%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO547+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 12:25:12 PM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 8 unt; 3 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 170 ( 65 ~; 58 |; 39 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 96 ( 78 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> coll(E,F,G) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
! [X0,X1,X2] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f102,plain,
! [A,C,D] :
( coll(C,D,A)
| ! [B] :
( ~ coll(A,B,D)
| ~ coll(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f369,plain,
? [A,B,C,O,D,E,F,G,NWPNT1] :
( ~ coll(E,F,G)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,F,G] :
( ~ coll(E,F,G)
& ? [A,B] :
( coll(G,A,B)
& ? [D] :
( perp(G,D,A,B)
& ? [C] :
( coll(F,A,C)
& perp(F,D,A,C)
& coll(E,B,C)
& perp(E,D,B,C)
& ? [O] :
( ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ coll(sK20_skl,sK21_skl,sK22_skl)
& coll(sK22_skl,sK23_skl,sK24_skl)
& perp(sK22_skl,sK25_skl,sK23_skl,sK24_skl)
& coll(sK21_skl,sK23_skl,sK26_skl)
& perp(sK21_skl,sK25_skl,sK23_skl,sK26_skl)
& coll(sK20_skl,sK24_skl,sK26_skl)
& perp(sK20_skl,sK25_skl,sK24_skl,sK26_skl)
& circle(sK27_skl,sK23_skl,sK25_skl,sK28_skl)
& circle(sK27_skl,sK23_skl,sK24_skl,sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(E,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(A,sK23_skl),skolemize(B,sK24_skl),skolemize(D,sK25_skl),skolemize(C,sK26_skl),skolemize(O,sK27_skl),skolemize(NWPNT1,sK28_skl)],[f370]) ).
fof(f375,plain,
coll(sK20_skl,sK24_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
coll(sK21_skl,sK23_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
coll(sK22_skl,sK23_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
~ coll(sK20_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
~ coll(sK21_skl,sK20_skl,sK22_skl),
inference(resolution,[status(thm)],[f100,f380]) ).
fof(f393,plain,
! [X0] :
( coll(X0,sK24_skl,sK22_skl)
| ~ coll(sK22_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f103,f379]) ).
fof(f394,plain,
! [X0] :
( coll(X0,sK26_skl,sK21_skl)
| ~ coll(sK21_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f103,f377]) ).
fof(f395,plain,
! [X0] :
( coll(X0,sK26_skl,sK20_skl)
| ~ coll(sK20_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f103,f375]) ).
fof(f396,plain,
! [X0,X1,X2,X3] :
( ~ coll(X1,X0,X3)
| coll(X2,X3,X0)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f103,f100]) ).
fof(f404,plain,
! [X0,X1] :
( coll(X1,sK22_skl,X0)
| ~ coll(X0,sK24_skl,X1)
| ~ coll(sK22_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f393,f103]) ).
fof(f405,plain,
! [X0,X1] :
( coll(X1,sK21_skl,X0)
| ~ coll(X0,sK26_skl,X1)
| ~ coll(sK21_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f394,f103]) ).
fof(f407,plain,
! [X0] :
( coll(X0,sK22_skl,sK24_skl)
| ~ coll(sK24_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f404,f379]) ).
fof(f411,plain,
! [X0] :
( coll(X0,sK21_skl,sK26_skl)
| ~ coll(sK26_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f405,f377]) ).
fof(f417,plain,
! [X0] :
( ~ coll(X0,sK22_skl,sK20_skl)
| ~ coll(sK22_skl,X0,sK21_skl) ),
inference(resolution,[status(thm)],[f396,f384]) ).
fof(f428,plain,
! [X0] :
( ~ coll(sK22_skl,X0,sK20_skl)
| ~ coll(sK22_skl,X0,sK21_skl) ),
inference(resolution,[status(thm)],[f417,f100]) ).
