%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO650+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 : n004.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 12:25:28 PM UTC 2026
% Result : Theorem 0.10s 0.50s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 30
% Syntax : Number of formulae : 148 ( 7 unt; 2 def)
% Number of atoms : 401 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 416 ( 163 ~; 153 |; 69 &)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 576 ( 556 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
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(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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
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(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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/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(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( coll(G,A,C)
& coll(G,D,F)
& coll(F,A,B)
& perp(F,D,A,B)
& perp(B,D,B,E)
& perp(C,D,C,E)
& perp(B,C,MIDPNT3,D)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,D)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,D)
& midp(MIDPNT1,A,B) )
=> para(G,E,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( coll(G,A,C)
& coll(G,D,F)
& coll(F,A,B)
& perp(F,D,A,B)
& perp(B,D,B,E)
& perp(C,D,C,E)
& perp(B,C,MIDPNT3,D)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,D)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,D)
& midp(MIDPNT1,A,B) )
=> para(G,E,A,B) ),
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(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(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(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(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(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,MIDPNT1,MIDPNT2,MIDPNT3] :
( ~ para(G,E,A,B)
& coll(G,A,C)
& coll(G,D,F)
& coll(F,A,B)
& perp(F,D,A,B)
& perp(B,D,B,E)
& perp(C,D,C,E)
& perp(B,C,MIDPNT3,D)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,D)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,D)
& midp(MIDPNT1,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,B,E,G] :
( ~ para(G,E,A,B)
& ? [C] :
( coll(G,A,C)
& ? [D,F] :
( coll(G,D,F)
& coll(F,A,B)
& perp(F,D,A,B)
& perp(B,D,B,E)
& perp(C,D,C,E)
& ? [MIDPNT3] :
( perp(B,C,MIDPNT3,D)
& midp(MIDPNT3,B,C)
& ? [MIDPNT2] :
( perp(A,C,MIDPNT2,D)
& midp(MIDPNT2,A,C)
& ? [MIDPNT1] :
( perp(A,B,MIDPNT1,D)
& midp(MIDPNT1,A,B) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK23_skl,sK22_skl,sK20_skl,sK21_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& coll(sK23_skl,sK25_skl,sK26_skl)
& coll(sK26_skl,sK20_skl,sK21_skl)
& perp(sK26_skl,sK25_skl,sK20_skl,sK21_skl)
& perp(sK21_skl,sK25_skl,sK21_skl,sK22_skl)
& perp(sK24_skl,sK25_skl,sK24_skl,sK22_skl)
& perp(sK21_skl,sK24_skl,sK27_skl,sK25_skl)
& midp(sK27_skl,sK21_skl,sK24_skl)
& perp(sK20_skl,sK24_skl,sK28_skl,sK25_skl)
& midp(sK28_skl,sK20_skl,sK24_skl)
& perp(sK20_skl,sK21_skl,sK29_skl,sK25_skl)
& midp(sK29_skl,sK20_skl,sK21_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(A,sK20_skl),skolemize(B,sK21_skl),skolemize(E,sK22_skl),skolemize(G,sK23_skl),skolemize(C,sK24_skl),skolemize(D,sK25_skl),skolemize(F,sK26_skl),skolemize(MIDPNT3,sK27_skl),skolemize(MIDPNT2,sK28_skl),skolemize(MIDPNT1,sK29_skl)],[f370]) ).
fof(f380,plain,
perp(sK26_skl,sK25_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
~ para(sK23_skl,sK22_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f520,plain,
! [X0,X1] :
( para(X0,X1,sK20_skl,sK21_skl)
| ~ perp(X0,X1,sK26_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f380,f117]) ).
fof(f521,plain,
perp(sK20_skl,sK21_skl,sK26_skl,sK25_skl),
inference(resolution,[status(thm)],[f380,f114]) ).
fof(f700,plain,
! [X0] :
( ~ midp(sK22_skl,X0,sK21_skl)
| ~ midp(sK23_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f201,f384]) ).
fof(f721,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f730,plain,
! [X0,X1,X2] :
( cong(X0,X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f721,f149]) ).
fof(f743,plain,
! [X0,X1,X2] :
( cong(X1,X0,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f730,f151]) ).
