%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO547+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 : n015.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 07:18:04 AM UTC 2026
% Result : Theorem 0.79s 0.59s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 58 ( 13 ~; 9 |; 31 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 54 ( 1 sgn 28 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(exemplo6GDDFULL012007,conjecture,
! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
file('theBenchmark.p',exemplo6GDDFULL012007) ).
fof(exemplo6GDDFULL012007_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012007]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,E,F,G,NWPNT1] :
( ~ coll(E,F,G)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012007_neg]) ).
fof(sk_exemplo6GDDFULL012007_neg,plain,
( ~ coll(sK0,sK1,sK2)
& coll(sK2,sK3,sK4)
& perp(sK2,sK7,sK3,sK4)
& coll(sK1,sK3,sK5)
& perp(sK1,sK7,sK3,sK5)
& coll(sK0,sK4,sK5)
& perp(sK0,sK7,sK4,sK5)
& circle(sK6,sK3,sK7,sK8)
& circle(sK6,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK3,sK4,sK5,sK7,sK8,sK0,sK1,sK2]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(O,sK6),skolemize(D,sK7),skolemize(E,sK0),skolemize(F,sK1),skolemize(G,sK2),skolemize(NWPNT1,sK8)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ coll(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012007_neg]) ).
cnf(c_178,negated_conjecture,
coll(sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012007_neg]) ).
cnf(c_180,negated_conjecture,
coll(sK1,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012007_neg]) ).
cnf(c_182,negated_conjecture,
coll(sK0,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012007_neg]) ).
cnf(c_280,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_281,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_282,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_336,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_280]) ).
cnf(c_447,plain,
coll(sK4,sK0,sK5),
inference(resolve,[status(thm)],[c_281,c_182]) ).
cnf(c_453,plain,
coll(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_336,c_182]) ).
cnf(c_454,plain,
coll(sK5,sK5,sK1),
inference(resolve,[status(thm)],[c_336,c_180]) ).
cnf(c_455,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_336,c_178]) ).
cnf(c_456,plain,
coll(sK5,sK5,sK4),
inference(resolve,[status(thm)],[c_447,c_336]) ).
cnf(c_482,plain,
( coll(A,sK0,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_453,c_280]) ).
cnf(c_487,plain,
( coll(sK1,A,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_454,c_280]) ).
cnf(c_490,plain,
( coll(A,sK2,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_455,c_280]) ).
cnf(c_492,plain,
coll(sK4,sK4,sK5),
inference(resolve,[status(thm)],[c_456,c_336]) ).
cnf(c_955,plain,
coll(sK1,sK0,sK5),
inference(resolve,[status(thm)],[c_482,c_454]) ).
cnf(c_960,plain,
coll(sK1,sK5,sK0),
inference(resolve,[status(thm)],[c_955,c_282]) ).
cnf(c_975,plain,
( coll(A,sK0,sK1)
| ~ coll(sK1,sK5,A) ),
inference(resolve,[status(thm)],[c_960,c_280]) ).
cnf(c_1224,plain,
coll(sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_490,c_492]) ).
cnf(c_1232,plain,
coll(sK5,sK4,sK2),
inference(resolve,[status(thm)],[c_1224,c_282]) ).
cnf(c_1247,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_1232,c_336]) ).
cnf(c_1274,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1247,c_336]) ).
cnf(c_1323,plain,
coll(sK1,sK2,sK5),
inference(resolve,[status(thm)],[c_1274,c_487]) ).
cnf(c_1383,plain,
coll(sK1,sK5,sK2),
inference(resolve,[status(thm)],[c_1323,c_282]) ).
cnf(c_2956,plain,
coll(sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_975,c_1383]) ).
cnf(c_2970,plain,
coll(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_2956,c_281]) ).
cnf(c_2993,plain,
coll(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_2970,c_282]) ).
cnf(c_2992,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_177,c_2993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO547+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:44:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1495185 was started by sandbox2 on n015,
% 0.10/0.36 % Fri Sep 25 13:44:28 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.79/0.59
% 0.79/0.59 % given #500 (A,wt=13): 494 -coll(c3,c3,A) | coll(A,c2,c3). [resolve(456,a,280,b)].
% 0.79/0.59
% 0.79/0.59 % SZS status Theorem for theBenchmark
% 0.79/0.59
% 0.79/0.59 % Proof 1 at 0.15 (+ 0.04) seconds.
% 0.79/0.59 % Length of proof is 33.
% 0.79/0.59 % Level of proof is 13.
% 0.79/0.59 % Maximum clause weight is 17.000.
% 0.79/0.59 % Given clauses 988.
% 0.79/0.59
% 0.79/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------