%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO659+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 12:25:29 PM UTC 2026
% Result : Theorem 5.03s 1.20s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 133 ( 12 unt; 2 def)
% Number of atoms : 368 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 376 ( 141 ~; 133 |; 77 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 508 ( 482 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(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,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4,NWPNT5] :
( ( circle(F,A,H,NWPNT5)
& coll(A,D,H)
& circle(F,B,G,NWPNT4)
& coll(B,E,G)
& perp(C,B,MIDPNT3,F)
& midp(MIDPNT3,C,B)
& perp(A,B,MIDPNT2,F)
& midp(MIDPNT2,A,B)
& perp(A,C,MIDPNT1,F)
& midp(MIDPNT1,A,C)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> para(D,E,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4,NWPNT5] :
( ( circle(F,A,H,NWPNT5)
& coll(A,D,H)
& circle(F,B,G,NWPNT4)
& coll(B,E,G)
& perp(C,B,MIDPNT3,F)
& midp(MIDPNT3,C,B)
& perp(A,B,MIDPNT2,F)
& midp(MIDPNT2,A,B)
& perp(A,C,MIDPNT1,F)
& midp(MIDPNT1,A,C)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> para(D,E,G,H) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
! [X0,X1,X2] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f102,plain,
! [A,C,D] :
( coll(C,D,A)
| ! [B] :
( ~ coll(A,B,D)
| ~ coll(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(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(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(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(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,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4,NWPNT5] :
( ~ para(D,E,G,H)
& circle(F,A,H,NWPNT5)
& coll(A,D,H)
& circle(F,B,G,NWPNT4)
& coll(B,E,G)
& perp(C,B,MIDPNT3,F)
& midp(MIDPNT3,C,B)
& perp(A,B,MIDPNT2,F)
& midp(MIDPNT2,A,B)
& perp(A,C,MIDPNT1,F)
& midp(MIDPNT1,A,C)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [D,E,G,H] :
( ~ para(D,E,G,H)
& ? [A,F] :
( ? [NWPNT5] : circle(F,A,H,NWPNT5)
& coll(A,D,H)
& ? [B] :
( ? [NWPNT4] : circle(F,B,G,NWPNT4)
& coll(B,E,G)
& ? [C,MIDPNT3] :
( perp(C,B,MIDPNT3,F)
& midp(MIDPNT3,C,B)
& ? [MIDPNT2] :
( perp(A,B,MIDPNT2,F)
& midp(MIDPNT2,A,B)
& ? [MIDPNT1] :
( perp(A,C,MIDPNT1,F)
& midp(MIDPNT1,A,C)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl)
& circle(sK25_skl,sK24_skl,sK23_skl,sK32_skl)
& coll(sK24_skl,sK20_skl,sK23_skl)
& circle(sK25_skl,sK26_skl,sK22_skl,sK31_skl)
& coll(sK26_skl,sK21_skl,sK22_skl)
& perp(sK27_skl,sK26_skl,sK28_skl,sK25_skl)
& midp(sK28_skl,sK27_skl,sK26_skl)
& perp(sK24_skl,sK26_skl,sK29_skl,sK25_skl)
& midp(sK29_skl,sK24_skl,sK26_skl)
& perp(sK24_skl,sK27_skl,sK30_skl,sK25_skl)
& midp(sK30_skl,sK24_skl,sK27_skl)
& coll(sK21_skl,sK24_skl,sK27_skl)
& perp(sK21_skl,sK26_skl,sK24_skl,sK27_skl)
& coll(sK20_skl,sK26_skl,sK27_skl)
& perp(sK20_skl,sK24_skl,sK26_skl,sK27_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,sK31_skl,sK32_skl]),skolemize(D,sK20_skl),skolemize(E,sK21_skl),skolemize(G,sK22_skl),skolemize(H,sK23_skl),skolemize(A,sK24_skl),skolemize(F,sK25_skl),skolemize(B,sK26_skl),skolemize(C,sK27_skl),skolemize(MIDPNT3,sK28_skl),skolemize(MIDPNT2,sK29_skl),skolemize(MIDPNT1,sK30_skl),skolemize(NWPNT4,sK31_skl),skolemize(NWPNT5,sK32_skl)],[f370]) ).
fof(f372,plain,
perp(sK20_skl,sK24_skl,sK26_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
perp(sK24_skl,sK26_skl,sK29_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
~ para(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f464,plain,
perp(sK20_skl,sK24_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f112,f372]) ).
fof(f468,plain,
perp(sK24_skl,sK26_skl,sK25_skl,sK29_skl),
inference(resolution,[status(thm)],[f379,f112]) ).
fof(f504,plain,
perp(sK29_skl,sK25_skl,sK24_skl,sK26_skl),
inference(resolution,[status(thm)],[f114,f379]) ).
fof(f512,plain,
! [X0,X1] :
( para(X0,X1,sK26_skl,sK27_skl)
| ~ perp(X0,X1,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f117,f372]) ).
