%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO649+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 : n001.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 12:25:27 PM UTC 2026
% Result : Theorem 0.23s 0.65s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 132 ( 10 unt; 2 def)
% Number of atoms : 363 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 373 ( 142 ~; 134 |; 72 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 536 ( 504 !; 32 ?)
% 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(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(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
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,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,MIDPNT6,MIDPNT7,MIDPNT8] :
( ( perp(F,G,F,H)
& perp(F,B,MIDPNT8,G)
& midp(MIDPNT8,F,B)
& perp(E,B,MIDPNT7,G)
& midp(MIDPNT7,E,B)
& perp(E,F,MIDPNT6,G)
& midp(MIDPNT6,E,F)
& coll(F,B,D)
& coll(F,C,E)
& circle(A,B,E,NWPNT5)
& circle(A,B,D,NWPNT4)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,F,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,MIDPNT6,MIDPNT7,MIDPNT8] :
( ( perp(F,G,F,H)
& perp(F,B,MIDPNT8,G)
& midp(MIDPNT8,F,B)
& perp(E,B,MIDPNT7,G)
& midp(MIDPNT7,E,B)
& perp(E,F,MIDPNT6,G)
& midp(MIDPNT6,E,F)
& coll(F,B,D)
& coll(F,C,E)
& circle(A,B,E,NWPNT5)
& circle(A,B,D,NWPNT4)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) )
=> para(H,F,C,D) ),
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(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(f137,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
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,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,MIDPNT6,MIDPNT7,MIDPNT8] :
( ~ para(H,F,C,D)
& perp(F,G,F,H)
& perp(F,B,MIDPNT8,G)
& midp(MIDPNT8,F,B)
& perp(E,B,MIDPNT7,G)
& midp(MIDPNT7,E,B)
& perp(E,F,MIDPNT6,G)
& midp(MIDPNT6,E,F)
& coll(F,B,D)
& coll(F,C,E)
& circle(A,B,E,NWPNT5)
& circle(A,B,D,NWPNT4)
& circle(A,B,C,NWPNT3)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [C,D,F,H] :
( ~ para(H,F,C,D)
& ? [G] :
( perp(F,G,F,H)
& ? [B,MIDPNT8] :
( perp(F,B,MIDPNT8,G)
& midp(MIDPNT8,F,B)
& ? [E,MIDPNT7] :
( perp(E,B,MIDPNT7,G)
& midp(MIDPNT7,E,B)
& ? [MIDPNT6] :
( perp(E,F,MIDPNT6,G)
& midp(MIDPNT6,E,F)
& coll(F,B,D)
& coll(F,C,E)
& ? [A] :
( ? [NWPNT5] : circle(A,B,E,NWPNT5)
& ? [NWPNT4] : circle(A,B,D,NWPNT4)
& ? [NWPNT3] : circle(A,B,C,NWPNT3)
& ? [NWPNT1,NWPNT2] : circle(A,B,NWPNT1,NWPNT2) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK23_skl,sK22_skl,sK20_skl,sK21_skl)
& perp(sK22_skl,sK24_skl,sK22_skl,sK23_skl)
& perp(sK22_skl,sK25_skl,sK26_skl,sK24_skl)
& midp(sK26_skl,sK22_skl,sK25_skl)
& perp(sK27_skl,sK25_skl,sK28_skl,sK24_skl)
& midp(sK28_skl,sK27_skl,sK25_skl)
& perp(sK27_skl,sK22_skl,sK29_skl,sK24_skl)
& midp(sK29_skl,sK27_skl,sK22_skl)
& coll(sK22_skl,sK25_skl,sK21_skl)
& coll(sK22_skl,sK20_skl,sK27_skl)
& circle(sK30_skl,sK25_skl,sK27_skl,sK35_skl)
& circle(sK30_skl,sK25_skl,sK21_skl,sK34_skl)
& circle(sK30_skl,sK25_skl,sK20_skl,sK33_skl)
& circle(sK30_skl,sK25_skl,sK31_skl,sK32_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,sK33_skl,sK34_skl,sK35_skl]),skolemize(C,sK20_skl),skolemize(D,sK21_skl),skolemize(F,sK22_skl),skolemize(H,sK23_skl),skolemize(G,sK24_skl),skolemize(B,sK25_skl),skolemize(MIDPNT8,sK26_skl),skolemize(E,sK27_skl),skolemize(MIDPNT7,sK28_skl),skolemize(MIDPNT6,sK29_skl),skolemize(A,sK30_skl),skolemize(NWPNT1,sK31_skl),skolemize(NWPNT2,sK32_skl),skolemize(NWPNT3,sK33_skl),skolemize(NWPNT4,sK34_skl),skolemize(NWPNT5,sK35_skl)],[f370]) ).
fof(f379,plain,
perp(sK27_skl,sK22_skl,sK29_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
perp(sK22_skl,sK24_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f385,plain,
~ para(sK23_skl,sK22_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f491,plain,
perp(sK22_skl,sK24_skl,sK23_skl,sK22_skl),
inference(resolution,[status(thm)],[f384,f112]) ).
fof(f492,plain,
perp(sK22_skl,sK23_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f114,f384]) ).
