%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO628+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 : n019.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 56.34s 7.73s
% Output : CNFRefutation 56.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 24 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 124 ( 29 ~; 25 |; 54 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 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 : 210 ( 17 sgn 92 !; 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(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(exemplo6GDDFULL8110991,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',exemplo6GDDFULL8110991) ).
fof(exemplo6GDDFULL8110991_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)],[exemplo6GDDFULL8110991]) ).
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)],[exemplo6GDDFULL8110991_neg]) ).
fof(sk_exemplo6GDDFULL8110991_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& perp(sK4,sK5,sK1,sK3)
& perp(sK6,sK11,sK2,sK3)
& coll(sK5,sK0,sK7)
& perp(sK5,sK2,sK0,sK7)
& coll(sK4,sK0,sK9)
& perp(sK4,sK2,sK0,sK9)
& circle(sK8,sK0,sK2,sK12)
& coll(sK11,sK0,sK9)
& perp(sK11,sK1,sK0,sK9)
& coll(sK6,sK0,sK7)
& perp(sK6,sK1,sK0,sK7)
& circle(sK8,sK0,sK1,sK10)
& circle(sK8,sK0,sK9,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK0,sK9,sK7,sK1,sK10,sK6,sK11,sK2,sK12,sK4,sK5,sK3]),skolemize(A,sK0),skolemize(B,sK9),skolemize(C,sK7),skolemize(O,sK8),skolemize(P1,sK1),skolemize(F,sK6),skolemize(G,sK11),skolemize(P,sK2),skolemize(G1,sK4),skolemize(F1,sK5),skolemize(K,sK3),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK12)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110991_neg]) ).
cnf(c_193,negated_conjecture,
perp(sK4,sK5,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110991_neg]) ).
cnf(c_202,negated_conjecture,
perp(sK6,sK1,sK0,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110991_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_264,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
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_295,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_298,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
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_494,plain,
( para(sK6,sK1,A,B)
| ~ perp(sK0,sK7,A,B) ),
inference(resolve,[status(thm)],[c_293,c_202]) ).
cnf(c_508,plain,
( para(A,B,sK1,sK3)
| ~ perp(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_293,c_193]) ).
cnf(c_512,plain,
perp(sK0,sK7,sK6,sK1),
inference(resolve,[status(thm)],[c_294,c_202]) ).
cnf(c_526,plain,
perp(sK4,sK5,sK3,sK1),
inference(resolve,[status(thm)],[c_295,c_193]) ).
cnf(c_946,plain,
perp(sK3,sK1,sK4,sK5),
inference(resolve,[status(thm)],[c_526,c_294]) ).
cnf(c_1643,plain,
para(sK6,sK1,sK6,sK1),
inference(resolve,[status(thm)],[c_494,c_512]) ).
cnf(c_1741,plain,
para(sK3,sK1,sK1,sK3),
inference(resolve,[status(thm)],[c_508,c_946]) ).
cnf(c_2190,plain,
eqangle(sK6,sK1,A,B,sK6,sK1,A,B),
inference(resolve,[status(thm)],[c_1643,c_263]) ).
cnf(c_3177,plain,
para(sK3,sK1,sK3,sK1),
inference(resolve,[status(thm)],[c_1741,c_298]) ).
cnf(c_4048,plain,
eqangle(sK3,sK1,A,B,sK3,sK1,A,B),
inference(resolve,[status(thm)],[c_3177,c_263]) ).
cnf(c_7217,plain,
eqangle(A,B,sK6,sK1,A,B,sK6,sK1),
inference(resolve,[status(thm)],[c_2190,c_284]) ).
cnf(c_14107,plain,
( cyclic(sK1,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_4048,c_260]) ).
cnf(c_15722,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_7217,c_264]) ).
cnf(c_15747,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_15722,c_241]) ).
cnf(c_16333,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_15747,c_355]) ).
cnf(c_16348,plain,
cyclic(sK1,A,sK3,sK3),
inference(resolve,[status(thm)],[c_16333,c_14107]) ).
cnf(c_17997,plain,
cyclic(sK1,sK3,A,sK3),
inference(resolve,[status(thm)],[c_16348,c_288]) ).
cnf(c_18832,plain,
cyclic(sK1,sK3,sK3,A),
inference(resolve,[status(thm)],[c_17997,c_289]) ).
cnf(c_18833,plain,
cyclic(sK3,sK1,A,sK3),
inference(resolve,[status(thm)],[c_17997,c_287]) ).
