%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO586+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 : n008.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 12:25:18 PM UTC 2026
% Result : Theorem 4.59s 1.11s
% Output : CNFRefutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 32
% Syntax : Number of formulae : 177 ( 39 unt; 0 def)
% Number of atoms : 396 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 373 ( 154 ~; 149 |; 37 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 660 ( 638 !; 22 ?)
% 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(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,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(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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
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(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(f50,axiom,
! [A,B,C,O,X] :
( ( eqangle(A,X,A,B,C,A,C,B)
& circle(O,A,B,C) )
=> perp(O,A,A,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
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(f70,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,E,I,NWPNT1] :
( ( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(I,E,C,D) ),
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(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(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(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
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(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(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(f148,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
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(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(f212,plain,
! [A,B,C,O,X] :
( perp(O,A,A,X)
| ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f213,plain,
! [A,O,X] :
( perp(O,A,A,X)
| ! [B,C] :
( ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f212]) ).
fof(f214,plain,
! [X0,X1,X2,X3,X4] :
( perp(X0,X1,X1,X4)
| ~ eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f217,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f218,plain,
! [B,C,M] :
( midp(M,B,C)
| ! [A,O] :
( ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f221,plain,
! [A,B,M] :
( cong(A,M,B,M)
| ! [C] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C) ) ),
inference(miniscoping,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f224,plain,
! [A,B,C] :
( perp(A,B,B,C)
| ! [O] :
( ~ coll(O,A,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f223]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
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(f250,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f251,plain,
! [C,D,M] :
( midp(M,C,D)
| ! [A,B] :
( ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( midp(X0,X3,X4)
| ~ para(X1,X4,X2,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
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(f261,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f262,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
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(f346,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f347,plain,
! [A,B,C] :
( ? [O] : circle(O,A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(miniscoping,[status(thm)],[f346]) ).
fof(f348,plain,
! [A,B,C] :
( circle(sK15_skl(C,B,A),A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(O,sK15_skl(C,B,A))],[f347]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ cyclic(X0,X2,X1,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f348]) ).
fof(f369,plain,
? [A,B,C,O,D,E,I,NWPNT1] :
( ~ perp(I,E,C,D)
& circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [C,D,E,I] :
( ~ perp(I,E,C,D)
& ? [A,B] :
( circle(I,A,B,E)
& coll(E,B,D)
& coll(E,A,C)
& ? [O] :
( ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK23_skl,sK22_skl,sK20_skl,sK21_skl)
& circle(sK23_skl,sK24_skl,sK25_skl,sK22_skl)
& coll(sK22_skl,sK25_skl,sK21_skl)
& coll(sK22_skl,sK24_skl,sK20_skl)
& circle(sK26_skl,sK24_skl,sK21_skl,sK27_skl)
& circle(sK26_skl,sK24_skl,sK25_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]),skolemize(C,sK20_skl),skolemize(D,sK21_skl),skolemize(E,sK22_skl),skolemize(I,sK23_skl),skolemize(A,sK24_skl),skolemize(B,sK25_skl),skolemize(O,sK26_skl),skolemize(NWPNT1,sK27_skl)],[f370]) ).
fof(f373,plain,
circle(sK26_skl,sK24_skl,sK21_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f376,plain,
circle(sK23_skl,sK24_skl,sK25_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
~ perp(sK23_skl,sK22_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f262,f122]) ).
fof(f380,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f260,f122]) ).
fof(f409,plain,
perp(sK11_skl(sK23_skl,sK24_skl),sK24_skl,sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f334,f376]) ).
fof(f414,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK23_skl)
| ~ perp(X0,X1,sK11_skl(sK23_skl,sK24_skl),sK24_skl) ),
inference(resolution,[status(thm)],[f409,f117]) ).
fof(f415,plain,
perp(sK24_skl,sK23_skl,sK11_skl(sK23_skl,sK24_skl),sK24_skl),
inference(resolution,[status(thm)],[f409,f114]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X1,X0,X2,X3)
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f191,f131]) ).
