%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO644+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 : n011.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 12:25:27 PM UTC 2026
% Result : Theorem 0.10s 0.49s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 45
% Syntax : Number of formulae : 246 ( 16 unt; 11 def)
% Number of atoms : 633 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 683 ( 296 ~; 285 |; 56 &)
% ( 11 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 12 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 769 ( 753 !; 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(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(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(f57,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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,A,C)
& coll(H,B,E)
& coll(G,D,F)
& coll(G,A,C)
& midp(F,B,A)
& midp(E,C,D)
& para(A,B,C,D)
& para(B,C,A,D) )
=> cong(A,G,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,A,C)
& coll(H,B,E)
& coll(G,D,F)
& coll(G,A,C)
& midp(F,B,A)
& midp(E,C,D)
& para(A,B,C,D)
& para(B,C,A,D) )
=> cong(A,G,G,H) ),
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(f118,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f119,plain,
! [A,B,E,F] :
( perp(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(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(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(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(f369,plain,
? [A,B,C,D,E,F,G,H] :
( ~ cong(A,G,G,H)
& coll(H,A,C)
& coll(H,B,E)
& coll(G,D,F)
& coll(G,A,C)
& midp(F,B,A)
& midp(E,C,D)
& para(A,B,C,D)
& para(B,C,A,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,G,H] :
( ~ cong(A,G,G,H)
& ? [C] :
( coll(H,A,C)
& ? [B,E] :
( coll(H,B,E)
& ? [D,F] :
( coll(G,D,F)
& coll(G,A,C)
& midp(F,B,A)
& midp(E,C,D)
& para(A,B,C,D)
& para(B,C,A,D) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cong(sK20_skl,sK21_skl,sK21_skl,sK22_skl)
& coll(sK22_skl,sK20_skl,sK23_skl)
& coll(sK22_skl,sK24_skl,sK25_skl)
& coll(sK21_skl,sK26_skl,sK27_skl)
& coll(sK21_skl,sK20_skl,sK23_skl)
& midp(sK27_skl,sK24_skl,sK20_skl)
& midp(sK25_skl,sK23_skl,sK26_skl)
& para(sK20_skl,sK24_skl,sK23_skl,sK26_skl)
& para(sK24_skl,sK23_skl,sK20_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]),skolemize(A,sK20_skl),skolemize(G,sK21_skl),skolemize(H,sK22_skl),skolemize(C,sK23_skl),skolemize(B,sK24_skl),skolemize(E,sK25_skl),skolemize(D,sK26_skl),skolemize(F,sK27_skl)],[f370]) ).
fof(f372,plain,
para(sK24_skl,sK23_skl,sK20_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
para(sK20_skl,sK24_skl,sK23_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
midp(sK27_skl,sK24_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
~ cong(sK20_skl,sK21_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f423,plain,
para(sK24_skl,sK23_skl,sK26_skl,sK20_skl),
inference(resolution,[status(thm)],[f105,f372]) ).
fof(f454,plain,
midp(sK27_skl,sK20_skl,sK24_skl),
inference(resolution,[status(thm)],[f122,f375]) ).
fof(f462,plain,
para(sK20_skl,sK26_skl,sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f107,f372]) ).
fof(f479,plain,
! [X0,X1] :
( para(X0,X1,sK23_skl,sK26_skl)
| ~ para(X0,X1,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f373,f110]) ).
fof(f481,plain,
para(sK20_skl,sK24_skl,sK26_skl,sK23_skl),
inference(resolution,[status(thm)],[f373,f105]) ).
fof(f506,plain,
! [X0,X1] :
( perp(sK20_skl,sK24_skl,X0,X1)
| ~ perp(sK23_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f120,f373]) ).
fof(f507,plain,
! [X0,X1] :
( perp(sK24_skl,sK23_skl,X0,X1)
| ~ perp(sK26_skl,sK20_skl,X0,X1) ),
inference(resolution,[status(thm)],[f120,f423]) ).
fof(f509,plain,
! [X0,X1] :
( perp(sK20_skl,sK26_skl,X0,X1)
| ~ perp(sK24_skl,sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f462,f120]) ).
fof(f519,plain,
para(sK26_skl,sK23_skl,sK20_skl,sK24_skl),
inference(resolution,[status(thm)],[f481,f107]) ).
fof(f604,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f614,plain,
! [X0,X1,X2] :
( cong(X0,X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f604,f149]) ).
