%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO625+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 : n013.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 12:25:24 PM UTC 2026
% Result : Theorem 7.24s 1.40s
% Output : CNFRefutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 49
% Syntax : Number of formulae : 258 ( 49 unt; 20 def)
% Number of atoms : 615 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 615 ( 258 ~; 248 |; 59 &)
% ( 20 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 21 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 734 ( 714 !; 20 ?)
% 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(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(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(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/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(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/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(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
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(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(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
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,I,C1,A1,B1,P,Q,N] :
( ( circle(N,P,A1,Q)
& midp(Q,C,I)
& midp(P,I,B)
& midp(B1,A,C)
& midp(A1,C,B)
& midp(C1,B,A)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> eqangle(B1,A1,A1,N,N,A1,A1,C1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,I,C1,A1,B1,P,Q,N] :
( ( circle(N,P,A1,Q)
& midp(Q,C,I)
& midp(P,I,B)
& midp(B1,A,C)
& midp(A1,C,B)
& midp(C1,B,A)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) )
=> eqangle(B1,A1,A1,N,N,A1,A1,C1) ),
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(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(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(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(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(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(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(f269,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f270,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q,U,V] :
( ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f270]) ).
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,I,C1,A1,B1,P,Q,N] :
( ~ eqangle(B1,A1,A1,N,N,A1,A1,C1)
& circle(N,P,A1,Q)
& midp(Q,C,I)
& midp(P,I,B)
& midp(B1,A,C)
& midp(A1,C,B)
& midp(C1,B,A)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [C1,A1,B1,N] :
( ~ eqangle(B1,A1,A1,N,N,A1,A1,C1)
& ? [P,Q] :
( circle(N,P,A1,Q)
& ? [C,I] :
( midp(Q,C,I)
& ? [B] :
( midp(P,I,B)
& ? [A] :
( midp(B1,A,C)
& midp(A1,C,B)
& midp(C1,B,A)
& eqangle(I,C,C,A,I,C,C,B)
& eqangle(I,B,B,C,I,B,B,A)
& eqangle(I,A,A,B,I,A,A,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK22_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK20_skl)
& circle(sK23_skl,sK24_skl,sK21_skl,sK25_skl)
& midp(sK25_skl,sK26_skl,sK27_skl)
& midp(sK24_skl,sK27_skl,sK28_skl)
& midp(sK22_skl,sK29_skl,sK26_skl)
& midp(sK21_skl,sK26_skl,sK28_skl)
& midp(sK20_skl,sK28_skl,sK29_skl)
& eqangle(sK27_skl,sK26_skl,sK26_skl,sK29_skl,sK27_skl,sK26_skl,sK26_skl,sK28_skl)
& eqangle(sK27_skl,sK28_skl,sK28_skl,sK26_skl,sK27_skl,sK28_skl,sK28_skl,sK29_skl)
& eqangle(sK27_skl,sK29_skl,sK29_skl,sK28_skl,sK27_skl,sK29_skl,sK29_skl,sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(C1,sK20_skl),skolemize(A1,sK21_skl),skolemize(B1,sK22_skl),skolemize(N,sK23_skl),skolemize(P,sK24_skl),skolemize(Q,sK25_skl),skolemize(C,sK26_skl),skolemize(I,sK27_skl),skolemize(B,sK28_skl),skolemize(A,sK29_skl)],[f370]) ).
fof(f372,plain,
eqangle(sK27_skl,sK29_skl,sK29_skl,sK28_skl,sK27_skl,sK29_skl,sK29_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
eqangle(sK27_skl,sK28_skl,sK28_skl,sK26_skl,sK27_skl,sK28_skl,sK28_skl,sK29_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
eqangle(sK27_skl,sK26_skl,sK26_skl,sK29_skl,sK27_skl,sK26_skl,sK26_skl,sK28_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
midp(sK20_skl,sK28_skl,sK29_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
midp(sK24_skl,sK27_skl,sK28_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ eqangle(sK22_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f383,plain,
midp(sK24_skl,sK28_skl,sK27_skl),
inference(resolution,[status(thm)],[f122,f378]) ).
