%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO583+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 : n026.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 7.58s 6.59s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 34
% Syntax : Number of formulae : 179 ( 8 unt; 7 def)
% Number of atoms : 517 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 585 ( 247 ~; 241 |; 62 &)
% ( 7 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 8 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 643 ( 621 !; 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(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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,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(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(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
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(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(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(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(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(f95,conjecture,
! [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ( coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(S,M,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ( coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(S,M,B,C) ),
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(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(f125,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f126,plain,
! [A,B,C,D] :
( cyclic(A,B,C,D)
| ! [O] :
( ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
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(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(f152,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f153,plain,
! [A,B,E,F] :
( cong(A,B,E,F)
| ! [C,D] :
( ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
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(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(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(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(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(f369,plain,
? [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ~ perp(S,M,B,C)
& coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,C,S,M] :
( ~ perp(S,M,B,C)
& ? [I] :
( coll(I,B,C)
& ? [A,D] :
( coll(I,A,D)
& ? [O,J] :
( cong(O,J,O,M)
& coll(O,J,M)
& ? [Q] :
( midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
& coll(sK24_skl,sK20_skl,sK21_skl)
& coll(sK24_skl,sK25_skl,sK26_skl)
& cong(sK27_skl,sK28_skl,sK27_skl,sK23_skl)
& coll(sK27_skl,sK28_skl,sK23_skl)
& midp(sK28_skl,sK22_skl,sK29_skl)
& midp(sK22_skl,sK25_skl,sK26_skl)
& midp(sK29_skl,sK21_skl,sK20_skl)
& circle(sK27_skl,sK25_skl,sK26_skl,sK30_skl)
& circle(sK27_skl,sK25_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,sK30_skl]),skolemize(B,sK20_skl),skolemize(C,sK21_skl),skolemize(S,sK22_skl),skolemize(M,sK23_skl),skolemize(I,sK24_skl),skolemize(A,sK25_skl),skolemize(D,sK26_skl),skolemize(O,sK27_skl),skolemize(J,sK28_skl),skolemize(Q,sK29_skl),skolemize(NWPNT1,sK30_skl)],[f370]) ).
fof(f373,plain,
circle(sK27_skl,sK25_skl,sK26_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
cong(sK27_skl,sK28_skl,sK27_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f510,plain,
cong(sK27_skl,sK23_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f151,f378]) ).
fof(f526,plain,
! [X0] :
( cyclic(sK23_skl,X0,sK28_skl,sK28_skl)
| ~ cong(sK27_skl,sK23_skl,sK27_skl,X0) ),
inference(resolution,[status(thm)],[f127,f510]) ).
fof(f618,plain,
! [X0,X1] :
( cong(X0,X1,sK27_skl,sK23_skl)
| ~ cong(X0,X1,sK27_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f154,f378]) ).
fof(f1486,plain,
cong(sK27_skl,sK23_skl,sK27_skl,sK23_skl),
inference(resolution,[status(thm)],[f618,f510]) ).
fof(f1659,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(f1662,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(f1827,plain,
! [X0,X1,X2] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f191,f186]) ).
fof(f1832,plain,
! [X0,X1,X2,X3] :
( perp(X3,X0,X0,X0)
| ~ circle(X3,X0,X1,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f191,f214]) ).
fof(f1859,plain,
cyclic(sK23_skl,sK23_skl,sK28_skl,sK28_skl),
inference(resolution,[status(thm)],[f526,f1486]) ).
fof(f2123,definition,
( sQ69_spl
<=> perp(sK27_skl,sK25_skl,sK25_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2124,plain,
( ~ sQ69_spl
| perp(sK27_skl,sK25_skl,sK25_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2123]) ).
fof(f2152,plain,
( ~ sQ69_spl
| perp(sK25_skl,sK25_skl,sK27_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2124,f114]) ).
fof(f3990,plain,
( perp(sK27_skl,sK25_skl,sK25_skl,sK25_skl)
| ~ cyclic(sK25_skl,sK26_skl,sK25_skl,sK30_skl) ),
inference(resolution,[status(thm)],[f1832,f373]) ).
