%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO565+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 : n007.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 12:25:15 PM UTC 2026
% Result : Theorem 12.67s 2.10s
% Output : CNFRefutation 10.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 43
% Syntax : Number of formulae : 230 ( 36 unt; 18 def)
% Number of atoms : 641 ( 0 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 669 ( 258 ~; 219 |; 148 &)
% ( 18 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 19 prp; 0-8 aty)
% Number of functors : 21 ( 21 usr; 20 con; 0-2 aty)
% Number of variables : 657 ( 614 !; 43 ?)
% 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(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(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/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(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(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(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(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(f92,axiom,
! [A,B,C,D,M] :
? [P] :
( ( midp(M,B,D)
& perp(C,A,C,D)
& perp(A,B,A,C) )
=> midp(P,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,H,O,OC,OA,OB,MIDPNT1,MIDPNT2,MIDPNT3,MIDPNT4,MIDPNT5,MIDPNT6,MIDPNT7,MIDPNT8,MIDPNT9,MIDPNT01,MIDPNT11,MIDPNT21] :
( ( perp(H,A,MIDPNT21,OB)
& midp(MIDPNT21,H,A)
& perp(C,A,MIDPNT11,OB)
& midp(MIDPNT11,C,A)
& perp(C,H,MIDPNT01,OB)
& midp(MIDPNT01,C,H)
& perp(H,C,MIDPNT9,OA)
& midp(MIDPNT9,H,C)
& perp(B,C,MIDPNT8,OA)
& midp(MIDPNT8,B,C)
& perp(B,H,MIDPNT7,OA)
& midp(MIDPNT7,B,H)
& perp(H,B,MIDPNT6,OC)
& midp(MIDPNT6,H,B)
& perp(A,B,MIDPNT5,OC)
& midp(MIDPNT5,A,B)
& perp(A,H,MIDPNT4,OC)
& midp(MIDPNT4,A,H)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) )
=> cong(H,OA,H,OB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,H,O,OC,OA,OB,MIDPNT1,MIDPNT2,MIDPNT3,MIDPNT4,MIDPNT5,MIDPNT6,MIDPNT7,MIDPNT8,MIDPNT9,MIDPNT01,MIDPNT11,MIDPNT21] :
( ( perp(H,A,MIDPNT21,OB)
& midp(MIDPNT21,H,A)
& perp(C,A,MIDPNT11,OB)
& midp(MIDPNT11,C,A)
& perp(C,H,MIDPNT01,OB)
& midp(MIDPNT01,C,H)
& perp(H,C,MIDPNT9,OA)
& midp(MIDPNT9,H,C)
& perp(B,C,MIDPNT8,OA)
& midp(MIDPNT8,B,C)
& perp(B,H,MIDPNT7,OA)
& midp(MIDPNT7,B,H)
& perp(H,B,MIDPNT6,OC)
& midp(MIDPNT6,H,B)
& perp(A,B,MIDPNT5,OC)
& midp(MIDPNT5,A,B)
& perp(A,H,MIDPNT4,OC)
& midp(MIDPNT4,A,H)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) )
=> cong(H,OA,H,OB) ),
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(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(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(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(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(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(f355,plain,
! [A,B,C,D,M] :
? [P] :
( midp(P,A,C)
| ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f356,plain,
! [A,C] :
( ? [P] : midp(P,A,C)
| ! [B,D] :
( ! [M] : ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ) ),
inference(miniscoping,[status(thm)],[f355]) ).
fof(f357,plain,
! [A,C] :
( midp(sK17_skl(C,A),A,C)
| ! [B,D] :
( ! [M] : ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(P,sK17_skl(C,A))],[f356]) ).