fof(f386,plain,
midp(sK20_skl,sK29_skl,sK28_skl),
inference(resolution,[status(thm)],[f122,f375]) ).
fof(f393,plain,
eqangle(sK28_skl,sK27_skl,sK28_skl,sK26_skl,sK27_skl,sK28_skl,sK28_skl,sK29_skl),
inference(resolution,[status(thm)],[f373,f138]) ).
fof(f414,plain,
eqangle(sK26_skl,sK29_skl,sK27_skl,sK26_skl,sK26_skl,sK28_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f140,f374]) ).
fof(f415,plain,
eqangle(sK28_skl,sK26_skl,sK27_skl,sK28_skl,sK28_skl,sK29_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f140,f373]) ).
fof(f416,plain,
eqangle(sK29_skl,sK28_skl,sK27_skl,sK29_skl,sK29_skl,sK26_skl,sK27_skl,sK29_skl),
inference(resolution,[status(thm)],[f140,f372]) ).
fof(f452,plain,
eqangle(sK27_skl,sK29_skl,sK27_skl,sK29_skl,sK29_skl,sK28_skl,sK29_skl,sK26_skl),
inference(resolution,[status(thm)],[f144,f372]) ).
fof(f520,plain,
eqangle(sK28_skl,sK27_skl,sK27_skl,sK28_skl,sK28_skl,sK26_skl,sK28_skl,sK29_skl),
inference(resolution,[status(thm)],[f393,f144]) ).
fof(f521,plain,
eqangle(sK27_skl,sK28_skl,sK28_skl,sK29_skl,sK28_skl,sK27_skl,sK28_skl,sK26_skl),
inference(resolution,[status(thm)],[f393,f142]) ).
fof(f738,plain,
( perp(sK27_skl,sK28_skl,sK28_skl,sK26_skl)
| ~ perp(sK27_skl,sK28_skl,sK28_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f274,f373]) ).
fof(f764,definition,
( sQ8_spl
<=> perp(sK27_skl,sK28_skl,sK28_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f767,definition,
( sQ9_spl
<=> perp(sK28_skl,sK27_skl,sK28_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f769,plain,
( sQ9_spl
| ~ perp(sK28_skl,sK27_skl,sK28_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f789,definition,
( sQ15_spl
<=> perp(sK27_skl,sK28_skl,sK28_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( ~ sQ15_spl
| perp(sK27_skl,sK28_skl,sK28_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f792,plain,
( sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f738,f764,f789]) ).
fof(f877,plain,
para(sK26_skl,sK29_skl,sK26_skl,sK28_skl),
inference(resolution,[status(thm)],[f186,f414]) ).
fof(f878,plain,
para(sK28_skl,sK26_skl,sK28_skl,sK29_skl),
inference(resolution,[status(thm)],[f186,f415]) ).
fof(f879,plain,
para(sK29_skl,sK28_skl,sK29_skl,sK26_skl),
inference(resolution,[status(thm)],[f186,f416]) ).
fof(f888,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X4,X5,X6,X7,X2,X3,X8,X9)
| ~ eqangle(X4,X5,X6,X7,X0,X1,X8,X9)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f147]) ).
fof(f889,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(f891,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(f902,definition,
( sQ23_spl
<=> perp(sK28_skl,sK26_skl,sK28_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( sQ23_spl
| ~ perp(sK28_skl,sK26_skl,sK28_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f902]) ).
fof(f973,plain,
para(sK26_skl,sK28_skl,sK26_skl,sK29_skl),
inference(resolution,[status(thm)],[f877,f107]) ).
fof(f974,plain,
para(sK26_skl,sK29_skl,sK28_skl,sK26_skl),
inference(resolution,[status(thm)],[f877,f105]) ).
