%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO561+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 : n005.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 12:25:14 PM UTC 2026
% Result : Theorem 3.18s 0.86s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 21
% Syntax : Number of formulae : 118 ( 27 unt; 0 def)
% Number of atoms : 325 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 318 ( 111 ~; 108 |; 77 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 538 ( 514 !; 24 ?)
% 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(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(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(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(f22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f42,axiom,
! [A,B,P,Q] :
( ( ~ coll(P,Q,A)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
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(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
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(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(f95,conjecture,
! [A,B,C,O,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ( coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) )
=> eqangle(A,D,D,E,D,E,E,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ( coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) )
=> eqangle(A,D,D,E,D,E,E,A) ),
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(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(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(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(f192,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| coll(P,Q,A)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| coll(X0,X3,X1)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
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(f369,plain,
? [A,B,C,O,P,Q,N,M,E,D,NWPNT1,NWPNT2] :
( ~ eqangle(A,D,D,E,D,E,E,A)
& coll(D,N,M)
& coll(D,A,B)
& coll(E,N,M)
& coll(E,A,C)
& circle(O,A,M,NWPNT2)
& coll(M,O,Q)
& circle(O,A,N,NWPNT1)
& coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,E,D] :
( ~ eqangle(A,D,D,E,D,E,E,A)
& ? [N,M] :
( coll(D,N,M)
& ? [B] :
( coll(D,A,B)
& coll(E,N,M)
& ? [C] :
( coll(E,A,C)
& ? [O] :
( ? [NWPNT2] : circle(O,A,M,NWPNT2)
& ? [Q] :
( coll(M,O,Q)
& ? [NWPNT1] : circle(O,A,N,NWPNT1)
& ? [P] :
( coll(N,O,P)
& coll(Q,A,B)
& perp(Q,O,A,B)
& coll(P,A,C)
& perp(P,O,A,C)
& circle(O,A,B,C) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK21_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
& coll(sK22_skl,sK23_skl,sK24_skl)
& coll(sK22_skl,sK20_skl,sK25_skl)
& coll(sK21_skl,sK23_skl,sK24_skl)
& coll(sK21_skl,sK20_skl,sK26_skl)
& circle(sK27_skl,sK20_skl,sK24_skl,sK31_skl)
& coll(sK24_skl,sK27_skl,sK28_skl)
& circle(sK27_skl,sK20_skl,sK23_skl,sK30_skl)
& coll(sK23_skl,sK27_skl,sK29_skl)
& coll(sK28_skl,sK20_skl,sK25_skl)
& perp(sK28_skl,sK27_skl,sK20_skl,sK25_skl)
& coll(sK29_skl,sK20_skl,sK26_skl)
& perp(sK29_skl,sK27_skl,sK20_skl,sK26_skl)
& circle(sK27_skl,sK20_skl,sK25_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,sK30_skl,sK31_skl]),skolemize(A,sK20_skl),skolemize(E,sK21_skl),skolemize(D,sK22_skl),skolemize(N,sK23_skl),skolemize(M,sK24_skl),skolemize(B,sK25_skl),skolemize(C,sK26_skl),skolemize(O,sK27_skl),skolemize(Q,sK28_skl),skolemize(P,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl)],[f370]) ).
fof(f373,plain,
perp(sK29_skl,sK27_skl,sK20_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f385,plain,
~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK21_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f405,plain,
perp(sK20_skl,sK26_skl,sK29_skl,sK27_skl),
inference(resolution,[status(thm)],[f114,f373]) ).
fof(f406,plain,
! [X0,X1] :
( para(sK29_skl,sK27_skl,X0,X1)
| ~ perp(sK20_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f373]) ).
fof(f536,plain,
para(sK29_skl,sK27_skl,sK29_skl,sK27_skl),
inference(resolution,[status(thm)],[f406,f405]) ).
fof(f817,plain,
! [X0,X1] : eqangle(sK29_skl,sK27_skl,X0,X1,sK29_skl,sK27_skl,X0,X1),
inference(resolution,[status(thm)],[f536,f189]) ).