fof(f4016,definition,
( sQ174_spl
<=> cyclic(sK25_skl,sK26_skl,sK25_skl,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f4018,plain,
( sQ174_spl
| ~ cyclic(sK25_skl,sK26_skl,sK25_skl,sK30_skl) ),
inference(component_clause,[status(thm)],[f4016]) ).
fof(f4019,plain,
( sQ69_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f3990,f4016,f2123]) ).
fof(f5119,plain,
! [X0,X1] :
( ~ sQ69_spl
| para(X0,X1,sK27_skl,sK25_skl)
| ~ perp(X0,X1,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2152,f117]) ).
fof(f6210,definition,
( sQ389_spl
<=> para(sK25_skl,sK20_skl,sK25_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f6211,plain,
( ~ sQ389_spl
| para(sK25_skl,sK20_skl,sK25_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f6210]) ).
fof(f6212,plain,
( sQ389_spl
| ~ para(sK25_skl,sK20_skl,sK25_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f6210]) ).
fof(f6749,definition,
! [X4,X5] :
( sQ424_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f6750,plain,
! [X0,X1] :
( ~ sQ424_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f6749]) ).
fof(f6766,plain,
! [X0] :
( ~ sQ389_spl
| midp(X0,sK21_skl,sK20_skl)
| ~ para(sK25_skl,sK21_skl,sK25_skl,sK20_skl)
| ~ midp(X0,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f6211,f252]) ).
fof(f6773,definition,
! [X0] :
( sQ425_spl
<=> ( midp(X0,sK21_skl,sK20_skl)
| ~ midp(X0,sK25_skl,sK25_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f6774,plain,
! [X0] :
( ~ sQ425_spl
| midp(X0,sK21_skl,sK20_skl)
| ~ midp(X0,sK25_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f6773]) ).
fof(f6776,definition,
( sQ426_spl
<=> para(sK25_skl,sK21_skl,sK25_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f6778,plain,
( sQ426_spl
| ~ para(sK25_skl,sK21_skl,sK25_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f6776]) ).
fof(f6779,plain,
( ~ sQ389_spl
| ~ sQ426_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f6766,f6773,f6776,f6210]) ).
fof(f7115,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1662,f186]) ).
fof(f7123,definition,
! [X2,X3] :
( sQ472_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f7124,plain,
! [X0,X1] :
( ~ sQ472_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f7123]) ).
fof(f7126,plain,
( sQ472_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f7115,f6749,f7123]) ).
fof(f7336,plain,
( ~ sQ424_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1859,f7344]) ).
fof(f7344,plain,
! [X0,X1,X2] :
( ~ sQ424_spl
| ~ cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1827,f6750]) ).
fof(f7346,plain,
~ sQ424_spl,
inference(contradiction_clause,[status(thm)],[f7336]) ).
fof(f7865,plain,
! [X0,X1] :
( ~ sQ472_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f7124,f256]) ).
fof(f7913,plain,
! [X0,X1] :
( ~ sQ472_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f7865,f100]) ).
fof(f7963,plain,
! [X0,X1] :
( ~ sQ472_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f7913,f98]) ).
fof(f7970,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f7963,f103]) ).
fof(f7973,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f7970,f7963]) ).
fof(f7981,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f7973]) ).
fof(f7982,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f7973]) ).
fof(f8079,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f7981,f1659]) ).
fof(f8093,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f8079,f7124]) ).
fof(f8103,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f8093,f136]) ).
fof(f8107,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f8103,f8093]) ).
fof(f8118,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ472_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,f8107]) ).
fof(f8119,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f8107]) ).
fof(f8120,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f8107]) ).
fof(f8121,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ472_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)],[f8118,f8107]) ).
fof(f8518,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ472_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f8121,f8107]) ).
fof(f8533,plain,
! [X0,X1] :
( ~ sQ472_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f8119,f8518]) ).
fof(f8590,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f8533,f8120]) ).
fof(f8591,plain,
! [X0,X1] :
( ~ sQ472_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f8533,f7982]) ).
fof(f8592,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f8533,f232]) ).
fof(f8599,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f8590,f8533]) ).