fof(f777,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(f1223,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X4,X5,X0,X1)
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(resolution,[status(thm)],[f142,f189]) ).
fof(f1812,plain,
para(sK20_skl,sK21_skl,sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f520,f521]) ).
fof(f2395,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f2435,plain,
! [X0,X1] :
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f2395,f743]) ).
fof(f2448,plain,
! [X0,X1] :
( para(X0,X1,X0,X0)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2435,f107]) ).
fof(f3083,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f777,f186]) ).
fof(f3084,definition,
! [X0,X1] :
( sQ167_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f3085,plain,
! [X0,X1] :
( ~ sQ167_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3084]) ).
fof(f3087,definition,
! [X2,X3] :
( sQ168_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f3088,plain,
! [X0,X1] :
( ~ sQ168_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3087]) ).
fof(f3090,plain,
( sQ168_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f3083,f3084,f3087]) ).
fof(f3107,plain,
( ~ sQ167_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1812,f3085]) ).
fof(f3131,plain,
~ sQ167_spl,
inference(contradiction_clause,[status(thm)],[f3107]) ).
fof(f3135,plain,
! [X0,X1] :
( ~ sQ168_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3088,f256]) ).
fof(f3139,plain,
! [X0,X1] :
( ~ sQ168_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f3088,f105]) ).
fof(f3179,plain,
! [X0,X1] :
( ~ sQ168_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3135,f100]) ).
fof(f3220,plain,
! [X0,X1] :
( ~ sQ168_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3179,f98]) ).
fof(f3222,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3220,f103]) ).
fof(f3225,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3222,f3220]) ).
fof(f3229,plain,
! [X0,X1,X2,X3] :
( ~ sQ168_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3225]) ).
fof(f3230,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3225]) ).
fof(f3231,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ168_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f3225]) ).
fof(f3368,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| ~ para(X2,X0,X2,X0)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3229,f1223]) ).
fof(f3377,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3368,f3088]) ).
fof(f3403,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f3377,f131]) ).
fof(f3408,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f3403,f133]) ).
fof(f3415,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f3408,f129]) ).
fof(f3423,plain,
! [X0,X1,X2,X3] :
( ~ sQ168_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f3415,f136]) ).
fof(f3427,plain,
! [X0,X1,X2,X3] :
( ~ sQ168_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3423,f3415]) ).
fof(f3435,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ168_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,f3427]) ).
fof(f3436,plain,
! [X0,X1,X2,X3] :
( ~ sQ168_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3427]) ).
fof(f3438,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ168_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)],[f3435,f3427]) ).
fof(f3496,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3231,f3139]) ).
fof(f3613,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ168_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3438,f3427]) ).
fof(f3614,plain,
! [X0,X1] :
( ~ sQ168_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3613,f3436]) ).
fof(f3639,plain,
! [X0,X1] :
( ~ sQ168_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3614,f3230]) ).
fof(f3650,plain,
! [X0,X1] :
( ~ sQ168_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3639,f3496]) ).
fof(f3654,plain,
! [X0,X1] :
( ~ sQ168_spl
| para(X0,X1,X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f2448,f3650]) ).
fof(f3663,plain,
! [X0,X1] :
( ~ sQ168_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3650,f122]) ).
fof(f3746,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3654,f3231]) ).
fof(f3753,plain,
! [X0,X1,X2] :
( ~ sQ168_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3746,f3663]) ).
fof(f3756,plain,
! [X0] :
( ~ sQ168_spl
| ~ midp(sK23_skl,X0,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f700,f3753]) ).
fof(f3800,plain,
( ~ sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3756,f3753]) ).
fof(f3801,plain,
~ sQ168_spl,
inference(contradiction_clause,[status(thm)],[f3800]) ).
fof(f3802,plain,
$false,
inference(sat_refutation,[status(thm)],[f3090,f3131,f3801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO650+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 18:13:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.50 % Refutation found
% 0.10/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54 % Elapsed time: 0.152823 seconds
% 0.20/0.54 % CPU time: 0.747308 seconds
% 0.20/0.54 % Total memory used: 91.506 MB
% 0.20/0.54 % Net memory used: 90.709 MB
%------------------------------------------------------------------------------