%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO598+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 : n020.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 12:25:20 PM UTC 2026
% Result : Theorem 8.89s 1.64s
% Output : CNFRefutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 25
% Syntax : Number of formulae : 130 ( 10 unt; 5 def)
% Number of atoms : 347 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 373 ( 156 ~; 143 |; 48 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 6 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 535 ( 515 !; 20 ?)
% 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(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(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(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(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(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(f95,conjecture,
! [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ( coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) )
=> eqangle(F,G,G,I,I,G,G,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ( coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) )
=> eqangle(F,G,G,I,I,G,G,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(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(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(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(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(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(f369,plain,
? [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ~ eqangle(F,G,G,I,I,G,G,E)
& coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,F,G,I] :
( ~ eqangle(F,G,G,I,I,G,G,E)
& ? [A,C] :
( coll(I,A,C)
& ? [H] :
( perp(I,H,A,C)
& ? [D] :
( ? [NWPNT1] : circle(D,A,H,NWPNT1)
& coll(H,D,G)
& ? [B] :
( midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK21_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK20_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& perp(sK23_skl,sK26_skl,sK24_skl,sK25_skl)
& circle(sK27_skl,sK24_skl,sK26_skl,sK29_skl)
& coll(sK26_skl,sK27_skl,sK22_skl)
& midp(sK22_skl,sK28_skl,sK24_skl)
& midp(sK21_skl,sK24_skl,sK25_skl)
& midp(sK20_skl,sK25_skl,sK28_skl)
& circle(sK27_skl,sK24_skl,sK28_skl,sK25_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(E,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(I,sK23_skl),skolemize(A,sK24_skl),skolemize(C,sK25_skl),skolemize(H,sK26_skl),skolemize(D,sK27_skl),skolemize(B,sK28_skl),skolemize(NWPNT1,sK29_skl)],[f370]) ).
fof(f375,plain,
midp(sK22_skl,sK28_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
perp(sK23_skl,sK26_skl,sK24_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
~ eqangle(sK21_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f417,plain,
midp(sK22_skl,sK24_skl,sK28_skl),
inference(resolution,[status(thm)],[f122,f375]) ).
fof(f440,plain,
perp(sK24_skl,sK25_skl,sK23_skl,sK26_skl),
inference(resolution,[status(thm)],[f378,f114]) ).
fof(f489,plain,
! [X0,X1] :
( para(X0,X1,sK23_skl,sK26_skl)
| ~ perp(X0,X1,sK24_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f440,f117]) ).
fof(f845,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X4,X5,X6,X7,X2,X3,X8,X9)
| ~ eqangle(X4,X5,X6,X7,X0,X1,X8,X9)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f147]) ).
fof(f846,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(f848,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(f1029,plain,
para(sK23_skl,sK26_skl,sK23_skl,sK26_skl),
inference(resolution,[status(thm)],[f489,f378]) ).
fof(f1359,definition,
( sQ45_spl
<=> perp(sK25_skl,sK25_skl,sK23_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1360,plain,
( ~ sQ45_spl
| perp(sK25_skl,sK25_skl,sK23_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f1359]) ).
fof(f1361,plain,
( sQ45_spl
| ~ perp(sK25_skl,sK25_skl,sK23_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f1359]) ).
fof(f1415,plain,
! [X0,X1] :
( ~ sQ45_spl
| para(X0,X1,sK23_skl,sK26_skl)
| ~ perp(X0,X1,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f1360,f117]) ).
fof(f2809,definition,
! [X0,X1] :
( sQ126_spl
<=> ~ midp(X0,sK24_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f2810,plain,
! [X0,X1] :
( ~ sQ126_spl
| ~ midp(X0,sK24_skl,X1) ),
inference(component_clause,[status(thm)],[f2809]) ).
fof(f2818,definition,
! [X0,X1,X2] :
( sQ128_spl
<=> ~ midp(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2819,plain,
! [X0,X1,X2] :
( ~ sQ128_spl
| ~ midp(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f2818]) ).
fof(f2826,plain,
( ~ sQ126_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f417,f2810]) ).
fof(f3042,definition,
! [X4,X5] :
( sQ161_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f3043,plain,
! [X0,X1] :
( ~ sQ161_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3042]) ).
