%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO630+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 : n012.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 12:25:25 PM UTC 2026
% Result : Theorem 2.30s 0.67s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 133 ( 20 unt; 0 def)
% Number of atoms : 352 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 352 ( 133 ~; 124 |; 70 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 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 : 561 ( 537 !; 24 ?)
% 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(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(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/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(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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A,B,C,D] :
( ( para(A,B,C,D)
& cyclic(A,B,C,D) )
=> eqangle(A,D,C,D,C,D,C,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(f65,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/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(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,D1,D,F,G,G1,F1,NWPNT1,NWPNT2] :
( ( coll(F1,A,C)
& perp(F1,D1,A,C)
& coll(G1,A,B)
& perp(G1,D1,A,B)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(D,D1,O)
& circle(O,D1,D,NWPNT2)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C) )
=> perp(G1,F1,G,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D1,D,F,G,G1,F1,NWPNT1,NWPNT2] :
( ( coll(F1,A,C)
& perp(F1,D1,A,C)
& coll(G1,A,B)
& perp(G1,D1,A,B)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(D,D1,O)
& circle(O,D1,D,NWPNT2)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C) )
=> perp(G1,F1,G,F) ),
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(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(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(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(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(f199,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f200,plain,
! [B,C,E,F] :
( para(E,F,B,C)
| ! [A] :
( ~ midp(F,A,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f226,plain,
! [A,B,C,D] :
( eqangle(A,D,C,D,C,D,C,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ para(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
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(f250,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f251,plain,
! [C,D,M] :
( midp(M,C,D)
| ! [A,B] :
( ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( midp(X0,X3,X4)
| ~ para(X1,X4,X2,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f255,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f256,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f369,plain,
? [A,B,C,O,D1,D,F,G,G1,F1,NWPNT1,NWPNT2] :
( ~ perp(G1,F1,G,F)
& coll(F1,A,C)
& perp(F1,D1,A,C)
& coll(G1,A,B)
& perp(G1,D1,A,B)
& coll(G,A,B)
& perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(D,D1,O)
& circle(O,D1,D,NWPNT2)
& circle(O,A,D1,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [F,G,G1,F1] :
( ~ perp(G1,F1,G,F)
& ? [A,C] :
( coll(F1,A,C)
& ? [D1] :
( perp(F1,D1,A,C)
& ? [B] :
( coll(G1,A,B)
& perp(G1,D1,A,B)
& coll(G,A,B)
& ? [D] :
( perp(G,D,A,B)
& coll(F,A,C)
& perp(F,D,A,C)
& ? [O] :
( coll(D,D1,O)
& ? [NWPNT2] : circle(O,D1,D,NWPNT2)
& ? [NWPNT1] : circle(O,A,D1,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK22_skl,sK23_skl,sK21_skl,sK20_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& perp(sK23_skl,sK26_skl,sK24_skl,sK25_skl)
& coll(sK22_skl,sK24_skl,sK27_skl)
& perp(sK22_skl,sK26_skl,sK24_skl,sK27_skl)
& coll(sK21_skl,sK24_skl,sK27_skl)
& perp(sK21_skl,sK28_skl,sK24_skl,sK27_skl)
& coll(sK20_skl,sK24_skl,sK25_skl)
& perp(sK20_skl,sK28_skl,sK24_skl,sK25_skl)
& coll(sK28_skl,sK26_skl,sK29_skl)
& circle(sK29_skl,sK26_skl,sK28_skl,sK31_skl)
& circle(sK29_skl,sK24_skl,sK26_skl,sK30_skl)
& circle(sK29_skl,sK24_skl,sK27_skl,sK25_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(F,sK20_skl),skolemize(G,sK21_skl),skolemize(G1,sK22_skl),skolemize(F1,sK23_skl),skolemize(A,sK24_skl),skolemize(C,sK25_skl),skolemize(D1,sK26_skl),skolemize(B,sK27_skl),skolemize(D,sK28_skl),skolemize(O,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl)],[f370]) ).
fof(f382,plain,
perp(sK23_skl,sK26_skl,sK24_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
~ perp(sK22_skl,sK23_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f384,f112]) ).
fof(f389,plain,
~ perp(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
inference(resolution,[status(thm)],[f114,f386]) ).
fof(f392,plain,
~ perp(sK20_skl,sK21_skl,sK23_skl,sK22_skl),
inference(resolution,[status(thm)],[f389,f112]) ).
fof(f397,plain,
~ perp(sK23_skl,sK22_skl,sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f392,f114]) ).
fof(f404,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f256,f107]) ).
fof(f406,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f260,f122]) ).
fof(f409,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X1,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f404,f105]) ).
fof(f415,plain,
! [X0,X1,X2] :
( ~ para(X1,X0,X0,X2)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f409,f107]) ).
fof(f422,plain,
! [X0,X1,X2] :
( ~ para(X1,X0,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f415,f105]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f186,f138]) ).
fof(f448,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X2,X3,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X0,X1,X4,X5) ),
inference(resolution,[status(thm)],[f140,f186]) ).
fof(f621,plain,
! [X0,X1,X2,X3,X4] :
( ~ midp(X3,X4,X1)
| para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f201,f122]) ).
