%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO572+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 07:18:08 AM UTC 2026
% Result : Theorem 2.75s 0.88s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 79 ( 30 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 43 ~; 39 |; 30 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 235 ( 28 sgn 94 !; 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(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(exemplo6GDDFULL214034,conjecture,
! [A,B,C,H,O,P,NWPNT1] :
( ( circle(O,B,P,NWPNT1)
& circle(O,H,B,C)
& perp(C,H,H,P)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) )
=> para(A,H,B,P) ),
file('theBenchmark.p',exemplo6GDDFULL214034) ).
fof(exemplo6GDDFULL214034_neg,negated_conjecture,
~ ! [A,B,C,H,O,P,NWPNT1] :
( ( circle(O,B,P,NWPNT1)
& circle(O,H,B,C)
& perp(C,H,H,P)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) )
=> para(A,H,B,P) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL214034]) ).
fof(nnf_95,plain,
? [A,B,C,H,O,P,NWPNT1] :
( ~ para(A,H,B,P)
& circle(O,B,P,NWPNT1)
& circle(O,H,B,C)
& perp(C,H,H,P)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL214034_neg]) ).
fof(sk_exemplo6GDDFULL214034_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& circle(sK5,sK2,sK3,sK6)
& circle(sK5,sK1,sK2,sK4)
& perp(sK4,sK1,sK1,sK3)
& perp(sK2,sK4,sK0,sK1)
& perp(sK0,sK4,sK2,sK1)
& perp(sK0,sK2,sK4,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK4,sK1,sK3,sK5,sK6]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK4),skolemize(H,sK1),skolemize(O,sK5),skolemize(P,sK3),skolemize(NWPNT1,sK6)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214034_neg]) ).
cnf(c_181,negated_conjecture,
perp(sK0,sK2,sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL214034_neg]) ).
cnf(c_220,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_230,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_238,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_239,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_242,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_243,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_263,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_265,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_266,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_267,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_268,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_272,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_273,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_274,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_276,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_277,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_278,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_334,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_278]) ).
cnf(c_432,plain,
( para(sK0,sK2,A,B)
| ~ perp(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_272,c_181]) ).
cnf(c_444,plain,
perp(sK4,sK1,sK0,sK2),
inference(resolve,[status(thm)],[c_273,c_181]) ).
cnf(c_456,plain,
perp(sK4,sK1,sK2,sK0),
inference(resolve,[status(thm)],[c_444,c_274]) ).
cnf(c_820,plain,
para(sK0,sK2,sK2,sK0),
inference(resolve,[status(thm)],[c_432,c_456]) ).
cnf(c_822,plain,
para(sK0,sK2,sK0,sK2),
inference(resolve,[status(thm)],[c_432,c_444]) ).
cnf(c_828,plain,
para(sK2,sK0,sK0,sK2),
inference(resolve,[status(thm)],[c_820,c_276]) ).
cnf(c_860,plain,
eqangle(sK0,sK2,A,B,sK0,sK2,A,B),
inference(resolve,[status(thm)],[c_822,c_242]) ).
cnf(c_916,plain,
para(sK2,sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_828,c_277]) ).
cnf(c_975,plain,
eqangle(sK2,sK0,A,B,sK2,sK0,A,B),
inference(resolve,[status(thm)],[c_916,c_242]) ).
cnf(c_1064,plain,
eqangle(A,B,sK0,sK2,A,B,sK0,sK2),
inference(resolve,[status(thm)],[c_860,c_263]) ).
cnf(c_1066,plain,
( cyclic(sK2,A,sK0,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_860,c_239]) ).
cnf(c_1067,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK0,sK0)
| ~ cyclic(sK2,A,sK0,A)
| ~ cyclic(sK2,A,sK0,sK2) ),
inference(resolve,[status(thm)],[c_860,c_238]) ).
cnf(c_1129,plain,
( cyclic(sK0,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_975,c_239]) ).
cnf(c_1172,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1064,c_243]) ).
