%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO646+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 : n009.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 12:25:27 PM UTC 2026
% Result : Theorem 1.06s 0.62s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 28
% Syntax : Number of formulae : 140 ( 7 unt; 2 def)
% Number of atoms : 375 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 392 ( 157 ~; 147 |; 59 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 14 con; 0-0 aty)
% Number of variables : 579 ( 551 !; 28 ?)
% 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(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ( circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,B,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ( circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(E,F,B,H) ),
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(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(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(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(f137,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f150,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f184,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f185,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
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(f190,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
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(f199,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f200,plain,
! [B,C,E,F] :
( para(E,F,B,C)
| ! [A] :
( ~ midp(F,A,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f206,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f255,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f256,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f369,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6] :
( ~ para(E,F,B,H)
& circle(A,C,H,NWPNT6)
& coll(C,G,H)
& midp(G,E,F)
& circle(A,B,F,NWPNT5)
& coll(F,D,E)
& circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,E,F,H] :
( ~ para(E,F,B,H)
& ? [A,C] :
( ? [NWPNT6] : circle(A,C,H,NWPNT6)
& ? [G] :
( coll(C,G,H)
& midp(G,E,F)
& ? [NWPNT5] : circle(A,B,F,NWPNT5)
& ? [D] :
( coll(F,D,E)
& ? [NWPNT4] : circle(A,B,E,NWPNT4)
& perp(A,C,C,D)
& ? [NWPNT3] : circle(A,B,C,NWPNT3)
& perp(A,B,B,D)
& ? [NWPNT1,NWPNT2] : circle(A,B,NWPNT1,NWPNT2) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK21_skl,sK22_skl,sK20_skl,sK23_skl)
& circle(sK24_skl,sK25_skl,sK23_skl,sK33_skl)
& coll(sK25_skl,sK26_skl,sK23_skl)
& midp(sK26_skl,sK21_skl,sK22_skl)
& circle(sK24_skl,sK20_skl,sK22_skl,sK32_skl)
& coll(sK22_skl,sK27_skl,sK21_skl)
& circle(sK24_skl,sK20_skl,sK21_skl,sK31_skl)
& perp(sK24_skl,sK25_skl,sK25_skl,sK27_skl)
& circle(sK24_skl,sK20_skl,sK25_skl,sK30_skl)
& perp(sK24_skl,sK20_skl,sK20_skl,sK27_skl)
& circle(sK24_skl,sK20_skl,sK28_skl,sK29_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,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(B,sK20_skl),skolemize(E,sK21_skl),skolemize(F,sK22_skl),skolemize(H,sK23_skl),skolemize(A,sK24_skl),skolemize(C,sK25_skl),skolemize(G,sK26_skl),skolemize(D,sK27_skl),skolemize(NWPNT1,sK28_skl),skolemize(NWPNT2,sK29_skl),skolemize(NWPNT3,sK30_skl),skolemize(NWPNT4,sK31_skl),skolemize(NWPNT5,sK32_skl),skolemize(NWPNT6,sK33_skl)],[f370]) ).
fof(f375,plain,
perp(sK24_skl,sK25_skl,sK25_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ para(sK21_skl,sK22_skl,sK20_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f466,plain,
perp(sK25_skl,sK27_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f114,f375]) ).
fof(f485,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK25_skl)
| ~ perp(X0,X1,sK25_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f117,f466]) ).
fof(f512,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f661,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| eqangle(X0,X1,X2,X3,X0,X1,X4,X5) ),
inference(resolution,[status(thm)],[f140,f189]) ).
fof(f721,plain,
! [X0] :
( ~ midp(sK22_skl,X0,sK23_skl)
| ~ midp(sK21_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f201,f382]) ).
fof(f1747,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f1788,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f485,f375]) ).
fof(f1912,plain,
! [X0,X1] :
( ~ midp(X0,X1,X0)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1747,f512]) ).
fof(f1927,plain,
! [X0,X1] :
( para(X0,X1,X0,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1912,f107]) ).
fof(f2430,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f661,f186]) ).
fof(f2431,definition,
! [X0,X1] :
( sQ74_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2432,plain,
! [X0,X1] :
( ~ sQ74_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2431]) ).
fof(f2434,definition,
! [X2,X3] :
( sQ75_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
! [X0,X1] :
( ~ sQ75_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2434]) ).
fof(f2437,plain,
( sQ75_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f2430,f2431,f2434]) ).
fof(f2439,plain,
( ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1788,f2432]) ).
fof(f2457,plain,
~ sQ74_spl,
inference(contradiction_clause,[status(thm)],[f2439]) ).
fof(f2463,plain,
! [X0,X1] :
( ~ sQ75_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2435,f256]) ).
fof(f2512,plain,
! [X0,X1] :
( ~ sQ75_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2463,f100]) ).
fof(f2561,plain,
! [X0,X1] :
( ~ sQ75_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2512,f98]) ).
fof(f2570,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2561,f103]) ).
fof(f2573,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2570,f2561]) ).
fof(f2575,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2573]) ).
fof(f2576,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f2573]) ).
fof(f2579,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ75_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f2573]) ).
fof(f2691,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| ~ para(X2,X1,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f2575,f661]) ).
fof(f2700,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2691,f2435]) ).
fof(f2707,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f2700,f131]) ).
fof(f2712,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f2707,f133]) ).
fof(f2719,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2712,f129]) ).
fof(f2727,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2719,f136]) ).
fof(f2731,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2727,f2719]) ).
fof(f2739,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ75_spl
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f2731]) ).
fof(f2740,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2731]) ).
fof(f2742,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ75_spl
| cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2739,f2731]) ).
fof(f2867,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f2740,f138]) ).
fof(f3082,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| eqangle(X0,X1,X0,X2,X1,X3,X3,X2) ),
inference(resolution,[status(thm)],[f2867,f142]) ).
fof(f3133,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2579,f2435]) ).
fof(f3220,plain,
! [X0,X1,X2,X3] :
( ~ sQ75_spl
| eqangle(X0,X1,X0,X2,X3,X1,X2,X3) ),
inference(resolution,[status(thm)],[f3082,f140]) ).
fof(f3344,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ75_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2742,f2731]) ).
fof(f3346,plain,
! [X0,X1] :
( ~ sQ75_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3344,f3220]) ).
fof(f3363,plain,
! [X0,X1] :
( ~ sQ75_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3346,f2576]) ).
fof(f3373,plain,
! [X0,X1] :
( ~ sQ75_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3363,f3133]) ).
fof(f3378,plain,
! [X0,X1] :
( ~ sQ75_spl
| para(X0,X1,X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1927,f3373]) ).
fof(f3499,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3378,f2579]) ).
fof(f3505,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3499,f3373]) ).
fof(f3557,plain,
! [X0] :
( ~ sQ75_spl
| ~ midp(sK22_skl,X0,sK23_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f721,f3505]) ).
fof(f3614,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3557,f3505]) ).
fof(f3615,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f3614]) ).
fof(f3616,plain,
$false,
inference(sat_refutation,[status(thm)],[f2437,f2457,f3615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO646+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 18:10:43 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 1.06/0.62 % Refutation found
% 1.06/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.06/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.06/0.64 % Elapsed time: 0.260049 seconds
% 1.06/0.64 % CPU time: 1.758079 seconds
% 1.06/0.64 % Total memory used: 108.942 MB
% 1.06/0.64 % Net memory used: 106.088 MB
%------------------------------------------------------------------------------