%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO627+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 : n002.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 07:18:15 AM UTC 2026
% Result : Theorem 47.19s 6.48s
% Output : CNFRefutation 47.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 24 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 119 ( 28 ~; 24 |; 54 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 191 ( 27 sgn 78 !; 13 ?)
% 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(exemplo6GDDFULL8110991F,conjecture,
! [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
( ( perp(G1,F1,P1,K)
& perp(F,G,P,K)
& coll(F1,A,C)
& perp(F1,P,A,C)
& coll(G1,A,B)
& perp(G1,P,A,B)
& circle(O,A,P,NWPNT2)
& coll(G,A,B)
& perp(G,P1,A,B)
& coll(F,A,C)
& perp(F,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,P1,P,K) ),
file('theBenchmark.p',exemplo6GDDFULL8110991F) ).
fof(exemplo6GDDFULL8110991F_neg,negated_conjecture,
~ ! [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
( ( perp(G1,F1,P1,K)
& perp(F,G,P,K)
& coll(F1,A,C)
& perp(F1,P,A,C)
& coll(G1,A,B)
& perp(G1,P,A,B)
& circle(O,A,P,NWPNT2)
& coll(G,A,B)
& perp(G,P1,A,B)
& coll(F,A,C)
& perp(F,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,P1,P,K) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110991F]) ).
fof(nnf_95,plain,
? [A,B,C,O,P1,F,G,P,G1,F1,K,NWPNT1,NWPNT2] :
( ~ cyclic(A,P1,P,K)
& perp(G1,F1,P1,K)
& perp(F,G,P,K)
& coll(F1,A,C)
& perp(F1,P,A,C)
& coll(G1,A,B)
& perp(G1,P,A,B)
& circle(O,A,P,NWPNT2)
& coll(G,A,B)
& perp(G,P1,A,B)
& coll(F,A,C)
& perp(F,P1,A,C)
& circle(O,A,P1,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110991F_neg]) ).
fof(sk_exemplo6GDDFULL8110991F_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& perp(sK11,sK12,sK1,sK3)
& perp(sK4,sK9,sK2,sK3)
& coll(sK12,sK0,sK5)
& perp(sK12,sK2,sK0,sK5)
& coll(sK11,sK0,sK7)
& perp(sK11,sK2,sK0,sK7)
& circle(sK6,sK0,sK2,sK10)
& coll(sK9,sK0,sK7)
& perp(sK9,sK1,sK0,sK7)
& coll(sK4,sK0,sK5)
& perp(sK4,sK1,sK0,sK5)
& circle(sK6,sK0,sK1,sK8)
& circle(sK6,sK0,sK7,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK0,sK7,sK5,sK1,sK8,sK4,sK9,sK2,sK10,sK11,sK12,sK3]),skolemize(A,sK0),skolemize(B,sK7),skolemize(C,sK5),skolemize(O,sK6),skolemize(P1,sK1),skolemize(F,sK4),skolemize(G,sK9),skolemize(P,sK2),skolemize(G1,sK11),skolemize(F1,sK12),skolemize(K,sK3),skolemize(NWPNT1,sK8),skolemize(NWPNT2,sK10)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110991F_neg]) ).
cnf(c_202,negated_conjecture,
perp(sK4,sK1,sK0,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110991F_neg]) ).
cnf(c_241,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_260,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_263,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_284,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_286,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_287,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_288,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_289,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_293,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_294,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_299,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_355,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_299]) ).
cnf(c_672,plain,
( para(sK4,sK1,A,B)
| ~ perp(sK0,sK5,A,B) ),
inference(resolve,[status(thm)],[c_293,c_202]) ).
cnf(c_690,plain,
perp(sK0,sK5,sK4,sK1),
inference(resolve,[status(thm)],[c_294,c_202]) ).
cnf(c_16242,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_672,c_690]) ).
cnf(c_16290,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_16242,c_263]) ).
cnf(c_16293,plain,
coll(sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_16242,c_241]) ).
cnf(c_16303,plain,
coll(sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_16293,c_355]) ).
cnf(c_16335,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_16303,c_355]) ).
cnf(c_16422,plain,
( cyclic(A,sK1,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK1,sK4,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_16335,c_260]) ).
cnf(c_37286,plain,
eqangle(A,B,sK4,sK1,A,B,sK4,sK1),
inference(resolve,[status(thm)],[c_16290,c_284]) ).
cnf(c_37289,plain,
cyclic(A,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_37286,c_16422]) ).
cnf(c_37293,plain,
cyclic(A,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_37289,c_288]) ).
cnf(c_37294,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_37289,c_287]) ).
cnf(c_37304,plain,
cyclic(A,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_37293,c_289]) ).