fof(f1647,plain,
! [X0,X1] : eqangle(sK29_skl,sK27_skl,sK29_skl,sK27_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f817,f144]) ).
fof(f1649,plain,
! [X0,X1] : eqangle(X0,X1,sK29_skl,sK27_skl,X0,X1,sK29_skl,sK27_skl),
inference(resolution,[status(thm)],[f817,f140]) ).
fof(f3008,plain,
! [X0] :
( cyclic(sK27_skl,sK27_skl,sK29_skl,X0)
| ~ coll(sK29_skl,X0,sK27_skl) ),
inference(resolution,[status(thm)],[f1647,f195]) ).
fof(f3009,plain,
! [X0] :
( cyclic(sK27_skl,sK27_skl,sK29_skl,X0)
| coll(sK29_skl,X0,sK27_skl) ),
inference(resolution,[status(thm)],[f1647,f193]) ).
fof(f3040,plain,
! [X0] : cyclic(sK27_skl,sK27_skl,sK29_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3009,f3008]) ).
fof(f3064,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1649,f186]) ).
fof(f3123,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f3064,f256]) ).
fof(f3234,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f3123,f100]) ).
fof(f3319,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f3234,f98]) ).
fof(f3400,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3319,f103]) ).
fof(f3405,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3422]) ).
fof(f3422,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3400,f3319]) ).
fof(f3699,plain,
! [X0,X1] :
( cyclic(sK27_skl,sK29_skl,X1,X0)
| ~ cyclic(sK27_skl,sK27_skl,sK29_skl,X0) ),
inference(resolution,[status(thm)],[f3040,f136]) ).
fof(f3713,plain,
! [X0,X1] : cyclic(sK27_skl,sK29_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3699,f3040]) ).
fof(f3726,plain,
! [X0,X1,X2] :
( cyclic(sK29_skl,X0,X2,X1)
| ~ cyclic(sK27_skl,sK29_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3713,f136]) ).
fof(f3737,plain,
! [X0,X1,X2] : cyclic(sK29_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3726,f3713]) ).
fof(f3748,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK29_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3737,f136]) ).
fof(f3753,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3765]) ).
fof(f3754,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,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f3765]) ).
fof(f3758,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3765]) ).
fof(f3765,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3748,f3737]) ).
fof(f3766,plain,
! [X0,X1,X2,X3,X4,X5] :
( 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)],[f3754,f3765]) ).
fof(f3792,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X1)
| ~ cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f3758,f3766]) ).
fof(f3803,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3792,f3765]) ).
fof(f3810,plain,
! [X0,X1,X2] :
( perp(X2,X0,X0,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3803,f3753]) ).
fof(f3817,plain,
! [X0,X1] : midp(X0,X1,X1),
inference(resolution,[status(thm)],[f3803,f3405]) ).
fof(f3832,plain,
! [X0,X1,X2,X3] :
( cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f3840]) ).
fof(f3840,plain,
! [X0,X1,X2] : perp(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3810,f3803]) ).
fof(f3908,plain,
! [X0,X1,X2] : cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[f3832,f3817]) ).
fof(f3909,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f3908]) ).
fof(f3911,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f3961]) ).
fof(f3961,plain,
! [X0,X1,X2,X3] : perp(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3909,f3908]) ).
fof(f3968,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f3973]) ).
fof(f3973,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3911,f3961]) ).
fof(f4127,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X8,X9,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f3968,f147]) ).
fof(f4130,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X0,X1,X4,X5),
inference(resolution,[status(thm)],[f3968,f140]) ).
fof(f4204,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7),
inference(resolution,[status(thm)],[f4130,f4127]) ).
fof(f4211,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f385,f4204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO561+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 17:29:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 3.18/0.86 % Refutation found
% 3.18/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.18/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.18/0.89 % Elapsed time: 0.521559 seconds
% 3.18/0.89 % CPU time: 3.741685 seconds
% 3.18/0.89 % Total memory used: 120.089 MB
% 3.18/0.89 % Net memory used: 115.566 MB
%------------------------------------------------------------------------------