%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO638+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 : n015.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 12:25:26 PM UTC 2026
% Result : Theorem 0.84s 0.56s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 31
% Syntax : Number of formulae : 162 ( 8 unt; 2 def)
% Number of atoms : 444 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 481 ( 199 ~; 191 |; 59 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 665 ( 643 !; 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(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(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
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(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(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(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(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(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,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(f95,conjecture,
! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) )
=> perp(C,H,D,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) )
=> perp(C,H,D,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(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(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(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(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(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(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(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
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(f369,plain,
? [A,B,E,G,D,C,F,H,NWPNT1,NWPNT2,NWPNT3] :
( ~ perp(C,H,D,H)
& coll(H,A,B)
& perp(H,F,A,B)
& midp(F,C,D)
& coll(C,G,D)
& para(A,D,C,B)
& perp(E,G,G,D)
& circle(E,A,G,NWPNT3)
& circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [D,C,H] :
( ~ perp(C,H,D,H)
& ? [A,B] :
( coll(H,A,B)
& ? [F] :
( perp(H,F,A,B)
& midp(F,C,D)
& ? [G] :
( coll(C,G,D)
& para(A,D,C,B)
& ? [E] :
( perp(E,G,G,D)
& ? [NWPNT3] : circle(E,A,G,NWPNT3)
& ? [NWPNT1,NWPNT2] : circle(E,A,NWPNT1,NWPNT2)
& midp(E,A,B) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK21_skl,sK22_skl,sK20_skl,sK22_skl)
& coll(sK22_skl,sK23_skl,sK24_skl)
& perp(sK22_skl,sK25_skl,sK23_skl,sK24_skl)
& midp(sK25_skl,sK21_skl,sK20_skl)
& coll(sK21_skl,sK26_skl,sK20_skl)
& para(sK23_skl,sK20_skl,sK21_skl,sK24_skl)
& perp(sK27_skl,sK26_skl,sK26_skl,sK20_skl)
& circle(sK27_skl,sK23_skl,sK26_skl,sK30_skl)
& circle(sK27_skl,sK23_skl,sK28_skl,sK29_skl)
& midp(sK27_skl,sK23_skl,sK24_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]),skolemize(D,sK20_skl),skolemize(C,sK21_skl),skolemize(H,sK22_skl),skolemize(A,sK23_skl),skolemize(B,sK24_skl),skolemize(F,sK25_skl),skolemize(G,sK26_skl),skolemize(E,sK27_skl),skolemize(NWPNT1,sK28_skl),skolemize(NWPNT2,sK29_skl),skolemize(NWPNT3,sK30_skl)],[f370]) ).
fof(f374,plain,
circle(sK27_skl,sK23_skl,sK26_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
perp(sK27_skl,sK26_skl,sK26_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ perp(sK21_skl,sK22_skl,sK20_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f493,plain,
perp(sK26_skl,sK20_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f114,f375]) ).
fof(f497,plain,
! [X0,X1] :
( para(X0,X1,sK26_skl,sK20_skl)
| ~ perp(X0,X1,sK27_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f117,f375]) ).
fof(f534,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f149,f260]) ).
fof(f607,plain,
! [X0,X1,X2] :
( ~ midp(X1,X2,X0)
| cong(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f151,f534]) ).
fof(f615,plain,
! [X0,X1,X2] :
( cong(X2,X0,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f607,f149]) ).
fof(f623,plain,
! [X0,X1,X2] :
( cong(X1,X0,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f615,f151]) ).
fof(f679,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(f1102,plain,
para(sK26_skl,sK20_skl,sK26_skl,sK20_skl),
inference(resolution,[status(thm)],[f497,f493]) ).
fof(f2510,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f679,f186]) ).
fof(f2511,definition,
! [X0,X1] :
( sQ84_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f2512,plain,
! [X0,X1] :
( ~ sQ84_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2511]) ).
fof(f2514,definition,
! [X2,X3] :
( sQ85_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f2515,plain,
! [X0,X1] :
( ~ sQ85_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2514]) ).
fof(f2517,plain,
( sQ85_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f2510,f2511,f2514]) ).
fof(f2535,plain,
( ~ sQ84_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1102,f2512]) ).
