%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO582+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 : n010.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 07:18:09 AM UTC 2026
% Result : Theorem 6.18s 1.31s
% Output : CNFRefutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 98 ( 36 unt; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 181 ( 65 ~; 61 |; 35 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 251 ( 29 sgn 96 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
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(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(ruleD57,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('theBenchmark.p',ruleD57) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('theBenchmark.p',ruleD67) ).
fof(ruleD68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('theBenchmark.p',ruleD68) ).
fof(exemplo6GDDFULL416044,conjecture,
! [A,B,C,O,D,A1,C1,NWPNT1] :
( ( coll(C1,A,B)
& perp(C,D,C,C1)
& coll(A1,C,D)
& perp(A,B,A,A1)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(D,B,A1,C1) ),
file('theBenchmark.p',exemplo6GDDFULL416044) ).
fof(exemplo6GDDFULL416044_neg,negated_conjecture,
~ ! [A,B,C,O,D,A1,C1,NWPNT1] :
( ( coll(C1,A,B)
& perp(C,D,C,C1)
& coll(A1,C,D)
& perp(A,B,A,A1)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(D,B,A1,C1) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL416044]) ).
fof(nnf_95,plain,
? [A,B,C,O,D,A1,C1,NWPNT1] :
( ~ para(D,B,A1,C1)
& coll(C1,A,B)
& perp(C,D,C,C1)
& coll(A1,C,D)
& perp(A,B,A,A1)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL416044_neg]) ).
fof(sk_exemplo6GDDFULL416044_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& coll(sK3,sK4,sK1)
& perp(sK6,sK0,sK6,sK3)
& coll(sK2,sK6,sK0)
& perp(sK4,sK1,sK4,sK2)
& circle(sK5,sK4,sK0,sK7)
& circle(sK5,sK4,sK1,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK4,sK1,sK6,sK0,sK7,sK2,sK3]),skolemize(A,sK4),skolemize(B,sK1),skolemize(C,sK6),skolemize(O,sK5),skolemize(D,sK0),skolemize(A1,sK2),skolemize(C1,sK3),skolemize(NWPNT1,sK7)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416044_neg]) ).
cnf(c_178,negated_conjecture,
coll(sK3,sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416044_neg]) ).
cnf(c_181,negated_conjecture,
perp(sK4,sK1,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL416044_neg]) ).
cnf(c_218,plain,
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD68]) ).
cnf(c_219,plain,
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD67]) ).
cnf(c_222,plain,
( midp(A,D,E)
| ~ para(B,E,C,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD64]) ).
cnf(c_229,plain,
( perp(B,A,A,D)
| ~ cyclic(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD57]) ).
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_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_278,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_279,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_280,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_320,plain,
( midp(A,D,D)
| ~ para(B,D,C,D)
| ~ midp(A,B,C) ),
inference(factor,[status(thm)],[c_222]) ).
cnf(c_328,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,E,D,E,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_238]) ).
cnf(c_329,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_265]) ).
cnf(c_334,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_278]) ).
cnf(c_496,plain,
( para(sK4,sK1,A,B)
| ~ perp(sK4,sK2,A,B) ),
inference(resolve,[status(thm)],[c_272,c_181]) ).
cnf(c_504,plain,
perp(sK4,sK2,sK4,sK1),
inference(resolve,[status(thm)],[c_273,c_181]) ).
cnf(c_517,plain,
coll(sK4,sK3,sK1),
inference(resolve,[status(thm)],[c_279,c_178]) ).
cnf(c_572,plain,
coll(sK1,sK1,sK4),
inference(resolve,[status(thm)],[c_517,c_334]) ).
cnf(c_841,plain,
coll(sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_572,c_334]) ).
cnf(c_1399,plain,
coll(sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_841,c_280]) ).
cnf(c_1402,plain,
( cyclic(A,sK1,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK1,sK4,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_841,c_239]) ).
cnf(c_2011,plain,
coll(sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_1399,c_279]) ).
cnf(c_2540,plain,
( midp(sK1,sK4,sK4)
| ~ cong(sK1,sK4,sK1,sK4) ),
inference(resolve,[status(thm)],[c_2011,c_219]) ).
cnf(c_3068,plain,
para(sK4,sK1,sK4,sK1),
inference(resolve,[status(thm)],[c_496,c_504]) ).
cnf(c_3120,plain,
( midp(A,sK1,sK1)
| ~ midp(A,sK4,sK4) ),
inference(resolve,[status(thm)],[c_3068,c_320]) ).
cnf(c_3123,plain,
eqangle(sK4,sK1,A,B,sK4,sK1,A,B),
inference(resolve,[status(thm)],[c_3068,c_242]) ).
cnf(c_3219,plain,
( cong(sK1,sK4,sK1,sK4)
| ~ cyclic(sK1,sK4,sK4,sK4)
| ~ cyclic(sK1,sK4,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3123,c_328]) ).
cnf(c_3222,plain,
eqangle(A,B,sK4,sK1,A,B,sK4,sK1),
inference(resolve,[status(thm)],[c_3123,c_263]) ).
cnf(c_3225,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,sK4)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3123,c_238]) ).
cnf(c_3233,plain,
cyclic(A,sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_3222,c_1402]) ).
cnf(c_3244,plain,
cyclic(A,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_3233,c_267]) ).
cnf(c_3245,plain,
cyclic(sK1,A,sK4,sK4),
inference(resolve,[status(thm)],[c_3233,c_266]) ).
