%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO612+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 : n015.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 07:18:13 AM UTC 2026
% Result : Theorem 18.47s 2.85s
% Output : CNFRefutation 18.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 61 ( 22 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 108 ( 29 ~; 25 |; 38 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 197 ( 16 sgn 84 !; 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(exemplo6GDDFULL618074,conjecture,
! [A,B,C,O,G,D,E,F,NWPNT1] :
( ( coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) )
=> cyclic(A,E,F,B) ),
file('theBenchmark.p',exemplo6GDDFULL618074) ).
fof(exemplo6GDDFULL618074_neg,negated_conjecture,
~ ! [A,B,C,O,G,D,E,F,NWPNT1] :
( ( coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) )
=> cyclic(A,E,F,B) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618074]) ).
fof(nnf_95,plain,
? [A,B,C,O,G,D,E,F,NWPNT1] :
( ~ cyclic(A,E,F,B)
& coll(F,B,C)
& perp(F,D,B,C)
& coll(E,A,C)
& perp(E,D,A,C)
& coll(D,C,G)
& circle(O,C,D,NWPNT1)
& coll(G,A,B)
& perp(G,C,A,B)
& circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618074_neg]) ).
fof(sk_exemplo6GDDFULL618074_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& coll(sK2,sK3,sK5)
& perp(sK2,sK7,sK3,sK5)
& coll(sK1,sK0,sK5)
& perp(sK1,sK7,sK0,sK5)
& coll(sK7,sK5,sK4)
& circle(sK6,sK5,sK7,sK8)
& coll(sK4,sK0,sK3)
& perp(sK4,sK5,sK0,sK3)
& circle(sK6,sK0,sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK0,sK3,sK5,sK4,sK7,sK8,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK3),skolemize(C,sK5),skolemize(O,sK6),skolemize(G,sK4),skolemize(D,sK7),skolemize(E,sK1),skolemize(F,sK2),skolemize(NWPNT1,sK8)],[nnf_95]) ).
cnf(c_177,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618074_neg]) ).
cnf(c_184,negated_conjecture,
perp(sK4,sK5,sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618074_neg]) ).
cnf(c_223,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_242,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_245,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_246,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_266,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_268,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_269,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_270,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_271,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_275,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_276,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_277,plain,
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD7]) ).
cnf(c_280,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_281,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_337,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_422,plain,
( para(sK4,sK5,A,B)
| ~ perp(sK0,sK3,A,B) ),
inference(resolve,[status(thm)],[c_275,c_184]) ).
cnf(c_427,plain,
( para(A,B,sK0,sK3)
| ~ perp(A,B,sK4,sK5) ),
inference(resolve,[status(thm)],[c_275,c_184]) ).
cnf(c_432,plain,
perp(sK0,sK3,sK4,sK5),
inference(resolve,[status(thm)],[c_276,c_184]) ).
cnf(c_437,plain,
perp(sK4,sK5,sK3,sK0),
inference(resolve,[status(thm)],[c_277,c_184]) ).
cnf(c_782,plain,
perp(sK3,sK0,sK4,sK5),
inference(resolve,[status(thm)],[c_437,c_276]) ).
cnf(c_1051,plain,
para(sK4,sK5,sK4,sK5),
inference(resolve,[status(thm)],[c_422,c_432]) ).
cnf(c_1076,plain,
para(sK3,sK0,sK0,sK3),
inference(resolve,[status(thm)],[c_427,c_782]) ).
cnf(c_1767,plain,
eqangle(sK4,sK5,A,B,sK4,sK5,A,B),
inference(resolve,[status(thm)],[c_1051,c_245]) ).
cnf(c_1836,plain,
para(sK3,sK0,sK3,sK0),
inference(resolve,[status(thm)],[c_1076,c_280]) ).
cnf(c_2527,plain,
eqangle(sK3,sK0,A,B,sK3,sK0,A,B),
inference(resolve,[status(thm)],[c_1836,c_245]) ).
