%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO655+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 : n002.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 12:25:28 PM UTC 2026
% Result : Theorem 1.64s 0.83s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 116 ( 9 unt; 2 def)
% Number of atoms : 322 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 337 ( 131 ~; 123 |; 62 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 461 ( 439 !; 22 ?)
% 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(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(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,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ( perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) )
=> para(F,G,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ( perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) )
=> para(F,G,A,C) ),
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(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(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,MIDPNT1,MIDPNT2,MIDPNT3,NWPNT4] :
( ~ para(F,G,A,C)
& perp(D,F,F,G)
& circle(D,B,F,NWPNT4)
& coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,C,F,G] :
( ~ para(F,G,A,C)
& ? [D] :
( perp(D,F,F,G)
& ? [B] :
( ? [NWPNT4] : circle(D,B,F,NWPNT4)
& ? [E] :
( coll(B,E,F)
& eqangle(C,B,B,E,E,B,B,A)
& coll(E,A,C)
& ? [MIDPNT3] :
( perp(A,C,MIDPNT3,D)
& midp(MIDPNT3,A,C)
& ? [MIDPNT2] :
( perp(B,C,MIDPNT2,D)
& midp(MIDPNT2,B,C)
& ? [MIDPNT1] :
( perp(B,A,MIDPNT1,D)
& midp(MIDPNT1,B,A) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl)
& perp(sK24_skl,sK22_skl,sK22_skl,sK23_skl)
& circle(sK24_skl,sK25_skl,sK22_skl,sK30_skl)
& coll(sK25_skl,sK26_skl,sK22_skl)
& eqangle(sK21_skl,sK25_skl,sK25_skl,sK26_skl,sK26_skl,sK25_skl,sK25_skl,sK20_skl)
& coll(sK26_skl,sK20_skl,sK21_skl)
& perp(sK20_skl,sK21_skl,sK27_skl,sK24_skl)
& midp(sK27_skl,sK20_skl,sK21_skl)
& perp(sK25_skl,sK21_skl,sK28_skl,sK24_skl)
& midp(sK28_skl,sK25_skl,sK21_skl)
& perp(sK25_skl,sK20_skl,sK29_skl,sK24_skl)
& midp(sK29_skl,sK25_skl,sK20_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]),skolemize(A,sK20_skl),skolemize(C,sK21_skl),skolemize(F,sK22_skl),skolemize(G,sK23_skl),skolemize(D,sK24_skl),skolemize(B,sK25_skl),skolemize(E,sK26_skl),skolemize(MIDPNT3,sK27_skl),skolemize(MIDPNT2,sK28_skl),skolemize(MIDPNT1,sK29_skl),skolemize(NWPNT4,sK30_skl)],[f370]) ).
fof(f373,plain,
perp(sK25_skl,sK20_skl,sK29_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
perp(sK24_skl,sK22_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f383,plain,
~ para(sK22_skl,sK23_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f492,plain,
perp(sK22_skl,sK23_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f114,f382]) ).
fof(f497,plain,
perp(sK29_skl,sK24_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f114,f373]) ).
fof(f498,plain,
! [X0,X1] :
( para(X0,X1,sK22_skl,sK23_skl)
| ~ perp(X0,X1,sK24_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f117,f382]) ).
fof(f503,plain,
! [X0,X1] :
( para(X0,X1,sK29_skl,sK24_skl)
| ~ perp(X0,X1,sK25_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f117,f373]) ).
fof(f510,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK22_skl)
| ~ perp(X0,X1,sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f492,f117]) ).
fof(f845,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(f847,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(f1335,plain,
para(sK29_skl,sK24_skl,sK29_skl,sK24_skl),
inference(resolution,[status(thm)],[f503,f497]) ).
fof(f2894,definition,
! [X4,X5] :
( sQ111_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f2895,plain,
! [X0,X1] :
( ~ sQ111_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2894]) ).