fof(f633,plain,
! [X0,X1,X2] :
( cong(X1,X0,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f614,f151]) ).
fof(f648,plain,
~ midp(sK21_skl,sK20_skl,sK22_skl),
inference(resolution,[status(thm)],[f633,f380]) ).
fof(f736,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(f737,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f138]) ).
fof(f883,plain,
! [X0] :
( midp(sK23_skl,X0,sK26_skl)
| ~ coll(sK23_skl,X0,sK26_skl)
| ~ midp(sK24_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f204,f372]) ).
fof(f962,plain,
para(sK26_skl,sK23_skl,sK23_skl,sK26_skl),
inference(resolution,[status(thm)],[f479,f519]) ).
fof(f991,plain,
para(sK26_skl,sK23_skl,sK26_skl,sK23_skl),
inference(resolution,[status(thm)],[f962,f105]) ).
fof(f1151,plain,
! [X0] :
( midp(X0,sK26_skl,sK23_skl)
| ~ para(sK24_skl,sK26_skl,sK20_skl,sK23_skl)
| ~ midp(X0,sK24_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f252,f372]) ).
fof(f1315,definition,
! [X0] :
( sQ46_spl
<=> ( midp(X0,sK26_skl,sK23_skl)
| ~ midp(X0,sK24_skl,sK20_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1316,plain,
! [X0] :
( ~ sQ46_spl
| midp(X0,sK26_skl,sK23_skl)
| ~ midp(X0,sK24_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f1315]) ).
fof(f1318,definition,
( sQ47_spl
<=> para(sK24_skl,sK26_skl,sK20_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1320,plain,
( sQ47_spl
| ~ para(sK24_skl,sK26_skl,sK20_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f1318]) ).
fof(f1321,plain,
( ~ sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1151,f1315,f1318]) ).
fof(f1955,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f736,f186]) ).
fof(f1956,definition,
! [X0,X1] :
( sQ48_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1957,plain,
! [X0,X1] :
( ~ sQ48_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1956]) ).
fof(f1959,definition,
! [X2,X3] :
( sQ49_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1960,plain,
! [X0,X1] :
( ~ sQ49_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1959]) ).
fof(f1962,plain,
( sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1955,f1956,f1959]) ).
fof(f1976,plain,
( ~ sQ48_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f991,f1957]) ).
fof(f1982,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f1976]) ).
fof(f1985,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| midp(X0,X2,X2)
| ~ para(X1,X2,X1,X2)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1960,f252]) ).
fof(f1987,plain,
! [X0,X1] :
( ~ sQ49_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1960,f256]) ).
fof(f1991,plain,
! [X0,X1] :
( ~ sQ49_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f1960,f105]) ).
fof(f1992,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1985,f1960]) ).
fof(f2031,plain,
! [X0,X1] :
( ~ sQ49_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1987,f100]) ).
fof(f2072,plain,
! [X0,X1] :
( ~ sQ49_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2031,f98]) ).
fof(f2074,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2072,f103]) ).
fof(f2077,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2074,f2072]) ).
fof(f2078,plain,
! [X0] :
( ~ sQ49_spl
| midp(sK23_skl,X0,sK26_skl)
| ~ midp(sK24_skl,X0,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f883,f2077]) ).
fof(f2080,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2077]) ).
fof(f2081,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f2077]) ).
fof(f2113,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| ~ para(X0,X2,X2,X0)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f2080,f737]) ).
fof(f2119,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2113,f1991]) ).
fof(f2132,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f2119,f131]) ).
fof(f2135,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f2132,f133]) ).
fof(f2141,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2135,f129]) ).
fof(f2147,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2141,f136]) ).
fof(f2151,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2147,f2141]) ).
fof(f2157,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ49_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,f2151]) ).
fof(f2158,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2151]) ).
fof(f2159,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ49_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)],[f2157,f2151]) ).
fof(f2180,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f2151]) ).
fof(f2194,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X2,X1,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2158,f144]) ).
fof(f2197,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f2158,f138]) ).
fof(f2207,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X2,X0,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2194,f138]) ).
fof(f2216,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X2,X0,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f2197,f140]) ).
fof(f2226,plain,
! [X0,X1,X2,X3] :
( ~ sQ49_spl
| eqangle(X0,X1,X1,X2,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2207,f140]) ).