fof(f358,plain,
! [X0,X1,X2,X3,X4] :
( midp(sK17_skl(X2,X0),X0,X2)
| ~ midp(X4,X1,X3)
| ~ perp(X2,X0,X2,X3)
| ~ perp(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f369,plain,
? [A,B,C,H,O,OC,OA,OB,MIDPNT1,MIDPNT2,MIDPNT3,MIDPNT4,MIDPNT5,MIDPNT6,MIDPNT7,MIDPNT8,MIDPNT9,MIDPNT01,MIDPNT11,MIDPNT21] :
( ~ cong(H,OA,H,OB)
& perp(H,A,MIDPNT21,OB)
& midp(MIDPNT21,H,A)
& perp(C,A,MIDPNT11,OB)
& midp(MIDPNT11,C,A)
& perp(C,H,MIDPNT01,OB)
& midp(MIDPNT01,C,H)
& perp(H,C,MIDPNT9,OA)
& midp(MIDPNT9,H,C)
& perp(B,C,MIDPNT8,OA)
& midp(MIDPNT8,B,C)
& perp(B,H,MIDPNT7,OA)
& midp(MIDPNT7,B,H)
& perp(H,B,MIDPNT6,OC)
& midp(MIDPNT6,H,B)
& perp(A,B,MIDPNT5,OC)
& midp(MIDPNT5,A,B)
& perp(A,H,MIDPNT4,OC)
& midp(MIDPNT4,A,H)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [H,OA,OB] :
( ~ cong(H,OA,H,OB)
& ? [A,MIDPNT21] :
( perp(H,A,MIDPNT21,OB)
& midp(MIDPNT21,H,A)
& ? [C,MIDPNT11] :
( perp(C,A,MIDPNT11,OB)
& midp(MIDPNT11,C,A)
& ? [MIDPNT01] :
( perp(C,H,MIDPNT01,OB)
& midp(MIDPNT01,C,H)
& ? [MIDPNT9] :
( perp(H,C,MIDPNT9,OA)
& midp(MIDPNT9,H,C)
& ? [B,MIDPNT8] :
( perp(B,C,MIDPNT8,OA)
& midp(MIDPNT8,B,C)
& ? [MIDPNT7] :
( perp(B,H,MIDPNT7,OA)
& midp(MIDPNT7,B,H)
& ? [OC,MIDPNT6] :
( perp(H,B,MIDPNT6,OC)
& midp(MIDPNT6,H,B)
& ? [MIDPNT5] :
( perp(A,B,MIDPNT5,OC)
& midp(MIDPNT5,A,B)
& ? [MIDPNT4] :
( perp(A,H,MIDPNT4,OC)
& midp(MIDPNT4,A,H)
& ? [O,MIDPNT3] :
( perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& ? [MIDPNT2] :
( perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& ? [MIDPNT1] :
( perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B)
& perp(B,C,A,H)
& perp(A,C,B,H)
& perp(A,B,C,H) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cong(sK20_skl,sK21_skl,sK20_skl,sK22_skl)
& perp(sK20_skl,sK23_skl,sK24_skl,sK22_skl)
& midp(sK24_skl,sK20_skl,sK23_skl)
& perp(sK25_skl,sK23_skl,sK26_skl,sK22_skl)
& midp(sK26_skl,sK25_skl,sK23_skl)
& perp(sK25_skl,sK20_skl,sK27_skl,sK22_skl)
& midp(sK27_skl,sK25_skl,sK20_skl)
& perp(sK20_skl,sK25_skl,sK28_skl,sK21_skl)
& midp(sK28_skl,sK20_skl,sK25_skl)
& perp(sK29_skl,sK25_skl,sK30_skl,sK21_skl)
& midp(sK30_skl,sK29_skl,sK25_skl)
& perp(sK29_skl,sK20_skl,sK31_skl,sK21_skl)
& midp(sK31_skl,sK29_skl,sK20_skl)
& perp(sK20_skl,sK29_skl,sK33_skl,sK32_skl)
& midp(sK33_skl,sK20_skl,sK29_skl)
& perp(sK23_skl,sK29_skl,sK34_skl,sK32_skl)
& midp(sK34_skl,sK23_skl,sK29_skl)
& perp(sK23_skl,sK20_skl,sK35_skl,sK32_skl)
& midp(sK35_skl,sK23_skl,sK20_skl)
& perp(sK29_skl,sK25_skl,sK37_skl,sK36_skl)
& midp(sK37_skl,sK29_skl,sK25_skl)
& perp(sK23_skl,sK25_skl,sK38_skl,sK36_skl)
& midp(sK38_skl,sK23_skl,sK25_skl)
& perp(sK23_skl,sK29_skl,sK39_skl,sK36_skl)
& midp(sK39_skl,sK23_skl,sK29_skl)
& perp(sK29_skl,sK25_skl,sK23_skl,sK20_skl)
& perp(sK23_skl,sK25_skl,sK29_skl,sK20_skl)
& perp(sK23_skl,sK29_skl,sK25_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,sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl]),skolemize(H,sK20_skl),skolemize(OA,sK21_skl),skolemize(OB,sK22_skl),skolemize(A,sK23_skl),skolemize(MIDPNT21,sK24_skl),skolemize(C,sK25_skl),skolemize(MIDPNT11,sK26_skl),skolemize(MIDPNT01,sK27_skl),skolemize(MIDPNT9,sK28_skl),skolemize(B,sK29_skl),skolemize(MIDPNT8,sK30_skl),skolemize(MIDPNT7,sK31_skl),skolemize(OC,sK32_skl),skolemize(MIDPNT6,sK33_skl),skolemize(MIDPNT5,sK34_skl),skolemize(MIDPNT4,sK35_skl),skolemize(O,sK36_skl),skolemize(MIDPNT3,sK37_skl),skolemize(MIDPNT2,sK38_skl),skolemize(MIDPNT1,sK39_skl)],[f370]) ).