fof(f1067,plain,
para(sK28_skl,sK29_skl,sK28_skl,sK26_skl),
inference(resolution,[status(thm)],[f878,f107]) ).
fof(f1068,plain,
para(sK28_skl,sK26_skl,sK29_skl,sK28_skl),
inference(resolution,[status(thm)],[f878,f105]) ).
fof(f1071,plain,
para(sK29_skl,sK26_skl,sK29_skl,sK28_skl),
inference(resolution,[status(thm)],[f879,f107]) ).
fof(f1072,plain,
para(sK29_skl,sK28_skl,sK26_skl,sK29_skl),
inference(resolution,[status(thm)],[f879,f105]) ).
fof(f1363,plain,
para(sK26_skl,sK28_skl,sK29_skl,sK26_skl),
inference(resolution,[status(thm)],[f973,f105]) ).
fof(f1366,plain,
para(sK28_skl,sK26_skl,sK26_skl,sK29_skl),
inference(resolution,[status(thm)],[f974,f107]) ).
fof(f1419,definition,
( sQ70_spl
<=> para(sK29_skl,sK26_skl,sK29_skl,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1421,plain,
( sQ70_spl
| ~ para(sK29_skl,sK26_skl,sK29_skl,sK28_skl) ),
inference(component_clause,[status(thm)],[f1419]) ).
fof(f1426,definition,
( sQ72_spl
<=> para(sK28_skl,sK29_skl,sK28_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( sQ72_spl
| ~ para(sK28_skl,sK29_skl,sK28_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f1426]) ).
fof(f1477,plain,
para(sK28_skl,sK29_skl,sK26_skl,sK28_skl),
inference(resolution,[status(thm)],[f1067,f105]) ).
fof(f1490,plain,
para(sK29_skl,sK28_skl,sK28_skl,sK26_skl),
inference(resolution,[status(thm)],[f1068,f107]) ).
fof(f1542,definition,
( sQ85_spl
<=> para(sK29_skl,sK28_skl,sK29_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1544,plain,
( sQ85_spl
| ~ para(sK29_skl,sK28_skl,sK29_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f1542]) ).
fof(f1546,plain,
( sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1544,f879]) ).
fof(f1547,plain,
sQ85_spl,
inference(contradiction_clause,[status(thm)],[f1546]) ).
fof(f1551,plain,
para(sK26_skl,sK29_skl,sK29_skl,sK28_skl),
inference(resolution,[status(thm)],[f1072,f107]) ).
fof(f1653,plain,
( para(sK27_skl,sK29_skl,sK27_skl,sK29_skl)
| ~ para(sK29_skl,sK28_skl,sK29_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f271,f452]) ).
fof(f1735,definition,
( sQ107_spl
<=> para(sK27_skl,sK29_skl,sK27_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1736,plain,
( ~ sQ107_spl
| para(sK27_skl,sK29_skl,sK27_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f1735]) ).
fof(f1738,plain,
( sQ107_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f1653,f1542,f1735]) ).
fof(f1888,plain,
para(sK29_skl,sK26_skl,sK26_skl,sK28_skl),
inference(resolution,[status(thm)],[f1363,f107]) ).
fof(f1901,plain,
para(sK28_skl,sK26_skl,sK29_skl,sK26_skl),
inference(resolution,[status(thm)],[f1366,f105]) ).
fof(f1911,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1428,f1067]) ).
fof(f1912,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f1911]) ).
fof(f1913,plain,
( sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1421,f1071]) ).
fof(f1914,plain,
sQ70_spl,
inference(contradiction_clause,[status(thm)],[f1913]) ).
fof(f1985,plain,
para(sK26_skl,sK28_skl,sK28_skl,sK29_skl),
inference(resolution,[status(thm)],[f1477,f107]) ).
fof(f1998,plain,
para(sK29_skl,sK28_skl,sK26_skl,sK28_skl),
inference(resolution,[status(thm)],[f1490,f105]) ).