fof(f2289,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ49_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2159,f2151]) ).
fof(f2290,plain,
! [X0,X1] :
( ~ sQ49_spl
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[f2289,f2226]) ).
fof(f2292,plain,
! [X0,X1] :
( ~ sQ49_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2289,f2216]) ).
fof(f2307,plain,
! [X0] :
( ~ sQ49_spl
| midp(X0,X0,X0) ),
inference(resolution,[status(thm)],[f2290,f2081]) ).
fof(f2315,plain,
! [X0,X1] :
( ~ sQ49_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2307,f1992]) ).
fof(f2318,plain,
( ~ sQ49_spl
| midp(sK23_skl,sK20_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f2315,f2078]) ).
fof(f2320,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2292,f2180]) ).
fof(f2329,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2320,f2292]) ).
fof(f2334,plain,
! [X0] :
( ~ sQ49_spl
| perp(sK20_skl,sK24_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f2329,f506]) ).
fof(f2338,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| perp(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f2329,f112]) ).
fof(f2358,plain,
! [X0] :
( ~ sQ49_spl
| perp(sK20_skl,sK24_skl,X0,sK26_skl) ),
inference(resolution,[status(thm)],[f2338,f506]) ).
fof(f2399,plain,
! [X0] :
( ~ sQ49_spl
| perp(sK26_skl,X0,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2334,f114]) ).
fof(f2421,plain,
! [X0] :
( ~ sQ49_spl
| perp(X0,sK26_skl,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2358,f114]) ).
fof(f2443,plain,
! [X0] :
( ~ sQ49_spl
| cong(sK26_skl,sK20_skl,sK26_skl,sK24_skl)
| ~ midp(X0,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2399,f230]) ).
fof(f2447,definition,
! [X0] :
( sQ52_spl
<=> ~ midp(X0,sK20_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2448,plain,
! [X0] :
( ~ sQ52_spl
| ~ midp(X0,sK20_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f2447]) ).
fof(f2450,definition,
( sQ53_spl
<=> cong(sK26_skl,sK20_skl,sK26_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f2451,plain,
( ~ sQ53_spl
| cong(sK26_skl,sK20_skl,sK26_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f2450]) ).
fof(f2453,plain,
( ~ sQ49_spl
| sQ53_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f2443,f2447,f2450,f1959]) ).
fof(f2454,plain,
( ~ sQ52_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f454,f2448]) ).
fof(f2455,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f2454]) ).
fof(f2493,definition,
! [X0] :
( sQ57_spl
<=> cong(X0,sK20_skl,X0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2494,plain,
! [X0] :
( ~ sQ57_spl
| cong(X0,sK20_skl,X0,sK24_skl) ),
inference(component_clause,[status(thm)],[f2493]) ).
fof(f2518,plain,
! [X0] :
( ~ sQ49_spl
| cong(X0,sK20_skl,X0,sK24_skl)
| ~ midp(sK26_skl,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2421,f230]) ).
fof(f2522,definition,
( sQ59_spl
<=> midp(sK26_skl,sK20_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2524,plain,
( sQ59_spl
| ~ midp(sK26_skl,sK20_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f2522]) ).
fof(f2525,plain,
( ~ sQ49_spl
| sQ57_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f2518,f2522,f2493,f1959]) ).
fof(f2526,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ57_spl
| midp(X0,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2494,f2081]) ).
fof(f2533,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ57_spl
| midp(X0,sK24_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f2526,f122]) ).
fof(f2534,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ49_spl
| ~ sQ57_spl
| midp(X0,sK26_skl,sK23_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1316,f2533]) ).
fof(f2538,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ49_spl
| ~ sQ57_spl
| midp(X0,sK23_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f2534,f122]) ).
fof(f2631,definition,
! [X0] :
( sQ60_spl
<=> ~ midp(X0,sK24_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2632,plain,
! [X0] :
( ~ sQ60_spl
| ~ midp(X0,sK24_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f2631]) ).
fof(f2698,plain,
( ~ sQ60_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f375,f2632]) ).
fof(f2699,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f2698]) ).
fof(f2920,plain,
( ~ sQ49_spl
| ~ sQ53_spl
| midp(sK26_skl,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2451,f2081]) ).
fof(f2927,plain,
( ~ sQ49_spl
| ~ sQ53_spl
| sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2920,f2524]) ).