cnf(c_3272,plain,
( cong(sK1,sK4,sK1,sK4)
| ~ cyclic(sK1,sK4,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3245,c_3219]) ).
cnf(c_3284,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A)
| ~ cyclic(sK1,A,sK4,sK1) ),
inference(resolve,[status(thm)],[c_3245,c_3225]) ).
cnf(c_3327,plain,
cyclic(A,sK4,sK4,sK1),
inference(resolve,[status(thm)],[c_3244,c_268]) ).
cnf(c_3328,plain,
cyclic(sK4,A,sK1,sK4),
inference(resolve,[status(thm)],[c_3244,c_266]) ).
cnf(c_3356,plain,
cong(sK1,sK4,sK1,sK4),
inference(resolve,[status(thm)],[c_3327,c_3272]) ).
cnf(c_3382,plain,
midp(sK1,sK4,sK4),
inference(resolve,[status(thm)],[c_3356,c_2540]) ).
cnf(c_3386,plain,
midp(sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3382,c_3120]) ).
cnf(c_3477,plain,
cong(sK1,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3386,c_218]) ).
cnf(c_3545,plain,
cyclic(sK1,sK4,A,sK4),
inference(resolve,[status(thm)],[c_3245,c_267]) ).
cnf(c_3710,plain,
cyclic(sK4,sK4,sK1,sK1),
inference(resolve,[status(thm)],[c_3327,c_329]) ).
cnf(c_3763,plain,
cyclic(sK4,sK1,A,sK4),
inference(resolve,[status(thm)],[c_3328,c_267]) ).
cnf(c_4064,plain,
( perp(A,sK1,sK1,sK1)
| ~ cyclic(sK1,sK1,A,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_3477,c_229]) ).
cnf(c_4164,plain,
cyclic(sK1,sK4,sK4,A),
inference(resolve,[status(thm)],[c_3545,c_268]) ).
cnf(c_4488,plain,
cyclic(sK4,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_3710,c_329]) ).
cnf(c_4496,plain,
( cyclic(sK4,sK1,sK1,A)
| ~ cyclic(sK4,sK4,sK1,A) ),
inference(resolve,[status(thm)],[c_3710,c_265]) ).
cnf(c_4557,plain,
( cyclic(sK1,A,sK4,B)
| ~ cyclic(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_3763,c_265]) ).
cnf(c_7296,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK1,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_4164,c_265]) ).
cnf(c_4688,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_4164,c_7296]) ).
cnf(c_4726,plain,
cyclic(sK4,sK1,sK1,A),
inference(resolve,[status(thm)],[c_4688,c_4496]) ).
cnf(c_7297,plain,
( cyclic(sK1,sK1,A,sK1)
| ~ cyclic(sK4,sK1,sK1,A) ),
inference(resolve,[status(thm)],[c_4488,c_265]) ).
cnf(c_4889,plain,
cyclic(sK1,sK1,A,sK1),
inference(resolve,[status(thm)],[c_4726,c_7297]) ).
cnf(c_4912,plain,
( perp(A,sK1,sK1,sK1)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_4889,c_4064]) ).
cnf(c_7298,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_4688,c_265]) ).
cnf(c_5119,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_4688,c_7298]) ).
cnf(c_5147,plain,
cyclic(sK1,A,sK4,B),
inference(resolve,[status(thm)],[c_5119,c_4557]) ).
cnf(c_7299,plain,
( cong(sK1,A,sK1,A)
| ~ cyclic(sK1,A,sK4,A) ),
inference(resolve,[status(thm)],[c_5147,c_3284]) ).
cnf(c_5153,plain,
cong(sK1,A,sK1,A),
inference(resolve,[status(thm)],[c_5147,c_7299]) ).
cnf(c_5176,plain,
perp(A,sK1,sK1,sK1),
inference(resolve,[status(thm)],[c_5153,c_4912]) ).
cnf(c_7300,plain,
( perp(sK1,sK1,A,B)
| ~ cong(sK1,A,sK1,A) ),
inference(resolve,[status(thm)],[c_5153,c_230]) ).
cnf(c_6797,plain,
perp(sK1,sK1,A,B),
inference(resolve,[status(thm)],[c_5153,c_7300]) ).
cnf(c_7301,plain,
( para(C,sK1,A,B)
| ~ perp(sK1,sK1,A,B) ),
inference(resolve,[status(thm)],[c_5176,c_272]) ).
cnf(c_7294,plain,
para(A,sK1,B,C),
inference(resolve,[status(thm)],[c_6797,c_7301]) ).
cnf(c_7295,plain,
$false,
inference(resolve,[status(thm)],[c_7294,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO582+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 13:43:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 894850 was started by sandbox2 on n010,
% 0.09/0.35 % Fri Sep 25 13:43:29 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 6.18/1.31
% 6.18/1.31 % given #500 (T,wt=14): 2906 -midp(c3,c7,c3) | cong(c5,c7,c5,c3). [resolve(2821,a,231,b)].
% 6.18/1.31
% 6.18/1.31 % SZS status Theorem for theBenchmark
% 6.18/1.31
% 6.18/1.31 % Proof 1 at 0.64 (+ 0.21) seconds.
% 6.18/1.31 % Length of proof is 89.
% 6.18/1.31 % Level of proof is 17.
% 6.18/1.31 % Maximum clause weight is 34.000.
% 6.18/1.31 % Given clauses 611.
% 6.18/1.31
% 6.18/1.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
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