Output : CNFRefutation 9.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 37 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 121 ( 37 ~; 33 |; 34 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 251 ( 32 sgn 102 !; 14 ?)
% 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(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(exemplo6GDDFULL012017,conjecture,
! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> cyclic(M,K,O,C) ),
file('theBenchmark.p',exemplo6GDDFULL012017) ).
fof(exemplo6GDDFULL012017_neg,negated_conjecture,
~ ! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> cyclic(M,K,O,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012017]) ).
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,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ~ cyclic(M,K,O,C)
& circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012017_neg]) ).
fof(sk_exemplo6GDDFULL012017_neg,plain,
( ~ cyclic(sK8,sK4,sK1,sK3)
& circle(sK5,sK4,sK8,sK12)
& circle(sK10,sK2,sK8,sK11)
& circle(sK5,sK4,sK6,sK7)
& circle(sK10,sK2,sK3,sK7)
& coll(sK7,sK3,sK6)
& coll(sK7,sK2,sK4)
& circle(sK1,sK2,sK6,sK9)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK6,sK9,sK7,sK10,sK5,sK8,sK11,sK12]),skolemize(A,sK2),skolemize(C,sK3),skolemize(K,sK4),skolemize(O,sK1),skolemize(N,sK6),skolemize(B,sK7),skolemize(G,sK10),skolemize(O1,sK5),skolemize(M,sK8),skolemize(NWPNT1,sK9),skolemize(NWPNT2,sK11),skolemize(NWPNT3,sK12)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012017_neg]) ).
cnf(c_112,negated_conjecture,
circle(sK5,sK4,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012017_neg]) ).
cnf(c_148,negated_conjecture,
perp(sK0(sK4,sK6,sK7,sK5),sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_112,c_102]) ).
cnf(c_190,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_237,negated_conjecture,
~ cyclic(sK8,sK4,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012017_neg]) ).
cnf(c_278,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_297,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_300,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_301,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_321,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_323,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_324,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_325,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_326,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_330,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_331,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_332,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_335,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_336,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_387,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_323]) ).
cnf(c_392,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_336]) ).
cnf(c_534,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_330,c_190]) ).
cnf(c_537,plain,
( para(A,B,sK4,sK5)
| ~ perp(A,B,sK0(sK4,sK6,sK7,sK5),sK4) ),
inference(resolve,[status(thm)],[c_330,c_148]) ).
cnf(c_540,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_331,c_190]) ).
cnf(c_543,plain,
perp(sK4,sK5,sK0(sK4,sK6,sK7,sK5),sK4),
inference(resolve,[status(thm)],[c_331,c_148]) ).
cnf(c_549,plain,
perp(sK0(sK4,sK6,sK7,sK5),sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_332,c_148]) ).
cnf(c_1046,plain,
perp(sK5,sK4,sK0(sK4,sK6,sK7,sK5),sK4),
inference(resolve,[status(thm)],[c_549,c_331]) ).
cnf(c_1269,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_534,c_540]) ).
cnf(c_1290,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1269,c_300]) ).
cnf(c_1336,plain,
para(sK5,sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_537,c_1046]) ).
cnf(c_1337,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_537,c_543]) ).
cnf(c_2213,plain,
para(sK5,sK4,sK5,sK4),
inference(resolve,[status(thm)],[c_1336,c_335]) ).
cnf(c_2228,plain,
eqangle(sK4,sK5,A,B,sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_1337,c_300]) ).
cnf(c_2823,plain,
eqangle(sK5,sK4,A,B,sK5,sK4,A,B),
inference(resolve,[status(thm)],[c_2213,c_300]) ).
cnf(c_5429,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_1290,c_321]) ).
cnf(c_5974,plain,
( cyclic(sK5,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_2228,c_297]) ).
cnf(c_6056,plain,
( cyclic(sK4,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_2823,c_297]) ).
cnf(c_6245,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_5429,c_301]) ).
cnf(c_6270,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_6245,c_278]) ).
cnf(c_6350,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_6270,c_392]) ).
cnf(c_6358,plain,
cyclic(sK4,A,sK5,sK5),
inference(resolve,[status(thm)],[c_6350,c_6056]) ).
cnf(c_6360,plain,
cyclic(sK5,A,sK4,sK4),
inference(resolve,[status(thm)],[c_6350,c_5974]) ).
cnf(c_6933,plain,
cyclic(A,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_6358,c_387]) ).
