%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO641+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 : n005.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 07:18:17 AM UTC 2026
% Result : Theorem 0.20s 5.73s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 79 ( 30 unt; 0 def)
% Number of atoms : 175 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 139 ( 43 ~; 39 |; 38 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 238 ( 28 sgn 96 !; 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(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
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(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(exemplo6GDDFULL81109107,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) )
=> para(U,V,B,C) ),
file('theBenchmark.p',exemplo6GDDFULL81109107) ).
fof(exemplo6GDDFULL81109107_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) )
=> para(U,V,B,C) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL81109107]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,U,V,NWPNT1] :
( ~ para(U,V,B,C)
& 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)],[exemplo6GDDFULL81109107_neg]) ).
fof(sk_exemplo6GDDFULL81109107_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& perp(sK3,sK5,sK4,sK1)
& perp(sK4,sK5,sK3,sK1)
& perp(sK4,sK3,sK5,sK1)
& perp(sK2,sK5,sK4,sK0)
& perp(sK4,sK5,sK2,sK0)
& perp(sK4,sK2,sK5,sK0)
& circle(sK6,sK4,sK5,sK7)
& circle(sK6,sK4,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK4,sK2,sK3,sK5,sK7,sK0,sK1]),skolemize(A,sK4),skolemize(B,sK2),skolemize(C,sK3),skolemize(O,sK6),skolemize(D,sK5),skolemize(U,sK0),skolemize(V,sK1),skolemize(NWPNT1,sK7)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109107_neg]) ).
cnf(c_183,negated_conjecture,
perp(sK4,sK2,sK5,sK0),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109107_neg]) ).
cnf(c_222,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_232,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_240,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_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_245,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
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_276,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_278,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_279,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
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_438,plain,
( para(sK4,sK2,A,B)
| ~ perp(sK5,sK0,A,B) ),
inference(resolve,[status(thm)],[c_274,c_183]) ).
cnf(c_454,plain,
perp(sK5,sK0,sK4,sK2),
inference(resolve,[status(thm)],[c_275,c_183]) ).
cnf(c_470,plain,
perp(sK5,sK0,sK2,sK4),
inference(resolve,[status(thm)],[c_454,c_276]) ).
cnf(c_1090,plain,
para(sK4,sK2,sK2,sK4),
inference(resolve,[status(thm)],[c_438,c_470]) ).
cnf(c_1091,plain,
para(sK4,sK2,sK4,sK2),
inference(resolve,[status(thm)],[c_438,c_454]) ).
cnf(c_1096,plain,
para(sK2,sK4,sK4,sK2),
inference(resolve,[status(thm)],[c_1090,c_278]) ).
cnf(c_1111,plain,
eqangle(sK4,sK2,A,B,sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1091,c_244]) ).
cnf(c_1150,plain,
para(sK2,sK4,sK2,sK4),
inference(resolve,[status(thm)],[c_1096,c_279]) ).
cnf(c_1165,plain,
eqangle(sK2,sK4,A,B,sK2,sK4,A,B),
inference(resolve,[status(thm)],[c_1150,c_244]) ).
cnf(c_1204,plain,
eqangle(A,B,sK4,sK2,A,B,sK4,sK2),
inference(resolve,[status(thm)],[c_1111,c_265]) ).
cnf(c_1206,plain,
( cyclic(sK2,A,sK4,sK4)
| ~ coll(sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_1111,c_241]) ).
cnf(c_1207,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,sK4)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1111,c_240]) ).
cnf(c_1227,plain,
( cyclic(sK4,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1165,c_241]) ).
cnf(c_1246,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1204,c_245]) ).
cnf(c_1271,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_1246,c_222]) ).
cnf(c_1293,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_1271,c_336]) ).
cnf(c_1301,plain,
cyclic(sK4,A,sK2,sK2),
inference(resolve,[status(thm)],[c_1293,c_1227]) ).
cnf(c_1302,plain,
cyclic(sK2,A,sK4,sK4),
inference(resolve,[status(thm)],[c_1293,c_1206]) ).
cnf(c_1317,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A)
| ~ cyclic(sK2,A,sK4,sK2) ),
inference(resolve,[status(thm)],[c_1302,c_1207]) ).
cnf(c_1372,plain,
cyclic(sK4,sK2,A,sK2),
inference(resolve,[status(thm)],[c_1301,c_269]) ).
cnf(c_1390,plain,
cyclic(sK2,sK4,A,sK4),
inference(resolve,[status(thm)],[c_1302,c_269]) ).
cnf(c_1517,plain,
cyclic(sK4,sK2,sK2,A),
inference(resolve,[status(thm)],[c_1372,c_270]) ).
cnf(c_1518,plain,
cyclic(sK2,sK4,A,sK2),
inference(resolve,[status(thm)],[c_1372,c_268]) ).
cnf(c_1613,plain,
cyclic(sK4,sK2,A,sK4),
inference(resolve,[status(thm)],[c_1390,c_268]) ).
cnf(c_1769,plain,
cyclic(sK2,sK4,sK2,A),
inference(resolve,[status(thm)],[c_1517,c_268]) ).
cnf(c_1784,plain,
cyclic(sK2,A,sK4,sK2),
inference(resolve,[status(thm)],[c_1518,c_269]) ).
cnf(c_1800,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK4,A) ),
inference(resolve,[status(thm)],[c_1784,c_1317]) ).
cnf(c_1896,plain,
( cyclic(sK2,A,sK4,B)
| ~ cyclic(sK4,sK2,A,B) ),
inference(resolve,[status(thm)],[c_1613,c_267]) ).
cnf(c_2492,plain,
( cyclic(sK4,sK2,A,B)
| ~ cyclic(sK2,sK4,sK2,A) ),
inference(resolve,[status(thm)],[c_1769,c_267]) ).
cnf(c_1957,plain,
cyclic(sK4,sK2,A,B),
inference(resolve,[status(thm)],[c_1769,c_2492]) ).
cnf(c_1971,plain,
cyclic(sK2,A,sK4,B),
inference(resolve,[status(thm)],[c_1957,c_1896]) ).
cnf(c_1975,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_1971,c_1800]) ).
cnf(c_2493,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_1975,c_232]) ).
cnf(c_2245,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_1975,c_2493]) ).
cnf(c_2489,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_2245,c_275]) ).
cnf(c_2494,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_2245,c_274]) ).
cnf(c_2490,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_2489,c_2494]) ).
cnf(c_2491,plain,
$false,
inference(resolve,[status(thm)],[c_2490,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO641+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n005.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 13:46:08 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 3611554 was started by sandbox on n005,
% 0.16/5.44 % Fri Sep 25 13:46:08 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.48
% 0.16/5.48 % From the command line: assign(max_seconds, 300).
% 0.20/5.73
% 0.20/5.73 % SZS status Theorem for theBenchmark
% 0.20/5.73
% 0.20/5.73 % Proof 1 at 0.17 (+ 0.06) seconds.
% 0.20/5.73 % Length of proof is 73.
% 0.20/5.73 % Level of proof is 19.
% 0.20/5.73 % Maximum clause weight is 34.000.
% 0.20/5.73 % Given clauses 471.
% 0.20/5.73
% 0.20/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------