%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO651+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 4.88s 1.46s
% Output : CNFRefutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 42
% Syntax : Number of formulae : 227 ( 14 unt; 11 def)
% Number of atoms : 609 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 665 ( 283 ~; 272 |; 67 &)
% ( 11 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 12 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 752 ( 734 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( para(A,C,F,D)
& perp(C,E,C,F)
& perp(B,C,MIDPNT3,E)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,E)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,E)
& midp(MIDPNT1,A,B)
& eqangle(A,C,C,D,D,C,C,B)
& coll(D,A,B) )
=> cong(C,F,D,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( para(A,C,F,D)
& perp(C,E,C,F)
& perp(B,C,MIDPNT3,E)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,E)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,E)
& midp(MIDPNT1,A,B)
& eqangle(A,C,C,D,D,C,C,B)
& coll(D,A,B) )
=> cong(C,F,D,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(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(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(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(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(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f206,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(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(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(f247,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f248,plain,
! [A,B,C,D] :
( para(A,C,B,D)
| ! [M] :
( ~ midp(M,C,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2,X3,X4] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
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(f272,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f273,plain,
! [A,B,C,D] :
( perp(A,B,C,D)
| ! [P,Q,U,V] :
( ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f272]) ).
fof(f274,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f273]) ).
fof(f369,plain,
? [A,B,C,D,E,F,MIDPNT1,MIDPNT2,MIDPNT3] :
( ~ cong(C,F,D,B)
& para(A,C,F,D)
& perp(C,E,C,F)
& perp(B,C,MIDPNT3,E)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,E)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,E)
& midp(MIDPNT1,A,B)
& eqangle(A,C,C,D,D,C,C,B)
& coll(D,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,C,D,F] :
( ~ cong(C,F,D,B)
& ? [A] :
( para(A,C,F,D)
& ? [E] :
( perp(C,E,C,F)
& ? [MIDPNT3] :
( perp(B,C,MIDPNT3,E)
& midp(MIDPNT3,B,C)
& ? [MIDPNT2] :
( perp(A,C,MIDPNT2,E)
& midp(MIDPNT2,A,C)
& ? [MIDPNT1] :
( perp(A,B,MIDPNT1,E)
& midp(MIDPNT1,A,B)
& eqangle(A,C,C,D,D,C,C,B)
& coll(D,A,B) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cong(sK21_skl,sK23_skl,sK22_skl,sK20_skl)
& para(sK24_skl,sK21_skl,sK23_skl,sK22_skl)
& perp(sK21_skl,sK25_skl,sK21_skl,sK23_skl)
& perp(sK20_skl,sK21_skl,sK26_skl,sK25_skl)
& midp(sK26_skl,sK20_skl,sK21_skl)
& perp(sK24_skl,sK21_skl,sK27_skl,sK25_skl)
& midp(sK27_skl,sK24_skl,sK21_skl)
& perp(sK24_skl,sK20_skl,sK28_skl,sK25_skl)
& midp(sK28_skl,sK24_skl,sK20_skl)
& eqangle(sK24_skl,sK21_skl,sK21_skl,sK22_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
& coll(sK22_skl,sK24_skl,sK20_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]),skolemize(B,sK20_skl),skolemize(C,sK21_skl),skolemize(D,sK22_skl),skolemize(F,sK23_skl),skolemize(A,sK24_skl),skolemize(E,sK25_skl),skolemize(MIDPNT3,sK26_skl),skolemize(MIDPNT2,sK27_skl),skolemize(MIDPNT1,sK28_skl)],[f370]) ).
fof(f373,plain,
eqangle(sK24_skl,sK21_skl,sK21_skl,sK22_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
midp(sK28_skl,sK24_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
perp(sK24_skl,sK20_skl,sK28_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f376,plain,
midp(sK27_skl,sK24_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ cong(sK21_skl,sK23_skl,sK22_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f396,plain,
midp(sK27_skl,sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f122,f376]) ).
fof(f397,plain,
midp(sK28_skl,sK20_skl,sK24_skl),
inference(resolution,[status(thm)],[f122,f374]) ).
fof(f497,plain,
perp(sK28_skl,sK25_skl,sK24_skl,sK20_skl),
inference(resolution,[status(thm)],[f114,f375]) ).
fof(f505,plain,
! [X0,X1] :
( para(X0,X1,sK28_skl,sK25_skl)
| ~ perp(X0,X1,sK24_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f117,f375]) ).
fof(f606,plain,
eqangle(sK21_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f138,f373]) ).
fof(f613,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f149,f260]) ).
fof(f620,plain,
! [X0,X1,X2] :
( ~ midp(X1,X2,X0)
| cong(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f151,f613]) ).
fof(f621,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f623,plain,
! [X0,X1,X2] :
( cong(X2,X0,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f620,f149]) ).
fof(f630,plain,
! [X0,X1,X2] :
( cong(X0,X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f621,f149]) ).
fof(f636,plain,
! [X0,X1,X2] :
( cong(X1,X0,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f623,f151]) ).
fof(f643,plain,
! [X0,X1,X2] :
( cong(X1,X0,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f630,f151]) ).