fof(f520,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X3,X4,X1)
| para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f201,f122]) ).
fof(f528,plain,
para(sK24_skl,sK23_skl,sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f414,f415]) ).
fof(f533,plain,
! [X0,X1] : eqangle(sK24_skl,sK23_skl,X0,X1,sK24_skl,sK23_skl,X0,X1),
inference(resolution,[status(thm)],[f528,f189]) ).
fof(f557,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK23_skl,X0,X1,sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f533,f140]) ).
fof(f615,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f557,f186]) ).
fof(f624,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[f615,f189]) ).
fof(f628,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f615,f256]) ).
fof(f642,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X1,X2,X3,X2,X3),
inference(resolution,[status(thm)],[f624,f144]) ).
fof(f645,plain,
! [X0,X1,X2] :
( midp(X2,X1,X2)
| ~ coll(X2,X1,X2)
| ~ circle(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f624,f219]) ).
fof(f661,plain,
! [X0,X1,X2] :
( midp(X2,X2,X2)
| ~ coll(X2,X2,X2)
| ~ circle(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f642,f219]) ).
fof(f664,plain,
! [X0,X1,X2] :
( midp(X2,X2,X2)
| ~ circle(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f661,f628]) ).
fof(f725,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f195,f100]) ).
fof(f726,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X2,X3)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f195,f98]) ).
fof(f801,plain,
! [X0,X1,X2] :
( cyclic(X1,X0,X0,X2)
| ~ eqangle(X0,X1,X0,X0,X2,X1,X2,X0) ),
inference(resolution,[status(thm)],[f725,f628]) ).
fof(f809,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X0,X3)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f726,f100]) ).
fof(f1552,plain,
! [X0,X1,X2] :
( cyclic(X1,X2,X0,X0)
| ~ eqangle(X0,X1,X0,X2,X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f809,f628]) ).
fof(f1556,plain,
! [X0,X1,X2] : cyclic(X0,X1,X2,X2),
inference(forward_subsumption_resolution,[status(thm)],[f1552,f624]) ).
fof(f1557,plain,
! [X0,X1,X2] : eqangle(X0,X1,X0,X2,X2,X1,X2,X2),
inference(resolution,[status(thm)],[f1556,f518]) ).
fof(f1571,plain,
! [X0,X1,X2] : eqangle(X0,X1,X0,X0,X2,X1,X2,X0),
inference(resolution,[status(thm)],[f1557,f142]) ).
fof(f1597,plain,
! [X0,X1,X2] : eqangle(X0,X0,X0,X1,X2,X0,X2,X1),
inference(resolution,[status(thm)],[f1571,f140]) ).
fof(f1704,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X1,X1)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1597,f214]) ).
fof(f2196,plain,
perp(sK26_skl,sK24_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f1704,f373]) ).
fof(f2665,plain,
! [X0,X1,X2] : cyclic(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f801,f1571]) ).
fof(f2798,plain,
! [X0,X1,X2] :
( midp(X1,X1,X1)
| ~ cyclic(X0,X1,X1,X2)
| ~ perp(X0,X1,X1,X1) ),
inference(resolution,[status(thm)],[f349,f664]) ).
fof(f2801,plain,
! [X0,X1] :
( midp(X1,X1,X1)
| ~ perp(X0,X1,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2798,f2665]) ).
fof(f2817,plain,
midp(sK24_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f2801,f2196]) ).
fof(f2823,plain,
! [X0,X1] :
( para(X0,sK24_skl,X1,sK24_skl)
| ~ midp(X0,sK24_skl,X1) ),
inference(resolution,[status(thm)],[f2817,f520]) ).
fof(f2830,plain,
! [X0,X1] :
( midp(sK24_skl,X0,X1)
| ~ para(sK24_skl,X1,sK24_skl,X0)
| ~ para(sK24_skl,X0,sK24_skl,X1) ),
inference(resolution,[status(thm)],[f2817,f252]) ).
