%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO585+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 : n004.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 07:18:10 AM UTC 2026
% Result : Theorem 0.82s 0.63s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 16 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 91 ( 24 ~; 20 |; 34 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 152 ( 12 sgn 68 !; 8 ?)
% 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(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(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(exemplo6GDDFULL416047,conjecture,
! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,U,D,V) ),
file('theBenchmark.p',exemplo6GDDFULL416047) ).
fof(exemplo6GDDFULL416047_neg,negated_conjecture,
~ ! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,U,D,V) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416047]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,U,V,NWPNT1] :
( ~ cyclic(A,U,D,V)
& perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416047_neg]) ).
fof(sk_exemplo6GDDFULL416047_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& perp(sK6,sK2,sK0,sK3)
& perp(sK0,sK2,sK6,sK3)
& perp(sK0,sK6,sK2,sK3)
& perp(sK4,sK2,sK0,sK1)
& perp(sK0,sK2,sK4,sK1)
& perp(sK0,sK4,sK2,sK1)
& circle(sK5,sK0,sK2,sK7)
& circle(sK5,sK0,sK4,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK0,sK4,sK6,sK2,sK7,sK1,sK3]),skolemize(A,sK0),skolemize(B,sK4),skolemize(C,sK6),skolemize(O,sK5),skolemize(D,sK2),skolemize(U,sK1),skolemize(V,sK3),skolemize(NWPNT1,sK7)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416047_neg]) ).
cnf(c_183,negated_conjecture,
perp(sK0,sK4,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416047_neg]) ).
cnf(c_222,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_241,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_244,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_265,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_267,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_268,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_269,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_270,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_274,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_275,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_280,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_336,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_280]) ).
cnf(c_490,plain,
( para(sK0,sK4,A,B)
| ~ perp(sK2,sK1,A,B) ),
inference(resolve,[status(thm)],[c_274,c_183]) ).
cnf(c_506,plain,
perp(sK2,sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_275,c_183]) ).
cnf(c_1479,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_490,c_506]) ).
cnf(c_1511,plain,
eqangle(sK0,sK4,A,B,sK0,sK4,A,B),
inference(resolve,[status(thm)],[c_1479,c_244]) ).
cnf(c_1514,plain,
coll(sK0,sK4,sK4),
inference(resolve,[status(thm)],[c_1479,c_222]) ).
cnf(c_1534,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_1514,c_336]) ).
cnf(c_1578,plain,
coll(sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_1534,c_336]) ).
cnf(c_1750,plain,
( cyclic(A,sK4,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK4,sK0,A,sK0,sK4) ),
inference(resolve,[status(thm)],[c_1578,c_241]) ).
cnf(c_2071,plain,
eqangle(A,B,sK0,sK4,A,B,sK0,sK4),
inference(resolve,[status(thm)],[c_1511,c_265]) ).
cnf(c_2082,plain,
cyclic(A,sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_2071,c_1750]) ).
cnf(c_2094,plain,
cyclic(sK4,A,sK0,sK0),
inference(resolve,[status(thm)],[c_2082,c_268]) ).
cnf(c_2325,plain,
cyclic(sK4,sK0,A,sK0),
inference(resolve,[status(thm)],[c_2094,c_269]) ).
cnf(c_2821,plain,
cyclic(sK4,sK0,sK0,A),
inference(resolve,[status(thm)],[c_2325,c_270]) ).
cnf(c_3442,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK4,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_2821,c_267]) ).
cnf(c_3111,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_2821,c_3442]) ).
cnf(c_3443,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_3111,c_267]) ).
cnf(c_3440,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_3111,c_3443]) ).
cnf(c_3441,plain,
$false,
inference(resolve,[status(thm)],[c_3440,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO585+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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 13:43:06 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 3295187 was started by sandbox on n004,
% 0.10/0.36 % Fri Sep 25 13:43:06 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.82/0.63
% 0.82/0.63 % SZS status Theorem for theBenchmark
% 0.82/0.63
% 0.82/0.63 % Proof 1 at 0.17 (+ 0.05) seconds.
% 0.82/0.63 % Length of proof is 42.
% 0.82/0.63 % Level of proof is 14.
% 0.82/0.63 % Maximum clause weight is 23.000.
% 0.82/0.63 % Given clauses 462.
% 0.82/0.63
% 0.82/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------