%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO562+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 : n018.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 1.33s 0.70s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 22
% Syntax : Number of formulae : 129 ( 8 unt; 2 def)
% Number of atoms : 362 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 390 ( 157 ~; 150 |; 60 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 575 ( 553 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(f95,conjecture,
! [A,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) )
=> eqangle(A,G,G,C,C,D,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ( coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) )
=> eqangle(A,G,G,C,C,D,D,E) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
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(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(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(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(f369,plain,
? [A,C,D,O,B,M,E,F,G,NWPNT1,NWPNT2] :
( ~ eqangle(A,G,G,C,C,D,D,E)
& coll(G,C,E)
& coll(G,A,B)
& coll(F,C,D)
& coll(F,A,B)
& circle(O,A,E,NWPNT2)
& coll(M,A,B)
& coll(M,C,O)
& circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,C,D,E,G] :
( ~ eqangle(A,G,G,C,C,D,D,E)
& coll(G,C,E)
& ? [B] :
( coll(G,A,B)
& ? [F] :
( coll(F,C,D)
& coll(F,A,B)
& ? [O] :
( ? [NWPNT2] : circle(O,A,E,NWPNT2)
& ? [M] :
( coll(M,A,B)
& coll(M,C,O)
& ? [NWPNT1] : circle(O,A,B,NWPNT1)
& perp(C,O,A,B)
& circle(O,A,C,D) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK24_skl,sK24_skl,sK21_skl,sK21_skl,sK22_skl,sK22_skl,sK23_skl)
& coll(sK24_skl,sK21_skl,sK23_skl)
& coll(sK24_skl,sK20_skl,sK25_skl)
& coll(sK26_skl,sK21_skl,sK22_skl)
& coll(sK26_skl,sK20_skl,sK25_skl)
& circle(sK27_skl,sK20_skl,sK23_skl,sK30_skl)
& coll(sK28_skl,sK20_skl,sK25_skl)
& coll(sK28_skl,sK21_skl,sK27_skl)
& circle(sK27_skl,sK20_skl,sK25_skl,sK29_skl)
& perp(sK21_skl,sK27_skl,sK20_skl,sK25_skl)
& circle(sK27_skl,sK20_skl,sK21_skl,sK22_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]),skolemize(A,sK20_skl),skolemize(C,sK21_skl),skolemize(D,sK22_skl),skolemize(E,sK23_skl),skolemize(G,sK24_skl),skolemize(B,sK25_skl),skolemize(F,sK26_skl),skolemize(O,sK27_skl),skolemize(M,sK28_skl),skolemize(NWPNT1,sK29_skl),skolemize(NWPNT2,sK30_skl)],[f370]) ).
fof(f373,plain,
perp(sK21_skl,sK27_skl,sK20_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ eqangle(sK20_skl,sK24_skl,sK24_skl,sK21_skl,sK21_skl,sK22_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
! [X0,X1] :
( para(X0,X1,sK20_skl,sK25_skl)
| ~ perp(X0,X1,sK21_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f117,f373]) ).
fof(f388,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X5,X4)
| para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f117,f112]) ).
fof(f390,plain,
! [X0,X1] :
( ~ perp(sK21_skl,sK27_skl,X0,X1)
| para(X0,X1,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f386,f114]) ).
fof(f391,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK27_skl,sK21_skl)
| para(X0,X1,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f386,f112]) ).
fof(f432,plain,
para(sK20_skl,sK25_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f390,f373]) ).
fof(f434,plain,
! [X0,X1] :
( ~ perp(sK21_skl,sK27_skl,X1,X0)
| para(X0,X1,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f390,f112]) ).
fof(f438,plain,
para(sK20_skl,sK25_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f432,f105]) ).
fof(f442,plain,
para(sK25_skl,sK20_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f438,f107]) ).
fof(f456,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)],[f186,f140]) ).
fof(f481,plain,
! [X0,X1] :
( ~ perp(sK27_skl,sK21_skl,X0,X1)
| para(X0,X1,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f391,f114]) ).
fof(f544,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X4,X5,X0,X1,X5,X4,X2,X3)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f456,f138]) ).
fof(f545,definition,
! [X0,X1] :
( sQ4_spl
<=> para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f546,plain,
! [X0,X1] :
( ~ sQ4_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X1,X2,X3,sK21_skl,sK22_skl,sK22_skl,sK23_skl)
| ~ eqangle(sK20_skl,sK24_skl,sK24_skl,sK21_skl,X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f147,f382]) ).
