%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO555+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 07:18:06 AM UTC 2026
% Result : Theorem 20.30s 6.53s
% Output : CNFRefutation 20.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 117 ( 25 ~; 21 |; 58 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 171 ( 13 sgn 74 !; 10 ?)
% 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(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(exemplo6GDDFULL012015,conjecture,
! [A,B,C,D,E,F,G,H,K,I] :
( ( coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(H,K,I,G) ),
file('theBenchmark.p',exemplo6GDDFULL012015) ).
fof(exemplo6GDDFULL012015_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,K,I] :
( ( coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(H,K,I,G) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012015]) ).
fof(nnf_95,plain,
? [A,B,C,D,E,F,G,H,K,I] :
( ~ cyclic(H,K,I,G)
& coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012015_neg]) ).
fof(sk_exemplo6GDDFULL012015_neg,plain,
( ~ cyclic(sK0,sK1,sK2,sK3)
& coll(sK2,sK5,sK8)
& perp(sK2,sK7,sK5,sK8)
& coll(sK1,sK5,sK8)
& perp(sK1,sK9,sK5,sK8)
& coll(sK0,sK5,sK6)
& perp(sK0,sK4,sK5,sK6)
& coll(sK3,sK8,sK6)
& perp(sK3,sK4,sK8,sK6)
& coll(sK4,sK5,sK8)
& perp(sK4,sK6,sK5,sK8)
& coll(sK9,sK5,sK6)
& perp(sK9,sK8,sK5,sK6)
& coll(sK7,sK8,sK6)
& perp(sK7,sK5,sK8,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK5,sK8,sK6,sK9,sK4,sK3,sK0,sK1,sK2]),skolemize(A,sK5),skolemize(B,sK8),skolemize(C,sK6),skolemize(D,sK7),skolemize(E,sK9),skolemize(F,sK4),skolemize(G,sK3),skolemize(H,sK0),skolemize(K,sK1),skolemize(I,sK2)],[nnf_95]) ).
cnf(c_147,negated_conjecture,
~ cyclic(sK0,sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012015_neg]) ).
cnf(c_153,negated_conjecture,
perp(sK0,sK4,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012015_neg]) ).
cnf(c_161,negated_conjecture,
perp(sK7,sK5,sK8,sK6),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012015_neg]) ).
cnf(c_200,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_219,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_222,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_223,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_243,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_245,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_247,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_248,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_252,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_253,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_258,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_314,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_258]) ).
cnf(c_401,plain,
( para(sK7,sK5,A,B)
| ~ perp(sK8,sK6,A,B) ),
inference(resolve,[status(thm)],[c_252,c_161]) ).
cnf(c_405,plain,
( para(sK0,sK4,A,B)
| ~ perp(sK5,sK6,A,B) ),
inference(resolve,[status(thm)],[c_252,c_153]) ).
cnf(c_415,plain,
perp(sK8,sK6,sK7,sK5),
inference(resolve,[status(thm)],[c_253,c_161]) ).
cnf(c_419,plain,
perp(sK5,sK6,sK0,sK4),
inference(resolve,[status(thm)],[c_253,c_153]) ).
cnf(c_916,plain,
para(sK7,sK5,sK7,sK5),
inference(resolve,[status(thm)],[c_401,c_415]) ).
cnf(c_1095,plain,
para(sK0,sK4,sK0,sK4),
inference(resolve,[status(thm)],[c_405,c_419]) ).
cnf(c_1139,plain,
eqangle(sK7,sK5,A,B,sK7,sK5,A,B),
inference(resolve,[status(thm)],[c_916,c_222]) ).
cnf(c_1564,plain,
eqangle(sK0,sK4,A,B,sK0,sK4,A,B),
inference(resolve,[status(thm)],[c_1095,c_222]) ).
cnf(c_5261,plain,
eqangle(A,B,sK7,sK5,A,B,sK7,sK5),
inference(resolve,[status(thm)],[c_1139,c_243]) ).
cnf(c_6216,plain,
( cyclic(sK4,A,sK0,sK0)
| ~ coll(sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_1564,c_219]) ).
cnf(c_8512,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_5261,c_223]) ).
cnf(c_8537,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_8512,c_200]) ).
cnf(c_8793,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_8537,c_314]) ).
