%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO544+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 : n005.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 12:25:12 PM UTC 2026
% Result : Theorem 11.16s 1.84s
% Output : CNFRefutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of formulae : 145 ( 9 unt; 2 def)
% Number of atoms : 398 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 427 ( 174 ~; 166 |; 58 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 559 ( 537 !; 22 ?)
% 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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,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(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(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(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
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(f95,conjecture,
! [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ( coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(S,M,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ( coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> perp(S,M,B,C) ),
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(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(f125,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f126,plain,
! [A,B,C,D] :
( cyclic(A,B,C,D)
| ! [O] :
( ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
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(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(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(f220,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f221,plain,
! [A,B,M] :
( cong(A,M,B,M)
| ! [C] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C) ) ),
inference(miniscoping,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
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(f369,plain,
? [A,B,C,O,D,Q,S,J,M,I,NWPNT1] :
( ~ perp(S,M,B,C)
& coll(I,B,C)
& coll(I,A,D)
& cong(O,J,O,M)
& coll(O,J,M)
& midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,C,S,M] :
( ~ perp(S,M,B,C)
& ? [I] :
( coll(I,B,C)
& ? [A,D] :
( coll(I,A,D)
& ? [O,J] :
( cong(O,J,O,M)
& coll(O,J,M)
& ? [Q] :
( midp(J,S,Q)
& midp(S,A,D)
& midp(Q,C,B)
& ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
& coll(sK24_skl,sK20_skl,sK21_skl)
& coll(sK24_skl,sK25_skl,sK26_skl)
& cong(sK27_skl,sK28_skl,sK27_skl,sK23_skl)
& coll(sK27_skl,sK28_skl,sK23_skl)
& midp(sK28_skl,sK22_skl,sK29_skl)
& midp(sK22_skl,sK25_skl,sK26_skl)
& midp(sK29_skl,sK21_skl,sK20_skl)
& circle(sK27_skl,sK25_skl,sK26_skl,sK30_skl)
& circle(sK27_skl,sK25_skl,sK20_skl,sK21_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(B,sK20_skl),skolemize(C,sK21_skl),skolemize(S,sK22_skl),skolemize(M,sK23_skl),skolemize(I,sK24_skl),skolemize(A,sK25_skl),skolemize(D,sK26_skl),skolemize(O,sK27_skl),skolemize(J,sK28_skl),skolemize(Q,sK29_skl),skolemize(NWPNT1,sK30_skl)],[f370]) ).
fof(f378,plain,
cong(sK27_skl,sK28_skl,sK27_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ perp(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f486,plain,
cong(sK27_skl,sK23_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f151,f378]) ).
fof(f551,plain,
! [X0] :
( cyclic(sK23_skl,X0,sK28_skl,sK28_skl)
| ~ cong(sK27_skl,sK23_skl,sK27_skl,X0) ),
inference(resolution,[status(thm)],[f486,f127]) ).
fof(f1007,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(f1009,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(f1012,plain,
! [X0,X1,X2] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f191,f186]) ).
fof(f1169,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f1597,plain,
cyclic(sK23_skl,sK28_skl,sK28_skl,sK28_skl),
inference(resolution,[status(thm)],[f551,f486]) ).
fof(f1687,plain,
cyclic(sK28_skl,sK23_skl,sK28_skl,sK28_skl),
inference(resolution,[status(thm)],[f1597,f133]) ).
fof(f1797,plain,
para(sK28_skl,sK28_skl,sK28_skl,sK28_skl),
inference(resolution,[status(thm)],[f1687,f1012]) ).
fof(f4009,definition,
! [X4,X5] :
( sQ312_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4010,plain,
! [X0,X1] :
( ~ sQ312_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f4009]) ).
fof(f4170,plain,
( ~ sQ312_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1797,f4010]) ).
fof(f4176,plain,
~ sQ312_spl,
inference(contradiction_clause,[status(thm)],[f4170]) ).
fof(f4209,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1009,f186]) ).
fof(f4217,definition,
! [X2,X3] :
( sQ333_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4218,plain,
! [X0,X1] :
( ~ sQ333_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f4217]) ).
fof(f4220,plain,
( sQ333_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f4209,f4009,f4217]) ).
fof(f4287,plain,
! [X0,X1] :
( ~ sQ333_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4218,f256]) ).
fof(f4290,plain,
! [X0,X1] :
( ~ sQ333_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f4218,f105]) ).
fof(f4310,plain,
! [X0,X1] :
( ~ sQ333_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4287,f100]) ).
fof(f4333,plain,
! [X0,X1] :
( ~ sQ333_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4310,f98]) ).
fof(f4335,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4333,f103]) ).
fof(f4338,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4335,f4333]) ).
fof(f4345,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ333_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f4338]) ).
fof(f4346,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f4338]) ).
fof(f4347,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f4338]) ).
fof(f4410,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f4345,f4290]) ).
fof(f4415,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4346,f1007]) ).
fof(f4429,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4415,f4218]) ).
fof(f4442,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4429,f136]) ).
fof(f4446,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4442,f4429]) ).
fof(f4487,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ333_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,f4446]) ).
fof(f4488,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f4446]) ).
fof(f4490,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f4446]) ).
fof(f4491,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ333_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)],[f4487,f4446]) ).
fof(f4633,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ333_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f4491,f4446]) ).
fof(f4648,plain,
! [X0,X1] :
( ~ sQ333_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4488,f4633]) ).
fof(f4680,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4648,f4490]) ).
fof(f4681,plain,
! [X0,X1] :
( ~ sQ333_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4648,f4347]) ).
fof(f4687,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4680,f4648]) ).
fof(f4711,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f4687]) ).
fof(f5467,plain,
! [X0,X1] :
( ~ sQ333_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4410,f4681]) ).
fof(f5479,plain,
! [X0,X1] :
( ~ sQ333_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f5467,f122]) ).
fof(f7379,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f260,f1169]) ).
fof(f7386,plain,
! [X0,X1] :
( ~ sQ333_spl
| para(X0,X0,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f7379,f5467]) ).
fof(f7389,plain,
! [X0,X1] :
( ~ sQ333_spl
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[f7386,f107]) ).
fof(f7539,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4345,f7389]) ).
fof(f7557,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f7539,f5479]) ).
fof(f7596,plain,
! [X0,X1,X2] :
( ~ sQ333_spl
| cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f4711,f7557]) ).
fof(f7741,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f7596]) ).
fof(f7748,plain,
! [X0,X1,X2,X3] :
( ~ sQ333_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f7741,f7596]) ).
fof(f7755,plain,
( ~ sQ333_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f381,f7748]) ).
fof(f7756,plain,
~ sQ333_spl,
inference(contradiction_clause,[status(thm)],[f7755]) ).
fof(f7757,plain,
$false,
inference(sat_refutation,[status(thm)],[f4176,f4220,f7756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO544+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 17:19:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 11.16/1.84 % Refutation found
% 11.16/1.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.16/1.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.16/1.88 % Elapsed time: 1.509673 seconds
% 11.16/1.88 % CPU time: 11.696923 seconds
% 11.16/1.88 % Total memory used: 198.764 MB
% 11.16/1.88 % Net memory used: 185.406 MB
%------------------------------------------------------------------------------