%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO648+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 : n017.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 10.28s 1.79s
% Output : CNFRefutation 10.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 119 ( 39 ~; 35 |; 30 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
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(exemplo6GDDFULLmoreE0213,conjecture,
! [A,B,C,D,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(A,C,E,NWPNT4)
& coll(C,A,E)
& perp(A,B,B,D)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(A,D,B,E) ),
file('theBenchmark.p',exemplo6GDDFULLmoreE0213) ).
fof(exemplo6GDDFULLmoreE0213_neg,negated_conjecture,
~ ! [A,B,C,D,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(A,C,E,NWPNT4)
& coll(C,A,E)
& perp(A,B,B,D)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(A,D,B,E) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULLmoreE0213]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ~ para(A,D,B,E)
& circle(A,C,E,NWPNT4)
& coll(C,A,E)
& perp(A,B,B,D)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULLmoreE0213_neg]) ).
fof(sk_exemplo6GDDFULLmoreE0213_neg,plain,
( ~ para(sK0,sK1,sK2,sK3)
& circle(sK0,sK4,sK3,sK8)
& coll(sK4,sK0,sK3)
& perp(sK0,sK2,sK2,sK1)
& perp(sK0,sK4,sK4,sK1)
& circle(sK0,sK2,sK4,sK7)
& circle(sK0,sK2,sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK5,sK6,sK4,sK7,sK1,sK3,sK8]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK4),skolemize(D,sK1),skolemize(E,sK3),skolemize(NWPNT1,sK5),skolemize(NWPNT2,sK6),skolemize(NWPNT3,sK7),skolemize(NWPNT4,sK8)],[nnf_95]) ).
cnf(c_192,negated_conjecture,
~ para(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0213_neg]) ).
cnf(c_193,negated_conjecture,
coll(sK4,sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0213_neg]) ).
cnf(c_195,negated_conjecture,
perp(sK0,sK4,sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULLmoreE0213_neg]) ).
cnf(c_244,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_252,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_253,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_256,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_277,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_279,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_280,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_281,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_282,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_286,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_287,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_292,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_294,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_348,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_292]) ).
cnf(c_568,plain,
( para(sK0,sK4,A,B)
| ~ perp(sK4,sK1,A,B) ),
inference(resolve,[status(thm)],[c_286,c_195]) ).
cnf(c_578,plain,
perp(sK4,sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_287,c_195]) ).
cnf(c_591,plain,
coll(sK4,sK3,sK0),
inference(resolve,[status(thm)],[c_294,c_193]) ).
cnf(c_637,plain,
coll(sK0,sK0,sK4),
inference(resolve,[status(thm)],[c_591,c_348]) ).
cnf(c_808,plain,
( cyclic(A,sK4,sK0,sK0)
| ~ eqangle(sK0,A,sK0,sK4,sK0,A,sK0,sK4) ),
inference(resolve,[status(thm)],[c_637,c_253]) ).
cnf(c_4102,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_568,c_578]) ).
cnf(c_4134,plain,
eqangle(sK0,sK4,A,B,sK0,sK4,A,B),
inference(resolve,[status(thm)],[c_4102,c_256]) ).
cnf(c_4215,plain,
eqangle(A,B,sK0,sK4,A,B,sK0,sK4),
inference(resolve,[status(thm)],[c_4134,c_277]) ).
cnf(c_4218,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK0,sK0)
| ~ cyclic(sK4,A,sK0,A)
| ~ cyclic(sK4,A,sK0,sK4) ),
inference(resolve,[status(thm)],[c_4134,c_252]) ).
cnf(c_4226,plain,
cyclic(A,sK4,sK0,sK0),
inference(resolve,[status(thm)],[c_4215,c_808]) ).
cnf(c_4237,plain,
cyclic(A,sK0,sK4,sK0),
inference(resolve,[status(thm)],[c_4226,c_281]) ).
