%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO634+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 : n012.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 12:25:25 PM UTC 2026
% Result : Theorem 2.33s 0.65s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 34
% Syntax : Number of formulae : 181 ( 13 unt; 6 def)
% Number of atoms : 504 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 542 ( 219 ~; 210 |; 78 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 7 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 670 ( 640 !; 30 ?)
% 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(f6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
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(f10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(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(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(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(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(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(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(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(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(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(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(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(f91,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) )
=> perp(D,G,P,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ( coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) )
=> perp(D,G,P,A) ),
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(f108,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f109,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ para(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
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(f118,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f119,plain,
! [A,B,E,F] :
( perp(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
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(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(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(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(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(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(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(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(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(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(f350,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f351,plain,
! [A,E,F] :
( ? [P] :
( perp(P,A,E,F)
& coll(P,E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(miniscoping,[status(thm)],[f350]) ).
fof(f352,plain,
! [A,E,F] :
( ( perp(sK16_skl(F,E,A),A,E,F)
& coll(sK16_skl(F,E,A),E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(P,sK16_skl(F,E,A))],[f351]) ).
fof(f354,plain,
! [X0,X1,X2,X3,X4] :
( perp(sK16_skl(X4,X3,X0),X0,X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f369,plain,
? [A,B,C,O,A1,P,Q,S,D,G,NWPNT1,NWPNT2] :
( ~ perp(D,G,P,A)
& coll(G,A,B)
& perp(G,Q,A,B)
& coll(D,B,C)
& perp(D,Q,B,C)
& coll(S,A,Q)
& coll(S,B,C)
& circle(O,A,Q,NWPNT2)
& eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,P,D,G] :
( ~ perp(D,G,P,A)
& ? [B] :
( coll(G,A,B)
& ? [Q] :
( perp(G,Q,A,B)
& ? [C] :
( coll(D,B,C)
& perp(D,Q,B,C)
& ? [S] :
( coll(S,A,Q)
& coll(S,B,C)
& ? [O] :
( ? [NWPNT2] : circle(O,A,Q,NWPNT2)
& ? [A1] :
( eqangle(Q,A,A,B,C,A,A,A1)
& coll(P,A,A1)
& ? [NWPNT1] : circle(O,A,P,NWPNT1)
& midp(A1,C,B)
& circle(O,A,B,C) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK22_skl,sK23_skl,sK21_skl,sK20_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& perp(sK23_skl,sK25_skl,sK20_skl,sK24_skl)
& coll(sK22_skl,sK24_skl,sK26_skl)
& perp(sK22_skl,sK25_skl,sK24_skl,sK26_skl)
& coll(sK27_skl,sK20_skl,sK25_skl)
& coll(sK27_skl,sK24_skl,sK26_skl)
& circle(sK28_skl,sK20_skl,sK25_skl,sK31_skl)
& eqangle(sK25_skl,sK20_skl,sK20_skl,sK24_skl,sK26_skl,sK20_skl,sK20_skl,sK29_skl)
& coll(sK21_skl,sK20_skl,sK29_skl)
& circle(sK28_skl,sK20_skl,sK21_skl,sK30_skl)
& midp(sK29_skl,sK26_skl,sK24_skl)
& circle(sK28_skl,sK20_skl,sK24_skl,sK26_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]),skolemize(A,sK20_skl),skolemize(P,sK21_skl),skolemize(D,sK22_skl),skolemize(G,sK23_skl),skolemize(B,sK24_skl),skolemize(Q,sK25_skl),skolemize(C,sK26_skl),skolemize(S,sK27_skl),skolemize(O,sK28_skl),skolemize(A1,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl)],[f370]) ).
fof(f373,plain,
midp(sK29_skl,sK26_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
perp(sK22_skl,sK25_skl,sK24_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
perp(sK23_skl,sK25_skl,sK20_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
~ perp(sK22_skl,sK23_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f472,plain,
midp(sK29_skl,sK24_skl,sK26_skl),
inference(resolution,[status(thm)],[f122,f373]) ).