cnf(c_3734,plain,
eqangle(A,B,sK4,sK5,A,B,sK4,sK5),
inference(resolve,[status(thm)],[c_1767,c_266]) ).
cnf(c_4402,plain,
( cyclic(sK0,A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_2527,c_242]) ).
cnf(c_4861,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_3734,c_246]) ).
cnf(c_4886,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_4861,c_223]) ).
cnf(c_5064,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_4886,c_337]) ).
cnf(c_5079,plain,
cyclic(sK0,A,sK3,sK3),
inference(resolve,[status(thm)],[c_5064,c_4402]) ).
cnf(c_6011,plain,
cyclic(sK0,sK3,A,sK3),
inference(resolve,[status(thm)],[c_5079,c_270]) ).
cnf(c_6774,plain,
cyclic(sK0,sK3,sK3,A),
inference(resolve,[status(thm)],[c_6011,c_271]) ).
cnf(c_6775,plain,
cyclic(sK3,sK0,A,sK3),
inference(resolve,[status(thm)],[c_6011,c_269]) ).
cnf(c_10984,plain,
( cyclic(sK3,sK3,A,B)
| ~ cyclic(sK0,sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_6774,c_268]) ).
cnf(c_8702,plain,
cyclic(sK3,sK3,A,B),
inference(resolve,[status(thm)],[c_6774,c_10984]) ).
cnf(c_8717,plain,
( cyclic(sK0,A,B,sK3)
| ~ cyclic(sK3,sK0,A,B) ),
inference(resolve,[status(thm)],[c_6775,c_268]) ).
cnf(c_10985,plain,
( cyclic(sK3,A,B,C)
| ~ cyclic(sK3,sK3,A,B) ),
inference(resolve,[status(thm)],[c_8702,c_268]) ).
cnf(c_10969,plain,
cyclic(sK3,A,B,C),
inference(resolve,[status(thm)],[c_8702,c_10985]) ).
cnf(c_10982,plain,
cyclic(sK0,A,B,sK3),
inference(resolve,[status(thm)],[c_10969,c_8717]) ).
cnf(c_10983,plain,
$false,
inference(resolve,[status(thm)],[c_10982,c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO612+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.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 13:47:43 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1506411 was started by sandbox on n015,
% 0.17/0.44 % Fri Sep 25 13:47:43 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 18.47/2.85
% 18.47/2.85 % given #500 (A,wt=13): 505 -coll(c3,c3,A) | coll(c7,A,c3). [resolve(460,a,281,a)].
% 18.47/2.85
% 18.47/2.85 % given #1000 (T,wt=10): 2811 para(c2,c3,c3,c5). [resolve(2719,a,280,a)].
% 18.47/2.85
% 18.47/2.85 % given #1500 (A,wt=24): 917 -perp(c1,c5,c3,c2) | perp(c3,f10(c3,c1,c2,c5),c2,c1). [resolve(824,a,194,a)].
% 18.47/2.85
% 18.47/2.85 % given #2000 (T,wt=13): 2285 -coll(c5,c4,A) | coll(c5,A,c5). [resolve(2158,a,281,a)].
% 18.47/2.85
% 18.47/2.85 % given #2500 (A,wt=33): 1942 perp(f17(f12(c1,c2,c3,c4),c4,c1,c4,c1),f12(c1,c2,c3,c4),c4,c1). [resolve(1933,a,355,a)].
% 18.47/2.85
% 18.47/2.85 % given #3000 (W,wt=10): 8413 para(c1,c1,c3,c3). [resolve(6658,a,279,a)].
% 18.47/2.85
% 18.47/2.85 % SZS status Theorem for theBenchmark
% 18.47/2.85
% 18.47/2.85 % Proof 1 at 1.70 (+ 0.62) seconds.
% 18.47/2.85 % Length of proof is 56.
% 18.47/2.85 % Level of proof is 15.
% 18.47/2.85 % Maximum clause weight is 23.000.
% 18.47/2.85 % Given clauses 3032.
% 18.47/2.85
% 18.47/2.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------