fof(f2040,plain,
para(sK26_skl,sK29_skl,sK28_skl,sK29_skl),
inference(resolution,[status(thm)],[f1551,f105]) ).
fof(f2098,plain,
( perp(sK28_skl,sK27_skl,sK27_skl,sK28_skl)
| ~ perp(sK28_skl,sK26_skl,sK28_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f520,f274]) ).
fof(f2108,definition,
( sQ129_spl
<=> perp(sK28_skl,sK27_skl,sK27_skl,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2109,plain,
( ~ sQ129_spl
| perp(sK28_skl,sK27_skl,sK27_skl,sK28_skl) ),
inference(component_clause,[status(thm)],[f2108]) ).
fof(f2111,plain,
( sQ129_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2098,f902,f2108]) ).
fof(f2365,plain,
( perp(sK27_skl,sK28_skl,sK28_skl,sK29_skl)
| ~ perp(sK28_skl,sK27_skl,sK28_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f521,f274]) ).
fof(f2372,plain,
( sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2365,f767,f764]) ).
fof(f2507,plain,
! [X0,X1] :
( ~ sQ15_spl
| para(X0,X1,sK28_skl,sK26_skl)
| ~ perp(X0,X1,sK27_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f790,f117]) ).
fof(f2566,plain,
para(sK29_skl,sK26_skl,sK28_skl,sK26_skl),
inference(resolution,[status(thm)],[f1888,f105]) ).
fof(f2584,definition,
( sQ156_spl
<=> para(sK28_skl,sK26_skl,sK29_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2586,plain,
( sQ156_spl
| ~ para(sK28_skl,sK26_skl,sK29_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f2584]) ).
fof(f2588,plain,
( sQ156_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2586,f1901]) ).
fof(f2589,plain,
sQ156_spl,
inference(contradiction_clause,[status(thm)],[f2588]) ).
fof(f2692,plain,
para(sK26_skl,sK28_skl,sK29_skl,sK28_skl),
inference(resolution,[status(thm)],[f1985,f105]) ).
fof(f2722,definition,
( sQ165_spl
<=> para(sK29_skl,sK28_skl,sK26_skl,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2724,plain,
( sQ165_spl
| ~ para(sK29_skl,sK28_skl,sK26_skl,sK28_skl) ),
inference(component_clause,[status(thm)],[f2722]) ).
fof(f2726,plain,
( sQ165_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2724,f1998]) ).
fof(f2727,plain,
sQ165_spl,
inference(contradiction_clause,[status(thm)],[f2726]) ).
fof(f2778,definition,
( sQ172_spl
<=> para(sK26_skl,sK29_skl,sK28_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2780,plain,
( sQ172_spl
| ~ para(sK26_skl,sK29_skl,sK28_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f2778]) ).
fof(f2782,plain,
( sQ172_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2780,f2040]) ).
fof(f2783,plain,
sQ172_spl,
inference(contradiction_clause,[status(thm)],[f2782]) ).
fof(f2838,plain,
! [X0] :
( ~ sQ129_spl
| cong(sK28_skl,X0,sK27_skl,X0)
| ~ midp(X0,sK28_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f2109,f222]) ).
fof(f3270,definition,
! [X4,X5] :
( sQ218_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3271,plain,
! [X0,X1] :
( ~ sQ218_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3270]) ).
fof(f3316,plain,
( ~ sQ107_spl
| ~ sQ218_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1736,f3271]) ).
fof(f3322,plain,
( ~ sQ107_spl
| ~ sQ218_spl ),
inference(contradiction_clause,[status(thm)],[f3316]) ).
fof(f3367,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f891,f186]) ).
fof(f3379,definition,
! [X2,X3] :
( sQ221_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f3380,plain,
! [X0,X1] :
( ~ sQ221_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3379]) ).
fof(f3382,plain,
( sQ221_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f3367,f3270,f3379]) ).
