%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO541+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 : 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 12:25:11 PM UTC 2026
% Result : Theorem 7.82s 6.44s
% Output : CNFRefutation 7.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 35
% Syntax : Number of formulae : 181 ( 11 unt; 5 def)
% Number of atoms : 475 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 514 ( 220 ~; 210 |; 48 &)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 666 ( 649 !; 17 ?)
% 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(f6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
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(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(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(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
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(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(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/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(f91,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
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(f108,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f109,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ para(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
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(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f148,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
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(f231,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f255,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f256,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(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(f350,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f351,plain,
! [A,E,F] :
( ? [P] :
( perp(P,A,E,F)
& coll(P,E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(miniscoping,[status(thm)],[f350]) ).
fof(f352,plain,
! [A,E,F] :
( ( perp(sK16_skl(F,E,A),A,E,F)
& coll(sK16_skl(F,E,A),E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(P,sK16_skl(F,E,A))],[f351]) ).
fof(f354,plain,
! [X0,X1,X2,X3,X4] :
( perp(sK16_skl(X4,X3,X0),X0,X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f369,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(F,G,D,E)
& midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [D,E,F,G] :
( ~ perp(F,G,D,E)
& midp(G,D,E)
& ? [B,C] :
( midp(F,C,B)
& ? [A] :
( coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
& midp(sK23_skl,sK20_skl,sK21_skl)
& midp(sK22_skl,sK25_skl,sK24_skl)
& coll(sK21_skl,sK26_skl,sK25_skl)
& perp(sK21_skl,sK24_skl,sK26_skl,sK25_skl)
& coll(sK20_skl,sK26_skl,sK24_skl)
& perp(sK20_skl,sK25_skl,sK26_skl,sK24_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(D,sK20_skl),skolemize(E,sK21_skl),skolemize(F,sK22_skl),skolemize(G,sK23_skl),skolemize(B,sK24_skl),skolemize(C,sK25_skl),skolemize(A,sK26_skl)],[f370]) ).
fof(f372,plain,
perp(sK20_skl,sK25_skl,sK26_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
perp(sK21_skl,sK24_skl,sK26_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
midp(sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f415,plain,
midp(sK23_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f122,f377]) ).
fof(f419,plain,
perp(sK26_skl,sK25_skl,sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f114,f374]) ).
fof(f420,plain,
perp(sK26_skl,sK24_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f114,f372]) ).
fof(f525,plain,
! [X0,X1] :
( perp(X0,X1,sK21_skl,sK24_skl)
| ~ para(X0,X1,sK26_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f419,f120]) ).
fof(f538,plain,
! [X0,X1] :
( para(X0,X1,sK20_skl,sK25_skl)
| ~ perp(X0,X1,sK26_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f420,f117]) ).
fof(f672,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f791,plain,
! [X0,X1,X2] :
( cong(X0,X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f672,f149]) ).
fof(f822,plain,
! [X0,X1,X2] :
( cong(X1,X0,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f791,f151]) ).
fof(f993,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f144]) ).
fof(f995,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)],[f189,f140]) ).
fof(f1023,plain,
para(sK20_skl,sK25_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f538,f372]) ).
fof(f1133,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ midp(X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1133,f822]) ).
fof(f1188,plain,
( perp(sK26_skl,sK26_skl,sK21_skl,sK24_skl)
| ~ midp(sK26_skl,sK26_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f1175,f525]) ).
fof(f1205,definition,
( sQ34_spl
<=> midp(sK26_skl,sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1207,plain,
( sQ34_spl
| ~ midp(sK26_skl,sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1208,definition,
( sQ35_spl
<=> perp(sK26_skl,sK26_skl,sK21_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1209,plain,
( ~ sQ35_spl
| perp(sK26_skl,sK26_skl,sK21_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f1208]) ).
fof(f1211,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f1188,f1205,f1208]) ).
fof(f1302,plain,
! [X0,X1] :
( ~ sQ35_spl
| para(X0,X1,sK21_skl,sK24_skl)
| ~ perp(X0,X1,sK26_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f1209,f117]) ).
fof(f2940,plain,
! [X0,X1,X2,X3,X4] :
( perp(sK16_skl(X4,X3,X0),X0,X4,X3)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f354,f112]) ).
fof(f3463,definition,
! [X4,X5] :
( sQ175_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f3464,plain,
! [X0,X1] :
( ~ sQ175_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3463]) ).
fof(f3510,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f995,f186]) ).
