%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO581+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 : n009.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 12:25:17 PM UTC 2026
% Result : Theorem 1.44s 0.75s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 30
% Syntax : Number of formulae : 159 ( 42 unt; 0 def)
% Number of atoms : 348 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 316 ( 127 ~; 122 |; 36 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 674 ( 662 !; 12 ?)
% 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(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
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(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(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/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(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/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(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
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(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,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,F,E,P] :
( ( coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) )
=> eqangle(A,C,C,P,P,C,C,B) ),
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(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(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(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f206,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
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(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,F,E,P] :
( ~ eqangle(A,C,C,P,P,C,C,B)
& coll(P,A,F)
& coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,B,C,P] :
( ~ eqangle(A,C,C,P,P,C,C,B)
& ? [F] :
( coll(P,A,F)
& ? [E] :
( coll(P,B,E)
& cong(A,E,E,F)
& eqangle(B,A,A,E,A,E,E,F)
& perp(C,A,C,B) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK21_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& coll(sK23_skl,sK21_skl,sK25_skl)
& cong(sK20_skl,sK25_skl,sK25_skl,sK24_skl)
& eqangle(sK21_skl,sK20_skl,sK20_skl,sK25_skl,sK20_skl,sK25_skl,sK25_skl,sK24_skl)
& perp(sK22_skl,sK20_skl,sK22_skl,sK21_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(C,sK22_skl),skolemize(P,sK23_skl),skolemize(F,sK24_skl),skolemize(E,sK25_skl)],[f370]) ).
fof(f372,plain,
perp(sK22_skl,sK20_skl,sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f414,plain,
perp(sK22_skl,sK20_skl,sK21_skl,sK22_skl),
inference(resolution,[status(thm)],[f112,f372]) ).
fof(f417,plain,
perp(sK22_skl,sK21_skl,sK22_skl,sK20_skl),
inference(resolution,[status(thm)],[f114,f372]) ).
fof(f435,plain,
! [X0,X1] :
( para(sK22_skl,sK21_skl,X0,X1)
| ~ perp(sK22_skl,sK20_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f417]) ).
fof(f1087,plain,
para(sK22_skl,sK21_skl,sK21_skl,sK22_skl),
inference(resolution,[status(thm)],[f435,f414]) ).
fof(f1088,plain,
para(sK22_skl,sK21_skl,sK22_skl,sK21_skl),
inference(resolution,[status(thm)],[f435,f372]) ).
fof(f1166,plain,
para(sK21_skl,sK22_skl,sK22_skl,sK21_skl),
inference(resolution,[status(thm)],[f1087,f107]) ).
fof(f1172,plain,
coll(sK22_skl,sK21_skl,sK21_skl),
inference(resolution,[status(thm)],[f1088,f256]) ).
fof(f1174,plain,
coll(sK21_skl,sK22_skl,sK21_skl),
inference(resolution,[status(thm)],[f1172,f100]) ).
fof(f1178,plain,
coll(sK21_skl,sK21_skl,sK22_skl),
inference(resolution,[status(thm)],[f1174,f98]) ).
fof(f1188,plain,
para(sK21_skl,sK22_skl,sK21_skl,sK22_skl),
inference(resolution,[status(thm)],[f1166,f105]) ).
fof(f1276,plain,
! [X0,X1] : eqangle(sK21_skl,sK22_skl,X0,X1,sK21_skl,sK22_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f1188]) ).
fof(f2358,plain,
! [X0,X1] : eqangle(X0,X1,sK21_skl,sK22_skl,X0,X1,sK21_skl,sK22_skl),
inference(resolution,[status(thm)],[f1276,f140]) ).
fof(f2719,plain,
! [X0] :
( cyclic(X0,sK22_skl,sK21_skl,sK21_skl)
| ~ coll(sK21_skl,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f2358,f195]) ).
fof(f2721,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f2358,f186]) ).
fof(f2729,plain,
! [X0] : cyclic(X0,sK22_skl,sK21_skl,sK21_skl),
inference(forward_subsumption_resolution,[status(thm)],[f2719,f1178]) ).
fof(f2736,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f2721,f256]) ).
fof(f2948,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f2736,f100]) ).
fof(f3132,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f2948,f98]) ).
fof(f3163,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3132,f103]) ).
fof(f3166,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3163,f3132]) ).
fof(f3169,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f3166]) ).
fof(f3192,plain,
! [X0] : cyclic(sK22_skl,X0,sK21_skl,sK21_skl),
inference(resolution,[status(thm)],[f2729,f133]) ).
