%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO643+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 : n016.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 22.26s 3.37s
% Output : CNFRefutation 20.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 24 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 106 ( 30 ~; 26 |; 34 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 205 ( 13 sgn 94 !; 12 ?)
% 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(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(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(exemplo6GDDFULL81109109F,conjecture,
! [A,B,C,D,E,F,G,H,I,J] :
( ( circle(J,B,A,E)
& circle(I,B,C,F)
& circle(H,A,C,D)
& circle(G,D,E,F)
& coll(F,C,D)
& coll(F,B,E)
& coll(E,A,D)
& coll(C,A,B) )
=> cyclic(I,J,H,G) ),
file('theBenchmark.p',exemplo6GDDFULL81109109F) ).
fof(exemplo6GDDFULL81109109F_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I,J] :
( ( circle(J,B,A,E)
& circle(I,B,C,F)
& circle(H,A,C,D)
& circle(G,D,E,F)
& coll(F,C,D)
& coll(F,B,E)
& coll(E,A,D)
& coll(C,A,B) )
=> cyclic(I,J,H,G) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL81109109F]) ).
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,H,I,J] :
( ~ cyclic(I,J,H,G)
& circle(J,B,A,E)
& circle(I,B,C,F)
& circle(H,A,C,D)
& circle(G,D,E,F)
& coll(F,C,D)
& coll(F,B,E)
& coll(E,A,D)
& coll(C,A,B) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL81109109F_neg]) ).
fof(sk_exemplo6GDDFULL81109109F_neg,plain,
( ~ cyclic(sK5,sK8,sK9,sK1)
& circle(sK8,sK6,sK10,sK3)
& circle(sK5,sK6,sK7,sK4)
& circle(sK9,sK10,sK7,sK2)
& circle(sK1,sK2,sK3,sK4)
& coll(sK4,sK7,sK2)
& coll(sK4,sK6,sK3)
& coll(sK3,sK10,sK2)
& coll(sK7,sK10,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK10,sK6,sK3,sK2,sK4,sK1,sK9,sK5,sK8]),skolemize(A,sK10),skolemize(B,sK6),skolemize(C,sK7),skolemize(D,sK2),skolemize(E,sK3),skolemize(F,sK4),skolemize(G,sK1),skolemize(H,sK9),skolemize(I,sK5),skolemize(J,sK8)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109109F_neg]) ).
cnf(c_111,negated_conjecture,
circle(sK5,sK6,sK7,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109109F_neg]) ).
cnf(c_132,negated_conjecture,
perp(sK0(sK6,sK7,sK4,sK5),sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_111,c_102]) ).
cnf(c_160,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_207,negated_conjecture,
~ cyclic(sK5,sK8,sK9,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL81109109F_neg]) ).
cnf(c_250,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_269,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_272,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_273,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_293,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_295,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_297,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_298,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_302,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_303,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_306,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_307,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_308,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_364,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_308]) ).
cnf(c_462,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_302,c_160]) ).
cnf(c_464,plain,
( para(A,B,sK6,sK5)
| ~ perp(A,B,sK0(sK6,sK7,sK4,sK5),sK6) ),
inference(resolve,[status(thm)],[c_302,c_132]) ).
cnf(c_466,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_303,c_160]) ).
cnf(c_468,plain,
perp(sK6,sK5,sK0(sK6,sK7,sK4,sK5),sK6),
inference(resolve,[status(thm)],[c_303,c_132]) ).
cnf(c_1112,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_466,c_462]) ).
cnf(c_1148,plain,
eqangle(sK2,sK1,A,B,sK2,sK1,A,B),
inference(resolve,[status(thm)],[c_1112,c_272]) ).
cnf(c_1188,plain,
para(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_468,c_464]) ).
cnf(c_2107,plain,
para(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_1188,c_307]) ).
cnf(c_3134,plain,
para(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_2107,c_306]) ).
cnf(c_3300,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_3134,c_307]) ).
