%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO549+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 4.48s 1.20s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 22
% Syntax : Number of formulae : 130 ( 11 unt; 2 def)
% Number of atoms : 379 ( 0 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 395 ( 146 ~; 138 |; 88 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 577 ( 545 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) )
=> eqangle(F,L,L,F1,F2,M,M,F3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) )
=> eqangle(F,L,L,F1,F2,M,M,F3) ),
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(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,D,O,C,P,F,P1,F2,F3,F1,L,M,NWPNT1,NWPNT2,NWPNT3] :
( ~ eqangle(F,L,L,F1,F2,M,M,F3)
& coll(M,A,B)
& perp(M,P1,A,B)
& coll(L,A,B)
& perp(L,P,A,B)
& coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& coll(F2,A,C)
& perp(F2,P1,A,C)
& circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& circle(O,A,P,NWPNT2)
& circle(O,A,C,NWPNT1)
& circle(O,A,B,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [F,F2,F3,F1,L,M] :
( ~ eqangle(F,L,L,F1,F2,M,M,F3)
& ? [A,B] :
( coll(M,A,B)
& ? [P1] :
( perp(M,P1,A,B)
& coll(L,A,B)
& ? [P] :
( perp(L,P,A,B)
& ? [D] :
( coll(F1,A,D)
& perp(F1,P,A,D)
& coll(F3,A,D)
& perp(F3,P1,A,D)
& ? [C] :
( coll(F2,A,C)
& perp(F2,P1,A,C)
& ? [O] :
( ? [NWPNT3] : circle(O,A,P1,NWPNT3)
& coll(F,A,C)
& perp(F,P,A,C)
& ? [NWPNT2] : circle(O,A,P,NWPNT2)
& ? [NWPNT1] : circle(O,A,C,NWPNT1)
& circle(O,A,B,D) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK24_skl,sK24_skl,sK23_skl,sK21_skl,sK25_skl,sK25_skl,sK22_skl)
& coll(sK25_skl,sK26_skl,sK27_skl)
& perp(sK25_skl,sK28_skl,sK26_skl,sK27_skl)
& coll(sK24_skl,sK26_skl,sK27_skl)
& perp(sK24_skl,sK29_skl,sK26_skl,sK27_skl)
& coll(sK23_skl,sK26_skl,sK30_skl)
& perp(sK23_skl,sK29_skl,sK26_skl,sK30_skl)
& coll(sK22_skl,sK26_skl,sK30_skl)
& perp(sK22_skl,sK28_skl,sK26_skl,sK30_skl)
& coll(sK21_skl,sK26_skl,sK31_skl)
& perp(sK21_skl,sK28_skl,sK26_skl,sK31_skl)
& circle(sK32_skl,sK26_skl,sK28_skl,sK35_skl)
& coll(sK20_skl,sK26_skl,sK31_skl)
& perp(sK20_skl,sK29_skl,sK26_skl,sK31_skl)
& circle(sK32_skl,sK26_skl,sK29_skl,sK34_skl)
& circle(sK32_skl,sK26_skl,sK31_skl,sK33_skl)
& circle(sK32_skl,sK26_skl,sK27_skl,sK30_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(F,sK20_skl),skolemize(F2,sK21_skl),skolemize(F3,sK22_skl),skolemize(F1,sK23_skl),skolemize(L,sK24_skl),skolemize(M,sK25_skl),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(P1,sK28_skl),skolemize(P,sK29_skl),skolemize(D,sK30_skl),skolemize(C,sK31_skl),skolemize(O,sK32_skl),skolemize(NWPNT1,sK33_skl),skolemize(NWPNT2,sK34_skl),skolemize(NWPNT3,sK35_skl)],[f370]) ).
fof(f384,plain,
perp(sK24_skl,sK29_skl,sK26_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
perp(sK25_skl,sK28_skl,sK26_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f388,plain,
~ eqangle(sK20_skl,sK24_skl,sK24_skl,sK23_skl,sK21_skl,sK25_skl,sK25_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f501,plain,
perp(sK24_skl,sK29_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f384,f112]) ).
fof(f502,plain,
perp(sK25_skl,sK28_skl,sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f386,f112]) ).
fof(f505,plain,
perp(sK26_skl,sK27_skl,sK25_skl,sK28_skl),
inference(resolution,[status(thm)],[f114,f386]) ).
fof(f506,plain,
perp(sK26_skl,sK27_skl,sK24_skl,sK29_skl),
inference(resolution,[status(thm)],[f114,f384]) ).
fof(f555,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK29_skl)
| ~ perp(X0,X1,sK26_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f117,f506]) ).
fof(f556,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK28_skl)
| ~ perp(X0,X1,sK26_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f117,f505]) ).
fof(f557,plain,
! [X0,X1] :
( para(X0,X1,sK27_skl,sK26_skl)
| ~ perp(X0,X1,sK25_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f117,f502]) ).
