%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO595+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 : n014.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 07:18:11 AM UTC 2026
% Result : Theorem 40.09s 5.64s
% Output : CNFRefutation 40.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 71 ( 27 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 115 ( 33 ~; 29 |; 35 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 224 ( 19 sgn 96 !; 11 ?)
% 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(ruleD11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('theBenchmark.p',ruleD11) ).
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(ruleD63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('theBenchmark.p',ruleD63) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(exemplo6GDDFULL416057,conjecture,
! [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,C,E,F) ),
file('theBenchmark.p',exemplo6GDDFULL416057) ).
fof(exemplo6GDDFULL416057_neg,negated_conjecture,
~ ! [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,C,E,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416057]) ).
fof(nnf_95,plain,
? [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ~ cyclic(B,C,E,F)
& circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416057_neg]) ).
fof(sk_exemplo6GDDFULL416057_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& circle(sK4,sK6,sK3,sK10)
& coll(sK3,sK5,sK1)
& circle(sK4,sK6,sK2,sK9)
& coll(sK2,sK5,sK0)
& circle(sK4,sK6,sK7,sK8)
& midp(sK4,sK5,sK6)
& coll(sK6,sK0,sK1)
& perp(sK6,sK5,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5,sK0,sK1,sK4,sK7,sK8,sK2,sK9,sK3,sK10]),skolemize(A,sK5),skolemize(B,sK0),skolemize(C,sK1),skolemize(D,sK6),skolemize(O,sK4),skolemize(E,sK2),skolemize(F,sK3),skolemize(NWPNT1,sK7),skolemize(NWPNT2,sK8),skolemize(NWPNT3,sK9),skolemize(NWPNT4,sK10)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416057_neg]) ).
cnf(c_195,negated_conjecture,
midp(sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416057_neg]) ).
cnf(c_197,negated_conjecture,
perp(sK6,sK5,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416057_neg]) ).
cnf(c_236,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_239,plain,
( para(B,D,C,E)
| ~ midp(A,D,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD63]) ).
cnf(c_255,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_258,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_259,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_279,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_281,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_282,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_283,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_284,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_286,plain,
( midp(A,C,B)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD11]) ).
cnf(c_288,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_289,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_290,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_293,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_294,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_345,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_350,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_440,plain,
( para(sK5,A,sK6,B)
| ~ midp(sK4,A,B) ),
inference(resolve,[status(thm)],[c_239,c_195]) ).
cnf(c_451,plain,
midp(sK4,sK6,sK5),
inference(resolve,[status(thm)],[c_286,c_195]) ).
cnf(c_456,plain,
( para(A,B,sK0,sK1)
| ~ perp(A,B,sK6,sK5) ),
inference(resolve,[status(thm)],[c_288,c_197]) ).
cnf(c_464,plain,
perp(sK6,sK5,sK1,sK0),
inference(resolve,[status(thm)],[c_290,c_197]) ).
cnf(c_955,plain,
perp(sK1,sK0,sK6,sK5),
inference(resolve,[status(thm)],[c_464,c_289]) ).
cnf(c_1754,plain,
para(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_440,c_451]) ).
cnf(c_1776,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_1754,c_293]) ).
cnf(c_1823,plain,
eqangle(sK5,sK6,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_1776,c_258]) ).
cnf(c_1889,plain,
para(sK1,sK0,sK0,sK1),
inference(resolve,[status(thm)],[c_456,c_955]) ).
cnf(c_2333,plain,
para(sK1,sK0,sK1,sK0),
inference(resolve,[status(thm)],[c_1889,c_293]) ).
cnf(c_2485,plain,
eqangle(sK1,sK0,A,B,sK1,sK0,A,B),
inference(resolve,[status(thm)],[c_2333,c_258]) ).
cnf(c_15452,plain,
eqangle(A,B,sK5,sK6,A,B,sK5,sK6),
inference(resolve,[status(thm)],[c_1823,c_279]) ).
cnf(c_15646,plain,
( cyclic(sK0,A,sK1,sK1)
| ~ coll(sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_2485,c_255]) ).