fof(f3393,plain,
! [X0,X1] :
( ~ sQ221_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3380,f256]) ).
fof(f3409,plain,
! [X0,X1] :
( ~ sQ221_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3393,f100]) ).
fof(f3425,plain,
! [X0,X1] :
( ~ sQ221_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3409,f98]) ).
fof(f3430,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3425,f103]) ).
fof(f3436,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3430,f3425]) ).
fof(f3479,plain,
! [X0,X1,X2,X3] :
( ~ sQ221_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3436]) ).
fof(f3480,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3436]) ).
fof(f3562,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3479,f889]) ).
fof(f3579,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3562,f3380]) ).
fof(f3600,plain,
! [X0,X1,X2,X3] :
( ~ sQ221_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3579,f136]) ).
fof(f3613,plain,
! [X0,X1,X2,X3] :
( ~ sQ221_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3600,f3579]) ).
fof(f3647,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ221_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,f3613]) ).
fof(f3648,plain,
! [X0,X1,X2,X3] :
( ~ sQ221_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3613]) ).
fof(f3650,plain,
! [X0,X1,X2,X3] :
( ~ sQ221_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3613]) ).
fof(f3651,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ221_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)],[f3647,f3613]) ).
fof(f3871,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ221_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3651,f3613]) ).
fof(f3895,plain,
! [X0,X1] :
( ~ sQ221_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3648,f3871]) ).
fof(f3919,plain,
! [X0,X1] :
( ~ sQ221_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3895,f3480]) ).
fof(f3950,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3650,f3895]) ).
fof(f3953,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3950,f3895]) ).
fof(f3998,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| perp(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f3953,f114]) ).
fof(f4008,plain,
! [X0,X1,X2] :
( ~ sQ221_spl
| perp(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f3998,f112]) ).
fof(f4018,plain,
( sQ23_spl
| ~ sQ221_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f904,f4008]) ).
fof(f4027,plain,
( sQ23_spl
| ~ sQ221_spl ),
inference(contradiction_clause,[status(thm)],[f4018]) ).
fof(f4029,plain,
! [X0] :
( ~ sQ129_spl
| ~ sQ221_spl
| cong(sK28_skl,X0,sK27_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2838,f3919]) ).
fof(f4072,plain,
! [X0,X1] :
( ~ sQ129_spl
| ~ sQ221_spl
| perp(sK28_skl,sK27_skl,X0,X1)
| ~ cong(sK28_skl,X0,sK27_skl,X0) ),
inference(resolution,[status(thm)],[f4029,f232]) ).
fof(f4076,plain,
! [X0,X1] :
( ~ sQ129_spl
| ~ sQ221_spl
| perp(sK28_skl,sK27_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4072,f4029]) ).
fof(f4150,plain,
! [X0,X1] :
( ~ sQ129_spl
| ~ sQ221_spl
| perp(X0,X1,sK28_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f4076,f114]) ).
fof(f4194,plain,
! [X0,X1] :
( ~ sQ129_spl
| ~ sQ221_spl
| perp(X0,X1,sK27_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f4150,f112]) ).
fof(f4195,definition,
! [X0] :
( sQ235_spl
<=> ~ midp(X0,sK28_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f4196,plain,
! [X0] :
( ~ sQ235_spl
| ~ midp(X0,sK28_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f4195]) ).
fof(f4202,plain,
( ~ sQ235_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f4196]) ).
fof(f4208,plain,
~ sQ235_spl,
inference(contradiction_clause,[status(thm)],[f4202]) ).
fof(f4269,definition,
! [X0,X1] :
( sQ239_spl
<=> ~ midp(X0,sK29_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f4270,plain,
! [X0,X1] :
( ~ sQ239_spl
| ~ midp(X0,sK29_skl,X1) ),
inference(component_clause,[status(thm)],[f4269]) ).
