%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO567+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 : n013.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 5.03s 1.20s
% Output : CNFRefutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 30 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 100 ( 31 ~; 27 |; 26 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 195 ( 18 sgn 78 !; 6 ?)
% 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(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(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
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(exemplo6GDDFULL214029,conjecture,
! [A,B,C,D,Q,P] :
( ( coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,Q,P,C) ),
file('theBenchmark.p',exemplo6GDDFULL214029) ).
fof(exemplo6GDDFULL214029_neg,negated_conjecture,
~ ! [A,B,C,D,Q,P] :
( ( coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,Q,P,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214029]) ).
fof(nnf_95,plain,
? [A,B,C,D,Q,P] :
( ~ cyclic(B,Q,P,C)
& coll(P,A,C)
& perp(P,D,A,C)
& coll(Q,A,B)
& perp(Q,D,A,B)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214029_neg]) ).
fof(sk_exemplo6GDDFULL214029_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& coll(sK2,sK5,sK3)
& perp(sK2,sK4,sK5,sK3)
& coll(sK1,sK5,sK0)
& perp(sK1,sK4,sK5,sK0)
& coll(sK4,sK0,sK3)
& perp(sK4,sK5,sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK0,sK3,sK1,sK2]),skolemize(A,sK5),skolemize(B,sK0),skolemize(C,sK3),skolemize(D,sK4),skolemize(Q,sK1),skolemize(P,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214029_neg]) ).
cnf(c_149,negated_conjecture,
perp(sK2,sK4,sK5,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214029_neg]) ).
cnf(c_153,negated_conjecture,
perp(sK4,sK5,sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214029_neg]) ).
cnf(c_192,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_211,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_214,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_215,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_235,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_237,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_238,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_239,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_240,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_244,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_245,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_246,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_249,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_250,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_306,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_250]) ).
cnf(c_349,plain,
( para(sK4,sK5,A,B)
| ~ perp(sK0,sK3,A,B) ),
inference(resolve,[status(thm)],[c_244,c_153]) ).
cnf(c_352,plain,
( para(A,B,sK0,sK3)
| ~ perp(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_244,c_153]) ).
cnf(c_354,plain,
( para(A,B,sK5,sK3)
| ~ perp(A,B,sK2,sK4) ),
inference(resolve,[status(thm)],[c_244,c_149]) ).
cnf(c_355,plain,
perp(sK0,sK3,sK4,sK5),
inference(resolve,[status(thm)],[c_245,c_153]) ).
cnf(c_358,plain,
perp(sK4,sK5,sK3,sK0),
inference(resolve,[status(thm)],[c_246,c_153]) ).
cnf(c_360,plain,
perp(sK2,sK4,sK3,sK5),
inference(resolve,[status(thm)],[c_246,c_149]) ).
cnf(c_628,plain,
perp(sK3,sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_358,c_245]) ).
cnf(c_656,plain,
perp(sK3,sK5,sK2,sK4),
inference(resolve,[status(thm)],[c_360,c_245]) ).
cnf(c_875,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_349,c_355]) ).
cnf(c_895,plain,
eqangle(sK4,sK5,A,B,sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_875,c_214]) ).
cnf(c_983,plain,
para(sK3,sK0,sK0,sK3),
inference(resolve,[status(thm)],[c_352,c_628]) ).
cnf(c_1016,plain,
para(sK3,sK5,sK5,sK3),
inference(resolve,[status(thm)],[c_354,c_656]) ).
cnf(c_1084,plain,
para(sK3,sK0,sK3,sK0),
inference(resolve,[status(thm)],[c_983,c_249]) ).
cnf(c_1158,plain,
para(sK3,sK5,sK3,sK5),
inference(resolve,[status(thm)],[c_1016,c_249]) ).
cnf(c_1198,plain,
eqangle(sK3,sK0,A,B,sK3,sK0,A,B),
inference(resolve,[status(thm)],[c_1084,c_214]) ).
cnf(c_1264,plain,
eqangle(sK3,sK5,A,B,sK3,sK5,A,B),
inference(resolve,[status(thm)],[c_1158,c_214]) ).
cnf(c_1658,plain,
eqangle(A,B,sK4,sK5,A,B,sK4,sK5),
inference(resolve,[status(thm)],[c_895,c_235]) ).
cnf(c_1828,plain,
( cyclic(sK0,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1198,c_211]) ).
cnf(c_1884,plain,
( cyclic(sK5,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_1264,c_211]) ).
cnf(c_1910,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1658,c_215]) ).
cnf(c_1935,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_1910,c_192]) ).
cnf(c_1975,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_1935,c_306]) ).
cnf(c_1983,plain,
cyclic(sK5,A,sK3,sK3),
inference(resolve,[status(thm)],[c_1975,c_1884]) ).
cnf(c_1986,plain,
cyclic(sK0,A,sK3,sK3),
inference(resolve,[status(thm)],[c_1975,c_1828]) ).
cnf(c_2202,plain,
cyclic(sK5,sK3,A,sK3),
inference(resolve,[status(thm)],[c_1983,c_239]) ).
cnf(c_2252,plain,
cyclic(sK0,sK3,A,sK3),
inference(resolve,[status(thm)],[c_1986,c_239]) ).
cnf(c_2479,plain,
cyclic(sK5,sK3,sK3,A),
inference(resolve,[status(thm)],[c_2202,c_240]) ).
cnf(c_2605,plain,
cyclic(sK3,sK0,A,sK3),
inference(resolve,[status(thm)],[c_2252,c_238]) ).
cnf(c_4462,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK5,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_2479,c_237]) ).
cnf(c_3064,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_2479,c_4462]) ).
cnf(c_3610,plain,
( cyclic(sK0,A,B,sK3)
| ~ cyclic(sK3,sK0,A,B) ),
inference(resolve,[status(thm)],[c_2605,c_237]) ).
cnf(c_4463,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_3064,c_237]) ).
cnf(c_4447,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_3064,c_4463]) ).
cnf(c_4460,plain,
cyclic(sK0,A,B,sK3),
inference(resolve,[status(thm)],[c_4447,c_3610]) ).
cnf(c_4461,plain,
$false,
inference(resolve,[status(thm)],[c_4460,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO567+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n013.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 13:41:51 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 541437 was started by sandbox2 on n013,
% 0.08/0.37 % Fri Sep 25 13:41:51 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.40
% 0.08/0.40 % From the command line: assign(max_seconds, 300).
% 5.03/1.20
% 5.03/1.20 % given #500 (T,wt=9): 1464 coll(c4,c5,c3). [resolve(1399,a,403,a)].
% 5.03/1.20
% 5.03/1.20 % given #1000 (A,wt=24): 682 -perp(c1,c3,c2,c4) | perp(c2,f11(c1,c2,c4,c3),c4,c1). [resolve(586,a,161,b)].
% 5.03/1.20
% 5.03/1.20 % SZS status Theorem for theBenchmark
% 5.03/1.20
% 5.03/1.20 % Proof 1 at 0.48 (+ 0.18) seconds.
% 5.03/1.20 % Length of proof is 66.
% 5.03/1.20 % Level of proof is 15.
% 5.03/1.20 % Maximum clause weight is 23.000.
% 5.03/1.20 % Given clauses 1326.
% 5.03/1.20
% 5.03/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------