fof(f3518,definition,
! [X2,X3] :
( sQ176_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f3519,plain,
! [X0,X1] :
( ~ sQ176_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3518]) ).
fof(f3521,plain,
( sQ176_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f3510,f3463,f3518]) ).
fof(f3577,plain,
( ~ sQ175_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1023,f3464]) ).
fof(f3591,plain,
~ sQ175_spl,
inference(contradiction_clause,[status(thm)],[f3577]) ).
fof(f3600,plain,
! [X0,X1] :
( ~ sQ176_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3519,f256]) ).
fof(f3603,plain,
! [X0,X1] :
( ~ sQ176_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f3519,f105]) ).
fof(f3633,plain,
! [X0,X1] :
( ~ sQ176_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3600,f100]) ).
fof(f3664,plain,
! [X0,X1] :
( ~ sQ176_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3633,f98]) ).
fof(f3669,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3664,f103]) ).
fof(f3672,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3669,f3664]) ).
fof(f3679,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ176_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f3672]) ).
fof(f3680,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3672]) ).
fof(f3681,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3672]) ).
fof(f3703,definition,
! [X3,X4,X5] :
( sQ180_spl
<=> ~ midp(X3,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f3704,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| ~ midp(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f3703]) ).
fof(f3750,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3679,f3603]) ).
fof(f3760,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3680,f993]) ).
fof(f3770,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3760,f3519]) ).
fof(f3810,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3770,f136]) ).
fof(f3814,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3810,f3770]) ).
fof(f3823,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ176_spl
| 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,f3814]) ).
fof(f3824,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3814]) ).
fof(f3825,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3814]) ).
fof(f3826,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ176_spl
| 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)],[f3823,f3814]) ).
fof(f3859,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ176_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3826,f3814]) ).
fof(f3869,plain,
! [X0,X1] :
( ~ sQ176_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3824,f3859]) ).
fof(f3883,plain,
! [X0,X1] :
( ~ sQ176_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3869,f3681]) ).
fof(f3886,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3869,f232]) ).
fof(f3895,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3886,f3869]) ).
fof(f3917,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3895,f114]) ).
fof(f3948,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3825,f3869]) ).
fof(f3959,plain,
! [X0,X1,X2] :
( ~ sQ176_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3948,f3869]) ).
fof(f4340,plain,
( ~ sQ180_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f415,f3704]) ).
fof(f4359,plain,
~ sQ180_spl,
inference(contradiction_clause,[status(thm)],[f4340]) ).
fof(f5410,plain,
! [X0,X1] :
( ~ sQ176_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3750,f3883]) ).
fof(f5416,plain,
( sQ34_spl
| ~ sQ176_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1207,f5410]) ).
fof(f5430,plain,
( sQ34_spl
| ~ sQ176_spl ),
inference(contradiction_clause,[status(thm)],[f5416]) ).
fof(f5436,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ sQ176_spl
| para(X0,X1,sK21_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1302,f3917]) ).
fof(f5547,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ sQ176_spl
| para(sK21_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f5436,f107]) ).
fof(f5594,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| perp(sK16_skl(X2,X1,X3),X3,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2940,f3959]) ).
fof(f5676,plain,
! [X0,X1,X2,X3] :
( ~ sQ35_spl
| ~ sQ176_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK21_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f5547,f110]) ).
fof(f5679,plain,
! [X0,X1,X2,X3] :
( ~ sQ35_spl
| ~ sQ176_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5676,f5436]) ).
fof(f5699,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ35_spl
| ~ sQ176_spl
| perp(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f5679]) ).
fof(f5902,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ176_spl
| ~ sQ35_spl
| ~ coll(X4,X3,X2)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f5699,f5594]) ).
fof(f5929,plain,
! [X0,X1,X2,X3] :
( ~ sQ176_spl
| ~ sQ35_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5902,f3672]) ).
fof(f5982,plain,
( ~ sQ176_spl
| ~ sQ35_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f378,f5929]) ).
fof(f5983,plain,
( ~ sQ176_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f5982]) ).
fof(f5984,plain,
$false,
inference(sat_refutation,[status(thm)],[f1211,f3521,f3591,f4359,f5430,f5983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO541+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 17:19:35 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 7.82/6.44 % Refutation found
% 7.82/6.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.82/6.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.82/6.48 % Elapsed time: 1.100335 seconds
% 7.82/6.48 % CPU time: 8.416374 seconds
% 7.82/6.48 % Total memory used: 169.465 MB
% 7.82/6.48 % Net memory used: 159.462 MB
%------------------------------------------------------------------------------