fof(f4272,definition,
! [X2,X3] :
( sQ240_spl
<=> ~ midp(X2,X3,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f4273,plain,
! [X0,X1] :
( ~ sQ240_spl
| ~ midp(X0,X1,sK27_skl) ),
inference(component_clause,[status(thm)],[f4272]) ).
fof(f4278,plain,
( ~ sQ240_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f4273]) ).
fof(f4286,plain,
~ sQ240_spl,
inference(contradiction_clause,[status(thm)],[f4278]) ).
fof(f4287,plain,
( ~ sQ239_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f4270]) ).
fof(f4295,plain,
~ sQ239_spl,
inference(contradiction_clause,[status(thm)],[f4287]) ).
fof(f4322,definition,
! [X0] :
( sQ241_spl
<=> ~ midp(X0,sK27_skl,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f4323,plain,
! [X0] :
( ~ sQ241_spl
| ~ midp(X0,sK27_skl,sK28_skl) ),
inference(component_clause,[status(thm)],[f4322]) ).
fof(f4329,plain,
( ~ sQ241_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f378,f4323]) ).
fof(f4336,plain,
~ sQ241_spl,
inference(contradiction_clause,[status(thm)],[f4329]) ).
fof(f4637,definition,
( sQ248_spl
<=> para(sK29_skl,sK26_skl,sK28_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f4639,plain,
( sQ248_spl
| ~ para(sK29_skl,sK26_skl,sK28_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f4637]) ).
fof(f4641,plain,
( sQ248_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4639,f2566]) ).
fof(f4642,plain,
sQ248_spl,
inference(contradiction_clause,[status(thm)],[f4641]) ).
fof(f4689,definition,
( sQ251_spl
<=> para(sK26_skl,sK28_skl,sK29_skl,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f4691,plain,
( sQ251_spl
| ~ para(sK26_skl,sK28_skl,sK29_skl,sK28_skl) ),
inference(component_clause,[status(thm)],[f4689]) ).
fof(f4693,plain,
( sQ251_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4691,f2692]) ).
fof(f4694,plain,
sQ251_spl,
inference(contradiction_clause,[status(thm)],[f4693]) ).
fof(f4913,plain,
( sQ9_spl
| ~ sQ129_spl
| ~ sQ221_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f4076]) ).
fof(f4914,plain,
( sQ9_spl
| ~ sQ129_spl
| ~ sQ221_spl ),
inference(contradiction_clause,[status(thm)],[f4913]) ).
fof(f4916,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| para(X0,X1,sK28_skl,sK26_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2507,f4194]) ).
fof(f4982,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| para(sK28_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4916,f107]) ).
fof(f4999,plain,
! [X0,X1,X2,X3] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK28_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f4982,f110]) ).
fof(f5002,plain,
! [X0,X1,X2,X3] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4999,f4916]) ).
fof(f5016,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f889,f5002]) ).
fof(f5017,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(backward_subsumption_resolution,[status(thm)],[f888,f5002]) ).
fof(f5604,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f5017,f5016]) ).
fof(f6109,plain,
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f381,f5604]) ).
fof(f6110,plain,
( ~ sQ15_spl
| ~ sQ129_spl
| ~ sQ221_spl ),
inference(contradiction_clause,[status(thm)],[f6109]) ).
fof(f6111,plain,
$false,
inference(sat_refutation,[status(thm)],[f792,f1547,f1738,f1912,f1914,f2111,f2372,f2589,f2727,f2783,f3322,f3382,f4027,f4208,f4286,f4295,f4336,f4642,f4694,f4914,f6110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO625+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 18:02:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 7.24/1.40 % Refutation found
% 7.24/1.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.24/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.24/1.43 % Elapsed time: 1.043507 seconds
% 7.24/1.43 % CPU time: 7.932651 seconds
% 7.24/1.43 % Total memory used: 158.025 MB
% 7.24/1.43 % Net memory used: 149.063 MB
%------------------------------------------------------------------------------