cnf(c_18707,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_15452,c_259]) ).
cnf(c_18726,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_18707,c_236]) ).
cnf(c_18995,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_18726,c_350]) ).
cnf(c_19007,plain,
cyclic(sK0,A,sK1,sK1),
inference(resolve,[status(thm)],[c_18995,c_15646]) ).
cnf(c_20045,plain,
cyclic(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_19007,c_345]) ).
cnf(c_20047,plain,
cyclic(sK0,sK1,A,sK1),
inference(resolve,[status(thm)],[c_19007,c_283]) ).
cnf(c_20293,plain,
cyclic(sK1,A,sK1,sK1),
inference(resolve,[status(thm)],[c_20045,c_282]) ).
cnf(c_20296,plain,
cyclic(sK0,sK1,sK1,A),
inference(resolve,[status(thm)],[c_20047,c_284]) ).
cnf(c_20909,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_20293,c_283]) ).
cnf(c_20913,plain,
cyclic(sK1,sK0,sK1,A),
inference(resolve,[status(thm)],[c_20296,c_282]) ).
cnf(c_22415,plain,
( cyclic(sK1,sK1,A,B)
| ~ cyclic(sK0,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_20296,c_281]) ).
cnf(c_20914,plain,
cyclic(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_20296,c_22415]) ).
cnf(c_22416,plain,
( cyclic(sK1,A,sK1,B)
| ~ cyclic(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_20909,c_281]) ).
cnf(c_22399,plain,
cyclic(sK1,A,sK1,B),
inference(resolve,[status(thm)],[c_20914,c_22416]) ).
cnf(c_22417,plain,
( cyclic(sK0,sK1,A,B)
| ~ cyclic(sK1,sK0,sK1,A) ),
inference(resolve,[status(thm)],[c_20913,c_281]) ).
cnf(c_22413,plain,
cyclic(sK0,sK1,A,B),
inference(resolve,[status(thm)],[c_22399,c_22417]) ).
cnf(c_22414,plain,
$false,
inference(resolve,[status(thm)],[c_22413,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO595+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:43:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 355479 was started by sandbox2 on n014,
% 0.17/0.43 % Fri Sep 25 13:43:32 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 40.09/5.64
% 40.09/5.64 % given #500 (A,wt=24): 454 -perp(c4,c5,A,B) | para(f12(c4,c6,c10,c5),c4,A,B). [resolve(288,a,131,a)].
% 40.09/5.64
% 40.09/5.64 % given #1000 (T,wt=13): 1820 -midp(A,c1,c1) | midp(A,c4,c4). [resolve(1776,a,336,b)].
% 40.09/5.64
% 40.09/5.64 % given #1500 (A,wt=33): 1024 para(f9(f12(c4,c7,c11,c5),c4,c1,c4,c5),c1,f12(c4,c7,c11,c5),c4). [resolve(415,a,439,a)].
% 40.09/5.64
% 40.09/5.64 % given #2000 (W,wt=10): 10867 cong(c5,c1,c5,c5). [resolve(10620,a,234,a)].
% 40.09/5.64
% 40.09/5.64 % given #2500 (T,wt=14): 5223 eqangle(c1,c4,A,B,c5,c5,A,B). [resolve(4815,a,258,a)].
% 40.09/5.64
% 40.09/5.64 % given #3000 (W,wt=14): 13356 eqangle(c5,c4,c5,c5,c1,c4,c1,c5). [resolve(12595,a,257,a)].
% 40.09/5.64
% 40.09/5.64 % given #3500 (T,wt=10): 20203 cyclic(c5,c1,c5,A). [back_unit_del(13390),unit_del(a,20177)].
% 40.09/5.64
% 40.09/5.64 % SZS status Theorem for theBenchmark
% 40.09/5.64
% 40.09/5.64 % Proof 1 at 3.75 (+ 1.35) seconds.
% 40.09/5.64 % Length of proof is 65.
% 40.09/5.64 % Level of proof is 16.
% 40.09/5.64 % Maximum clause weight is 23.000.
% 40.09/5.64 % Given clauses 3816.
% 40.09/5.64
% 40.09/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------