%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO615+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 : n003.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 12:25:22 PM UTC 2026
% Result : Theorem 1.37s 0.79s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 23
% Syntax : Number of formulae : 120 ( 33 unt; 0 def)
% Number of atoms : 290 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 260 ( 90 ~; 85 |; 61 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 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 : 554 ( 530 !; 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(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(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(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(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/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(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(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(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5] :
( ( coll(G,F,A)
& circle(E,F,G,NWPNT5)
& circle(E,B,F,NWPNT4)
& coll(F,A,C)
& circle(E,B,NWPNT2,NWPNT3)
& perp(A,B,B,E)
& perp(B,D,NWPNT1,E)
& midpoint(NWPNT1,B,D)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) )
=> eqangle(F,D,D,C,C,D,D,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5] :
( ( coll(G,F,A)
& circle(E,F,G,NWPNT5)
& circle(E,B,F,NWPNT4)
& coll(F,A,C)
& circle(E,B,NWPNT2,NWPNT3)
& perp(A,B,B,E)
& perp(B,D,NWPNT1,E)
& midpoint(NWPNT1,B,D)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) )
=> eqangle(F,D,D,C,C,D,D,G) ),
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(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(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(f141,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f146,plain,
! [A,B,C,D,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ! [P,Q,U,V] :
( ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(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(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(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(f369,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5] :
( ~ eqangle(F,D,D,C,C,D,D,G)
& coll(G,F,A)
& circle(E,F,G,NWPNT5)
& circle(E,B,F,NWPNT4)
& coll(F,A,C)
& circle(E,B,NWPNT2,NWPNT3)
& perp(A,B,B,E)
& perp(B,D,NWPNT1,E)
& midpoint(NWPNT1,B,D)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [C,D,F,G] :
( ~ eqangle(F,D,D,C,C,D,D,G)
& ? [A] :
( coll(G,F,A)
& ? [E] :
( ? [NWPNT5] : circle(E,F,G,NWPNT5)
& ? [B] :
( ? [NWPNT4] : circle(E,B,F,NWPNT4)
& coll(F,A,C)
& ? [NWPNT2,NWPNT3] : circle(E,B,NWPNT2,NWPNT3)
& perp(A,B,B,E)
& ? [NWPNT1] :
( perp(B,D,NWPNT1,E)
& midpoint(NWPNT1,B,D)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK22_skl,sK21_skl,sK21_skl,sK20_skl,sK20_skl,sK21_skl,sK21_skl,sK23_skl)
& coll(sK23_skl,sK22_skl,sK24_skl)
& circle(sK25_skl,sK22_skl,sK23_skl,sK31_skl)
& circle(sK25_skl,sK26_skl,sK22_skl,sK30_skl)
& coll(sK22_skl,sK24_skl,sK20_skl)
& circle(sK25_skl,sK26_skl,sK28_skl,sK29_skl)
& perp(sK24_skl,sK26_skl,sK26_skl,sK25_skl)
& perp(sK26_skl,sK21_skl,sK27_skl,sK25_skl)
& midpoint(sK27_skl,sK26_skl,sK21_skl)
& eqangle(sK21_skl,sK20_skl,sK20_skl,sK24_skl,sK21_skl,sK20_skl,sK20_skl,sK26_skl)
& eqangle(sK21_skl,sK26_skl,sK26_skl,sK20_skl,sK21_skl,sK26_skl,sK26_skl,sK24_skl)
& eqangle(sK21_skl,sK24_skl,sK24_skl,sK26_skl,sK21_skl,sK24_skl,sK24_skl,sK20_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl,sK30_skl,sK31_skl]),skolemize(C,sK20_skl),skolemize(D,sK21_skl),skolemize(F,sK22_skl),skolemize(G,sK23_skl),skolemize(A,sK24_skl),skolemize(E,sK25_skl),skolemize(B,sK26_skl),skolemize(NWPNT1,sK27_skl),skolemize(NWPNT2,sK28_skl),skolemize(NWPNT3,sK29_skl),skolemize(NWPNT4,sK30_skl),skolemize(NWPNT5,sK31_skl)],[f370]) ).
fof(f376,plain,
perp(sK26_skl,sK21_skl,sK27_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f383,plain,
~ eqangle(sK22_skl,sK21_skl,sK21_skl,sK20_skl,sK20_skl,sK21_skl,sK21_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f427,plain,
perp(sK27_skl,sK25_skl,sK26_skl,sK21_skl),
inference(resolution,[status(thm)],[f114,f376]) ).
fof(f435,plain,
perp(sK27_skl,sK25_skl,sK21_skl,sK26_skl),
inference(resolution,[status(thm)],[f427,f112]) ).
fof(f446,plain,
! [X0,X1] :
( para(sK26_skl,sK21_skl,X0,X1)
| ~ perp(sK27_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f376]) ).
fof(f961,plain,
para(sK26_skl,sK21_skl,sK21_skl,sK26_skl),
inference(resolution,[status(thm)],[f446,f435]) ).