fof(f375,plain,
midp(sK39_skl,sK23_skl,sK29_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
midp(sK38_skl,sK23_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
midp(sK37_skl,sK29_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
midp(sK35_skl,sK23_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f385,plain,
midp(sK33_skl,sK20_skl,sK29_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f391,plain,
midp(sK28_skl,sK20_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f393,plain,
midp(sK27_skl,sK25_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f394,plain,
perp(sK25_skl,sK20_skl,sK27_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f398,plain,
perp(sK20_skl,sK23_skl,sK24_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f399,plain,
~ cong(sK20_skl,sK21_skl,sK20_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f402,plain,
midp(sK27_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f122,f393]) ).
fof(f403,plain,
midp(sK28_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f122,f391]) ).
fof(f406,plain,
midp(sK33_skl,sK29_skl,sK20_skl),
inference(resolution,[status(thm)],[f122,f385]) ).
fof(f408,plain,
midp(sK35_skl,sK20_skl,sK23_skl),
inference(resolution,[status(thm)],[f122,f381]) ).
fof(f410,plain,
midp(sK38_skl,sK25_skl,sK23_skl),
inference(resolution,[status(thm)],[f122,f377]) ).
fof(f800,plain,
perp(sK25_skl,sK20_skl,sK22_skl,sK27_skl),
inference(resolution,[status(thm)],[f394,f112]) ).
fof(f820,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK22_skl)
| ~ perp(X0,X1,sK20_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f398,f117]) ).
fof(f821,plain,
perp(sK24_skl,sK22_skl,sK20_skl,sK23_skl),
inference(resolution,[status(thm)],[f398,f114]) ).
fof(f822,plain,
perp(sK20_skl,sK23_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f398,f112]) ).
fof(f1126,plain,
perp(sK22_skl,sK27_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f800,f114]) ).
fof(f1158,plain,
! [X0,X1] :
( para(X0,X1,sK20_skl,sK23_skl)
| ~ perp(X0,X1,sK24_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f821,f117]) ).
fof(f1169,plain,
! [X0,X1] :
( para(X0,X1,sK22_skl,sK24_skl)
| ~ perp(X0,X1,sK20_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f822,f117]) ).
fof(f1170,plain,
perp(sK22_skl,sK24_skl,sK20_skl,sK23_skl),
inference(resolution,[status(thm)],[f822,f114]) ).
fof(f1524,definition,
( sQ138_spl
<=> midp(sK22_skl,sK20_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
( ~ sQ138_spl
| midp(sK22_skl,sK20_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f1524]) ).
fof(f1534,plain,
perp(sK22_skl,sK27_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f1126,f112]) ).
fof(f2070,plain,
para(sK22_skl,sK24_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f820,f1170]) ).
fof(f2209,plain,
( cong(sK22_skl,sK20_skl,sK22_skl,sK25_skl)
| ~ midp(sK27_skl,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f1534,f230]) ).
fof(f2213,definition,
( sQ209_spl
<=> midp(sK27_skl,sK20_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2215,plain,
( sQ209_spl
| ~ midp(sK27_skl,sK20_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2213]) ).
fof(f2216,definition,
( sQ210_spl
<=> cong(sK22_skl,sK20_skl,sK22_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2217,plain,
( ~ sQ210_spl
| cong(sK22_skl,sK20_skl,sK22_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f2216]) ).
fof(f2219,plain,
( sQ210_spl
| ~ sQ209_spl ),
inference(split_clause,[status(thm)],[f2209,f2213,f2216]) ).
fof(f2220,plain,
( sQ209_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2215,f402]) ).
