%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO554+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 : n019.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 2.10s 0.80s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 77 ( 16 ~; 12 |; 40 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 143 ( 7 sgn 69 !; 16 ?)
% 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(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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(exemplo6GDDFULL012014,conjecture,
! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) )
=> coll(D,F,G) ),
file('theBenchmark.p',exemplo6GDDFULL012014) ).
fof(exemplo6GDDFULL012014_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) )
=> coll(D,F,G) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012014]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ coll(D,F,G)
& circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012014_neg]) ).
fof(sk_exemplo6GDDFULL012014_neg,plain,
( ~ coll(sK0,sK1,sK2)
& circle(sK5,sK3,sK2,sK15)
& circle(sK4,sK3,sK2,sK14)
& circle(sK5,sK3,sK1,sK13)
& coll(sK5,sK11,sK1)
& circle(sK5,sK3,sK11,sK12)
& coll(sK3,sK0,sK11)
& circle(sK4,sK3,sK0,sK10)
& circle(sK5,sK3,sK8,sK9)
& circle(sK4,sK3,sK6,sK7)
& perp(sK3,sK4,sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK0,sK10,sK11,sK12,sK1,sK13,sK2,sK14,sK15]),skolemize(A,sK4),skolemize(B,sK5),skolemize(C,sK3),skolemize(D,sK0),skolemize(E,sK11),skolemize(F,sK1),skolemize(G,sK2),skolemize(NWPNT1,sK6),skolemize(NWPNT2,sK7),skolemize(NWPNT3,sK8),skolemize(NWPNT4,sK9),skolemize(NWPNT5,sK10),skolemize(NWPNT6,sK12),skolemize(NWPNT7,sK13),skolemize(NWPNT8,sK14),skolemize(NWPNT9,sK15)],[nnf_95]) ).
cnf(c_252,negated_conjecture,
~ coll(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012014_neg]) ).
cnf(c_255,negated_conjecture,
perp(sK3,sK4,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012014_neg]) ).
cnf(c_294,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_316,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_317,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_337,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_346,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_347,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_352,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_408,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_352]) ).
cnf(c_574,plain,
( para(sK3,sK4,A,B)
| ~ perp(sK3,sK5,A,B) ),
inference(resolve,[status(thm)],[c_346,c_255]) ).
cnf(c_590,plain,
perp(sK3,sK5,sK3,sK4),
inference(resolve,[status(thm)],[c_347,c_255]) ).
cnf(c_1328,plain,
para(sK3,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_574,c_590]) ).
cnf(c_1352,plain,
eqangle(sK3,sK4,A,B,sK3,sK4,A,B),
inference(resolve,[status(thm)],[c_1328,c_316]) ).
cnf(c_3187,plain,
eqangle(A,B,sK3,sK4,A,B,sK3,sK4),
inference(resolve,[status(thm)],[c_1352,c_337]) ).
cnf(c_3629,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3187,c_317]) ).
cnf(c_3658,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_3629,c_294]) ).
cnf(c_3691,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_3658,c_408]) ).
cnf(c_3832,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_3691,c_352]) ).
cnf(c_3830,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_3691,c_3832]) ).
cnf(c_3831,plain,
$false,
inference(resolve,[status(thm)],[c_3830,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO554+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:41:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2885882 was started by sandbox on n019,
% 0.10/0.37 % Fri Sep 25 13:41:50 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 2.10/0.80
% 2.10/0.80 % given #500 (W,wt=13): 658 -coll(c4,c4,A) | coll(c3,A,c4). [resolve(624,a,352,a)].
% 2.10/0.80
% 2.10/0.80 % given #1000 (T,wt=13): 1432 -coll(c1,c2,A) | coll(c3,A,c1). [resolve(1389,a,352,a)].
% 2.10/0.80
% 2.10/0.80 % SZS status Theorem for theBenchmark
% 2.10/0.80
% 2.10/0.80 % Proof 1 at 0.20 (+ 0.09) seconds.
% 2.10/0.80 % Length of proof is 28.
% 2.10/0.80 % Level of proof is 10.
% 2.10/0.80 % Maximum clause weight is 23.000.
% 2.10/0.80 % Given clauses 1319.
% 2.10/0.80
% 2.10/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------