%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO620+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 : n016.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 07:18:14 AM UTC 2026
% Result : Theorem 2.02s 0.79s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 23 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 68 ( 14 ~; 10 |; 39 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 52 ( 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(exemplo6GDDFULL8110982,conjecture,
! [A,B,C,O,I,E,J,L] :
( ( coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) )
=> coll(I,L,J) ),
file('theBenchmark.p',exemplo6GDDFULL8110982) ).
fof(exemplo6GDDFULL8110982_neg,negated_conjecture,
~ ! [A,B,C,O,I,E,J,L] :
( ( coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) )
=> coll(I,L,J) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110982]) ).
fof(nnf_95,plain,
? [A,B,C,O,I,E,J,L] :
( ~ coll(I,L,J)
& coll(L,B,O)
& perp(L,C,B,O)
& coll(J,A,E)
& perp(J,C,A,E)
& perp(A,O,A,E)
& coll(I,A,O)
& perp(I,C,A,O)
& eqangle(O,C,C,A,O,C,C,B)
& eqangle(O,B,B,C,O,B,B,A)
& eqangle(O,A,A,B,O,A,A,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110982_neg]) ).
fof(sk_exemplo6GDDFULL8110982_neg,plain,
( ~ coll(sK0,sK1,sK2)
& coll(sK1,sK3,sK4)
& perp(sK1,sK7,sK3,sK4)
& coll(sK2,sK5,sK6)
& perp(sK2,sK7,sK5,sK6)
& perp(sK5,sK4,sK5,sK6)
& coll(sK0,sK5,sK4)
& perp(sK0,sK7,sK5,sK4)
& eqangle(sK4,sK7,sK7,sK5,sK4,sK7,sK7,sK3)
& eqangle(sK4,sK3,sK3,sK7,sK4,sK3,sK3,sK5)
& eqangle(sK4,sK5,sK5,sK3,sK4,sK5,sK5,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK3,sK7,sK0,sK6,sK2,sK1]),skolemize(A,sK5),skolemize(B,sK3),skolemize(C,sK7),skolemize(O,sK4),skolemize(I,sK0),skolemize(E,sK6),skolemize(J,sK2),skolemize(L,sK1)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ coll(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110982_neg]) ).
cnf(c_148,negated_conjecture,
coll(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110982_neg]) ).
cnf(c_150,negated_conjecture,
coll(sK2,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110982_neg]) ).
cnf(c_153,negated_conjecture,
coll(sK0,sK5,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110982_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_408,plain,
( coll(A,sK4,sK0)
| ~ coll(sK0,sK5,A) ),
inference(resolve,[status(thm)],[c_254,c_153]) ).
cnf(c_414,plain,
coll(sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_256,c_153]) ).
cnf(c_415,plain,
coll(sK2,sK6,sK5),
inference(resolve,[status(thm)],[c_256,c_150]) ).
cnf(c_417,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_310,c_153]) ).
cnf(c_419,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_310,c_148]) ).
cnf(c_432,plain,
coll(sK5,sK5,sK0),
inference(resolve,[status(thm)],[c_414,c_310]) ).
cnf(c_436,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_415,c_310]) ).
cnf(c_461,plain,
( coll(A,sK0,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_417,c_254]) ).
cnf(c_470,plain,
( coll(sK1,A,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_419,c_254]) ).
cnf(c_497,plain,
( coll(sK0,A,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_432,c_254]) ).
cnf(c_1118,plain,
coll(sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_461,c_419]) ).
cnf(c_1123,plain,
coll(sK1,sK4,sK0),
inference(resolve,[status(thm)],[c_1118,c_256]) ).
cnf(c_1159,plain,
( coll(A,sK0,sK1)
| ~ coll(sK1,sK4,A) ),
inference(resolve,[status(thm)],[c_1123,c_254]) ).
cnf(c_1527,plain,
coll(sK0,sK2,sK5),
inference(resolve,[status(thm)],[c_497,c_436]) ).
cnf(c_1543,plain,
coll(sK0,sK5,sK2),
inference(resolve,[status(thm)],[c_1527,c_256]) ).
cnf(c_1576,plain,
coll(sK2,sK4,sK0),
inference(resolve,[status(thm)],[c_1543,c_408]) ).
cnf(c_1663,plain,
coll(sK2,sK0,sK4),
inference(resolve,[status(thm)],[c_1576,c_256]) ).
cnf(c_1767,plain,
coll(sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1663,c_310]) ).
cnf(c_1943,plain,
coll(sK1,sK2,sK4),
inference(resolve,[status(thm)],[c_1767,c_470]) ).
cnf(c_2086,plain,
coll(sK1,sK4,sK2),
inference(resolve,[status(thm)],[c_1943,c_256]) ).
cnf(c_3480,plain,
coll(sK2,sK0,sK1),
inference(resolve,[status(thm)],[c_1159,c_2086]) ).
cnf(c_3484,plain,
coll(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_3480,c_255]) ).
cnf(c_3499,plain,
coll(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_3484,c_256]) ).
cnf(c_3498,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_3499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO620+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 13:49:43 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2515393 was started by sandbox2 on n016,
% 0.16/0.43 % Fri Sep 25 13:49:43 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 2.02/0.79
% 2.02/0.79 % given #500 (W,wt=9): 1453 coll(c3,c3,c1). [resolve(1446,a,310,a)].
% 2.02/0.79
% 2.02/0.79 % given #1000 (T,wt=10): 3112 para(c1,c3,c3,c2). [resolve(2813,a,252,a)].
% 2.02/0.79
% 2.02/0.79 % SZS status Theorem for theBenchmark
% 2.02/0.79
% 2.02/0.79 % Proof 1 at 0.23 (+ 0.07) seconds.
% 2.02/0.79 % Length of proof is 35.
% 2.02/0.79 % Level of proof is 14.
% 2.02/0.79 % Maximum clause weight is 17.000.
% 2.02/0.79 % Given clauses 1054.
% 2.02/0.79
% 2.02/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------