fof(f559,plain,
! [X0,X1] :
( para(X0,X1,sK27_skl,sK26_skl)
| ~ perp(X0,X1,sK24_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f117,f501]) ).
fof(f1420,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(f1421,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(f1423,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(f2971,plain,
para(sK24_skl,sK29_skl,sK24_skl,sK29_skl),
inference(resolution,[status(thm)],[f555,f384]) ).
fof(f4727,definition,
! [X4,X5] :
( sQ256_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f4728,plain,
! [X0,X1] :
( ~ sQ256_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f4727]) ).
fof(f4940,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1423,f186]) ).
fof(f4952,definition,
! [X2,X3] :
( sQ259_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f4953,plain,
! [X0,X1] :
( ~ sQ259_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f4952]) ).
fof(f4955,plain,
( sQ259_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f4940,f4727,f4952]) ).
fof(f4984,plain,
( ~ sQ256_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2971,f4728]) ).
fof(f5004,plain,
~ sQ256_spl,
inference(contradiction_clause,[status(thm)],[f4984]) ).
fof(f5007,plain,
! [X0,X1] :
( ~ sQ259_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4953,f256]) ).
fof(f5063,plain,
! [X0,X1] :
( ~ sQ259_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f5007,f100]) ).
fof(f5116,plain,
! [X0,X1] :
( ~ sQ259_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f5063,f98]) ).
fof(f5124,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f5116,f103]) ).
fof(f5127,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f5124,f5116]) ).
fof(f5132,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f5127]) ).
fof(f5546,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5132,f1421]) ).
fof(f5559,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f5546,f4953]) ).
fof(f5576,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5559,f136]) ).
fof(f5580,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5576,f5559]) ).
fof(f5588,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ259_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,f5580]) ).
fof(f5589,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f5580]) ).
fof(f5591,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ259_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)],[f5588,f5580]) ).
fof(f5721,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ259_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f5591,f5580]) ).
fof(f5723,plain,
! [X0,X1] :
( ~ sQ259_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f5721,f5589]) ).
fof(f5731,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f5723,f232]) ).
fof(f5736,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f5731,f5723]) ).
fof(f5761,plain,
! [X0] :
( ~ sQ259_spl
| para(X0,X0,sK25_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f5736,f556]) ).
fof(f5775,plain,
! [X0] :
( ~ sQ259_spl
| para(X0,X0,sK27_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f5736,f559]) ).
fof(f5874,plain,
! [X0] :
( ~ sQ259_spl
| para(sK25_skl,sK28_skl,X0,X0) ),
inference(resolution,[status(thm)],[f5761,f107]) ).
fof(f5915,plain,
! [X0] :
( ~ sQ259_spl
| para(sK27_skl,sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f5775,f107]) ).
fof(f5921,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| perp(sK25_skl,sK28_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5874,f120]) ).
fof(f5925,plain,
! [X0,X1] :
( ~ sQ259_spl
| perp(sK25_skl,sK28_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5921,f5736]) ).
fof(f6025,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| perp(sK27_skl,sK26_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5915,f120]) ).
fof(f6029,plain,
! [X0,X1] :
( ~ sQ259_spl
| perp(sK27_skl,sK26_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f6025,f5736]) ).
fof(f6140,plain,
! [X0,X1] :
( ~ sQ259_spl
| perp(X0,X1,sK25_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f5925,f114]) ).
fof(f6418,plain,
! [X0,X1] :
( ~ sQ259_spl
| para(X0,X1,sK27_skl,sK26_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f557,f6140]) ).
fof(f6571,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK27_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f6418,f120]) ).
fof(f6575,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f6571,f6029]) ).
fof(f6577,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ259_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f6575]) ).
fof(f6582,plain,
! [X0,X1,X2,X3] :
( ~ sQ259_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f6577,f6575]) ).
fof(f6589,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ259_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1421,f6582]) ).
fof(f6590,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ259_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)],[f1420,f6582]) ).
fof(f6958,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ259_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f6590,f6589]) ).
fof(f7125,plain,
( ~ sQ259_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f388,f6958]) ).
fof(f7126,plain,
~ sQ259_spl,
inference(contradiction_clause,[status(thm)],[f7125]) ).
fof(f7127,plain,
$false,
inference(sat_refutation,[status(thm)],[f4955,f5004,f7126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO549+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n003.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sun Sep 20 17:27:01 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.53 % Drodi V4.1.1
% 4.48/1.20 % Refutation found
% 4.48/1.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.48/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.48/1.21 % Elapsed time: 0.681708 seconds
% 4.48/1.21 % CPU time: 5.110744 seconds
% 4.48/1.21 % Total memory used: 140.593 MB
% 4.48/1.21 % Net memory used: 133.217 MB
%------------------------------------------------------------------------------