fof(f962,plain,
para(sK26_skl,sK21_skl,sK26_skl,sK21_skl),
inference(resolution,[status(thm)],[f446,f427]) ).
fof(f1050,plain,
para(sK21_skl,sK26_skl,sK26_skl,sK21_skl),
inference(resolution,[status(thm)],[f961,f107]) ).
fof(f1056,plain,
coll(sK26_skl,sK21_skl,sK21_skl),
inference(resolution,[status(thm)],[f962,f256]) ).
fof(f1058,plain,
coll(sK21_skl,sK26_skl,sK21_skl),
inference(resolution,[status(thm)],[f1056,f100]) ).
fof(f1062,plain,
coll(sK21_skl,sK21_skl,sK26_skl),
inference(resolution,[status(thm)],[f1058,f98]) ).
fof(f1074,plain,
para(sK21_skl,sK26_skl,sK21_skl,sK26_skl),
inference(resolution,[status(thm)],[f1050,f105]) ).
fof(f1344,plain,
! [X0,X1] : eqangle(sK21_skl,sK26_skl,X0,X1,sK21_skl,sK26_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f1074]) ).
fof(f2352,plain,
! [X0,X1] : eqangle(X0,X1,sK21_skl,sK26_skl,X0,X1,sK21_skl,sK26_skl),
inference(resolution,[status(thm)],[f1344,f140]) ).
fof(f3110,plain,
! [X0] :
( cyclic(X0,sK26_skl,sK21_skl,sK21_skl)
| ~ coll(sK21_skl,sK21_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f2352,f195]) ).
fof(f3121,plain,
! [X0] : cyclic(X0,sK26_skl,sK21_skl,sK21_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3110,f1062]) ).
fof(f3628,plain,
! [X0] : cyclic(sK26_skl,X0,sK21_skl,sK21_skl),
inference(resolution,[status(thm)],[f3121,f133]) ).
fof(f3634,plain,
! [X0] : cyclic(sK26_skl,sK21_skl,X0,sK21_skl),
inference(resolution,[status(thm)],[f3628,f131]) ).
fof(f3645,plain,
! [X0] : cyclic(sK26_skl,sK21_skl,sK21_skl,X0),
inference(resolution,[status(thm)],[f3634,f129]) ).
fof(f3668,plain,
! [X0,X1] :
( cyclic(sK21_skl,sK21_skl,X1,X0)
| ~ cyclic(sK26_skl,sK21_skl,sK21_skl,X0) ),
inference(resolution,[status(thm)],[f3645,f136]) ).
fof(f3672,plain,
! [X0,X1] : cyclic(sK21_skl,sK21_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3668,f3645]) ).
fof(f3674,plain,
! [X0,X1,X2] :
( cyclic(sK21_skl,X0,X2,X1)
| ~ cyclic(sK21_skl,sK21_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3672,f136]) ).
fof(f3678,plain,
! [X0,X1,X2] : cyclic(sK21_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3674,f3672]) ).
fof(f3680,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK21_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3678,f136]) ).
fof(f3684,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3680,f3678]) ).
fof(f3687,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,f3684]) ).
fof(f3688,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3684]) ).
fof(f3689,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)],[f3687,f3684]) ).
fof(f3764,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2),
inference(resolution,[status(thm)],[f3688,f138]) ).
fof(f3923,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3689,f3684]) ).
fof(f3933,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f3923,f3764]) ).
fof(f3943,plain,
! [X0,X1,X2] :
( perp(X0,X0,X2,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3933,f232]) ).
fof(f3950,plain,
! [X0,X1,X2] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3943,f3933]) ).
fof(f3982,plain,
! [X0,X1,X2] : perp(X0,X1,X2,X2),
inference(resolution,[status(thm)],[f3950,f114]) ).
fof(f4006,plain,
! [X0,X1,X2,X3,X4] :
( para(X3,X4,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3982,f117]) ).
fof(f4009,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4006,f3950]) ).
fof(f4021,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f4009]) ).
fof(f4207,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5),
inference(resolution,[status(thm)],[f4021,f144]) ).
fof(f4389,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X0,X1,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f4207,f142]) ).
fof(f4648,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X1,X0,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f4389,f138]) ).
fof(f4883,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X5,X4),
inference(resolution,[status(thm)],[f4648,f142]) ).
fof(f5231,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X6,X7,X8,X9,X2,X3,X4,X5)
| ~ eqangle(X0,X1,X1,X0,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[f4883,f147]) ).
fof(f5236,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7),
inference(forward_subsumption_resolution,[status(thm)],[f5231,f4648]) ).
fof(f5977,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f383,f5236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO615+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 18:00:14 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 1.37/0.79 % Refutation found
% 1.37/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.37/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.83 % Elapsed time: 0.449443 seconds
% 0.26/0.83 % CPU time: 3.257449 seconds
% 0.26/0.83 % Total memory used: 117.809 MB
% 0.26/0.83 % Net memory used: 114.198 MB
%------------------------------------------------------------------------------