fof(f858,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(f860,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(f1117,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1117,f643]) ).
fof(f1222,plain,
para(sK28_skl,sK25_skl,sK28_skl,sK25_skl),
inference(resolution,[status(thm)],[f505,f497]) ).
fof(f2337,plain,
( perp(sK21_skl,sK24_skl,sK21_skl,sK22_skl)
| ~ perp(sK22_skl,sK21_skl,sK21_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f274,f606]) ).
fof(f2348,definition,
( sQ143_spl
<=> perp(sK22_skl,sK21_skl,sK21_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2350,plain,
( sQ143_spl
| ~ perp(sK22_skl,sK21_skl,sK21_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f2348]) ).
fof(f2359,definition,
( sQ146_spl
<=> perp(sK21_skl,sK24_skl,sK21_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2360,plain,
( ~ sQ146_spl
| perp(sK21_skl,sK24_skl,sK21_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f2359]) ).
fof(f2362,plain,
( sQ146_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f2337,f2348,f2359]) ).
fof(f2953,plain,
( ~ sQ146_spl
| cong(sK21_skl,sK21_skl,sK21_skl,sK22_skl)
| ~ midp(sK24_skl,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f2360,f230]) ).
fof(f2957,definition,
( sQ163_spl
<=> midp(sK24_skl,sK21_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2959,plain,
( sQ163_spl
| ~ midp(sK24_skl,sK21_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f2957]) ).
fof(f2960,definition,
( sQ164_spl
<=> cong(sK21_skl,sK21_skl,sK21_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2961,plain,
( ~ sQ164_spl
| cong(sK21_skl,sK21_skl,sK21_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f2960]) ).
fof(f2963,plain,
( ~ sQ146_spl
| sQ164_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f2953,f2957,f2960,f2359]) ).
fof(f3117,definition,
( sQ181_spl
<=> cong(sK21_skl,sK22_skl,sK21_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f3118,plain,
( ~ sQ181_spl
| cong(sK21_skl,sK22_skl,sK21_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f3117]) ).
fof(f3181,definition,
! [X4,X5] :
( sQ187_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f3182,plain,
! [X0,X1] :
( ~ sQ187_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3181]) ).
fof(f3322,definition,
( sQ198_spl
<=> midp(sK21_skl,sK22_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f3323,plain,
( ~ sQ198_spl
| midp(sK21_skl,sK22_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f3322]) ).
fof(f3345,plain,
( ~ sQ181_spl
| midp(sK21_skl,sK22_skl,sK21_skl)
| ~ coll(sK21_skl,sK22_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f3118,f258]) ).
fof(f3354,definition,
( sQ201_spl
<=> coll(sK21_skl,sK22_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f3356,plain,
( sQ201_spl
| ~ coll(sK21_skl,sK22_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f3354]) ).
fof(f3357,plain,
( ~ sQ181_spl
| sQ198_spl
| ~ sQ201_spl ),
inference(split_clause,[status(thm)],[f3345,f3354,f3322,f3117]) ).
fof(f3459,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f860,f186]) ).
fof(f3467,definition,
! [X2,X3] :
( sQ206_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f3468,plain,
! [X0,X1] :
( ~ sQ206_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3467]) ).
fof(f3470,plain,
( sQ206_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f3459,f3181,f3467]) ).
fof(f3471,plain,
( ~ sQ187_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1222,f3182]) ).
fof(f3485,plain,
~ sQ187_spl,
inference(contradiction_clause,[status(thm)],[f3471]) ).
fof(f3488,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| midp(X0,X2,X2)
| ~ para(X1,X2,X1,X2)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3468,f252]) ).
fof(f3490,plain,
! [X0,X1] :
( ~ sQ206_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3468,f256]) ).
fof(f3494,plain,
! [X0,X1] :
( ~ sQ206_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f3468,f105]) ).
fof(f3495,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3488,f3468]) ).
fof(f3522,plain,
! [X0,X1] :
( ~ sQ206_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3490,f100]) ).
fof(f3524,plain,
( sQ201_spl
| ~ sQ206_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3356,f3522]) ).
fof(f3552,plain,
! [X0,X1] :
( ~ sQ206_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3522,f98]) ).
fof(f3553,plain,
( sQ201_spl
| ~ sQ206_spl ),
inference(contradiction_clause,[status(thm)],[f3524]) ).
fof(f3555,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3552,f103]) ).
fof(f3558,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3555,f3552]) ).
fof(f3563,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3558]) ).
fof(f3564,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3558]) ).
fof(f3565,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ206_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f3558]) ).
fof(f3703,plain,
( ~ sQ198_spl
| midp(sK21_skl,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f3323,f122]) ).
fof(f3869,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ midp(X1,X0,X0)
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3563,f636]) ).
fof(f3926,plain,
( ~ sQ164_spl
| cong(sK21_skl,sK22_skl,sK21_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f2961,f151]) ).
fof(f4068,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3564,f858]) ).
fof(f4078,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4068,f3468]) ).
fof(f4099,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3565,f3494]) ).
fof(f4112,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4078,f136]) ).
fof(f4116,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4112,f4078]) ).