fof(f2545,plain,
~ sQ84_spl,
inference(contradiction_clause,[status(thm)],[f2535]) ).
fof(f2549,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| midp(X0,X2,X2)
| ~ para(X1,X2,X1,X2)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2515,f252]) ).
fof(f2552,plain,
! [X0,X1] :
( ~ sQ85_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2515,f256]) ).
fof(f2556,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2549,f2515]) ).
fof(f2627,plain,
! [X0,X1] :
( ~ sQ85_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2552,f100]) ).
fof(f2700,plain,
! [X0,X1] :
( ~ sQ85_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2627,f98]) ).
fof(f2712,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2700,f103]) ).
fof(f2715,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2712,f2700]) ).
fof(f2717,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2715]) ).
fof(f2718,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f2715]) ).
fof(f2720,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ85_spl
| midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f219,f2715]) ).
fof(f2721,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ85_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f2715]) ).
fof(f2759,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ para(X2,X1,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f2717,f679]) ).
fof(f2768,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2759,f2515]) ).
fof(f2773,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ midp(X1,X0,X0)
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2718,f623]) ).
fof(f2783,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f2768,f131]) ).
fof(f2788,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f2783,f133]) ).
fof(f2795,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2788,f129]) ).
fof(f2803,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2795,f136]) ).
fof(f2807,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2803,f2795]) ).
fof(f2815,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ85_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,f2807]) ).
fof(f2816,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2807]) ).
fof(f2817,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f2807]) ).
fof(f2818,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ85_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)],[f2815,f2807]) ).
fof(f2899,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X2,X1,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2816,f144]) ).
fof(f2954,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| midp(X3,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f2720,f2816]) ).
fof(f2973,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X2,X0,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2899,f138]) ).
fof(f3042,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X2,X1,X3,X0,X2,X3) ),
inference(resolution,[status(thm)],[f2973,f142]) ).
fof(f3115,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X2,X1,X0,X3,X3,X2) ),
inference(resolution,[status(thm)],[f3042,f140]) ).
fof(f3171,plain,
! [X0,X1,X2,X3] :
( ~ sQ85_spl
| eqangle(X0,X1,X2,X0,X1,X3,X3,X2) ),
inference(resolution,[status(thm)],[f3115,f138]) ).
fof(f3204,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2721,f2515]) ).
fof(f3263,plain,
( ~ sQ85_spl
| midp(sK30_skl,sK26_skl,sK30_skl) ),
inference(resolution,[status(thm)],[f2954,f374]) ).
fof(f3265,plain,
! [X0] :
( ~ sQ85_spl
| midp(X0,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f3263,f3204]) ).
fof(f3271,plain,
! [X0] :
( ~ sQ85_spl
| midp(sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f3265,f2556]) ).
fof(f3275,plain,
! [X0] :
( ~ sQ85_spl
| midp(X0,sK26_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3271,f2773]) ).
fof(f3286,plain,
! [X0,X1] :
( ~ sQ85_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3275,f2556]) ).
fof(f3292,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ85_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2818,f2807]) ).
fof(f3293,plain,
! [X0,X1] :
( ~ sQ85_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3292,f3171]) ).
fof(f3325,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| ~ midp(X0,X2,X2)
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2817,f260]) ).
fof(f3327,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3325,f3286]) ).
fof(f3424,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3327,f3293]) ).
fof(f3436,plain,
! [X0,X1,X2] :
( ~ sQ85_spl
| perp(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f3424,f112]) ).
fof(f3531,plain,
( ~ sQ85_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f381,f3436]) ).
fof(f3542,plain,
~ sQ85_spl,
inference(contradiction_clause,[status(thm)],[f3531]) ).
fof(f3543,plain,
$false,
inference(sat_refutation,[status(thm)],[f2517,f2545,f3542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO638+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 18:13:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.84/0.56 % Refutation found
% 0.84/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.84/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.84/0.58 % Elapsed time: 0.202146 seconds
% 0.84/0.58 % CPU time: 1.329961 seconds
% 0.84/0.58 % Total memory used: 104.462 MB
% 0.84/0.58 % Net memory used: 102.792 MB
%------------------------------------------------------------------------------