%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO653+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 : n009.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 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 33
% Syntax : Number of formulae : 183 ( 9 unt; 2 def)
% Number of atoms : 494 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 537 ( 226 ~; 216 |; 61 &)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 777 ( 761 !; 16 ?)
% 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(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
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(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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f49,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,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(f54,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
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(f95,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,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(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(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(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(f145,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f146,plain,
! [A,B,C,D,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ! [P,Q,U,V] :
( ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
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(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(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(f209,plain,
! [A,B,C,O,X] :
( eqangle(A,X,A,B,C,A,C,B)
| ~ perp(O,A,A,X)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f210,plain,
! [A,B,C,X] :
( eqangle(A,X,A,B,C,A,C,B)
| ! [O] :
( ~ perp(O,A,A,X)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f209]) ).
fof(f211,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ perp(X0,X1,X1,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
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(f223,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f224,plain,
! [A,B,C] :
( perp(A,B,B,C)
| ! [O] :
( ~ coll(O,A,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f223]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f228,plain,
! [A,B,M,O] :
( cong(O,A,O,B)
| ~ perp(O,M,A,B)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f229,plain,
! [A,B,O] :
( cong(O,A,O,B)
| ! [M] :
( ~ perp(O,M,A,B)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
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(f369,plain,
? [A,B,C,D,E,F,G,H] :
( ~ para(G,H,A,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,B,G,H] :
( ~ para(G,H,A,B)
& ? [C,F] :
( coll(H,C,F)
& ? [E] :
( coll(H,B,E)
& coll(G,A,E)
& ? [D] :
( coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& coll(sK23_skl,sK21_skl,sK26_skl)
& coll(sK22_skl,sK20_skl,sK26_skl)
& coll(sK22_skl,sK27_skl,sK25_skl)
& coll(sK25_skl,sK20_skl,sK21_skl)
& para(sK20_skl,sK27_skl,sK25_skl,sK26_skl)
& coll(sK26_skl,sK24_skl,sK27_skl)
& para(sK20_skl,sK24_skl,sK21_skl,sK27_skl)
& para(sK20_skl,sK21_skl,sK24_skl,sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(G,sK22_skl),skolemize(H,sK23_skl),skolemize(C,sK24_skl),skolemize(F,sK25_skl),skolemize(E,sK26_skl),skolemize(D,sK27_skl)],[f370]) ).
fof(f375,plain,
para(sK20_skl,sK27_skl,sK25_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f496,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK26_skl)
| ~ para(X0,X1,sK20_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f375,f110]) ).
fof(f498,plain,
para(sK20_skl,sK27_skl,sK26_skl,sK25_skl),
inference(resolution,[status(thm)],[f375,f105]) ).
fof(f515,plain,
para(sK26_skl,sK25_skl,sK20_skl,sK27_skl),
inference(resolution,[status(thm)],[f498,f107]) ).
fof(f643,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f149,f260]) ).
fof(f700,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(f806,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(resolution,[status(thm)],[f144,f189]) ).
fof(f951,plain,
para(sK26_skl,sK25_skl,sK25_skl,sK26_skl),
inference(resolution,[status(thm)],[f496,f515]) ).
fof(f956,plain,
para(sK26_skl,sK25_skl,sK26_skl,sK25_skl),
inference(resolution,[status(thm)],[f951,f105]) ).
fof(f1121,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f700,f186]) ).
fof(f1122,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1122]) ).
fof(f1125,definition,
! [X2,X3] :
( sQ1_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1126,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1125]) ).
fof(f1128,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1121,f1122,f1125]) ).
fof(f1129,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f956,f1123]) ).
fof(f1135,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1129]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1126,f256]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1139,f100]) ).
fof(f1209,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1175,f98]) ).
fof(f1210,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1209,f103]) ).
fof(f1213,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1210,f1209]) ).
fof(f1301,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f1213]) ).
fof(f1303,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1301,f806]) ).
fof(f1308,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1303,f1126]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1308,f136]) ).
fof(f1338,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1334,f1308]) ).
fof(f1344,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_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,f1338]) ).
fof(f1345,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f1338]) ).
fof(f1347,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_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)],[f1344,f1338]) ).
