%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO559+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:25:14 PM UTC 2026
% Result : Theorem 1.49s 0.61s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 21 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 188 ( 70 ~; 67 |; 36 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 310 ( 287 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( ~ coll(P,Q,A)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ( coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) )
=> para(C,D,E,F) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f104,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f143,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f187,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f188,plain,
! [A,B,C,D] :
( ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f192,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| coll(P,Q,A)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| coll(X0,X3,X1)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f197,plain,
! [A,B,P,Q] :
( cong(A,B,P,Q)
| ! [C,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) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f231,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f331,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f332,plain,
! [A,O] :
( ? [P] : perp(P,A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(miniscoping,[status(thm)],[f331]) ).
fof(f333,plain,
! [A,O] :
( perp(sK11_skl(O,A),A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( perp(sK11_skl(X0,X1),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f369,plain,
? [A,B,C,O,F,P,E,D,NWPNT1,NWPNT2] :
( ~ para(C,D,E,F)
& coll(D,B,F)
& circle(O,B,D,NWPNT2)
& coll(E,A,C)
& circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [C,F,E,D] :
( ~ para(C,D,E,F)
& ? [B] :
( coll(D,B,F)
& ? [O] :
( ? [NWPNT2] : circle(O,B,D,NWPNT2)
& ? [A] :
( coll(E,A,C)
& ? [P] :
( ? [NWPNT1] : circle(P,A,E,NWPNT1)
& circle(P,A,B,F)
& circle(O,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK20_skl,sK23_skl,sK22_skl,sK21_skl)
& coll(sK23_skl,sK24_skl,sK21_skl)
& circle(sK25_skl,sK24_skl,sK23_skl,sK29_skl)
& coll(sK22_skl,sK26_skl,sK20_skl)
& circle(sK27_skl,sK26_skl,sK22_skl,sK28_skl)
& circle(sK27_skl,sK26_skl,sK24_skl,sK21_skl)
& circle(sK25_skl,sK26_skl,sK24_skl,sK20_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,sK29_skl]),skolemize(C,sK20_skl),skolemize(F,sK21_skl),skolemize(E,sK22_skl),skolemize(D,sK23_skl),skolemize(B,sK24_skl),skolemize(O,sK25_skl),skolemize(A,sK26_skl),skolemize(P,sK27_skl),skolemize(NWPNT1,sK28_skl),skolemize(NWPNT2,sK29_skl)],[f370]) ).
fof(f374,plain,
circle(sK27_skl,sK26_skl,sK22_skl,sK28_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
~ para(sK20_skl,sK23_skl,sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f701,plain,
perp(sK11_skl(sK27_skl,sK26_skl),sK26_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f334,f374]) ).
fof(f706,plain,
perp(sK26_skl,sK27_skl,sK11_skl(sK27_skl,sK26_skl),sK26_skl),
inference(resolution,[status(thm)],[f701,f114]) ).
fof(f707,plain,
perp(sK11_skl(sK27_skl,sK26_skl),sK26_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f701,f112]) ).
fof(f714,plain,
! [X0,X1] :
( para(sK26_skl,sK27_skl,X0,X1)
| ~ perp(sK11_skl(sK27_skl,sK26_skl),sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f706,f117]) ).
fof(f1609,plain,
para(sK26_skl,sK27_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f714,f707]) ).
fof(f1610,plain,
para(sK26_skl,sK27_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f714,f701]) ).
fof(f1615,plain,
para(sK27_skl,sK26_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f1609,f107]) ).
fof(f1619,plain,
! [X0,X1] : eqangle(sK26_skl,sK27_skl,X0,X1,sK26_skl,sK27_skl,X0,X1),
inference(resolution,[status(thm)],[f1610,f189]) ).
fof(f1639,plain,
para(sK27_skl,sK26_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f1615,f105]) ).
fof(f1642,plain,
! [X0,X1] : eqangle(sK27_skl,sK26_skl,X0,X1,sK27_skl,sK26_skl,X0,X1),
inference(resolution,[status(thm)],[f1639,f189]) ).
fof(f1944,plain,
! [X0,X1] : eqangle(sK26_skl,sK27_skl,sK26_skl,sK27_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1619,f144]) ).
fof(f2054,plain,
! [X0] :
( cong(sK26_skl,X0,sK26_skl,X0)
| ~ cyclic(sK26_skl,X0,sK27_skl,sK27_skl)
| ~ cyclic(sK26_skl,X0,sK27_skl,X0)
| ~ cyclic(sK26_skl,X0,sK27_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f1642,f198]) ).
fof(f2282,plain,
! [X0] :
( cyclic(sK27_skl,sK27_skl,sK26_skl,X0)
| ~ coll(sK26_skl,X0,sK27_skl) ),
inference(resolution,[status(thm)],[f1944,f195]) ).
fof(f2283,plain,
! [X0] :
( cyclic(sK27_skl,sK27_skl,sK26_skl,X0)
| coll(sK26_skl,X0,sK27_skl) ),
inference(resolution,[status(thm)],[f1944,f193]) ).
fof(f2295,plain,
! [X0] : cyclic(sK27_skl,sK27_skl,sK26_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f2283,f2282]) ).
fof(f2328,plain,
! [X0,X1] :
( cyclic(sK27_skl,sK26_skl,X1,X0)
| ~ cyclic(sK27_skl,sK27_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f2295,f136]) ).
fof(f2332,plain,
! [X0,X1] : cyclic(sK27_skl,sK26_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f2328,f2295]) ).
fof(f2335,plain,
! [X0,X1,X2] :
( cyclic(sK26_skl,X0,X2,X1)
| ~ cyclic(sK27_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2332,f136]) ).
fof(f2339,plain,
! [X0] :
( cong(sK26_skl,X0,sK26_skl,X0)
| ~ cyclic(sK26_skl,X0,sK27_skl,X0)
| ~ cyclic(sK26_skl,X0,sK27_skl,sK26_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f2054,f2340]) ).
fof(f2340,plain,
! [X0,X1,X2] : cyclic(sK26_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f2335,f2332]) ).
fof(f2342,plain,
! [X0] :
( cong(sK26_skl,X0,sK26_skl,X0)
| ~ cyclic(sK26_skl,X0,sK27_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2339,f2340]) ).
fof(f2346,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK26_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2340,f136]) ).
fof(f2354,plain,
! [X0] : cong(sK26_skl,X0,sK26_skl,X0),
inference(backward_subsumption_resolution,[status(thm)],[f2342,f2358]) ).
fof(f2358,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f2346,f2340]) ).
fof(f2365,plain,
! [X0,X1] :
( perp(sK26_skl,sK26_skl,X1,X0)
| ~ cong(sK26_skl,X0,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f2354,f232]) ).
fof(f2372,plain,
! [X0,X1] : perp(sK26_skl,sK26_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f2365,f2354]) ).
fof(f2387,plain,
! [X0,X1] : perp(X0,X1,sK26_skl,sK26_skl),
inference(resolution,[status(thm)],[f2372,f114]) ).
fof(f2431,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ perp(sK26_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2387,f117]) ).
fof(f2437,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f2431,f2372]) ).
fof(f2438,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f378,f2437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO559+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.32 % Computer : n019.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sun Sep 20 17:32:20 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.34 % Drodi V4.1.1
% 1.49/0.61 % Refutation found
% 1.49/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.49/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.49/0.63 % Elapsed time: 0.284679 seconds
% 1.49/0.63 % CPU time: 1.974021 seconds
% 1.49/0.63 % Total memory used: 108.724 MB
% 1.49/0.63 % Net memory used: 105.925 MB
%------------------------------------------------------------------------------