cnf(c_23205,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK1,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_18832,c_286]) ).
cnf(c_20939,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_18832,c_23205]) ).
cnf(c_20951,plain,
cyclic(sK3,A,sK1,sK3),
inference(resolve,[status(thm)],[c_18833,c_288]) ).
cnf(c_23206,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_20939,c_286]) ).
cnf(c_23170,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_20939,c_23206]) ).
cnf(c_23207,plain,
( cyclic(A,sK1,B,sK3)
| ~ cyclic(sK3,A,sK1,B) ),
inference(resolve,[status(thm)],[c_20951,c_286]) ).
cnf(c_23203,plain,
cyclic(A,sK1,B,sK3),
inference(resolve,[status(thm)],[c_23170,c_23207]) ).
cnf(c_23204,plain,
$false,
inference(resolve,[status(thm)],[c_23203,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO628+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 13:45:35 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2893495 was started by sandbox on n019,
% 0.18/0.45 % Fri Sep 25 13:45:35 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.49
% 0.18/0.49 % From the command line: assign(max_seconds, 300).
% 56.34/7.73
% 56.34/7.73 % given #500 (T,wt=9): 1424 coll(c7,c9,c2). [resolve(1422,a,300,a)].
% 56.34/7.73
% 56.34/7.73 % given #1000 (A,wt=13): 765 -coll(c9,c1,A) | coll(c1,A,c9). [resolve(705,a,299,a)].
% 56.34/7.73
% 56.34/7.73 % given #1500 (T,wt=13): 1391 -coll(c6,c6,A) | coll(c10,A,c6). [resolve(1375,a,299,a)].
% 56.34/7.73
% 56.34/7.73 % given #2000 (A,wt=24): 1123 -perp(c9,c5,c11,c10) | perp(c11,f10(c11,c9,c10,c5),c10,c9). [resolve(946,a,212,a)].
% 56.34/7.73
% 56.34/7.73 % given #2500 (W,wt=9): 5597 coll(c11,c11,c7). [resolve(5543,a,355,a)].
% 56.34/7.73
% 56.34/7.73 % given #3000 (T,wt=9): 6863 coll(c9,c11,c5). [resolve(6815,a,300,a)].
% 56.34/7.73
% 56.34/7.73 % given #3500 (W,wt=13): 2846 -coll(c1,c3,A) | coll(c8,A,c1). [resolve(2777,a,299,a)].
% 56.34/7.73
% 56.34/7.73 % given #4000 (T,wt=13): 3765 -coll(c4,c9,A) | coll(c4,A,c4). [resolve(3639,a,299,a)].
% 56.34/7.73
% 56.34/7.73 % given #4500 (A,wt=28): 3417 coll(f17(f12(c1,c8,c13,c4),c4,c1,c1,c10),c1,c10). [resolve(3327,a,382,a)].
% 56.34/7.73
% 56.34/7.73 % given #5000 (T,wt=13): 5825 -coll(c7,c11,A) | coll(c1,A,c7). [resolve(5652,a,299,a)].
% 56.34/7.73
% 56.34/7.73 % given #5500 (A,wt=22): 3971 -coll(A,c7,c6) | -coll(A,c6,c7) | eqratio(A,c7,c7,c6,A,c6,c6,c7). [resolve(3012,a,242,a)].
% 56.34/7.73
% 56.34/7.73 % given #6000 (T,wt=13): 8383 -coll(c4,c11,A) | coll(A,c4,c4). [resolve(8361,a,299,b)].
% 56.34/7.73
% 56.34/7.73 % given #6500 (A,wt=18): 4437 -midp(A,c3,c9) | -para(c3,c8,c9,c2) | midp(A,c8,c2). [resolve(4345,a,243,c)].
% 56.34/7.73
% 56.34/7.73 % given #7000 (W,wt=10): 20188 perp(c8,c8,c10,c10). [resolve(18527,a,345,a)].
% 56.34/7.73
% 56.34/7.73 % SZS status Theorem for theBenchmark
% 56.34/7.73
% 56.34/7.73 % Proof 1 at 5.42 (+ 1.75) seconds.
% 56.34/7.73 % Length of proof is 57.
% 56.34/7.73 % Level of proof is 15.
% 56.34/7.73 % Maximum clause weight is 23.000.
% 56.34/7.73 % Given clauses 7069.
% 56.34/7.73
% 56.34/7.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------