fof(f480,plain,
perp(sK24_skl,sK26_skl,sK22_skl,sK25_skl),
inference(resolution,[status(thm)],[f380,f114]) ).
fof(f504,plain,
! [X0,X1] :
( perp(X0,X1,sK20_skl,sK24_skl)
| ~ para(X0,X1,sK23_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f382,f120]) ).
fof(f506,plain,
perp(sK20_skl,sK24_skl,sK23_skl,sK25_skl),
inference(resolution,[status(thm)],[f382,f114]) ).
fof(f510,plain,
! [X0,X1] :
( para(X0,X1,sK22_skl,sK25_skl)
| ~ perp(X0,X1,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f480,f117]) ).
fof(f530,plain,
! [X0,X1] :
( para(X0,X1,sK23_skl,sK25_skl)
| ~ perp(X0,X1,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f506,f117]) ).
fof(f623,plain,
! [X0,X1,X2] :
( cong(X0,X1,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f260,f149]) ).
fof(f638,plain,
! [X0,X1,X2] :
( cong(X2,X0,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f623,f151]) ).
fof(f931,plain,
! [X0,X1] :
( ~ cong(X0,X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f186,f206]) ).
fof(f937,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f144]) ).
fof(f939,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f140]) ).
fof(f971,plain,
! [X0,X1,X2,X3] :
( midp(X1,X0,X1)
| ~ coll(X1,X0,X1)
| ~ circle(X3,X2,X0,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f191,f219]) ).
fof(f1106,plain,
! [X0,X1] :
( ~ midp(X0,X1,X0)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f931,f638]) ).
fof(f1169,definition,
( sQ47_spl
<=> perp(sK23_skl,sK23_skl,sK20_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1170,plain,
( ~ sQ47_spl
| perp(sK23_skl,sK23_skl,sK20_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f1169]) ).
fof(f1313,plain,
( perp(sK23_skl,sK23_skl,sK20_skl,sK24_skl)
| ~ midp(sK23_skl,sK25_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f1106,f504]) ).
fof(f1320,definition,
( sQ55_spl
<=> midp(sK23_skl,sK25_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
( sQ55_spl
| ~ midp(sK23_skl,sK25_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f1320]) ).
fof(f1323,plain,
( sQ47_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f1313,f1320,f1169]) ).
fof(f1343,plain,
! [X0,X1] :
( ~ sQ47_spl
| para(X0,X1,sK20_skl,sK24_skl)
| ~ perp(X0,X1,sK23_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f1170,f117]) ).
fof(f1874,plain,
para(sK22_skl,sK25_skl,sK22_skl,sK25_skl),
inference(resolution,[status(thm)],[f510,f380]) ).
fof(f2577,plain,
para(sK23_skl,sK25_skl,sK23_skl,sK25_skl),
inference(resolution,[status(thm)],[f530,f382]) ).
fof(f2792,definition,
! [X0,X1,X2] :
( sQ146_spl
<=> ~ midp(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2793,plain,
! [X0,X1,X2] :
( ~ sQ146_spl
| ~ midp(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f2792]) ).
fof(f2922,definition,
! [X4,X5] :
( sQ148_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2923,plain,
! [X0,X1] :
( ~ sQ148_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2922]) ).
fof(f2935,plain,
( ~ sQ148_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1874,f2923]) ).
fof(f2945,plain,
~ sQ148_spl,
inference(contradiction_clause,[status(thm)],[f2935]) ).
fof(f2980,definition,
( sQ154_spl
<=> para(sK23_skl,sK25_skl,sK23_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2982,plain,
( sQ154_spl
| ~ para(sK23_skl,sK25_skl,sK23_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2980]) ).
fof(f2986,plain,
( sQ154_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2982,f2577]) ).
fof(f2987,plain,
sQ154_spl,
inference(contradiction_clause,[status(thm)],[f2986]) ).
fof(f3226,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f939,f186]) ).
fof(f3237,definition,
! [X2,X3] :
( sQ191_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f3238,plain,
! [X0,X1] :
( ~ sQ191_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3237]) ).
fof(f3240,plain,
( sQ191_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f3226,f2922,f3237]) ).
