%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO645+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 : n026.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 07:18:18 AM UTC 2026
% Result : Theorem 25.81s 4.22s
% Output : CNFRefutation 25.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 123 ( 39 ~; 35 |; 34 &)
% ( 0 <=>; 15 =>; 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 : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 200 ( 28 sgn 80 !; 9 ?)
% 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(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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(exemplo6GDDFULLmoreE0091,conjecture,
! [A,B,C,D,E,F,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(A,B,F,NWPNT3)
& coll(F,B,D)
& circle(A,B,E,NWPNT2)
& coll(E,B,C)
& circle(A,C,D,NWPNT1)
& perp(A,D,D,B)
& perp(A,C,C,B) )
=> para(C,D,E,F) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0091) ).
fof(exemplo6GDDFULLmoreE0091_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(A,B,F,NWPNT3)
& coll(F,B,D)
& circle(A,B,E,NWPNT2)
& coll(E,B,C)
& circle(A,C,D,NWPNT1)
& perp(A,D,D,B)
& perp(A,C,C,B) )
=> para(C,D,E,F) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0091]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,NWPNT1,NWPNT2,NWPNT3] :
( ~ para(C,D,E,F)
& circle(A,B,F,NWPNT3)
& coll(F,B,D)
& circle(A,B,E,NWPNT2)
& coll(E,B,C)
& circle(A,C,D,NWPNT1)
& perp(A,D,D,B)
& perp(A,C,C,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0091_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0091_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& circle(sK4,sK5,sK3,sK8)
& coll(sK3,sK5,sK1)
& circle(sK4,sK5,sK2,sK7)
& coll(sK2,sK5,sK0)
& circle(sK4,sK0,sK1,sK6)
& perp(sK4,sK1,sK1,sK5)
& perp(sK4,sK0,sK0,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK0,sK5,sK1,sK6,sK2,sK7,sK3,sK8]),skolemize(A,sK4),skolemize(B,sK5),skolemize(C,sK0),skolemize(D,sK1),skolemize(E,sK2),skolemize(F,sK3),skolemize(NWPNT1,sK6),skolemize(NWPNT2,sK7),skolemize(NWPNT3,sK8)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0091_neg]) ).
cnf(c_196,negated_conjecture,
perp(sK4,sK0,sK0,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0091_neg]) ).
cnf(c_235,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_245,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_253,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_254,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_257,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_278,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_280,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_281,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_282,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_283,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_287,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_288,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_293,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_349,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_293]) ).
cnf(c_595,plain,
( para(sK4,sK0,A,B)
| ~ perp(sK0,sK5,A,B) ),
inference(resolve,[status(thm)],[c_287,c_196]) ).
cnf(c_605,plain,
perp(sK0,sK5,sK4,sK0),
inference(resolve,[status(thm)],[c_288,c_196]) ).
cnf(c_7064,plain,
para(sK4,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_595,c_605]) ).
cnf(c_7096,plain,
eqangle(sK4,sK0,A,B,sK4,sK0,A,B),
inference(resolve,[status(thm)],[c_7064,c_257]) ).
cnf(c_7099,plain,
coll(sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_7064,c_235]) ).
cnf(c_7127,plain,
coll(sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_7099,c_349]) ).
cnf(c_7181,plain,
coll(sK4,sK4,sK0),
inference(resolve,[status(thm)],[c_7127,c_349]) ).
cnf(c_7627,plain,
( cyclic(A,sK0,sK4,sK4)
| ~ eqangle(sK4,A,sK4,sK0,sK4,A,sK4,sK0) ),
inference(resolve,[status(thm)],[c_7181,c_254]) ).
cnf(c_11202,plain,
eqangle(A,B,sK4,sK0,A,B,sK4,sK0),
inference(resolve,[status(thm)],[c_7096,c_278]) ).
cnf(c_11205,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK4,sK4)
| ~ cyclic(sK0,A,sK4,A)
| ~ cyclic(sK0,A,sK4,sK0) ),
inference(resolve,[status(thm)],[c_7096,c_253]) ).
cnf(c_11213,plain,
cyclic(A,sK0,sK4,sK4),
inference(resolve,[status(thm)],[c_11202,c_7627]) ).