fof(f3207,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f847,f186]) ).
fof(f3215,definition,
! [X2,X3] :
( sQ133_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f3216,plain,
! [X0,X1] :
( ~ sQ133_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3215]) ).
fof(f3218,plain,
( sQ133_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f3207,f2894,f3215]) ).
fof(f3219,plain,
( ~ sQ111_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1335,f2895]) ).
fof(f3237,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f3219]) ).
fof(f3240,plain,
! [X0,X1] :
( ~ sQ133_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3216,f256]) ).
fof(f3279,plain,
! [X0,X1] :
( ~ sQ133_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3240,f100]) ).
fof(f3315,plain,
! [X0,X1] :
( ~ sQ133_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3279,f98]) ).
fof(f3317,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3315,f103]) ).
fof(f3320,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3317,f3315]) ).
fof(f3324,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3320]) ).
fof(f3730,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3324,f845]) ).
fof(f3740,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3730,f3216]) ).
fof(f3750,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3740,f136]) ).
fof(f3754,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3750,f3740]) ).
fof(f3761,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ133_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,f3754]) ).
fof(f3762,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3754]) ).
fof(f3764,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ133_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)],[f3761,f3754]) ).
fof(f4169,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ133_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3764,f3754]) ).
fof(f4171,plain,
! [X0,X1] :
( ~ sQ133_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4169,f3762]) ).
fof(f4183,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4171,f232]) ).
fof(f4189,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4183,f4171]) ).
fof(f4199,plain,
! [X0] :
( ~ sQ133_spl
| para(X0,X0,sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f4189,f498]) ).
fof(f4265,plain,
! [X0] :
( ~ sQ133_spl
| para(sK22_skl,sK23_skl,X0,X0) ),
inference(resolution,[status(thm)],[f4199,f107]) ).
fof(f4331,plain,
! [X0] :
( ~ sQ133_spl
| para(X0,X0,sK24_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f510,f4189]) ).
fof(f4341,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| perp(sK22_skl,sK23_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4265,f120]) ).
fof(f4345,plain,
! [X0,X1] :
( ~ sQ133_spl
| perp(sK22_skl,sK23_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4341,f4189]) ).
fof(f4448,plain,
! [X0] :
( ~ sQ133_spl
| para(sK24_skl,sK22_skl,X0,X0) ),
inference(resolution,[status(thm)],[f4331,f107]) ).
fof(f4462,plain,
! [X0,X1] :
( ~ sQ133_spl
| perp(X0,X1,sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f4345,f114]) ).
fof(f4760,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| perp(sK24_skl,sK22_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4448,f120]) ).
fof(f4764,plain,
! [X0,X1] :
( ~ sQ133_spl
| perp(sK24_skl,sK22_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4760,f4189]) ).
fof(f4771,plain,
! [X0,X1] :
( ~ sQ133_spl
| para(X0,X1,sK24_skl,sK22_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f510,f4462]) ).
fof(f5023,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK24_skl,sK22_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4771,f120]) ).
fof(f5027,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5023,f4764]) ).
fof(f5028,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ133_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f5027]) ).
fof(f5037,plain,
! [X0,X1,X2,X3] :
( ~ sQ133_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5028,f5027]) ).
fof(f5046,plain,
( ~ sQ133_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f5037]) ).
fof(f5047,plain,
~ sQ133_spl,
inference(contradiction_clause,[status(thm)],[f5046]) ).
fof(f5048,plain,
$false,
inference(sat_refutation,[status(thm)],[f3218,f3237,f5047]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO655+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 18:22:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 1.64/0.83 % Refutation found
% 1.64/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.64/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.53/0.86 % Elapsed time: 0.492098 seconds
% 2.53/0.86 % CPU time: 3.609972 seconds
% 2.53/0.86 % Total memory used: 126.938 MB
% 2.53/0.86 % Net memory used: 122.241 MB
%------------------------------------------------------------------------------