%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO603+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 : n005.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 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 19 ~; 15 |; 20 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 93 ( 1 sgn 49 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
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(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(exemplo6GDDFULL618065,conjecture,
! [A,B,C,D,E,F,G] :
( ( circle(G,A,E,F)
& coll(F,A,C)
& para(B,C,F,E)
& coll(E,A,B)
& circle(D,A,B,C) )
=> coll(A,G,D) ),
file('theBenchmark.p',exemplo6GDDFULL618065) ).
fof(exemplo6GDDFULL618065_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( circle(G,A,E,F)
& coll(F,A,C)
& para(B,C,F,E)
& coll(E,A,B)
& circle(D,A,B,C) )
=> coll(A,G,D) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL618065]) ).
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] :
( ~ coll(A,G,D)
& circle(G,A,E,F)
& coll(F,A,C)
& para(B,C,F,E)
& coll(E,A,B)
& circle(D,A,B,C) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL618065_neg]) ).
fof(sk_exemplo6GDDFULL618065_neg,plain,
( ~ coll(sK2,sK5,sK1)
& circle(sK5,sK2,sK6,sK7)
& coll(sK7,sK2,sK4)
& para(sK3,sK4,sK7,sK6)
& coll(sK6,sK2,sK3)
& circle(sK1,sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK6,sK7,sK5]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK4),skolemize(D,sK1),skolemize(E,sK6),skolemize(F,sK7),skolemize(G,sK5)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK1,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618065_neg]) ).
cnf(c_110,negated_conjecture,
circle(sK5,sK2,sK6,sK7),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618065_neg]) ).
cnf(c_116,negated_conjecture,
perp(sK0(sK2,sK6,sK7,sK5),sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_130,negated_conjecture,
perp(sK0(sK2,sK3,sK4,sK1),sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_177,negated_conjecture,
~ coll(sK2,sK5,sK1),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL618065_neg]) ).
cnf(c_219,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_271,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_272,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_277,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_278,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_279,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_333,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_277]) ).
cnf(c_399,plain,
( para(A,B,sK2,sK1)
| ~ perp(A,B,sK0(sK2,sK3,sK4,sK1),sK2) ),
inference(resolve,[status(thm)],[c_271,c_130]) ).
cnf(c_400,plain,
( para(A,B,sK2,sK5)
| ~ perp(A,B,sK0(sK2,sK6,sK7,sK5),sK2) ),
inference(resolve,[status(thm)],[c_271,c_116]) ).
cnf(c_401,plain,
perp(sK2,sK1,sK0(sK2,sK3,sK4,sK1),sK2),
inference(resolve,[status(thm)],[c_272,c_130]) ).
cnf(c_402,plain,
perp(sK2,sK5,sK0(sK2,sK6,sK7,sK5),sK2),
inference(resolve,[status(thm)],[c_272,c_116]) ).
cnf(c_815,plain,
para(sK2,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_401,c_399]) ).
cnf(c_831,plain,
para(sK2,sK5,sK2,sK5),
inference(resolve,[status(thm)],[c_402,c_400]) ).
cnf(c_1033,plain,
coll(sK2,sK1,sK1),
inference(resolve,[status(thm)],[c_815,c_219]) ).
cnf(c_1040,plain,
coll(sK1,sK1,sK2),
inference(resolve,[status(thm)],[c_1033,c_333]) ).
cnf(c_1048,plain,
coll(sK2,sK2,sK1),
inference(resolve,[status(thm)],[c_1040,c_333]) ).
cnf(c_1063,plain,
( coll(A,sK1,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_1048,c_277]) ).
cnf(c_1305,plain,
coll(sK2,sK5,sK5),
inference(resolve,[status(thm)],[c_831,c_219]) ).
cnf(c_1312,plain,
coll(sK5,sK5,sK2),
inference(resolve,[status(thm)],[c_1305,c_333]) ).
cnf(c_1320,plain,
coll(sK2,sK2,sK5),
inference(resolve,[status(thm)],[c_1312,c_333]) ).
cnf(c_2823,plain,
coll(sK5,sK1,sK2),
inference(resolve,[status(thm)],[c_1063,c_1320]) ).
cnf(c_2826,plain,
coll(sK5,sK2,sK1),
inference(resolve,[status(thm)],[c_2823,c_279]) ).
cnf(c_2834,plain,
coll(sK2,sK5,sK1),
inference(resolve,[status(thm)],[c_2826,c_278]) ).
cnf(c_2833,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_177,c_2834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO603+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 13:43:53 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 3608463 was started by sandbox2 on n005,
% 0.10/5.37 % Fri Sep 25 13:43:53 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 0.14/5.58
% 0.14/5.58 % given #500 (T,wt=9): 1117 coll(c6,c6,c4). [resolve(1081,a,333,a)].
% 0.14/5.58
% 0.14/5.58 % given #1000 (A,wt=36): 823 -perp(f12(c1,c2,c3,c4),c4,c1,c1) | coll(f10(f12(c1,c2,c3,c4),c1,c1,c4),c1,c1). [resolve(401,a,191,b)].
% 0.14/5.58
% 0.14/5.58 % SZS status Theorem for theBenchmark
% 0.14/5.58
% 0.14/5.58 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.14/5.58 % Length of proof is 37.
% 0.14/5.58 % Level of proof is 11.
% 0.14/5.58 % Maximum clause weight is 24.000.
% 0.14/5.58 % Given clauses 1025.
% 0.14/5.58
% 0.14/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------