%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO622+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 : n009.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 07:18:14 AM UTC 2026
% Result : Theorem 38.67s 6.03s
% Output : CNFRefutation 38.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 25 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 139 ( 46 ~; 42 |; 32 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 254 ( 32 sgn 104 !; 7 ?)
% 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(ruleD10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('theBenchmark.p',ruleD10) ).
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(ruleD21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('theBenchmark.p',ruleD21) ).
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(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD73) ).
fof(exemplo6GDDFULL8110985,conjecture,
! [A,B,C,D,E,F,NWPNT1] :
( ( coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) )
=> perp(E,F,B,C) ),
file('theBenchmark.p',exemplo6GDDFULL8110985) ).
fof(exemplo6GDDFULL8110985_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,NWPNT1] :
( ( coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) )
=> perp(E,F,B,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL8110985]) ).
cnf(c_112,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_117,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_118,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_119,plain,
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD10]) ).
cnf(c_122,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_123,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_124,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_125,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_127,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_129,plain,
( eqangle(A,B,E,F,C,D,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD21]) ).
cnf(c_147,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_148,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_151,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_152,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,F,D,F,E)
| ~ cyclic(A,B,C,F)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD43]) ).
cnf(c_160,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_170,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_176,plain,
( para(A,B,C,D)
| ~ para(E,F,V6,V7)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD73]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,NWPNT1] :
( ~ perp(E,F,B,C)
& coll(F,A,D)
& perp(A,E,NWPNT1,F)
& midpoint(NWPNT1,A,E)
& coll(E,B,C)
& eqangle(E,A,A,C,E,A,A,B)
& circle(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL8110985_neg]) ).
fof(sk_exemplo6GDDFULL8110985_neg,plain,
( ~ perp(sK0,sK4,sK3,sK2)
& coll(sK4,sK1,sK5)
& perp(sK1,sK0,sK6,sK4)
& midpoint(sK6,sK1,sK0)
& coll(sK0,sK3,sK2)
& eqangle(sK0,sK1,sK1,sK2,sK0,sK1,sK1,sK3)
& circle(sK5,sK1,sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK1,sK3,sK2,sK0,sK6,sK4]),skolemize(A,sK1),skolemize(B,sK3),skolemize(C,sK2),skolemize(D,sK5),skolemize(E,sK0),skolemize(F,sK4),skolemize(NWPNT1,sK6)],[nnf_95]) ).
cnf(c_209,negated_conjecture,
eqangle(sK0,sK1,sK1,sK2,sK0,sK1,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110985_neg]) ).
cnf(c_213,negated_conjecture,
~ perp(sK0,sK4,sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL8110985_neg]) ).
cnf(c_266,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_112]) ).
cnf(c_334,plain,
eqangle(sK0,sK1,sK0,sK1,sK1,sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_209,c_129]) ).
cnf(c_336,plain,
eqangle(sK1,sK2,sK0,sK1,sK1,sK3,sK0,sK1),
inference(resolve,[status(thm)],[c_209,c_127]) ).
cnf(c_1655,plain,
( para(sK0,sK1,sK0,sK1)
| ~ para(sK1,sK2,sK1,sK3) ),
inference(resolve,[status(thm)],[c_334,c_176]) ).
cnf(c_2161,plain,
para(sK1,sK2,sK1,sK3),
inference(resolve,[status(thm)],[c_336,c_147]) ).
cnf(c_2165,plain,
para(sK0,sK1,sK0,sK1),
inference(resolve,[status(thm)],[c_2161,c_1655]) ).
cnf(c_3457,plain,
coll(sK0,sK1,sK1),
inference(resolve,[status(thm)],[c_2165,c_170]) ).
cnf(c_3461,plain,
eqangle(sK0,sK1,A,B,sK0,sK1,A,B),
inference(resolve,[status(thm)],[c_2165,c_148]) ).
cnf(c_3483,plain,
coll(sK1,sK1,sK0),
inference(resolve,[status(thm)],[c_3457,c_266]) ).
cnf(c_3523,plain,
coll(sK0,sK0,sK1),
inference(resolve,[status(thm)],[c_3483,c_266]) ).