cnf(c_1197,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_1172,c_220]) ).
cnf(c_1220,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_1197,c_334]) ).
cnf(c_1228,plain,
cyclic(sK0,A,sK2,sK2),
inference(resolve,[status(thm)],[c_1220,c_1129]) ).
cnf(c_1229,plain,
cyclic(sK2,A,sK0,sK0),
inference(resolve,[status(thm)],[c_1220,c_1066]) ).
cnf(c_1244,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK0,A)
| ~ cyclic(sK2,A,sK0,sK2) ),
inference(resolve,[status(thm)],[c_1229,c_1067]) ).
cnf(c_1331,plain,
cyclic(sK0,sK2,A,sK2),
inference(resolve,[status(thm)],[c_1228,c_267]) ).
cnf(c_1349,plain,
cyclic(sK2,sK0,A,sK0),
inference(resolve,[status(thm)],[c_1229,c_267]) ).
cnf(c_1476,plain,
cyclic(sK0,sK2,sK2,A),
inference(resolve,[status(thm)],[c_1331,c_268]) ).
cnf(c_1477,plain,
cyclic(sK2,sK0,A,sK2),
inference(resolve,[status(thm)],[c_1331,c_266]) ).
cnf(c_1572,plain,
cyclic(sK0,sK2,A,sK0),
inference(resolve,[status(thm)],[c_1349,c_266]) ).
cnf(c_1728,plain,
cyclic(sK2,sK0,sK2,A),
inference(resolve,[status(thm)],[c_1476,c_266]) ).
cnf(c_1743,plain,
cyclic(sK2,A,sK0,sK2),
inference(resolve,[status(thm)],[c_1477,c_267]) ).
cnf(c_1759,plain,
( cong(sK2,A,sK2,A)
| ~ cyclic(sK2,A,sK0,A) ),
inference(resolve,[status(thm)],[c_1743,c_1244]) ).
cnf(c_1855,plain,
( cyclic(sK2,A,sK0,B)
| ~ cyclic(sK0,sK2,A,B) ),
inference(resolve,[status(thm)],[c_1572,c_265]) ).
cnf(c_2448,plain,
( cyclic(sK0,sK2,A,B)
| ~ cyclic(sK2,sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_1728,c_265]) ).
cnf(c_1916,plain,
cyclic(sK0,sK2,A,B),
inference(resolve,[status(thm)],[c_1728,c_2448]) ).
cnf(c_1930,plain,
cyclic(sK2,A,sK0,B),
inference(resolve,[status(thm)],[c_1916,c_1855]) ).
cnf(c_1934,plain,
cong(sK2,A,sK2,A),
inference(resolve,[status(thm)],[c_1930,c_1759]) ).
cnf(c_2449,plain,
( perp(sK2,sK2,A,B)
| ~ cong(sK2,A,sK2,A) ),
inference(resolve,[status(thm)],[c_1934,c_230]) ).
cnf(c_2200,plain,
perp(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_1934,c_2449]) ).
cnf(c_2445,plain,
perp(A,B,sK2,sK2),
inference(resolve,[status(thm)],[c_2200,c_273]) ).
cnf(c_2450,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK2,sK2) ),
inference(resolve,[status(thm)],[c_2200,c_272]) ).
cnf(c_2446,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_2445,c_2450]) ).
cnf(c_2447,plain,
$false,
inference(resolve,[status(thm)],[c_2446,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO572+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 13:45:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3407338 was started by sandbox2 on n002,
% 0.16/0.43 % Fri Sep 25 13:45:04 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 2.75/0.88
% 2.75/0.88 % SZS status Theorem for theBenchmark
% 2.75/0.88
% 2.75/0.88 % Proof 1 at 0.30 (+ 0.09) seconds.
% 2.75/0.88 % Length of proof is 73.
% 2.75/0.88 % Level of proof is 19.
% 2.75/0.88 % Maximum clause weight is 34.000.
% 2.75/0.88 % Given clauses 456.
% 2.75/0.88
% 2.75/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------