%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO568+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 : n010.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 12:25:15 PM UTC 2026
% Result : Theorem 8.03s 1.45s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 119 ( 10 unt; 2 def)
% Number of atoms : 341 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 366 ( 144 ~; 136 |; 63 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-3 aty)
% Number of variables : 501 ( 480 !; 21 ?)
% 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(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(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(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(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(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,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B) )
=> perp(A,O,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ( coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B) )
=> perp(A,O,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(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f119,plain,
! [A,B,E,F] :
( perp(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(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(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(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(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,O,D,E,MIDPNT1,MIDPNT2,MIDPNT3] :
( ~ perp(A,O,D,E)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,O,D,E] :
( ~ perp(A,O,D,E)
& ? [C] :
( coll(E,A,C)
& ? [B] :
( perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B)
& ? [MIDPNT3] :
( perp(B,C,MIDPNT3,O)
& midp(MIDPNT3,B,C)
& ? [MIDPNT2] :
( perp(A,C,MIDPNT2,O)
& midp(MIDPNT2,A,C)
& ? [MIDPNT1] :
( perp(A,B,MIDPNT1,O)
& midp(MIDPNT1,A,B) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ perp(sK20_skl,sK21_skl,sK22_skl,sK23_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& perp(sK23_skl,sK25_skl,sK20_skl,sK24_skl)
& coll(sK22_skl,sK20_skl,sK25_skl)
& perp(sK22_skl,sK24_skl,sK20_skl,sK25_skl)
& perp(sK25_skl,sK24_skl,sK26_skl,sK21_skl)
& midp(sK26_skl,sK25_skl,sK24_skl)
& perp(sK20_skl,sK24_skl,sK27_skl,sK21_skl)
& midp(sK27_skl,sK20_skl,sK24_skl)
& perp(sK20_skl,sK25_skl,sK28_skl,sK21_skl)
& midp(sK28_skl,sK20_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]),skolemize(A,sK20_skl),skolemize(O,sK21_skl),skolemize(D,sK22_skl),skolemize(E,sK23_skl),skolemize(C,sK24_skl),skolemize(B,sK25_skl),skolemize(MIDPNT3,sK26_skl),skolemize(MIDPNT2,sK27_skl),skolemize(MIDPNT1,sK28_skl)],[f370]) ).
fof(f377,plain,
perp(sK25_skl,sK24_skl,sK26_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ perp(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f450,plain,
perp(sK26_skl,sK21_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f377,f114]) ).
fof(f626,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK24_skl)
| ~ perp(X0,X1,sK26_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f450,f117]) ).
fof(f628,plain,
perp(sK26_skl,sK21_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f450,f112]) ).
fof(f769,plain,
perp(sK24_skl,sK25_skl,sK26_skl,sK21_skl),
inference(resolution,[status(thm)],[f628,f114]) ).
fof(f1141,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(f1143,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(f1504,plain,
para(sK24_skl,sK25_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f626,f769]) ).
fof(f2024,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f1504,f105]) ).
fof(f3690,definition,
! [X4,X5] :
( sQ268_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3691,plain,
! [X0,X1] :
( ~ sQ268_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3690]) ).
fof(f3912,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1143,f186]) ).
fof(f3920,definition,
! [X2,X3] :
( sQ273_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3921,plain,
! [X0,X1] :
( ~ sQ273_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3920]) ).
fof(f3923,plain,
( sQ273_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3912,f3690,f3920]) ).
fof(f4050,plain,
( ~ sQ268_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2024,f3691]) ).
fof(f4069,plain,
~ sQ268_spl,
inference(contradiction_clause,[status(thm)],[f4050]) ).
fof(f4085,plain,
! [X0,X1] :
( ~ sQ273_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3921,f256]) ).
fof(f4116,plain,
! [X0,X1] :
( ~ sQ273_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4085,f100]) ).
fof(f4143,plain,
! [X0,X1] :
( ~ sQ273_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4116,f98]) ).
fof(f4146,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4143,f103]) ).
fof(f4149,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4146,f4143]) ).
fof(f4150,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ273_spl
| perp(sK16_skl(X3,X4,X0),X0,X4,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f354,f4149]) ).
fof(f4157,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f4149]) ).
fof(f4193,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ273_spl
| perp(X3,X4,X6,X5)
| ~ para(X3,X4,sK16_skl(X5,X6,X0),X0)
| ~ perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f4150,f120]) ).
fof(f4194,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ273_spl
| para(X3,X4,X6,X5)
| ~ perp(X3,X4,sK16_skl(X5,X6,X0),X0)
| ~ perp(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f4150,f117]) ).
fof(f4282,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4157,f1141]) ).
fof(f4291,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4282,f3921]) ).
fof(f4310,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4291,f136]) ).
fof(f4314,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4310,f4291]) ).
fof(f4421,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ273_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,f4314]) ).
fof(f4422,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f4314]) ).
fof(f4423,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f4314]) ).
fof(f4424,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ273_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)],[f4421,f4314]) ).
fof(f4572,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ273_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f4424,f4314]) ).
fof(f4602,plain,
! [X0,X1] :
( ~ sQ273_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4422,f4572]) ).
fof(f4627,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4602,f4423]) ).
fof(f4635,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4627,f4602]) ).
fof(f4680,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| perp(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f4635,f112]) ).
fof(f7032,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ273_spl
| perp(X0,X1,X3,X2)
| ~ para(X0,X1,sK16_skl(X2,X3,X4),X4) ),
inference(forward_subsumption_resolution,[status(thm)],[f4193,f4635]) ).
fof(f7253,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ273_spl
| para(X0,X1,X3,X2)
| ~ perp(X0,X1,sK16_skl(X2,X3,X4),X4) ),
inference(forward_subsumption_resolution,[status(thm)],[f4194,f4635]) ).
fof(f7268,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f7253,f4680]) ).
fof(f7298,plain,
! [X0,X1,X2,X3] :
( ~ sQ273_spl
| perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f7032,f7268]) ).
fof(f7320,plain,
( ~ sQ273_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f382,f7298]) ).
fof(f7323,plain,
~ sQ273_spl,
inference(contradiction_clause,[status(thm)],[f7320]) ).
fof(f7324,plain,
$false,
inference(sat_refutation,[status(thm)],[f3923,f4069,f7323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO568+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 17:30:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 8.03/1.45 % Refutation found
% 8.03/1.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.03/1.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.03/1.48 % Elapsed time: 1.101073 seconds
% 8.03/1.48 % CPU time: 8.378549 seconds
% 8.03/1.48 % Total memory used: 168.240 MB
% 8.03/1.48 % Net memory used: 157.941 MB
%------------------------------------------------------------------------------