cnf(c_11224,plain,
cyclic(A,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_11213,c_282]) ).
cnf(c_11225,plain,
cyclic(sK0,A,sK4,sK4),
inference(resolve,[status(thm)],[c_11213,c_281]) ).
cnf(c_11263,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK4,A)
| ~ cyclic(sK0,A,sK4,sK0) ),
inference(resolve,[status(thm)],[c_11225,c_11205]) ).
cnf(c_11313,plain,
cyclic(sK4,A,sK0,sK4),
inference(resolve,[status(thm)],[c_11224,c_281]) ).
cnf(c_11549,plain,
cyclic(sK0,sK4,A,sK4),
inference(resolve,[status(thm)],[c_11225,c_282]) ).
cnf(c_11787,plain,
cyclic(sK4,sK0,A,sK4),
inference(resolve,[status(thm)],[c_11313,c_282]) ).
cnf(c_12181,plain,
cyclic(sK0,sK4,sK4,A),
inference(resolve,[status(thm)],[c_11549,c_283]) ).
cnf(c_12600,plain,
( cyclic(sK0,A,sK4,B)
| ~ cyclic(sK4,sK0,A,B) ),
inference(resolve,[status(thm)],[c_11787,c_280]) ).
cnf(c_22855,plain,
( cyclic(sK4,sK4,A,B)
| ~ cyclic(sK0,sK4,sK4,A) ),
inference(resolve,[status(thm)],[c_12181,c_280]) ).
cnf(c_12735,plain,
cyclic(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_12181,c_22855]) ).
cnf(c_22856,plain,
( cyclic(sK4,A,B,C)
| ~ cyclic(sK4,sK4,A,B) ),
inference(resolve,[status(thm)],[c_12735,c_280]) ).
cnf(c_13205,plain,
cyclic(sK4,A,B,C),
inference(resolve,[status(thm)],[c_12735,c_22856]) ).
cnf(c_13233,plain,
cyclic(sK0,A,sK4,B),
inference(resolve,[status(thm)],[c_13205,c_12600]) ).
cnf(c_22857,plain,
( cong(sK0,A,sK0,A)
| ~ cyclic(sK0,A,sK4,A) ),
inference(resolve,[status(thm)],[c_13233,c_11263]) ).
cnf(c_13255,plain,
cong(sK0,A,sK0,A),
inference(resolve,[status(thm)],[c_13233,c_22857]) ).
cnf(c_22858,plain,
( perp(sK0,sK0,A,B)
| ~ cong(sK0,A,sK0,A) ),
inference(resolve,[status(thm)],[c_13255,c_245]) ).
cnf(c_16517,plain,
perp(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_13255,c_22858]) ).
cnf(c_22852,plain,
perp(A,B,sK0,sK0),
inference(resolve,[status(thm)],[c_16517,c_288]) ).
cnf(c_22859,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK0,sK0) ),
inference(resolve,[status(thm)],[c_16517,c_287]) ).
cnf(c_22853,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_22852,c_22859]) ).
cnf(c_22854,plain,
$false,
inference(resolve,[status(thm)],[c_22853,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO645+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n026.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 13:49:11 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2667321 was started by sandbox2 on n026,
% 0.18/0.44 % Fri Sep 25 13:49:11 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 25.81/4.22
% 25.81/4.22 % given #500 (W,wt=13): 2558 -coll(c2,c5,A) | coll(c5,A,c2). [resolve(2072,a,293,a)].
% 25.81/4.22
% 25.81/4.22 % given #1000 (T,wt=9): 7144 coll(c3,c1,c3). [resolve(7099,a,294,a)].
% 25.81/4.22
% 25.81/4.22 % given #1500 (W,wt=9): 18658 midp(c4,c6,c3). [resolve(18395,a,285,a)].
% 25.81/4.22
% 25.81/4.22 % SZS status Theorem for theBenchmark
% 25.81/4.22
% 25.81/4.22 % Proof 1 at 2.79 (+ 0.86) seconds.
% 25.81/4.22 % Length of proof is 57.
% 25.81/4.22 % Level of proof is 19.
% 25.81/4.22 % Maximum clause weight is 34.000.
% 25.81/4.22 % Given clauses 1631.
% 25.81/4.22
% 25.81/4.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------