fof(f2221,plain,
sQ209_spl,
inference(contradiction_clause,[status(thm)],[f2220]) ).
fof(f2380,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(f2382,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(f3316,plain,
para(sK22_skl,sK24_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f2070,f105]) ).
fof(f3545,plain,
( ~ sQ210_spl
| midp(sK22_skl,sK20_skl,sK25_skl)
| ~ coll(sK22_skl,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2217,f258]) ).
fof(f3554,definition,
( sQ266_spl
<=> coll(sK22_skl,sK20_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3556,plain,
( sQ266_spl
| ~ coll(sK22_skl,sK20_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f3554]) ).
fof(f3557,plain,
( ~ sQ210_spl
| sQ138_spl
| ~ sQ266_spl ),
inference(split_clause,[status(thm)],[f3545,f3554,f1524,f2216]) ).
fof(f8843,definition,
! [X4,X5] :
( sQ882_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ882_spl])],[split_symbol_definition]) ).
fof(f8844,plain,
! [X0,X1] :
( ~ sQ882_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f8843]) ).
fof(f9284,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2382,f186]) ).
fof(f9292,definition,
! [X2,X3] :
( sQ895_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ895_spl])],[split_symbol_definition]) ).
fof(f9293,plain,
! [X0,X1] :
( ~ sQ895_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f9292]) ).
fof(f9295,plain,
( sQ895_spl
| sQ882_spl ),
inference(split_clause,[status(thm)],[f9284,f8843,f9292]) ).
fof(f9656,plain,
( ~ sQ882_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3316,f8844]) ).
fof(f9694,plain,
~ sQ882_spl,
inference(contradiction_clause,[status(thm)],[f9656]) ).
fof(f9695,plain,
! [X0,X1] :
( ~ sQ895_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f9293,f256]) ).
fof(f9752,plain,
! [X0,X1] :
( ~ sQ895_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f9695,f100]) ).
fof(f9804,plain,
! [X0,X1] :
( ~ sQ895_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f9752,f98]) ).
fof(f9807,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f9804,f103]) ).
fof(f9812,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f9807,f9804]) ).
fof(f9820,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f9812]) ).
fof(f9824,plain,
( sQ266_spl
| ~ sQ895_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3556,f9812]) ).
fof(f9853,plain,
( sQ266_spl
| ~ sQ895_spl ),
inference(contradiction_clause,[status(thm)],[f9824]) ).
fof(f9936,definition,
! [X3,X4,X5] :
( sQ962_spl
<=> ~ midp(X3,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ962_spl])],[split_symbol_definition]) ).
fof(f9937,plain,
! [X0,X1,X2] :
( ~ sQ962_spl
| ~ midp(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f9936]) ).
fof(f9968,plain,
( ~ sQ138_spl
| ~ sQ962_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1525,f9937]) ).
fof(f9997,plain,
( ~ sQ138_spl
| ~ sQ962_spl ),
inference(contradiction_clause,[status(thm)],[f9968]) ).
fof(f10473,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f9820,f2380]) ).
fof(f10482,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f10473,f9293]) ).
fof(f10518,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f10482,f136]) ).
fof(f10522,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f10518,f10482]) ).
fof(f10531,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ895_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,f10522]) ).
fof(f10532,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f10522]) ).
fof(f10533,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f10522]) ).
fof(f10534,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ895_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)],[f10531,f10522]) ).
fof(f10946,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ895_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f10534,f10522]) ).
fof(f10956,plain,
! [X0,X1] :
( ~ sQ895_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f10532,f10946]) ).
fof(f11229,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f10956,f232]) ).
fof(f11233,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f11229,f10956]) ).
fof(f11235,plain,
! [X0] :
( ~ sQ895_spl
| para(X0,X0,sK20_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f11233,f1158]) ).
fof(f11252,plain,
! [X0] :
( ~ sQ895_spl
| para(X0,X0,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f11233,f1169]) ).
fof(f11321,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f10533,f10956]) ).
fof(f11323,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f11321,f10956]) ).
fof(f11440,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f11323,f114]) ).
fof(f11490,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f11440,f112]) ).
fof(f11540,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ895_spl
| midp(sK17_skl(X2,X0),X0,X2)
| ~ midp(X3,X1,X4)
| ~ perp(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f358,f11490]) ).
fof(f11590,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ895_spl
| midp(sK17_skl(X3,X4),X4,X3)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f11540,f11490]) ).