fof(f8600,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f8592,f8533]) ).
fof(f8679,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f8599]) ).
fof(f8689,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f8600,f114]) ).
fof(f9158,plain,
( sQ174_spl
| ~ sQ472_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4018,f8107]) ).
fof(f9159,plain,
( sQ174_spl
| ~ sQ472_spl ),
inference(contradiction_clause,[status(thm)],[f9158]) ).
fof(f9160,plain,
! [X0] :
( ~ sQ425_spl
| ~ sQ472_spl
| midp(X0,sK21_skl,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6774,f8591]) ).
fof(f9191,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ sQ472_spl
| para(X0,X1,sK27_skl,sK25_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f5119,f8689]) ).
fof(f9195,plain,
! [X0] :
( ~ sQ425_spl
| ~ sQ472_spl
| midp(X0,sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f9160,f122]) ).
fof(f9220,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ sQ472_spl
| para(sK27_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f9191,f107]) ).
fof(f9264,plain,
! [X0,X1,X2,X3] :
( ~ sQ69_spl
| ~ sQ472_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK27_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f9220,f110]) ).
fof(f9267,plain,
! [X0,X1,X2,X3] :
( ~ sQ69_spl
| ~ sQ472_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f9264,f9191]) ).
fof(f9270,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ69_spl
| ~ sQ472_spl
| midp(X0,X4,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f252,f9267]) ).
fof(f9280,plain,
( sQ426_spl
| ~ sQ69_spl
| ~ sQ472_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6778,f9267]) ).
fof(f9288,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ69_spl
| ~ sQ472_spl
| midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f9270,f9267]) ).
fof(f9290,plain,
( sQ426_spl
| ~ sQ69_spl
| ~ sQ472_spl ),
inference(contradiction_clause,[status(thm)],[f9280]) ).
fof(f9329,plain,
! [X0,X1,X2] :
( ~ sQ425_spl
| ~ sQ472_spl
| ~ sQ69_spl
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f9288,f9195]) ).
fof(f9339,plain,
! [X0,X1,X2] :
( ~ sQ472_spl
| ~ sQ425_spl
| ~ sQ69_spl
| cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f8679,f9329]) ).
fof(f9466,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| ~ sQ425_spl
| ~ sQ69_spl
| perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f9339]) ).
fof(f9475,plain,
! [X0,X1,X2,X3] :
( ~ sQ472_spl
| ~ sQ425_spl
| ~ sQ69_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f9466,f9339]) ).
fof(f9520,plain,
( sQ389_spl
| ~ sQ69_spl
| ~ sQ472_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6212,f9267]) ).
fof(f9521,plain,
( sQ389_spl
| ~ sQ69_spl
| ~ sQ472_spl ),
inference(contradiction_clause,[status(thm)],[f9520]) ).
fof(f9570,plain,
( ~ sQ472_spl
| ~ sQ425_spl
| ~ sQ69_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f381,f9475]) ).
fof(f9571,plain,
( ~ sQ472_spl
| ~ sQ425_spl
| ~ sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f9570]) ).
fof(f9572,plain,
$false,
inference(sat_refutation,[status(thm)],[f4019,f6779,f7126,f7346,f9159,f9290,f9521,f9571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO583+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.51 % Computer : n026.cluster.edu
% 0.08/5.51 % Model : x86_64 x86_64
% 0.08/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.51 % Memory : 8046.5625MB
% 0.08/5.51 % OS : Linux 6.8.0-71-generic
% 0.08/5.52 % CPULimit : 300
% 0.08/5.52 % WCLimit : 300
% 0.08/5.52 % DateTime : Sun Sep 20 17:43:56 UTC 2026
% 0.08/5.52 % CPUTime :
% 0.08/5.53 % Drodi V4.1.1
% 7.58/6.59 % Refutation found
% 7.58/6.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.58/6.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.51/6.62 % Elapsed time: 1.089098 seconds
% 3.51/6.62 % CPU time: 8.383514 seconds
% 3.51/6.62 % Total memory used: 169.813 MB
% 3.51/6.62 % Net memory used: 159.448 MB
%------------------------------------------------------------------------------