cnf(c_3435,plain,
eqangle(sK5,sK6,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_3300,c_272]) ).
cnf(c_4192,plain,
eqangle(A,B,sK2,sK1,A,B,sK2,sK1),
inference(resolve,[status(thm)],[c_1148,c_293]) ).
cnf(c_10576,plain,
( cyclic(sK6,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_3435,c_269]) ).
cnf(c_10802,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_4192,c_273]) ).
cnf(c_10827,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_10802,c_250]) ).
cnf(c_10970,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_10827,c_364]) ).
cnf(c_10979,plain,
cyclic(sK6,A,sK5,sK5),
inference(resolve,[status(thm)],[c_10970,c_10576]) ).
cnf(c_11557,plain,
cyclic(sK6,sK5,A,sK5),
inference(resolve,[status(thm)],[c_10979,c_297]) ).
cnf(c_11822,plain,
cyclic(sK6,sK5,sK5,A),
inference(resolve,[status(thm)],[c_11557,c_298]) ).
cnf(c_13577,plain,
( cyclic(sK5,sK5,A,B)
| ~ cyclic(sK6,sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_11822,c_295]) ).
cnf(c_12475,plain,
cyclic(sK5,sK5,A,B),
inference(resolve,[status(thm)],[c_11822,c_13577]) ).
cnf(c_13578,plain,
( cyclic(sK5,A,B,C)
| ~ cyclic(sK5,sK5,A,B) ),
inference(resolve,[status(thm)],[c_12475,c_295]) ).
cnf(c_13575,plain,
cyclic(sK5,A,B,C),
inference(resolve,[status(thm)],[c_12475,c_13578]) ).
cnf(c_13576,plain,
$false,
inference(resolve,[status(thm)],[c_13575,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO643+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n016.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 13:50:43 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2518669 was started by sandbox on n016,
% 0.07/0.35 % Fri Sep 25 13:50:43 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 22.26/3.37
% 22.26/3.37 % given #500 (W,wt=9): 943 coll(c4,c6,c5). [resolve(874,a,310,a)].
% 22.26/3.37
% 22.26/3.37 % given #1000 (T,wt=9): 2323 coll(c1,c3,c9). [resolve(2229,a,310,a)].
% 22.26/3.37
% 22.26/3.37 % given #1500 (W,wt=13): 1075 -coll(c6,c1,A) | coll(A,c2,c6). [resolve(1030,a,308,b)].
% 22.26/3.37
% 22.26/3.37 % given #2000 (T,wt=13): 1689 -coll(c8,c1,A) | coll(c8,A,c8). [resolve(1675,a,308,a)].
% 22.26/3.37
% 22.26/3.37 % given #2500 (W,wt=13): 2238 -coll(c9,c2,A) | coll(A,c3,c9). [resolve(2183,a,308,b)].
% 22.26/3.37
% 22.26/3.37 % given #3000 (T,wt=13): 2930 -coll(c10,c4,A) | coll(A,c4,c10). [resolve(2878,a,308,b)].
% 22.26/3.37
% 22.26/3.37 % given #3500 (W,wt=13): 4455 -coll(c10,c5,A) | coll(A,c7,c10). [resolve(4413,a,308,b)].
% 22.26/3.37
% 22.26/3.37 % given #4000 (T,wt=13): 8453 -coll(c9,c7,A) | coll(A,c8,c9). [resolve(8444,a,308,b)].
% 22.26/3.37
% 22.26/3.37 % SZS status Theorem for theBenchmark
% 22.26/3.37
% 22.26/3.37 % Proof 1 at 2.39 (+ 0.54) seconds.
% 22.26/3.37 % Length of proof is 57.
% 22.26/3.37 % Level of proof is 15.
% 22.26/3.37 % Maximum clause weight is 24.000.
% 22.26/3.37 % Given clauses 4485.
% 22.26/3.37
% 22.26/3.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------