fof(f11595,plain,
! [X0] :
( ~ sQ895_spl
| para(sK20_skl,sK23_skl,X0,X0) ),
inference(resolution,[status(thm)],[f11235,f107]) ).
fof(f11704,plain,
! [X0] :
( ~ sQ895_spl
| para(sK22_skl,sK24_skl,X0,X0) ),
inference(resolution,[status(thm)],[f11252,f107]) ).
fof(f11761,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ895_spl
| midp(sK17_skl(X3,X4),X3,X4)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f11590,f122]) ).
fof(f11762,definition,
! [X3,X4] :
( sQ966_spl
<=> midp(sK17_skl(X3,X4),X3,X4) ),
introduced(definition,[new_symbols(definition,[sQ966_spl])],[split_symbol_definition]) ).
fof(f11763,plain,
! [X0,X1] :
( ~ sQ966_spl
| midp(sK17_skl(X0,X1),X0,X1) ),
inference(component_clause,[status(thm)],[f11762]) ).
fof(f11765,plain,
( ~ sQ895_spl
| sQ966_spl
| sQ962_spl ),
inference(split_clause,[status(thm)],[f11761,f9936,f11762,f9292]) ).
fof(f11862,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(sK20_skl,sK23_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f11595,f120]) ).
fof(f11866,plain,
! [X0,X1] :
( ~ sQ895_spl
| perp(sK20_skl,sK23_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f11862,f11233]) ).
fof(f11989,plain,
! [X0,X1,X2] :
( ~ sQ895_spl
| perp(sK22_skl,sK24_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f11704,f120]) ).
fof(f11993,plain,
! [X0,X1] :
( ~ sQ895_spl
| perp(sK22_skl,sK24_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f11989,f11233]) ).
fof(f12094,plain,
! [X0,X1] :
( ~ sQ966_spl
| midp(sK17_skl(X0,X1),X1,X0) ),
inference(resolution,[status(thm)],[f11763,f122]) ).
fof(f12191,plain,
! [X0,X1] :
( ~ sQ895_spl
| perp(X0,X1,sK20_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f11866,f114]) ).
fof(f14208,plain,
! [X0,X1] :
( ~ sQ895_spl
| para(X0,X1,sK22_skl,sK24_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1169,f12191]) ).
fof(f14214,definition,
! [X0] :
( sQ1034_spl
<=> ~ midp(X0,sK20_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ1034_spl])],[split_symbol_definition]) ).
fof(f14215,plain,
! [X0] :
( ~ sQ1034_spl
| ~ midp(X0,sK20_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f14214]) ).
fof(f14221,plain,
( ~ sQ1034_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f408,f14215]) ).
fof(f14229,plain,
~ sQ1034_spl,
inference(contradiction_clause,[status(thm)],[f14221]) ).
fof(f14236,definition,
! [X0] :
( sQ1036_spl
<=> ~ midp(X0,sK25_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ1036_spl])],[split_symbol_definition]) ).
fof(f14237,plain,
! [X0] :
( ~ sQ1036_spl
| ~ midp(X0,sK25_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f14236]) ).
fof(f14243,plain,
( ~ sQ1036_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f14237]) ).
fof(f14251,plain,
~ sQ1036_spl,
inference(contradiction_clause,[status(thm)],[f14243]) ).
fof(f14260,definition,
! [X0] :
( sQ1038_spl
<=> ~ midp(X0,sK25_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ1038_spl])],[split_symbol_definition]) ).
fof(f14261,plain,
! [X0] :
( ~ sQ1038_spl
| ~ midp(X0,sK25_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f14260]) ).
fof(f14267,plain,
( ~ sQ1038_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f403,f14261]) ).
fof(f14275,plain,
~ sQ1038_spl,
inference(contradiction_clause,[status(thm)],[f14267]) ).
fof(f14283,definition,
! [X0] :
( sQ1040_spl
<=> ~ midp(X0,sK20_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ1040_spl])],[split_symbol_definition]) ).
fof(f14284,plain,
! [X0] :
( ~ sQ1040_spl
| ~ midp(X0,sK20_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f14283]) ).
fof(f14290,plain,
( ~ sQ1040_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f391,f14284]) ).
fof(f14298,plain,
~ sQ1040_spl,
inference(contradiction_clause,[status(thm)],[f14290]) ).