cnf(c_8816,plain,
cyclic(sK4,A,sK0,sK0),
inference(resolve,[status(thm)],[c_8793,c_6216]) ).
cnf(c_10059,plain,
cyclic(sK4,sK0,A,sK0),
inference(resolve,[status(thm)],[c_8816,c_247]) ).
cnf(c_10849,plain,
cyclic(sK4,sK0,sK0,A),
inference(resolve,[status(thm)],[c_10059,c_248]) ).
cnf(c_15271,plain,
( cyclic(sK0,sK0,A,B)
| ~ cyclic(sK4,sK0,sK0,A) ),
inference(resolve,[status(thm)],[c_10849,c_245]) ).
cnf(c_13029,plain,
cyclic(sK0,sK0,A,B),
inference(resolve,[status(thm)],[c_10849,c_15271]) ).
cnf(c_15272,plain,
( cyclic(sK0,A,B,C)
| ~ cyclic(sK0,sK0,A,B) ),
inference(resolve,[status(thm)],[c_13029,c_245]) ).
cnf(c_15269,plain,
cyclic(sK0,A,B,C),
inference(resolve,[status(thm)],[c_13029,c_15272]) ).
cnf(c_15270,plain,
$false,
inference(resolve,[status(thm)],[c_15269,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO555+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.37 % Computer : n016.cluster.edu
% 0.06/0.37 % Model : x86_64 x86_64
% 0.06/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.37 % Memory : 8046.5625MB
% 0.06/0.37 % OS : Linux 6.8.0-71-generic
% 0.06/0.38 % CPULimit : 300
% 0.06/0.38 % WCLimit : 300
% 0.06/0.38 % DateTime : Fri Sep 25 13:46:15 UTC 2026
% 0.06/0.38 % CPUTime :
% 0.06/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.38 % Process 2505293 was started by sandbox on n016,
% 0.06/0.38 % Fri Sep 25 13:46:15 2026
% 0.06/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 20.30/6.53
% 20.30/6.53 % given #500 (T,wt=9): 1387 coll(c6,c3,c6). [resolve(1382,a,260,a)].
% 20.30/6.53
% 20.30/6.53 % given #1000 (A,wt=13): 718 -coll(c2,c4,A) | coll(c2,A,c2). [resolve(584,a,258,a)].
% 20.30/6.53
% 20.30/6.53 % given #1500 (T,wt=10): 2080 para(c4,c10,c6,c3). [resolve(1238,a,256,a)].
% 20.30/6.53
% 20.30/6.53 % given #2000 (A,wt=15): 1124 -perp(c3,c6,A,B) | para(c1,c2,A,B). [resolve(902,a,252,a)].
% 20.30/6.53
% 20.30/6.53 % given #2500 (T,wt=13): 2825 -coll(c5,c5,A) | coll(c6,A,c5). [resolve(2460,a,258,a)].
% 20.30/6.53
% 20.30/6.53 % given #3000 (A,wt=32): 1607 -coll(A,c8,c5) | -coll(A,c6,c2) | -coll(B,c8,c6) | coll(A,B,f20(c8,c6,c5,c2,A,B)). [resolve(1096,a,163,a)].
% 20.30/6.53
% 20.30/6.53 % given #3500 (W,wt=13): 3720 -coll(c6,c10,A) | coll(A,c10,c6). [resolve(3359,a,258,b)].
% 20.30/6.53
% 20.30/6.53 % given #4000 (T,wt=13): 4975 -coll(c9,c7,A) | coll(A,c5,c9). [resolve(4946,a,258,b)].
% 20.30/6.53
% 20.30/6.53 % given #4500 (W,wt=14): 4303 eqangle(c5,c9,A,B,c6,c3,A,B). [resolve(2016,a,222,a)].
% 20.30/6.53
% 20.30/6.53 % given #5000 (T,wt=10): 10485 cyclic(c1,c4,A,c1). [resolve(9911,a,246,a)].
% 20.30/6.53
% 20.30/6.53 % SZS status Theorem for theBenchmark
% 20.30/6.53
% 20.30/6.53 % Proof 1 at 2.13 (+ 0.67) seconds.
% 20.30/6.53 % Length of proof is 46.
% 20.30/6.53 % Level of proof is 14.
% 20.30/6.53 % Maximum clause weight is 23.000.
% 20.30/6.53 % Given clauses 5262.
% 20.30/6.53
% 20.30/6.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------