cnf(c_4238,plain,
cyclic(sK4,A,sK0,sK0),
inference(resolve,[status(thm)],[c_4226,c_280]) ).
cnf(c_4276,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK0,A)
| ~ cyclic(sK4,A,sK0,sK4) ),
inference(resolve,[status(thm)],[c_4238,c_4218]) ).
cnf(c_4326,plain,
cyclic(sK0,A,sK4,sK0),
inference(resolve,[status(thm)],[c_4237,c_280]) ).
cnf(c_4524,plain,
cyclic(sK4,sK0,A,sK0),
inference(resolve,[status(thm)],[c_4238,c_281]) ).
cnf(c_4752,plain,
cyclic(sK0,sK4,A,sK0),
inference(resolve,[status(thm)],[c_4326,c_281]) ).
cnf(c_5148,plain,
cyclic(sK4,sK0,sK0,A),
inference(resolve,[status(thm)],[c_4524,c_282]) ).
cnf(c_5547,plain,
( cyclic(sK4,A,sK0,B)
| ~ cyclic(sK0,sK4,A,B) ),
inference(resolve,[status(thm)],[c_4752,c_279]) ).
cnf(c_11027,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK4,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_5148,c_279]) ).
cnf(c_5678,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_5148,c_11027]) ).
cnf(c_11028,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_5678,c_279]) ).
cnf(c_6139,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_5678,c_11028]) ).
cnf(c_6167,plain,
cyclic(sK4,A,sK0,B),
inference(resolve,[status(thm)],[c_6139,c_5547]) ).
cnf(c_11029,plain,
( cong(sK4,A,sK4,A)
| ~ cyclic(sK4,A,sK0,A) ),
inference(resolve,[status(thm)],[c_6167,c_4276]) ).
cnf(c_6183,plain,
cong(sK4,A,sK4,A),
inference(resolve,[status(thm)],[c_6167,c_11029]) ).
cnf(c_11030,plain,
( perp(sK4,sK4,A,B)
| ~ cong(sK4,A,sK4,A) ),
inference(resolve,[status(thm)],[c_6183,c_244]) ).
cnf(c_7801,plain,
perp(sK4,sK4,A,B),
inference(resolve,[status(thm)],[c_6183,c_11030]) ).
cnf(c_11024,plain,
perp(A,B,sK4,sK4),
inference(resolve,[status(thm)],[c_7801,c_287]) ).
cnf(c_11031,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK4,sK4) ),
inference(resolve,[status(thm)],[c_7801,c_286]) ).
cnf(c_11025,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_11024,c_11031]) ).
cnf(c_11026,plain,
$false,
inference(resolve,[status(thm)],[c_11025,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO648+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:41:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2411240 was started by sandbox on n017,
% 0.09/0.37 % Fri Sep 25 13:41:48 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 10.28/1.79
% 10.28/1.79 % given #500 (A,wt=59): 397 -cyclic(c1,c4,c2,A) | -cong(f16(c1,c4,c2,A),c1,f16(c1,c4,c2,A),B) | -cong(C,c1,C,c4) | f16(c1,c4,c2,A) = C | coll(f13(c1,c4,c2,B,f16(c1,c4,c2,A),C),c1,c2). [resolve(194,a,161,a)].
% 10.28/1.79
% 10.28/1.79 % given #1000 (T,wt=10): 7088 cong(c9,c3,c9,c4). [back_unit_del(6992),unit_del(a,7060),unit_del(b,7060)].
% 10.28/1.79
% 10.28/1.79 % SZS status Theorem for theBenchmark
% 10.28/1.79
% 10.28/1.79 % Proof 1 at 0.92 (+ 0.31) seconds.
% 10.28/1.79 % Length of proof is 57.
% 10.28/1.79 % Level of proof is 17.
% 10.28/1.79 % Maximum clause weight is 34.000.
% 10.28/1.79 % Given clauses 1045.
% 10.28/1.79
% 10.28/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------