cnf(c_6935,plain,
cyclic(sK4,sK5,A,sK5),
inference(resolve,[status(thm)],[c_6358,c_325]) ).
cnf(c_6969,plain,
cyclic(sK5,sK4,A,sK4),
inference(resolve,[status(thm)],[c_6360,c_325]) ).
cnf(c_7168,plain,
cyclic(sK5,A,sK5,sK5),
inference(resolve,[status(thm)],[c_6933,c_324]) ).
cnf(c_7181,plain,
cyclic(sK4,sK5,sK5,A),
inference(resolve,[status(thm)],[c_6935,c_326]) ).
cnf(c_7282,plain,
cyclic(sK4,sK5,A,sK4),
inference(resolve,[status(thm)],[c_6969,c_324]) ).
cnf(c_7702,plain,
cyclic(sK5,sK5,A,sK5),
inference(resolve,[status(thm)],[c_7168,c_325]) ).
cnf(c_7716,plain,
cyclic(sK5,sK4,sK5,A),
inference(resolve,[status(thm)],[c_7181,c_324]) ).
cnf(c_9974,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK4,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_7181,c_323]) ).
cnf(c_7717,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_7181,c_9974]) ).
cnf(c_8177,plain,
( cyclic(sK5,A,sK4,B)
| ~ cyclic(sK4,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7282,c_323]) ).
cnf(c_9975,plain,
( cyclic(sK5,A,sK5,B)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7702,c_323]) ).
cnf(c_8613,plain,
cyclic(sK5,A,sK5,B),
inference(resolve,[status(thm)],[c_7717,c_9975]) ).
cnf(c_9976,plain,
( cyclic(sK4,sK5,A,B)
| ~ cyclic(sK5,sK4,sK5,A) ),
inference(resolve,[status(thm)],[c_7716,c_323]) ).
cnf(c_8681,plain,
cyclic(sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_8613,c_9976]) ).
cnf(c_8694,plain,
cyclic(sK5,A,sK4,B),
inference(resolve,[status(thm)],[c_8681,c_8177]) ).
cnf(c_9977,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_7717,c_323]) ).
cnf(c_8700,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_7717,c_9977]) ).
cnf(c_9978,plain,
( cyclic(A,sK4,B,C)
| ~ cyclic(sK5,A,sK4,B) ),
inference(resolve,[status(thm)],[c_8694,c_323]) ).
cnf(c_9972,plain,
cyclic(A,sK4,B,C),
inference(resolve,[status(thm)],[c_8700,c_9978]) ).
cnf(c_9973,plain,
$false,
inference(resolve,[status(thm)],[c_9972,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO557+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:44:28 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2657477 was started by sandbox2 on n026,
% 0.19/0.44 % Fri Sep 25 13:44:28 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 9.94/1.91
% 9.94/1.91 % given #500 (T,wt=13): 655 -coll(c2,c6,A) | coll(c2,A,c2). [resolve(607,a,336,a)].
% 9.94/1.91
% 9.94/1.91 % given #1000 (A,wt=40): 972 -perp(f12(c3,c5,c6,c8),c8,c3,c3) | coll(f11(f12(c3,c5,c6,c8),c3,c3,c8),c3,f12(c3,c5,c6,c8)). [resolve(543,a,248,b)].
% 9.94/1.91
% 9.94/1.91 % given #1500 (T,wt=13): 1686 -coll(c3,c2,A) | coll(c4,A,c3). [resolve(1550,a,336,a)].
% 9.94/1.91
% 9.94/1.91 % given #2000 (A,wt=27): 1234 coll(f11(c1,c1,c4,f12(c1,c5,c10,c4)),c4,c1). [resolve(1112,a,366,a)].
% 9.94/1.91
% 9.94/1.91 % given #2500 (T,wt=9): 6418 coll(c3,A,c8). [back_unit_del(2250),unit_del(a,6350)].
% 9.94/1.91
% 9.94/1.91 % SZS status Theorem for theBenchmark
% 9.94/1.91
% 9.94/1.91 % Proof 1 at 1.11 (+ 0.27) seconds.
% 9.94/1.91 % Length of proof is 75.
% 9.94/1.91 % Level of proof is 18.
% 9.94/1.91 % Maximum clause weight is 24.000.
% 9.94/1.91 % Given clauses 2818.
% 9.94/1.91
% 9.94/1.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------