fof(f821,plain,
! [X0,X1,X2,X3] :
( ~ para(X2,X3,X3,X2)
| para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f544,f189]) ).
fof(f825,definition,
! [X2,X3] :
( sQ7_spl
<=> ~ para(X2,X3,X3,X2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f826,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ para(X0,X1,X1,X0) ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f828,plain,
( sQ7_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f821,f545,f825]) ).
fof(f869,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X2,X1,X2,X0,X3,X1,X3)
| cyclic(X2,X3,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f193,f144]) ).
fof(f911,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f826]) ).
fof(f912,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f911]) ).
fof(f1002,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X3,X1,X3,X0,X2,X1,X2)
| cyclic(X3,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f195,f144]) ).
fof(f1837,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X0,X2)
| cyclic(X2,X2,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f869,f189]) ).
fof(f1841,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| cyclic(X2,X2,X0,X1)
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1837,f546]) ).
fof(f2035,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X0,X2)
| cyclic(X2,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1002,f189]) ).
fof(f2039,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| cyclic(X2,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2035,f546]) ).
fof(f2095,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2039,f1841]) ).
fof(f2101,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2095,f136]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2101,f2095]) ).
fof(f2107,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f2106]) ).
fof(f2108,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f2106]) ).
fof(f2109,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2106]) ).
fof(f2135,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| cong(X0,X1,X4,X5)
| ~ eqangle(X2,X0,X2,X1,X3,X4,X3,X5)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2108,f2106]) ).
fof(f2139,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2135,f2106]) ).
fof(f2166,plain,
! [X0,X1] :
( ~ sQ4_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2109,f2139]) ).
fof(f2189,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2166,f2107]) ).
fof(f2194,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2166,f232]) ).
fof(f2201,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2189,f2166]) ).
fof(f2202,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2194,f2166]) ).
fof(f2232,plain,
! [X0] :
( ~ sQ4_spl
| para(sK21_skl,X0,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2201,f481]) ).
fof(f2244,plain,
! [X0] :
( ~ sQ4_spl
| para(X0,X0,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2202,f391]) ).
fof(f2271,plain,
! [X0] :
( ~ sQ4_spl
| para(sK20_skl,sK25_skl,X0,X0) ),
inference(resolution,[status(thm)],[f2244,f107]) ).
fof(f2289,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(sK20_skl,sK25_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2271,f120]) ).
fof(f2294,plain,
! [X0,X1] :
( ~ sQ4_spl
| perp(sK20_skl,sK25_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2289,f2202]) ).
fof(f2347,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(sK21_skl,X2,X0,X1)
| ~ perp(sK20_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2232,f120]) ).
fof(f2351,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| perp(sK21_skl,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2347,f2294]) ).
fof(f2352,plain,
! [X0,X1] :
( ~ sQ4_spl
| para(X0,X1,sK20_skl,sK25_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f434,f2351]) ).
fof(f2393,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK20_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2352,f120]) ).
fof(f2399,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2393,f2294]) ).
fof(f2404,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ perp(X4,X5,X3,X2)
| para(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f388,f2399]) ).
fof(f2408,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2404,f2399]) ).
fof(f2416,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f2408]) ).
fof(f2556,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ eqangle(X0,X1,sK24_skl,sK21_skl,sK21_skl,sK22_skl,sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f2416,f553]) ).
fof(f2580,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ eqangle(sK24_skl,sK21_skl,X0,X1,sK22_skl,sK23_skl,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f2556,f140]) ).
fof(f2604,plain,
( ~ sQ4_spl
| $false ),
inference(resolution,[status(thm)],[f2580,f2416]) ).
fof(f2610,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f2604]) ).
fof(f2611,plain,
$false,
inference(sat_refutation,[status(thm)],[f828,f912,f2610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO562+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 : n018.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 17:30:28 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 1.33/0.70 % Refutation found
% 1.33/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.70 % Elapsed time: 0.335663 seconds
% 1.33/0.70 % CPU time: 2.347895 seconds
% 1.33/0.70 % Total memory used: 112.873 MB
% 1.33/0.70 % Net memory used: 109.109 MB
%------------------------------------------------------------------------------