%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO566+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 : n017.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 07:18:07 AM UTC 2026
% Result : Theorem 2.59s 0.87s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 21 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 66 ( 13 ~; 9 |; 39 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 51 ( 1 sgn 26 !; 8 ?)
% 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(exemplo6GDDFULL214028,conjecture,
! [A,B,C,F,H,T,Q,P] :
( ( coll(P,A,C)
& perp(P,F,A,C)
& coll(Q,A,H)
& perp(Q,F,A,H)
& coll(T,B,C)
& perp(T,F,B,C)
& perp(A,C,B,H)
& perp(B,C,A,H)
& coll(F,A,B)
& perp(F,C,A,B) )
=> coll(P,Q,T) ),
file('theBenchmark.p',exemplo6GDDFULL214028) ).
fof(exemplo6GDDFULL214028_neg,negated_conjecture,
~ ! [A,B,C,F,H,T,Q,P] :
( ( coll(P,A,C)
& perp(P,F,A,C)
& coll(Q,A,H)
& perp(Q,F,A,H)
& coll(T,B,C)
& perp(T,F,B,C)
& perp(A,C,B,H)
& perp(B,C,A,H)
& coll(F,A,B)
& perp(F,C,A,B) )
=> coll(P,Q,T) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214028]) ).
fof(nnf_95,plain,
? [A,B,C,F,H,T,Q,P] :
( ~ coll(P,Q,T)
& coll(P,A,C)
& perp(P,F,A,C)
& coll(Q,A,H)
& perp(Q,F,A,H)
& coll(T,B,C)
& perp(T,F,B,C)
& perp(A,C,B,H)
& perp(B,C,A,H)
& coll(F,A,B)
& perp(F,C,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214028_neg]) ).
fof(sk_exemplo6GDDFULL214028_neg,plain,
( ~ coll(sK0,sK1,sK2)
& coll(sK0,sK3,sK4)
& perp(sK0,sK7,sK3,sK4)
& coll(sK1,sK3,sK5)
& perp(sK1,sK7,sK3,sK5)
& coll(sK2,sK6,sK4)
& perp(sK2,sK7,sK6,sK4)
& perp(sK3,sK4,sK6,sK5)
& perp(sK6,sK4,sK3,sK5)
& coll(sK7,sK3,sK6)
& perp(sK7,sK4,sK3,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK4,sK3,sK6,sK5,sK2,sK1,sK0]),skolemize(A,sK3),skolemize(B,sK6),skolemize(C,sK4),skolemize(F,sK7),skolemize(H,sK5),skolemize(T,sK2),skolemize(Q,sK1),skolemize(P,sK0)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ coll(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214028_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK0,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214028_neg]) ).
cnf(c_150,negated_conjecture,
coll(sK1,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214028_neg]) ).
cnf(c_152,negated_conjecture,
coll(sK2,sK6,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214028_neg]) ).
cnf(c_254,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_255,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_256,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_310,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_254]) ).
cnf(c_405,plain,
( coll(sK4,A,sK0)
| ~ coll(sK0,sK3,A) ),
inference(resolve,[status(thm)],[c_254,c_148]) ).
cnf(c_416,plain,
coll(sK1,sK5,sK3),
inference(resolve,[status(thm)],[c_256,c_150]) ).
cnf(c_417,plain,
coll(sK0,sK4,sK3),
inference(resolve,[status(thm)],[c_256,c_148]) ).
cnf(c_419,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_310,c_152]) ).
cnf(c_421,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_310,c_148]) ).
cnf(c_476,plain,
coll(sK3,sK3,sK1),
inference(resolve,[status(thm)],[c_416,c_310]) ).
cnf(c_480,plain,
coll(sK3,sK3,sK0),
inference(resolve,[status(thm)],[c_417,c_310]) ).
cnf(c_490,plain,
( coll(A,sK2,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_419,c_254]) ).
cnf(c_553,plain,
( coll(A,sK1,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_476,c_254]) ).
cnf(c_2459,plain,
coll(sK0,sK2,sK4),
inference(resolve,[status(thm)],[c_490,c_421]) ).
cnf(c_2497,plain,
coll(sK0,sK4,sK2),
inference(resolve,[status(thm)],[c_2459,c_256]) ).
cnf(c_2571,plain,
( coll(A,sK2,sK0)
| ~ coll(sK0,sK4,A) ),
inference(resolve,[status(thm)],[c_2497,c_254]) ).
cnf(c_2783,plain,
coll(sK0,sK1,sK3),
inference(resolve,[status(thm)],[c_553,c_480]) ).
cnf(c_2947,plain,
coll(sK0,sK3,sK1),
inference(resolve,[status(thm)],[c_2783,c_256]) ).
cnf(c_3112,plain,
coll(sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_2947,c_405]) ).
cnf(c_3253,plain,
coll(sK4,sK0,sK1),
inference(resolve,[status(thm)],[c_3112,c_256]) ).
cnf(c_3378,plain,
coll(sK0,sK4,sK1),
inference(resolve,[status(thm)],[c_3253,c_255]) ).
cnf(c_3801,plain,
coll(sK1,sK2,sK0),
inference(resolve,[status(thm)],[c_2571,c_3378]) ).
cnf(c_3806,plain,
coll(sK1,sK0,sK2),
inference(resolve,[status(thm)],[c_3801,c_256]) ).
cnf(c_3817,plain,
coll(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_3806,c_255]) ).
cnf(c_3816,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_3817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO566+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 13:37:47 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.38 % Process 2397185 was started by sandbox2 on n017,
% 0.13/0.38 % Fri Sep 25 13:37:47 2026
% 0.13/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.41
% 0.13/0.41 % From the command line: assign(max_seconds, 300).
% 2.59/0.87
% 2.59/0.87 % given #500 (W,wt=10): 1272 para(c3,c1,c1,c3). [resolve(389,a,928,a)].
% 2.59/0.87
% 2.59/0.87 % given #1000 (T,wt=9): 3370 coll(c6,c7,c7). [resolve(3240,a,255,a)].
% 2.59/0.87
% 2.59/0.87 % SZS status Theorem for theBenchmark
% 2.59/0.87
% 2.59/0.87 % Proof 1 at 0.31 (+ 0.12) seconds.
% 2.59/0.87 % Length of proof is 32.
% 2.59/0.87 % Level of proof is 12.
% 2.59/0.87 % Maximum clause weight is 17.000.
% 2.59/0.87 % Given clauses 1380.
% 2.59/0.87
% 2.59/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------