fof(f1350,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ1_spl
| eqangle(X0,X1,X2,X3,X7,X5,X7,X6)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X4,X6) ),
inference(resolution,[status(thm)],[f1345,f147]) ).
fof(f1351,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X2,X1,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f1345,f144]) ).
fof(f1355,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f1345,f138]) ).
fof(f1364,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X2,X0,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f1351,f138]) ).
fof(f1381,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X2,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f1364,f140]) ).
fof(f1384,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f1347,f1338]) ).
fof(f1385,plain,
! [X0,X1] :
( ~ sQ1_spl
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[f1384,f1364]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ sQ1_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1384,f1355]) ).
fof(f1397,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cong(X0,X1,X3,X3)
| ~ cong(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f1385,f154]) ).
fof(f1400,plain,
! [X0,X1] :
( ~ sQ1_spl
| circle(X0,X0,X1,X0)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1385,f124]) ).
fof(f1403,plain,
! [X0,X1] :
( ~ sQ1_spl
| cong(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f1386,f149]) ).
fof(f1499,plain,
! [X0] :
( ~ midp(sK23_skl,X0,sK21_skl)
| ~ midp(sK22_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f201,f381]) ).
fof(f1516,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f1213]) ).
fof(f1543,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1516,f1126]) ).
fof(f1621,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ midp(X0,X1,X0)
| cong(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f1397,f643]) ).
fof(f1675,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cong(X2,X2,X0,X1)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1621,f151]) ).
fof(f1716,plain,
! [X0] :
( ~ sQ1_spl
| circle(X0,X0,X0,X0) ),
inference(resolution,[status(thm)],[f1400,f1403]) ).
fof(f1737,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X0,X2,X3,X2,X3) ),
inference(resolution,[status(thm)],[f1350,f1381]) ).
fof(f1770,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X0,X1,X2,X3,X3,X2) ),
inference(resolution,[status(thm)],[f1737,f142]) ).
fof(f1813,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X0,X2,X3,X3,X2) ),
inference(resolution,[status(thm)],[f1770,f138]) ).
fof(f1868,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f1213]) ).
fof(f1871,plain,
! [X0] :
( ~ sQ1_spl
| midp(X0,X0,X0)
| ~ circle(X0,X0,X0,X0) ),
inference(resolution,[status(thm)],[f1868,f1813]) ).
fof(f1902,plain,
! [X0] :
( ~ sQ1_spl
| midp(X0,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1871,f1716]) ).
fof(f1919,plain,
! [X0,X1] :
( ~ sQ1_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1902,f1543]) ).
fof(f1923,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cong(X0,X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1675,f1919]) ).
fof(f1928,plain,
! [X0,X1] :
( ~ sQ1_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1919,f122]) ).
fof(f1984,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| circle(X0,X0,X1,X2)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1923,f124]) ).
fof(f1985,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| circle(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1984,f1923]) ).
fof(f2077,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| perp(X1,X2,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f1213]) ).
fof(f2078,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f2077,f1985]) ).
fof(f2112,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ circle(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f211,f2078]) ).
fof(f2122,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cong(X2,X0,X2,X1)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2078,f230]) ).
fof(f2128,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cong(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2122,f1928]) ).
fof(f2130,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| circle(X0,X1,X3,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f124,f2128]) ).
fof(f2134,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2130,f2128]) ).
fof(f2189,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X0,X2,X3,X0,X3,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2112,f2134]) ).
fof(f2200,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[f2189,f186]) ).
fof(f2206,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2200,f1516]) ).
fof(f2212,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2206,f1919]) ).
fof(f2213,plain,
! [X0] :
( ~ sQ1_spl
| ~ midp(sK23_skl,X0,sK21_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1499,f2212]) ).
fof(f2218,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2213,f2212]) ).
fof(f2219,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f2218]) ).
fof(f2220,plain,
$false,
inference(sat_refutation,[status(thm)],[f1128,f1135,f2219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO653+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 18:12:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.102031 seconds
% 0.14/0.47 % CPU time: 0.496444 seconds
% 0.14/0.47 % Total memory used: 90.956 MB
% 0.14/0.47 % Net memory used: 90.171 MB
%------------------------------------------------------------------------------