fof(f2928,plain,
( ~ sQ49_spl
| ~ sQ53_spl
| sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f2927]) ).
fof(f3050,plain,
! [X0] :
( ~ sQ49_spl
| perp(sK20_skl,sK26_skl,X0,sK23_skl) ),
inference(resolution,[status(thm)],[f509,f2338]) ).
fof(f3062,plain,
! [X0] :
( ~ sQ49_spl
| perp(X0,sK23_skl,sK20_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3050,f114]) ).
fof(f3129,plain,
! [X0] :
( ~ sQ49_spl
| cong(X0,sK20_skl,X0,sK26_skl)
| ~ midp(sK23_skl,sK20_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3062,f230]) ).
fof(f3133,definition,
( sQ81_spl
<=> midp(sK23_skl,sK20_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3135,plain,
( sQ81_spl
| ~ midp(sK23_skl,sK20_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f3133]) ).
fof(f3136,definition,
! [X0] :
( sQ82_spl
<=> cong(X0,sK20_skl,X0,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3137,plain,
! [X0] :
( ~ sQ82_spl
| cong(X0,sK20_skl,X0,sK26_skl) ),
inference(component_clause,[status(thm)],[f3136]) ).
fof(f3139,plain,
( ~ sQ49_spl
| sQ82_spl
| ~ sQ81_spl ),
inference(split_clause,[status(thm)],[f3129,f3133,f3136,f1959]) ).
fof(f3140,plain,
( sQ81_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3135,f2318]) ).
fof(f3141,plain,
( sQ81_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f3140]) ).
fof(f3147,plain,
! [X0] :
( ~ sQ82_spl
| cong(X0,sK20_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f3137,f149]) ).
fof(f3164,plain,
! [X0] :
( ~ sQ82_spl
| cong(sK26_skl,X0,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f3147,f151]) ).
fof(f3181,plain,
! [X0] :
( ~ sQ82_spl
| cong(sK26_skl,X0,sK20_skl,X0) ),
inference(resolution,[status(thm)],[f3164,f149]) ).
fof(f3191,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(sK26_skl,sK20_skl,X0,X1)
| ~ cong(sK26_skl,X0,sK20_skl,X0) ),
inference(resolution,[status(thm)],[f3181,f232]) ).
fof(f3196,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(sK26_skl,sK20_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3191,f3181]) ).
fof(f3203,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(sK24_skl,sK23_skl,X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f507,f3196]) ).
fof(f3217,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(X0,X1,sK24_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f3203,f114]) ).
fof(f3244,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(X0,X1,sK23_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f3217,f112]) ).
fof(f3248,plain,
! [X0,X1] :
( ~ sQ82_spl
| perp(sK23_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3244,f114]) ).
fof(f3255,plain,
! [X0,X1,X2,X3] :
( ~ sQ82_spl
| para(X0,X1,X2,X3)
| ~ perp(X0,X1,sK23_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f3248,f117]) ).
fof(f3257,plain,
! [X0,X1,X2,X3] :
( ~ sQ82_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3255,f3244]) ).
fof(f3264,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ82_spl
| midp(X0,X4,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f252,f3257]) ).
fof(f3269,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ82_spl
| midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3264,f3257]) ).
fof(f3326,plain,
! [X0,X1,X2] :
( ~ sQ46_spl
| ~ sQ49_spl
| ~ sQ57_spl
| ~ sQ82_spl
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3269,f2538]) ).
fof(f3347,plain,
( ~ sQ46_spl
| ~ sQ49_spl
| ~ sQ57_spl
| ~ sQ82_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f648,f3326]) ).
fof(f3353,plain,
( ~ sQ46_spl
| ~ sQ49_spl
| ~ sQ57_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3347]) ).
fof(f3354,plain,
( sQ47_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1320,f3257]) ).
fof(f3355,plain,
( sQ47_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3354]) ).
fof(f3356,plain,
$false,
inference(sat_refutation,[status(thm)],[f1321,f1962,f1982,f2453,f2455,f2525,f2699,f2928,f3139,f3141,f3353,f3355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO644+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 18:11:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.49 % Refutation found
% 0.10/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.52 % Elapsed time: 0.144189 seconds
% 0.10/0.52 % CPU time: 0.786599 seconds
% 0.10/0.52 % Total memory used: 93.180 MB
% 0.10/0.52 % Net memory used: 92.329 MB
%------------------------------------------------------------------------------