fof(f541,plain,
perp(sK27_skl,sK26_skl,sK20_skl,sK24_skl),
inference(resolution,[status(thm)],[f464,f114]) ).
fof(f549,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK29_skl)
| ~ perp(X0,X1,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f468,f117]) ).
fof(f559,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK26_skl)
| ~ perp(X0,X1,sK29_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f504,f117]) ).
fof(f778,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X2,X3,X4,X5)
| eqangle(X0,X1,X2,X3,X0,X1,X4,X5) ),
inference(resolution,[status(thm)],[f140,f189]) ).
fof(f1902,plain,
para(sK27_skl,sK26_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f512,f541]) ).
fof(f2145,plain,
para(sK27_skl,sK26_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f1902,f105]) ).
fof(f3303,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f778,f186]) ).
fof(f3304,definition,
! [X0,X1] :
( sQ170_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f3305,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3304]) ).
fof(f3307,definition,
! [X2,X3] :
( sQ171_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f3308,plain,
! [X0,X1] :
( ~ sQ171_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3307]) ).
fof(f3310,plain,
( sQ171_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f3303,f3304,f3307]) ).
fof(f3312,plain,
( ~ sQ170_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2145,f3305]) ).
fof(f3334,plain,
~ sQ170_spl,
inference(contradiction_clause,[status(thm)],[f3312]) ).
fof(f3338,plain,
! [X0,X1] :
( ~ sQ171_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3308,f256]) ).
fof(f3390,plain,
! [X0,X1] :
( ~ sQ171_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3338,f100]) ).
fof(f3439,plain,
! [X0,X1] :
( ~ sQ171_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3390,f98]) ).
fof(f3442,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3439,f103]) ).
fof(f3445,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3442,f3439]) ).
fof(f3448,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3445]) ).
fof(f3495,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| ~ para(X2,X1,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3448,f778]) ).
fof(f3504,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3495,f3308]) ).
fof(f3511,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f3504,f131]) ).
fof(f3516,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f3511,f133]) ).
fof(f3523,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f3516,f129]) ).
fof(f3531,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f3523,f136]) ).
fof(f3535,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3531,f3523]) ).
fof(f3543,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ171_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,f3535]) ).
fof(f3544,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3535]) ).
fof(f3546,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ171_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)],[f3543,f3535]) ).
fof(f3716,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ171_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3546,f3535]) ).
fof(f3755,plain,
! [X0,X1] :
( ~ sQ171_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3544,f3716]) ).
fof(f3768,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3755,f232]) ).
fof(f3775,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3768,f3755]) ).
fof(f3778,plain,
! [X0] :
( ~ sQ171_spl
| para(X0,X0,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3775,f559]) ).
fof(f3786,plain,
! [X0] :
( ~ sQ171_spl
| para(X0,X0,sK25_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f3775,f549]) ).
fof(f3815,plain,
! [X0] :
( ~ sQ171_spl
| para(sK24_skl,sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f3778,f107]) ).
fof(f3871,plain,
! [X0] :
( ~ sQ171_spl
| para(sK25_skl,sK29_skl,X0,X0) ),
inference(resolution,[status(thm)],[f3786,f107]) ).
fof(f3900,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| perp(sK24_skl,sK26_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3815,f120]) ).
fof(f3904,plain,
! [X0,X1] :
( ~ sQ171_spl
| perp(sK24_skl,sK26_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3900,f3775]) ).
fof(f4070,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| perp(sK25_skl,sK29_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3871,f120]) ).
fof(f4074,plain,
! [X0,X1] :
( ~ sQ171_spl
| perp(sK25_skl,sK29_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4070,f3775]) ).
fof(f4115,plain,
! [X0,X1] :
( ~ sQ171_spl
| perp(X0,X1,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f3904,f114]) ).
fof(f4339,plain,
! [X0,X1] :
( ~ sQ171_spl
| para(X0,X1,sK25_skl,sK29_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f549,f4115]) ).
fof(f4664,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK25_skl,sK29_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4339,f120]) ).
fof(f4668,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4664,f4074]) ).
fof(f4669,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ171_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f4668]) ).
fof(f4675,plain,
! [X0,X1,X2,X3] :
( ~ sQ171_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4669,f4668]) ).
fof(f4682,plain,
( ~ sQ171_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f4675]) ).
fof(f4685,plain,
~ sQ171_spl,
inference(contradiction_clause,[status(thm)],[f4682]) ).
fof(f4686,plain,
$false,
inference(sat_refutation,[status(thm)],[f3310,f3334,f4685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO659+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 : n010.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 18:15:25 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 5.03/1.20 % Refutation found
% 5.03/1.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.03/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.01/1.24 % Elapsed time: 0.777558 seconds
% 4.01/1.24 % CPU time: 5.796972 seconds
% 4.01/1.24 % Total memory used: 130.423 MB
% 4.01/1.24 % Net memory used: 125.756 MB
%------------------------------------------------------------------------------