fof(f3198,plain,
! [X0] : cyclic(sK22_skl,sK21_skl,X0,sK21_skl),
inference(resolution,[status(thm)],[f3192,f131]) ).
fof(f3209,plain,
! [X0] : cyclic(sK22_skl,sK21_skl,sK21_skl,X0),
inference(resolution,[status(thm)],[f3198,f129]) ).
fof(f3226,plain,
! [X0,X1] :
( cyclic(sK21_skl,sK21_skl,X1,X0)
| ~ cyclic(sK22_skl,sK21_skl,sK21_skl,X0) ),
inference(resolution,[status(thm)],[f3209,f136]) ).
fof(f3230,plain,
! [X0,X1] : cyclic(sK21_skl,sK21_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3226,f3209]) ).
fof(f3231,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f3166]) ).
fof(f3247,plain,
! [X0,X1,X2] :
( cyclic(sK21_skl,X0,X2,X1)
| ~ cyclic(sK21_skl,sK21_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3230,f136]) ).
fof(f3251,plain,
! [X0,X1,X2] : cyclic(sK21_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3247,f3230]) ).
fof(f3253,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK21_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3251,f136]) ).
fof(f3257,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3253,f3251]) ).
fof(f3260,plain,
! [X0,X1,X2,X3] :
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ para(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f227,f3257]) ).
fof(f3261,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,f3257]) ).
fof(f3262,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3257]) ).
fof(f3263,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)],[f3261,f3257]) ).
fof(f3362,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2),
inference(resolution,[status(thm)],[f3262,f138]) ).
fof(f3514,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)],[f3263,f3257]) ).
fof(f3518,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f3514,f3362]) ).
fof(f3547,plain,
! [X0,X1] : midp(X0,X1,X1),
inference(resolution,[status(thm)],[f3518,f3231]) ).
fof(f3548,plain,
! [X0,X1,X2] :
( perp(X0,X0,X2,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3518,f232]) ).
fof(f3555,plain,
! [X0,X1,X2] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3548,f3518]) ).
fof(f3582,plain,
! [X0,X1,X2] : perp(X0,X1,X2,X2),
inference(resolution,[status(thm)],[f3555,f114]) ).
fof(f3627,plain,
! [X0,X1,X2,X3,X4] :
( para(X3,X4,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3582,f117]) ).
fof(f3630,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3627,f3555]) ).
fof(f3631,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f3169,f3630]) ).
fof(f3633,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X1,X2,X1,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f3260,f3630]) ).
fof(f3635,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f3630]) ).
fof(f3644,plain,
! [X0,X1,X2] : midp(X0,X1,X2),
inference(resolution,[status(thm)],[f3631,f3547]) ).
fof(f3652,plain,
! [X0,X1,X2] : cong(X0,X1,X0,X2),
inference(backward_subsumption_resolution,[status(thm)],[f260,f3644]) ).
fof(f3666,plain,
! [X0,X1,X2] : eqangle(X0,X1,X1,X2,X1,X2,X0,X2),
inference(backward_subsumption_resolution,[status(thm)],[f206,f3652]) ).
fof(f3737,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X7,X1,X0,X1,X3,X4,X5,X6)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[f3633,f147]) ).
fof(f3839,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5),
inference(resolution,[status(thm)],[f3635,f144]) ).
fof(f3859,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( eqangle(X2,X0,X0,X1,X3,X4,X5,X6)
| ~ eqangle(X0,X1,X2,X1,X3,X4,X5,X6) ),
inference(resolution,[status(thm)],[f3666,f147]) ).
fof(f4017,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X0,X1,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f3839,f142]) ).
fof(f4342,plain,
! [X0,X1,X2,X3,X4,X5,X6] : eqangle(X0,X1,X2,X1,X3,X4,X5,X6),
inference(resolution,[status(thm)],[f3737,f4017]) ).
fof(f4968,plain,
! [X0,X1,X2,X3,X4,X5,X6] : eqangle(X0,X1,X1,X2,X3,X4,X5,X6),
inference(backward_subsumption_resolution,[status(thm)],[f3859,f4342]) ).
fof(f4978,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f377,f4968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO581+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 17:38:42 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 1.44/0.75 % Refutation found
% 1.44/0.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.44/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.77 % Elapsed time: 0.396432 seconds
% 1.44/0.77 % CPU time: 2.850674 seconds
% 1.44/0.77 % Total memory used: 110.612 MB
% 1.44/0.77 % Net memory used: 106.598 MB
%------------------------------------------------------------------------------