fof(f4123,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ206_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,f4116]) ).
fof(f4124,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f4116]) ).
fof(f4125,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f4116]) ).
fof(f4126,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ206_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)],[f4123,f4116]) ).
fof(f4240,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ206_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f4126,f4116]) ).
fof(f4331,plain,
( ~ sQ198_spl
| ~ sQ206_spl
| midp(sK22_skl,sK21_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f4099,f3703]) ).
fof(f4342,plain,
( ~ sQ206_spl
| midp(sK24_skl,sK21_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f4099,f396]) ).
fof(f4353,plain,
! [X0] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(sK22_skl,X0,X0) ),
inference(resolution,[status(thm)],[f4331,f3495]) ).
fof(f4356,plain,
! [X0] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,sK22_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f4353,f3869]) ).
fof(f4393,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4356,f3495]) ).
fof(f4396,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4393,f4099]) ).
fof(f4398,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ sQ198_spl
| para(X0,X0,X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1147,f4396]) ).
fof(f4404,plain,
! [X0,X1] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4396,f122]) ).
fof(f4420,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4398,f3565]) ).
fof(f4426,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ sQ198_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4420,f4404]) ).
fof(f4434,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ206_spl
| ~ sQ198_spl
| para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f249,f4426]) ).
fof(f4465,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| ~ sQ198_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4434,f4426]) ).
fof(f4505,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ206_spl
| ~ sQ198_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f858,f4465]) ).
fof(f4517,definition,
! [X0,X1] :
( sQ237_spl
<=> ~ midp(X0,sK24_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f4518,plain,
! [X0,X1] :
( ~ sQ237_spl
| ~ midp(X0,sK24_skl,X1) ),
inference(component_clause,[status(thm)],[f4517]) ).
fof(f4520,definition,
! [X2,X3,X4] :
( sQ238_spl
<=> ~ midp(X2,X3,X4) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f4521,plain,
! [X0,X1,X2] :
( ~ sQ238_spl
| ~ midp(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f4520]) ).
fof(f4550,plain,
! [X0,X1] :
( ~ sQ206_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4124,f4240]) ).
fof(f4631,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ sQ198_spl
| cong(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f4505,f4240]) ).
fof(f4638,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| ~ sQ198_spl
| cong(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4631,f151]) ).
fof(f4640,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ206_spl
| ~ sQ198_spl
| cong(X0,X1,X3,X4)
| ~ cong(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f4638,f154]) ).
fof(f4643,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| ~ sQ198_spl
| cong(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4640,f4631]) ).
fof(f4645,plain,
( ~ sQ206_spl
| ~ sQ198_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f382,f4643]) ).
fof(f4646,plain,
( ~ sQ206_spl
| ~ sQ198_spl ),
inference(contradiction_clause,[status(thm)],[f4645]) ).
fof(f4662,plain,
( ~ sQ164_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f3926,f3117,f2960]) ).
fof(f5019,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4125,f4550]) ).
fof(f5022,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f5019,f4550]) ).
fof(f5038,plain,
( sQ143_spl
| ~ sQ206_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2350,f5022]) ).
fof(f5043,plain,
( sQ143_spl
| ~ sQ206_spl ),
inference(contradiction_clause,[status(thm)],[f5038]) ).
fof(f5081,plain,
( ~ sQ237_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f374,f4518]) ).
fof(f5090,plain,
~ sQ237_spl,
inference(contradiction_clause,[status(thm)],[f5081]) ).
fof(f5091,plain,
( ~ sQ238_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f397,f4521]) ).
fof(f5107,plain,
~ sQ238_spl,
inference(contradiction_clause,[status(thm)],[f5091]) ).
fof(f5144,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f232,f4550]) ).
fof(f5145,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f5144,f4550]) ).
fof(f5163,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f5145,f114]) ).
fof(f5293,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ206_spl
| para(X0,X1,X3,X4)
| ~ perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f117,f5145]) ).
fof(f5298,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5293,f5163]) ).
fof(f5471,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ206_spl
| midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3565,f5298]) ).
fof(f5478,plain,
! [X0,X1] :
( ~ sQ206_spl
| midp(X0,sK21_skl,X1) ),
inference(resolution,[status(thm)],[f5471,f4342]) ).
fof(f5516,plain,
( sQ163_spl
| ~ sQ206_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2959,f5478]) ).
fof(f5521,plain,
( sQ163_spl
| ~ sQ206_spl ),
inference(contradiction_clause,[status(thm)],[f5516]) ).
fof(f5522,plain,
$false,
inference(sat_refutation,[status(thm)],[f2362,f2963,f3357,f3470,f3485,f3553,f4646,f4662,f5043,f5090,f5107,f5521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO651+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 18:18:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.41 % Drodi V4.1.1
% 4.88/1.46 % Refutation found
% 4.88/1.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.88/1.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.88/1.50 % Elapsed time: 1.112124 seconds
% 4.88/1.50 % CPU time: 8.167410 seconds
% 4.88/1.50 % Total memory used: 130.849 MB
% 4.88/1.50 % Net memory used: 125.644 MB
%------------------------------------------------------------------------------