%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO601+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 07:18:12 AM UTC 2026
% Result : Theorem 5.00s 1.14s
% Output : CNFRefutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 28 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 97 ( 33 ~; 29 |; 18 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 214 ( 19 sgn 92 !; 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(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
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(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(exemplo6GDDFULL618063f,conjecture,
! [A,B,C,D,E,F,G] :
( ( circle(G,B,A,C)
& circle(F,A,D,B)
& circle(E,A,D,C)
& coll(D,B,C) )
=> cyclic(A,F,G,E) ),
file('theBenchmark.p',exemplo6GDDFULL618063f) ).
fof(exemplo6GDDFULL618063f_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( circle(G,B,A,C)
& circle(F,A,D,B)
& circle(E,A,D,C)
& coll(D,B,C) )
=> cyclic(A,F,G,E) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618063f]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G] :
( ~ cyclic(A,F,G,E)
& circle(G,B,A,C)
& circle(F,A,D,B)
& circle(E,A,D,C)
& coll(D,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618063f_neg]) ).
fof(sk_exemplo6GDDFULL618063f_neg,plain,
( ~ cyclic(sK2,sK5,sK7,sK1)
& circle(sK7,sK6,sK2,sK4)
& circle(sK5,sK2,sK3,sK6)
& circle(sK1,sK2,sK3,sK4)
& coll(sK3,sK6,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK6,sK4,sK1,sK2,sK5,sK7]),skolemize(A,sK2),skolemize(B,sK6),skolemize(C,sK4),skolemize(D,sK3),skolemize(E,sK1),skolemize(F,sK5),skolemize(G,sK7)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618063f_neg]) ).
cnf(c_110,negated_conjecture,
circle(sK5,sK2,sK3,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618063f_neg]) ).
cnf(c_131,negated_conjecture,
perp(sK0(sK2,sK3,sK6,sK5),sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_145,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_192,negated_conjecture,
~ cyclic(sK2,sK5,sK7,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618063f_neg]) ).
cnf(c_232,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_251,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_254,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_255,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_275,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_277,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_278,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_279,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_280,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_284,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_285,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_286,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_289,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_290,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_341,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_277]) ).
cnf(c_346,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_290]) ).
cnf(c_422,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_284,c_145]) ).
cnf(c_423,plain,
( para(A,B,sK2,sK5)
| ~ perp(A,B,sK0(sK2,sK3,sK6,sK5),sK2) ),
inference(resolve,[status(thm)],[c_284,c_131]) ).
cnf(c_425,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_285,c_145]) ).
cnf(c_429,plain,
perp(sK0(sK2,sK3,sK6,sK5),sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_286,c_131]) ).
cnf(c_564,plain,
perp(sK5,sK2,sK0(sK2,sK3,sK6,sK5),sK2),
inference(resolve,[status(thm)],[c_429,c_285]) ).
cnf(c_980,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_422,c_425]) ).
cnf(c_981,plain,
para(sK5,sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_423,c_564]) ).
cnf(c_1005,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_980,c_254]) ).
cnf(c_1053,plain,
para(sK5,sK2,sK5,sK2),
inference(resolve,[status(thm)],[c_981,c_289]) ).
cnf(c_1318,plain,
eqangle(sK5,sK2,A,B,sK5,sK2,A,B),
inference(resolve,[status(thm)],[c_1053,c_254]) ).
cnf(c_1942,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_1005,c_275]) ).
cnf(c_2021,plain,
( cyclic(sK2,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1318,c_251]) ).
cnf(c_2068,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_1942,c_255]) ).
cnf(c_2093,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_2068,c_232]) ).
cnf(c_2124,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_2093,c_346]) ).
cnf(c_2133,plain,
cyclic(sK2,A,sK5,sK5),
inference(resolve,[status(thm)],[c_2124,c_2021]) ).
cnf(c_2349,plain,
cyclic(A,sK5,sK5,sK5),
inference(resolve,[status(thm)],[c_2133,c_341]) ).
cnf(c_2351,plain,
cyclic(sK2,sK5,A,sK5),
inference(resolve,[status(thm)],[c_2133,c_279]) ).
cnf(c_2583,plain,
cyclic(sK5,A,sK5,sK5),
inference(resolve,[status(thm)],[c_2349,c_278]) ).
cnf(c_2596,plain,
cyclic(sK2,sK5,sK5,A),
inference(resolve,[status(thm)],[c_2351,c_280]) ).
cnf(c_3191,plain,
cyclic(sK5,sK5,A,sK5),
inference(resolve,[status(thm)],[c_2583,c_279]) ).
cnf(c_3205,plain,
cyclic(sK5,sK2,sK5,A),
inference(resolve,[status(thm)],[c_2596,c_278]) ).
cnf(c_3989,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK2,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_2596,c_277]) ).
cnf(c_3206,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_2596,c_3989]) ).
cnf(c_3990,plain,
( cyclic(sK5,A,sK5,B)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_3191,c_277]) ).
cnf(c_3935,plain,
cyclic(sK5,A,sK5,B),
inference(resolve,[status(thm)],[c_3206,c_3990]) ).
cnf(c_3991,plain,
( cyclic(sK2,sK5,A,B)
| ~ cyclic(sK5,sK2,sK5,A) ),
inference(resolve,[status(thm)],[c_3205,c_277]) ).
cnf(c_3987,plain,
cyclic(sK2,sK5,A,B),
inference(resolve,[status(thm)],[c_3935,c_3991]) ).
cnf(c_3988,plain,
$false,
inference(resolve,[status(thm)],[c_3987,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO601+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:46:41 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2661760 was started by sandbox2 on n026,
% 0.17/0.43 % Fri Sep 25 13:46:41 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 5.00/1.14
% 5.00/1.14 % given #500 (T,wt=9): 1213 coll(c2,c4,c7). [resolve(1182,a,291,a)].
% 5.00/1.14
% 5.00/1.14 % SZS status Theorem for theBenchmark
% 5.00/1.14
% 5.00/1.14 % Proof 1 at 0.45 (+ 0.19) seconds.
% 5.00/1.14 % Length of proof is 64.
% 5.00/1.14 % Level of proof is 16.
% 5.00/1.14 % Maximum clause weight is 24.000.
% 5.00/1.14 % Given clauses 979.
% 5.00/1.14
% 5.00/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------