fof(f446,definition,
( sQ0_spl
<=> coll(sK20_skl,sK26_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ0_spl
| coll(sK20_skl,sK26_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ0_spl
| ~ coll(sK20_skl,sK26_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f454,plain,
( sQ0_spl
| ~ coll(sK26_skl,sK20_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f448,f100]) ).
fof(f458,plain,
( sQ0_spl
| ~ coll(sK26_skl,sK22_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f454,f98]) ).
fof(f463,plain,
( sQ0_spl
| ~ coll(sK22_skl,sK26_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f458,f100]) ).
fof(f468,plain,
( sQ0_spl
| ~ coll(sK20_skl,sK24_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f463,f395]) ).
fof(f475,plain,
( sQ0_spl
| ~ coll(sK20_skl,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f468,f98]) ).
fof(f482,plain,
( sQ0_spl
| ~ coll(sK24_skl,sK24_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f475,f407]) ).
fof(f495,plain,
! [X0] :
( sQ0_spl
| ~ coll(X0,sK20_skl,sK24_skl)
| ~ coll(sK20_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f482,f396]) ).
fof(f498,plain,
! [X0] :
( sQ0_spl
| ~ coll(X0,sK20_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f100]) ).
fof(f500,plain,
! [X0] :
( sQ0_spl
| ~ coll(sK20_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f498,f100]) ).
fof(f505,plain,
! [X0] :
( sQ0_spl
| ~ coll(sK20_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f500,f98]) ).
fof(f509,plain,
( sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f375,f505]) ).
fof(f514,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f539,plain,
( ~ coll(sK20_skl,sK24_skl,sK22_skl)
| ~ coll(sK22_skl,sK26_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f428,f395]) ).
fof(f543,definition,
( sQ2_spl
<=> coll(sK22_skl,sK26_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( sQ2_spl
| ~ coll(sK22_skl,sK26_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,definition,
( sQ3_spl
<=> coll(sK20_skl,sK24_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ3_spl
| ~ coll(sK20_skl,sK24_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f539,f543,f546]) ).
fof(f553,plain,
( sQ2_spl
| ~ coll(sK22_skl,sK21_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f545,f98]) ).
fof(f560,plain,
( sQ2_spl
| ~ coll(sK26_skl,sK26_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f553,f411]) ).
fof(f573,plain,
! [X0] :
( sQ2_spl
| ~ coll(X0,sK22_skl,sK26_skl)
| ~ coll(sK22_skl,X0,sK26_skl) ),
inference(resolution,[status(thm)],[f560,f396]) ).
fof(f576,plain,
! [X0] :
( sQ2_spl
| ~ coll(X0,sK22_skl,sK26_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f100]) ).
fof(f579,plain,
! [X0] :
( sQ2_spl
| ~ coll(X0,sK26_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f576,f98]) ).
fof(f584,plain,
( ~ sQ0_spl
| sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f447,f579]) ).
fof(f588,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f592,plain,
( sQ3_spl
| ~ coll(sK20_skl,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f548,f98]) ).
fof(f601,plain,
( sQ3_spl
| ~ coll(sK24_skl,sK24_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f592,f407]) ).
fof(f614,plain,
! [X0] :
( sQ3_spl
| ~ coll(X0,sK20_skl,sK24_skl)
| ~ coll(sK20_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f601,f396]) ).
fof(f617,plain,
! [X0] :
( sQ3_spl
| ~ coll(X0,sK20_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f614,f100]) ).
fof(f619,plain,
! [X0] :
( sQ3_spl
| ~ coll(sK20_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f617,f100]) ).
fof(f624,plain,
! [X0] :
( sQ3_spl
| ~ coll(sK20_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f619,f98]) ).
fof(f628,plain,
( sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f375,f624]) ).
fof(f633,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f634,plain,
$false,
inference(sat_refutation,[status(thm)],[f514,f549,f588,f633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO547+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 17:23:29 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.064771 seconds
% 0.12/0.43 % CPU time: 0.302934 seconds
% 0.12/0.43 % Total memory used: 74.593 MB
% 0.12/0.43 % Net memory used: 74.390 MB
%------------------------------------------------------------------------------