cnf(c_3619,plain,
( cyclic(A,sK1,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK1,sK0,A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_3523,c_151]) ).
cnf(c_16763,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,sK0)
| ~ cyclic(sK1,A,sK0,A)
| ~ cyclic(sK1,A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_3461,c_152]) ).
cnf(c_16766,plain,
eqangle(A,B,sK0,sK1,A,B,sK0,sK1),
inference(resolve,[status(thm)],[c_3461,c_127]) ).
cnf(c_16767,plain,
cyclic(A,sK1,sK0,sK0),
inference(resolve,[status(thm)],[c_16766,c_3619]) ).
cnf(c_16785,plain,
cyclic(sK1,A,sK0,sK0),
inference(resolve,[status(thm)],[c_16767,c_124]) ).
cnf(c_16788,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,A)
| ~ cyclic(sK1,A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_16785,c_16763]) ).
cnf(c_16820,plain,
cyclic(sK1,sK0,A,sK0),
inference(resolve,[status(thm)],[c_16785,c_123]) ).
cnf(c_17926,plain,
cyclic(sK0,sK1,A,sK0),
inference(resolve,[status(thm)],[c_16820,c_124]) ).
cnf(c_17927,plain,
cyclic(sK1,sK0,sK0,A),
inference(resolve,[status(thm)],[c_16820,c_122]) ).
cnf(c_19185,plain,
( cyclic(sK1,A,sK0,B)
| ~ cyclic(sK0,sK1,A,B) ),
inference(resolve,[status(thm)],[c_17926,c_125]) ).
cnf(c_28591,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK1,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_17927,c_125]) ).
cnf(c_19196,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_17927,c_28591]) ).
cnf(c_28592,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_19196,c_125]) ).
cnf(c_19821,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_19196,c_28592]) ).
cnf(c_19822,plain,
cyclic(sK1,A,sK0,B),
inference(resolve,[status(thm)],[c_19821,c_19185]) ).
cnf(c_28593,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK0,A) ),
inference(resolve,[status(thm)],[c_19822,c_16788]) ).
cnf(c_19841,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_19822,c_28593]) ).
cnf(c_28594,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_19841,c_160]) ).
cnf(c_22219,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_19841,c_28594]) ).
cnf(c_28583,plain,
( perp(A,B,C,D)
| ~ para(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_22219,c_119]) ).
cnf(c_28584,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK1,sK1) ),
inference(resolve,[status(thm)],[c_22219,c_118]) ).
cnf(c_28585,plain,
perp(A,B,sK1,sK1),
inference(resolve,[status(thm)],[c_22219,c_117]) ).
cnf(c_28586,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_28585,c_28584]) ).
cnf(c_28589,plain,
perp(A,B,C,D),
inference(resolve,[status(thm)],[c_28586,c_28583]) ).
cnf(c_28590,plain,
$false,
inference(resolve,[status(thm)],[c_28589,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO622+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 13:44:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1724098 was started by sandbox2 on n009,
% 0.08/0.36 % Fri Sep 25 13:44:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 38.67/6.03
% 38.67/6.03 % given #500 (W,wt=9): 8386 coll(c4,c3,c3). [resolve(7260,a,111,a)].
% 38.67/6.03
% 38.67/6.03 % given #1000 (T,wt=13): 7215 -coll(c5,c1,A) | coll(A,c4,c5). [resolve(6173,a,112,b)].
% 38.67/6.03
% 38.67/6.03 % given #1500 (T,wt=14): 2030 -cong(c5,c2,c5,c2) | midp(c5,c2,c2). [resolve(1365,a,171,b)].
% 38.67/6.03
% 38.67/6.03 % SZS status Theorem for theBenchmark
% 38.67/6.03
% 38.67/6.03 % Proof 1 at 4.22 (+ 1.32) seconds.
% 38.67/6.03 % Length of proof is 68.
% 38.67/6.03 % Level of proof is 21.
% 38.67/6.03 % Maximum clause weight is 34.000.
% 38.67/6.03 % Given clauses 1918.
% 38.67/6.03
% 38.67/6.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------