cnf(c_37314,plain,
cyclic(sK1,sK4,A,sK4),
inference(resolve,[status(thm)],[c_37294,c_288]) ).
cnf(c_37461,plain,
cyclic(sK4,A,sK4,sK1),
inference(resolve,[status(thm)],[c_37304,c_287]) ).
cnf(c_37479,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_37314,c_289]) ).
cnf(c_37899,plain,
cyclic(sK4,sK4,A,sK1),
inference(resolve,[status(thm)],[c_37461,c_288]) ).
cnf(c_38680,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_37479,c_286]) ).
cnf(c_37919,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_37479,c_38680]) ).
cnf(c_38681,plain,
( cyclic(sK4,A,B,sK1)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_37899,c_286]) ).
cnf(c_38286,plain,
cyclic(sK4,A,B,sK1),
inference(resolve,[status(thm)],[c_37919,c_38681]) ).
cnf(c_38682,plain,
( cyclic(sK4,A,sK1,B)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_37899,c_286]) ).
cnf(c_38287,plain,
cyclic(sK4,A,sK1,B),
inference(resolve,[status(thm)],[c_37919,c_38682]) ).
cnf(c_38683,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_37919,c_286]) ).
cnf(c_38328,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_37919,c_38683]) ).
cnf(c_38684,plain,
( cyclic(A,B,sK1,C)
| ~ cyclic(sK4,A,B,C) ),
inference(resolve,[status(thm)],[c_38286,c_286]) ).
cnf(c_38670,plain,
cyclic(A,B,sK1,C),
inference(resolve,[status(thm)],[c_38328,c_38684]) ).
cnf(c_38685,plain,
( cyclic(A,sK1,B,C)
| ~ cyclic(sK4,A,sK1,B) ),
inference(resolve,[status(thm)],[c_38287,c_286]) ).
cnf(c_38678,plain,
cyclic(A,sK1,B,C),
inference(resolve,[status(thm)],[c_38670,c_38685]) ).
cnf(c_38679,plain,
$false,
inference(resolve,[status(thm)],[c_38678,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO627+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 13:48:06 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3412866 was started by sandbox2 on n002,
% 0.16/0.43 % Fri Sep 25 13:48:06 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 47.19/6.48
% 47.19/6.48 % given #500 (A,wt=41): 403 -perp(A,c2,c2,c1) | -cyclic(A,c1,c2,B) | -eqangle(A,c1,A,c2,f16(A,c1,c2,B),c1,f16(A,c1,c2,B),c9) | midp(c9,c1,c2). [resolve(197,a,157,c)].
% 47.19/6.48
% 47.19/6.48 % given #1000 (T,wt=13): 6862 -coll(c6,c6,A) | coll(A,c9,c6). [resolve(6506,a,299,b)].
% 47.19/6.48
% 47.19/6.48 % given #1500 (W,wt=14): 1347 -cong(c1,c2,c1,c7) | midp(c1,c2,c7). [resolve(804,a,240,b)].
% 47.19/6.48
% 47.19/6.48 % given #2000 (T,wt=9): 16927 coll(c3,c5,c9). [resolve(16532,a,8386,a)].
% 47.19/6.48
% 47.19/6.48 % given #2500 (W,wt=9): 24354 coll(c8,c11,c11). [resolve(21467,a,241,a)].
% 47.19/6.48
% 47.19/6.48 % given #3000 (T,wt=9): 30464 coll(c2,c4,c5). [resolve(30225,a,17049,a)].
% 47.19/6.48
% 47.19/6.48 % given #3500 (T,wt=9): 32708 coll(c11,c8,c6). [resolve(20829,a,25356,a)].
% 47.19/6.48
% 47.19/6.48 % given #4000 (A,wt=18): 1151 -midp(A,c2,B) | -para(A,c2,B,c9) | midp(c2,c2,c9). [resolve(750,a,257,c)].
% 47.19/6.48
% 47.19/6.48 % given #4500 (T,wt=13): 27551 -coll(c9,c3,A) | coll(A,c11,c9). [resolve(26976,a,299,b)].
% 47.19/6.48
% 47.19/6.48 % given #5000 (W,wt=13): 34214 -coll(c11,c8,A) | coll(A,c5,c11). [resolve(34199,a,299,b)].
% 47.19/6.48
% 47.19/6.48 % SZS status Theorem for theBenchmark
% 47.19/6.48
% 47.19/6.48 % Proof 1 at 4.74 (+ 1.20) seconds.
% 47.19/6.48 % Length of proof is 50.
% 47.19/6.48 % Level of proof is 16.
% 47.19/6.48 % Maximum clause weight is 23.000.
% 47.19/6.48 % Given clauses 5294.
% 47.19/6.48
% 47.19/6.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------