fof(f2843,plain,
! [X0,X1] :
( midp(sK24_skl,X1,X0)
| ~ para(sK24_skl,X0,sK24_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2830,f107]) ).
fof(f2991,plain,
! [X0] : midp(sK24_skl,X0,X0),
inference(resolution,[status(thm)],[f2843,f615]) ).
fof(f3011,plain,
! [X0] : cong(sK24_skl,X0,sK24_skl,X0),
inference(resolution,[status(thm)],[f2991,f380]) ).
fof(f3039,plain,
! [X0] : cong(sK24_skl,X0,X0,sK24_skl),
inference(resolution,[status(thm)],[f3011,f149]) ).
fof(f3065,plain,
! [X0] : cong(X0,sK24_skl,sK24_skl,X0),
inference(resolution,[status(thm)],[f3039,f151]) ).
fof(f3132,plain,
! [X0] : cong(X0,sK24_skl,X0,sK24_skl),
inference(resolution,[status(thm)],[f3065,f149]) ).
fof(f3163,plain,
! [X0] :
( midp(X0,sK24_skl,sK24_skl)
| ~ coll(X0,sK24_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f3132,f258]) ).
fof(f3176,plain,
! [X0] : midp(X0,sK24_skl,sK24_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3163,f628]) ).
fof(f3178,plain,
! [X0] : para(X0,sK24_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f3176,f2823]) ).
fof(f3208,plain,
! [X0] : para(sK24_skl,sK24_skl,X0,sK24_skl),
inference(resolution,[status(thm)],[f3178,f107]) ).
fof(f3222,plain,
! [X0] : para(sK24_skl,sK24_skl,sK24_skl,X0),
inference(resolution,[status(thm)],[f3208,f105]) ).
fof(f3225,plain,
! [X0] : midp(sK24_skl,X0,sK24_skl),
inference(resolution,[status(thm)],[f3222,f2843]) ).
fof(f3271,plain,
! [X0] : cong(sK24_skl,sK24_skl,sK24_skl,X0),
inference(resolution,[status(thm)],[f3225,f380]) ).
fof(f3378,plain,
! [X0,X1] :
( circle(sK24_skl,sK24_skl,X0,X1)
| ~ cong(sK24_skl,sK24_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f3271,f124]) ).
fof(f3381,plain,
! [X0,X1] : circle(sK24_skl,sK24_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3378,f3271]) ).
fof(f3384,plain,
! [X0,X1] :
( midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3381,f645]) ).
fof(f3868,plain,
! [X0,X1] :
( ~ coll(X1,X0,X0)
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3384,f100]) ).
fof(f3870,plain,
! [X0,X1] : midp(X0,X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3868,f628]) ).
fof(f3891,plain,
! [X0,X1] : cong(X0,X0,X0,X1),
inference(resolution,[status(thm)],[f3870,f380]) ).
fof(f3893,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f3870,f378]) ).
fof(f3970,plain,
! [X0,X1,X2] :
( circle(X0,X0,X1,X2)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f3891,f124]) ).
fof(f3975,plain,
! [X0,X1,X2] : circle(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3970,f3891]) ).
fof(f4060,plain,
! [X0,X1,X2] :
( perp(X0,X2,X2,X1)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3975,f225]) ).
fof(f4061,plain,
! [X0,X1,X2] : perp(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f4060,f3893]) ).
fof(f4394,plain,
! [X0,X1,X2,X3] :
( cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f4061]) ).
fof(f4810,plain,
! [X0,X1,X2] : cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[f4394,f3870]) ).
fof(f4812,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f4810]) ).
fof(f4836,plain,
! [X0,X1,X2,X3] : perp(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4812,f4810]) ).
fof(f4877,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f377,f4836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO586+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 17:40:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 4.59/1.11 % Refutation found
% 4.59/1.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.59/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.41/1.13 % Elapsed time: 0.736819 seconds
% 2.41/1.13 % CPU time: 5.581168 seconds
% 2.41/1.13 % Total memory used: 143.239 MB
% 2.41/1.13 % Net memory used: 135.751 MB
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