fof(f625,plain,
! [X0,X1,X2,X3] :
( ~ para(X1,X0,X2,X3)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f445,f189]) ).
fof(f667,plain,
! [X0,X1,X2,X3] :
( ~ para(X1,X0,X3,X2)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f625,f105]) ).
fof(f682,plain,
! [X0,X1,X2,X3] :
( ~ para(X3,X2,X1,X0)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f667,f107]) ).
fof(f707,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X0,X2)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f195,f100]) ).
fof(f743,plain,
! [X0,X1,X2,X3] :
( ~ coll(X3,X2,X0)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f707,f98]) ).
fof(f758,plain,
! [X0,X1,X2,X3] :
( ~ coll(X2,X3,X0)
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f743,f100]) ).
fof(f791,plain,
! [X0,X1,X2,X3] :
( ~ para(X3,X2,X0,X1)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f682,f105]) ).
fof(f902,plain,
! [X0,X1,X2,X3] :
( ~ para(X2,X3,X2,X3)
| para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f448,f189]) ).
fof(f909,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X4,X5,X2,X3)
| ~ perp(X2,X3,X4,X5)
| para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f902,f117]) ).
fof(f913,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| para(X0,X1,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f909,f114]) ).
fof(f938,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f913,f382]) ).
fof(f948,plain,
! [X0,X1] : para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[f938,f791]) ).
fof(f953,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f938,f422]) ).
fof(f976,plain,
! [X0,X1,X2] :
( cyclic(X1,X2,X0,X0)
| ~ eqangle(X0,X1,X0,X2,X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f953,f758]) ).
fof(f978,plain,
! [X0,X1,X2] :
( cyclic(X1,X0,X0,X2)
| ~ eqangle(X0,X1,X0,X0,X2,X1,X2,X0) ),
inference(resolution,[status(thm)],[f953,f743]) ).
fof(f1039,plain,
! [X0,X1,X2] :
( ~ para(X2,X0,X2,X0)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f976,f189]) ).
fof(f1047,plain,
! [X0,X1,X2] : cyclic(X0,X1,X2,X2),
inference(forward_subsumption_resolution,[status(thm)],[f1039,f938]) ).
fof(f1048,plain,
! [X0,X1,X2] :
( eqangle(X0,X2,X2,X2,X2,X2,X2,X1)
| ~ para(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f1047,f227]) ).
fof(f1056,plain,
! [X0,X1,X2] :
( ~ eqangle(X1,X0,X2,X0,X1,X1,X2,X1)
| cyclic(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f978,f144]) ).
fof(f1131,plain,
! [X0] : eqangle(X0,X0,X0,X0,X0,X0,X0,X0),
inference(resolution,[status(thm)],[f1048,f948]) ).
fof(f1192,plain,
! [X0,X1] :
( ~ para(X0,X0,X0,X0)
| cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1056,f189]) ).
fof(f1199,plain,
! [X0,X1] : cyclic(X0,X0,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f1192,f948]) ).
fof(f1201,plain,
! [X0,X1,X2] :
( cong(X0,X0,X1,X2)
| ~ eqangle(X0,X0,X0,X0,X2,X1,X2,X2)
| ~ cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1199,f198]) ).
fof(f1205,plain,
! [X0,X1,X2] :
( cong(X0,X0,X2,X1)
| ~ eqangle(X0,X0,X0,X0,X1,X2,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1201,f1199]) ).
fof(f1417,plain,
! [X0] : cong(X0,X0,X0,X0),
inference(resolution,[status(thm)],[f1205,f1131]) ).
fof(f1431,plain,
! [X0] :
( midp(X0,X0,X0)
| ~ coll(X0,X0,X0) ),
inference(resolution,[status(thm)],[f1417,f258]) ).
fof(f1442,plain,
! [X0] : midp(X0,X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f1431,f953]) ).
fof(f1450,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ para(X0,X2,X0,X1)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f1442,f252]) ).
fof(f1452,plain,
! [X0,X1,X2] :
( para(X0,X1,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1442,f621]) ).
fof(f1464,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ para(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1450,f107]) ).
fof(f1466,plain,
! [X0,X1] : midp(X0,X1,X1),
inference(resolution,[status(thm)],[f1464,f938]) ).
fof(f1481,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1466,f406]) ).
fof(f1488,plain,
! [X0,X1,X2] :
( perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1481,f232]) ).
fof(f1500,plain,
! [X0,X1,X2] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f1488,f1481]) ).
fof(f1564,plain,
! [X0,X1] : para(X0,X1,X1,X1),
inference(resolution,[status(thm)],[f1452,f1466]) ).
fof(f1577,plain,
! [X0,X1,X2,X3] :
( perp(X3,X0,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1564,f120]) ).
fof(f1585,plain,
! [X0,X1,X2,X3] : perp(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f1577,f1500]) ).
fof(f1780,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f397,f1585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO630+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 18:06:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 2.30/0.67 % Refutation found
% 2.30/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.30/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.30/0.69 % Elapsed time: 0.380488 seconds
% 2.30/0.69 % CPU time: 2.658611 seconds
% 2.30/0.69 % Total memory used: 130.815 MB
% 2.30/0.69 % Net memory used: 125.441 MB
%------------------------------------------------------------------------------