fof(f495,plain,
perp(sK29_skl,sK24_skl,sK27_skl,sK22_skl),
inference(resolution,[status(thm)],[f114,f379]) ).
fof(f499,plain,
! [X0,X1] :
( para(X0,X1,sK29_skl,sK24_skl)
| ~ perp(X0,X1,sK27_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f117,f379]) ).
fof(f509,plain,
! [X0,X1] :
( para(X0,X1,sK23_skl,sK22_skl)
| ~ perp(X0,X1,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f491,f117]) ).
fof(f512,plain,
! [X0,X1] :
( para(X0,X1,sK22_skl,sK24_skl)
| ~ perp(X0,X1,sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f492,f117]) ).
fof(f651,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(f1203,plain,
para(sK29_skl,sK24_skl,sK29_skl,sK24_skl),
inference(resolution,[status(thm)],[f499,f495]) ).
fof(f2535,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f651,f186]) ).
fof(f2536,definition,
! [X0,X1] :
( sQ116_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f2537,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2536]) ).
fof(f2539,definition,
! [X2,X3] :
( sQ117_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f2540,plain,
! [X0,X1] :
( ~ sQ117_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2539]) ).
fof(f2542,plain,
( sQ117_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f2535,f2536,f2539]) ).
fof(f2544,plain,
( ~ sQ116_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1203,f2537]) ).
fof(f2554,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f2544]) ).
fof(f2557,plain,
! [X0,X1] :
( ~ sQ117_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2540,f256]) ).
fof(f2603,plain,
! [X0,X1] :
( ~ sQ117_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2557,f100]) ).
fof(f2646,plain,
! [X0,X1] :
( ~ sQ117_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2603,f98]) ).
fof(f2649,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2646,f103]) ).
fof(f2652,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2649,f2646]) ).
fof(f2653,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2652]) ).
fof(f2720,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| ~ para(X2,X1,X2,X1)
| cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f2653,f651]) ).
fof(f2729,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| cyclic(X0,X1,X2,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2720,f2540]) ).
fof(f2750,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| cyclic(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f2729,f131]) ).
fof(f2755,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| cyclic(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f2750,f133]) ).
fof(f2762,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2755,f129]) ).
fof(f2770,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f2762,f136]) ).
fof(f2774,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2770,f2762]) ).
fof(f2782,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ117_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,f2774]) ).
fof(f2783,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2774]) ).
fof(f2785,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ117_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)],[f2782,f2774]) ).
fof(f2937,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f2783,f138]) ).
fof(f3098,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ117_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2785,f2774]) ).
fof(f3099,plain,
! [X0,X1] :
( ~ sQ117_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3098,f2937]) ).
fof(f3127,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3099,f232]) ).
fof(f3133,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3127,f3099]) ).
fof(f3165,plain,
! [X0] :
( ~ sQ117_spl
| para(X0,X0,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f3133,f512]) ).
fof(f3168,plain,
! [X0] :
( ~ sQ117_spl
| para(X0,X0,sK23_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f3133,f509]) ).
fof(f3254,plain,
! [X0] :
( ~ sQ117_spl
| para(sK22_skl,sK24_skl,X0,X0) ),
inference(resolution,[status(thm)],[f3165,f107]) ).
fof(f3272,plain,
! [X0] :
( ~ sQ117_spl
| para(sK23_skl,sK22_skl,X0,X0) ),
inference(resolution,[status(thm)],[f3168,f107]) ).
fof(f3317,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| perp(sK22_skl,sK24_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3254,f120]) ).
fof(f3321,plain,
! [X0,X1] :
( ~ sQ117_spl
| perp(sK22_skl,sK24_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3317,f3133]) ).
fof(f3344,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| perp(sK23_skl,sK22_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3272,f120]) ).
fof(f3348,plain,
! [X0,X1] :
( ~ sQ117_spl
| perp(sK23_skl,sK22_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3344,f3133]) ).
fof(f3448,plain,
! [X0,X1] :
( ~ sQ117_spl
| perp(X0,X1,sK22_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f3321,f114]) ).
fof(f3659,plain,
! [X0,X1] :
( ~ sQ117_spl
| para(X0,X1,sK23_skl,sK22_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f509,f3448]) ).
fof(f3935,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK23_skl,sK22_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3659,f120]) ).
fof(f3939,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3935,f3348]) ).
fof(f3940,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ117_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f3939]) ).
fof(f3948,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3940,f3939]) ).
fof(f3955,plain,
( ~ sQ117_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f385,f3948]) ).
fof(f3959,plain,
~ sQ117_spl,
inference(contradiction_clause,[status(thm)],[f3955]) ).
fof(f3960,plain,
$false,
inference(sat_refutation,[status(thm)],[f2542,f2554,f3959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO649+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 18:17:42 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.23/0.65 % Refutation found
% 0.23/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.68 % Elapsed time: 0.244193 seconds
% 0.23/0.68 % CPU time: 1.630747 seconds
% 0.23/0.68 % Total memory used: 100.949 MB
% 0.23/0.68 % Net memory used: 99.395 MB
%------------------------------------------------------------------------------