%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO631+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 : n010.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 07:18:16 AM UTC 2026
% Result : Theorem 46.05s 14.12s
% Output : CNFRefutation 46.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 22 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 122 ( 28 ~; 24 |; 54 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 204 ( 13 sgn 92 !; 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(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(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(exemplo6GDDFULL8110994,conjecture,
! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ( coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(P,G,I,H) ),
file('theBenchmark.p',exemplo6GDDFULL8110994) ).
fof(exemplo6GDDFULL8110994_neg,negated_conjecture,
~ ! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ( coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(P,G,I,H) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110994]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ~ cyclic(P,G,I,H)
& coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110994_neg]) ).
fof(sk_exemplo6GDDFULL8110994_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& coll(sK2,sK3,sK4)
& coll(sK2,sK7,sK1)
& coll(sK4,sK5,sK6)
& perp(sK4,sK0,sK5,sK6)
& coll(sK3,sK10,sK5)
& perp(sK3,sK0,sK10,sK5)
& coll(sK1,sK8,sK10)
& perp(sK1,sK0,sK8,sK10)
& coll(sK7,sK8,sK6)
& perp(sK7,sK0,sK8,sK6)
& circle(sK9,sK8,sK0,sK12)
& circle(sK9,sK8,sK6,sK11)
& circle(sK9,sK8,sK10,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK8,sK10,sK5,sK6,sK11,sK0,sK12,sK7,sK1,sK3,sK4,sK2]),skolemize(A,sK8),skolemize(B,sK10),skolemize(C,sK5),skolemize(O,sK9),skolemize(D,sK6),skolemize(P,sK0),skolemize(F,sK7),skolemize(G,sK1),skolemize(H,sK3),skolemize(E,sK4),skolemize(I,sK2),skolemize(NWPNT1,sK11),skolemize(NWPNT2,sK12)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110994_neg]) ).
cnf(c_196,negated_conjecture,
perp(sK4,sK0,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110994_neg]) ).
cnf(c_202,negated_conjecture,
perp(sK7,sK0,sK8,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110994_neg]) ).
cnf(c_241,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_260,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_263,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_264,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_284,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_286,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_288,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_289,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_293,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_294,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_295,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_297,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_298,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_299,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_355,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_299]) ).
cnf(c_439,plain,
( para(sK7,sK0,A,B)
| ~ perp(sK8,sK6,A,B) ),
inference(resolve,[status(thm)],[c_293,c_202]) ).
cnf(c_442,plain,
( para(sK4,sK0,A,B)
| ~ perp(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_293,c_196]) ).
cnf(c_453,plain,
perp(sK8,sK6,sK7,sK0),
inference(resolve,[status(thm)],[c_294,c_202]) ).
cnf(c_456,plain,
perp(sK5,sK6,sK4,sK0),
inference(resolve,[status(thm)],[c_294,c_196]) ).
cnf(c_956,plain,
perp(sK5,sK6,sK0,sK4),
inference(resolve,[status(thm)],[c_456,c_295]) ).
cnf(c_1339,plain,
para(sK7,sK0,sK7,sK0),
inference(resolve,[status(thm)],[c_439,c_453]) ).
cnf(c_1364,plain,
para(sK4,sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_442,c_956]) ).
cnf(c_1616,plain,
eqangle(sK7,sK0,A,B,sK7,sK0,A,B),
inference(resolve,[status(thm)],[c_1339,c_263]) ).
cnf(c_3619,plain,
para(sK0,sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_1364,c_297]) ).
cnf(c_4698,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_3619,c_298]) ).
cnf(c_4873,plain,
eqangle(sK0,sK4,A,B,sK0,sK4,A,B),
inference(resolve,[status(thm)],[c_4698,c_263]) ).
cnf(c_6675,plain,
eqangle(A,B,sK7,sK0,A,B,sK7,sK0),
inference(resolve,[status(thm)],[c_1616,c_284]) ).
cnf(c_8825,plain,
( cyclic(sK4,A,sK0,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_4873,c_260]) ).
cnf(c_9060,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_6675,c_264]) ).
cnf(c_9085,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_9060,c_241]) ).
cnf(c_9338,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_9085,c_355]) ).
cnf(c_9347,plain,
cyclic(sK4,A,sK0,sK0),
inference(resolve,[status(thm)],[c_9338,c_8825]) ).
cnf(c_10276,plain,
cyclic(sK4,sK0,A,sK0),
inference(resolve,[status(thm)],[c_9347,c_288]) ).
cnf(c_10580,plain,
cyclic(sK4,sK0,sK0,A),
inference(resolve,[status(thm)],[c_10276,c_289]) ).
cnf(c_13059,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK4,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_10580,c_286]) ).
cnf(c_11383,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_10580,c_13059]) ).
cnf(c_13060,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_11383,c_286]) ).
cnf(c_13057,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_11383,c_13060]) ).
cnf(c_13058,plain,
$false,
inference(resolve,[status(thm)],[c_13057,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.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 13:45:59 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 903694 was started by sandbox on n010,
% 0.11/0.36 % Fri Sep 25 13:45:59 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 46.05/14.12
% 46.05/14.12 % given #500 (T,wt=10): 523 -coll(c9,c11,A) | coll(c10,A,c9). [resolve(484,a,299,a)].
% 46.05/14.12
% 46.05/14.12 % given #1000 (W,wt=6): 2269 coll(c11,c2,c9). [resolve(647,a,592,a)].
% 46.05/14.12
% 46.05/14.12 % given #1500 (T,wt=6): 3794 coll(c4,c4,c4). [resolve(3774,a,355,a)].
% 46.05/14.12
% 46.05/14.12 % given #2000 (W,wt=10): 1517 -coll(c10,c1,A) | coll(A,c5,c10). [resolve(1461,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #2500 (T,wt=10): 2064 -coll(c5,c2,A) | coll(A,c9,c5). [resolve(1863,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #3000 (W,wt=10): 2582 -coll(c11,c3,A) | coll(A,c7,c11). [resolve(2228,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #3500 (T,wt=10): 3041 -coll(c3,c8,A) | coll(A,c10,c3). [resolve(2763,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #4000 (W,wt=10): 3909 -coll(c4,c1,A) | coll(c5,A,c4). [resolve(3845,a,299,a)].
% 46.05/14.12
% 46.05/14.12 % given #4500 (T,wt=10): 5068 -coll(c3,c11,A) | coll(A,c1,c3). [resolve(5043,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #5000 (W,wt=10): 6212 -coll(c2,c5,A) | coll(A,c4,c2). [resolve(6202,a,299,b)].
% 46.05/14.12
% 46.05/14.12 % given #5500 (T,wt=6): 9526 coll(c3,A,c2). [back_unit_del(715),unit_del(a,9338)].
% 46.05/14.12
% 46.05/14.12 % SZS status Theorem for theBenchmark
% 46.05/14.12
% 46.05/14.12 % Proof 1 at 1.99 (+ 0.65) seconds.
% 46.05/14.12 % Length of proof is 55.
% 46.05/14.12 % Level of proof is 14.
% 46.05/14.12 % Maximum clause weight is 20.000.
% 46.05/14.12 % Given clauses 5854.
% 46.05/14.12
% 46.05/14.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------