fof(f14309,definition,
! [X0] :
( sQ1042_spl
<=> ~ midp(X0,sK29_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ1042_spl])],[split_symbol_definition]) ).
fof(f14310,plain,
! [X0] :
( ~ sQ1042_spl
| ~ midp(X0,sK29_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f14309]) ).
fof(f14316,plain,
( ~ sQ1042_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f379,f14310]) ).
fof(f14325,plain,
~ sQ1042_spl,
inference(contradiction_clause,[status(thm)],[f14316]) ).
fof(f14368,definition,
! [X0] :
( sQ1044_spl
<=> ~ midp(X0,sK29_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ1044_spl])],[split_symbol_definition]) ).
fof(f14369,plain,
! [X0] :
( ~ sQ1044_spl
| ~ midp(X0,sK29_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f14368]) ).
fof(f14375,plain,
( ~ sQ1044_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f406,f14369]) ).
fof(f14383,plain,
~ sQ1044_spl,
inference(contradiction_clause,[status(thm)],[f14375]) ).
fof(f14391,definition,
! [X0] :
( sQ1046_spl
<=> ~ midp(X0,sK20_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ1046_spl])],[split_symbol_definition]) ).
fof(f14392,plain,
! [X0] :
( ~ sQ1046_spl
| ~ midp(X0,sK20_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f14391]) ).
fof(f14398,plain,
( ~ sQ1046_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f385,f14392]) ).
fof(f14406,plain,
~ sQ1046_spl,
inference(contradiction_clause,[status(thm)],[f14398]) ).
fof(f14417,definition,
! [X0] :
( sQ1048_spl
<=> ~ midp(X0,sK23_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ1048_spl])],[split_symbol_definition]) ).
fof(f14418,plain,
! [X0] :
( ~ sQ1048_spl
| ~ midp(X0,sK23_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f14417]) ).
fof(f14424,plain,
( ~ sQ1048_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f375,f14418]) ).
fof(f14432,plain,
~ sQ1048_spl,
inference(contradiction_clause,[status(thm)],[f14424]) ).
fof(f14504,definition,
! [X0] :
( sQ1050_spl
<=> ~ midp(X0,sK23_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ1050_spl])],[split_symbol_definition]) ).
fof(f14505,plain,
! [X0] :
( ~ sQ1050_spl
| ~ midp(X0,sK23_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f14504]) ).
fof(f14511,plain,
( ~ sQ1050_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f381,f14505]) ).
fof(f14519,plain,
~ sQ1050_spl,
inference(contradiction_clause,[status(thm)],[f14511]) ).
fof(f14529,definition,
! [X0] :
( sQ1052_spl
<=> ~ midp(X0,sK23_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ1052_spl])],[split_symbol_definition]) ).
fof(f14530,plain,
! [X0] :
( ~ sQ1052_spl
| ~ midp(X0,sK23_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f14529]) ).
fof(f14536,plain,
( ~ sQ1052_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f377,f14530]) ).
fof(f14544,plain,
~ sQ1052_spl,
inference(contradiction_clause,[status(thm)],[f14536]) ).
fof(f14966,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK22_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f14208,f120]) ).
fof(f14970,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f14966,f11993]) ).
fof(f14977,plain,
! [X0,X1,X2,X3] :
( ~ sQ895_spl
| cong(X3,X1,X3,X2)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f230,f14970]) ).
fof(f15036,plain,
! [X0] :
( ~ sQ895_spl
| ~ midp(X0,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f14977,f399]) ).
fof(f15043,plain,
( ~ sQ966_spl
| ~ sQ895_spl
| $false ),
inference(resolution,[status(thm)],[f15036,f12094]) ).
fof(f15047,plain,
( ~ sQ966_spl
| ~ sQ895_spl ),
inference(contradiction_clause,[status(thm)],[f15043]) ).
fof(f15048,plain,
$false,
inference(sat_refutation,[status(thm)],[f2219,f2221,f3557,f9295,f9694,f9853,f9997,f11765,f14229,f14251,f14275,f14298,f14325,f14383,f14406,f14432,f14519,f14544,f15047]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO565+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 17:31:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 12.67/2.10 % Refutation found
% 12.67/2.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.67/2.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.13/2.15 % Elapsed time: 1.758102 seconds
% 10.13/2.15 % CPU time: 13.649154 seconds
% 10.13/2.15 % Total memory used: 214.192 MB
% 10.13/2.15 % Net memory used: 199.324 MB
%------------------------------------------------------------------------------