fof(f3249,plain,
! [X0,X1] :
( ~ sQ191_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3238,f256]) ).
fof(f3271,plain,
! [X0,X1] :
( ~ sQ191_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3249,f100]) ).
fof(f3293,plain,
! [X0,X1] :
( ~ sQ191_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3271,f98]) ).
fof(f3295,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3293,f103]) ).
fof(f3298,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3295,f3293]) ).
fof(f3299,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ191_spl
| perp(sK16_skl(X3,X4,X0),X0,X4,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f354,f3298]) ).
fof(f3303,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3298]) ).
fof(f3376,plain,
( ~ sQ146_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f472,f2793]) ).
fof(f3388,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3303,f937]) ).
fof(f3404,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3388,f3238]) ).
fof(f3425,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3404,f136]) ).
fof(f3429,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3425,f3404]) ).
fof(f3457,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ perp(X0,X1,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f349,f3429]) ).
fof(f3459,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ191_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,f3429]) ).
fof(f3460,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3429]) ).
fof(f3461,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3429]) ).
fof(f3462,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ191_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)],[f3459,f3429]) ).
fof(f3688,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ191_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3462,f3429]) ).
fof(f3710,plain,
! [X0,X1] :
( ~ sQ191_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3460,f3688]) ).
fof(f3731,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3710,f3461]) ).
fof(f3733,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3710,f232]) ).
fof(f3739,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3731,f3710]) ).
fof(f3740,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3733,f3710]) ).
fof(f3744,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| circle(sK15_skl(X0,X1,X2),X2,X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3457,f3739]) ).
fof(f3745,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(sK16_skl(X0,X1,X2),X2,X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3299,f3739]) ).
fof(f3783,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3740,f114]) ).
fof(f4022,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| midp(X3,X2,X3)
| ~ coll(X3,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f971,f3429]) ).
fof(f4023,plain,
! [X0,X1] :
( ~ sQ191_spl
| midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4022,f3744]) ).
fof(f4028,plain,
! [X0,X1] :
( ~ sQ191_spl
| midp(X0,X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4023,f3298]) ).
fof(f4078,plain,
( sQ55_spl
| ~ sQ191_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1322,f4028]) ).
fof(f4081,plain,
( sQ55_spl
| ~ sQ191_spl ),
inference(contradiction_clause,[status(thm)],[f4078]) ).
fof(f4083,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ sQ191_spl
| para(X0,X1,sK20_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1343,f3783]) ).
fof(f4084,plain,
~ sQ146_spl,
inference(contradiction_clause,[status(thm)],[f3376]) ).
fof(f4143,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ sQ191_spl
| para(sK20_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4083,f107]) ).
fof(f4209,plain,
! [X0,X1,X2,X3] :
( ~ sQ47_spl
| ~ sQ191_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f4143,f110]) ).
fof(f4213,plain,
! [X0,X1,X2,X3] :
( ~ sQ47_spl
| ~ sQ191_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4209,f4083]) ).
fof(f4224,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ47_spl
| ~ sQ191_spl
| perp(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f4213]) ).
fof(f4312,plain,
! [X0,X1,X2,X3] :
( ~ sQ191_spl
| ~ sQ47_spl
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f4224,f3745]) ).
fof(f4378,plain,
( ~ sQ191_spl
| ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f384,f4312]) ).
fof(f4379,plain,
( ~ sQ191_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f4378]) ).
fof(f4380,plain,
$false,
inference(sat_refutation,[status(thm)],[f1323,f2945,f2987,f3240,f4081,f4084,f4379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO634+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.28 % Computer : n012.cluster.edu
% 0.02/0.28 % Model : x86_64 x86_64
% 0.02/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.28 % Memory : 8046.5625MB
% 0.02/0.28 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 18:06:37 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 2.33/0.65 % Refutation found
% 2.33/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.33/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.33/0.67 % Elapsed time: 0.375908 seconds
% 2.33/0.67 % CPU time: 2.676229 seconds
% 2.33/0.67 % Total memory used: 137.452 MB
% 2.33/0.67 % Net memory used: 131.461 MB
%------------------------------------------------------------------------------