fof(f3055,plain,
( ~ sQ161_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1029,f3043]) ).
fof(f3067,plain,
~ sQ161_spl,
inference(contradiction_clause,[status(thm)],[f3055]) ).
fof(f3212,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f848,f186]) ).
fof(f3224,definition,
! [X2,X3] :
( sQ167_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f3225,plain,
! [X0,X1] :
( ~ sQ167_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3224]) ).
fof(f3227,plain,
( sQ167_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f3212,f3042,f3224]) ).
fof(f3233,plain,
! [X0,X1] :
( ~ sQ167_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3225,f256]) ).
fof(f3255,plain,
! [X0,X1] :
( ~ sQ167_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3233,f100]) ).
fof(f3278,plain,
! [X0,X1] :
( ~ sQ167_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3255,f98]) ).
fof(f3282,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3278,f103]) ).
fof(f3286,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3282,f3278]) ).
fof(f3292,plain,
! [X0,X1,X2,X3] :
( ~ sQ167_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3286]) ).
fof(f3315,plain,
~ sQ126_spl,
inference(contradiction_clause,[status(thm)],[f2826]) ).
fof(f3344,plain,
( ~ sQ128_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f417,f2819]) ).
fof(f3350,plain,
~ sQ128_spl,
inference(contradiction_clause,[status(thm)],[f3344]) ).
fof(f3360,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3292,f846]) ).
fof(f3376,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3360,f3225]) ).
fof(f3390,plain,
! [X0,X1,X2,X3] :
( ~ sQ167_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3376,f136]) ).
fof(f3394,plain,
! [X0,X1,X2,X3] :
( ~ sQ167_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3390,f3376]) ).
fof(f3402,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ167_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,f3394]) ).
fof(f3403,plain,
! [X0,X1,X2,X3] :
( ~ sQ167_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3394]) ).
fof(f3405,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ167_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)],[f3402,f3394]) ).
fof(f3646,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ167_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3405,f3394]) ).
fof(f3663,plain,
! [X0,X1] :
( ~ sQ167_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3403,f3646]) ).
fof(f3700,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3663,f232]) ).
fof(f3706,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3700,f3663]) ).
fof(f3752,plain,
! [X0,X1,X2] :
( ~ sQ167_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3706,f114]) ).
fof(f3877,plain,
! [X0,X1] :
( ~ sQ45_spl
| ~ sQ167_spl
| para(X0,X1,sK23_skl,sK26_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1415,f3752]) ).
fof(f3882,plain,
( sQ45_spl
| ~ sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1361,f3706]) ).
fof(f3883,plain,
( sQ45_spl
| ~ sQ167_spl ),
inference(contradiction_clause,[status(thm)],[f3882]) ).
fof(f3953,plain,
! [X0,X1] :
( ~ sQ45_spl
| ~ sQ167_spl
| para(sK23_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3877,f107]) ).
fof(f4106,plain,
! [X0,X1,X2,X3] :
( ~ sQ45_spl
| ~ sQ167_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK23_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3953,f110]) ).
fof(f4109,plain,
! [X0,X1,X2,X3] :
( ~ sQ45_spl
| ~ sQ167_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4106,f3877]) ).
fof(f4117,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ45_spl
| ~ sQ167_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f846,f4109]) ).
fof(f4118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ45_spl
| ~ sQ167_spl
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(backward_subsumption_resolution,[status(thm)],[f845,f4109]) ).
fof(f4336,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ45_spl
| ~ sQ167_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f4118,f4117]) ).
fof(f4702,plain,
( ~ sQ45_spl
| ~ sQ167_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f380,f4336]) ).
fof(f4703,plain,
( ~ sQ45_spl
| ~ sQ167_spl ),
inference(contradiction_clause,[status(thm)],[f4702]) ).
fof(f4704,plain,
$false,
inference(sat_refutation,[status(thm)],[f3067,f3227,f3315,f3350,f3883,f4703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO598+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 17:45:02 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 8.89/1.64 % Refutation found
% 8.89/1.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.89/1.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.89/1.67 % Elapsed time: 1.206071 seconds
% 8.89/1.67 % CPU time: 9.203934 seconds
% 8.89/1.67 % Total memory used: 150.219 MB
% 8.89/1.67 % Net memory used: 142.377 MB
%------------------------------------------------------------------------------