%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO560+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 : n026.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 12:25:14 PM UTC 2026
% Result : Theorem 1.15s 0.77s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of formulae : 133 ( 12 unt; 2 def)
% Number of atoms : 344 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 358 ( 147 ~; 139 |; 48 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 551 ( 537 !; 14 ?)
% 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(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,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,H,G] :
( ( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> eqangle(E,G,G,H,H,G,G,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(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(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,H,G] :
( ~ eqangle(E,G,G,H,H,G,G,D)
& coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& 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,H,G] :
( ~ eqangle(E,G,G,H,H,G,G,D)
& ? [A,B] :
( coll(G,A,B)
& perp(G,H,A,B)
& coll(H,B,E)
& coll(H,A,D)
& ? [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,
( ~ eqangle(sK21_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK20_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& perp(sK23_skl,sK22_skl,sK24_skl,sK25_skl)
& coll(sK22_skl,sK25_skl,sK21_skl)
& coll(sK22_skl,sK24_skl,sK20_skl)
& coll(sK21_skl,sK24_skl,sK26_skl)
& perp(sK21_skl,sK25_skl,sK24_skl,sK26_skl)
& coll(sK20_skl,sK25_skl,sK26_skl)
& perp(sK20_skl,sK24_skl,sK25_skl,sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(D,sK20_skl),skolemize(E,sK21_skl),skolemize(H,sK22_skl),skolemize(G,sK23_skl),skolemize(A,sK24_skl),skolemize(B,sK25_skl),skolemize(C,sK26_skl)],[f370]) ).
fof(f372,plain,
perp(sK20_skl,sK24_skl,sK25_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
perp(sK21_skl,sK25_skl,sK24_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
~ eqangle(sK21_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f426,plain,
perp(sK21_skl,sK25_skl,sK26_skl,sK24_skl),
inference(resolution,[status(thm)],[f112,f374]) ).
fof(f427,plain,
perp(sK20_skl,sK24_skl,sK26_skl,sK25_skl),
inference(resolution,[status(thm)],[f112,f372]) ).
fof(f479,plain,
perp(sK26_skl,sK24_skl,sK21_skl,sK25_skl),
inference(resolution,[status(thm)],[f114,f426]) ).
fof(f481,plain,
perp(sK26_skl,sK25_skl,sK20_skl,sK24_skl),
inference(resolution,[status(thm)],[f114,f427]) ).
fof(f525,plain,
! [X0,X1] :
( para(X0,X1,sK21_skl,sK25_skl)
| ~ perp(X0,X1,sK26_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f117,f479]) ).
fof(f541,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK26_skl)
| ~ perp(X0,X1,sK21_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f117,f374]) ).
fof(f543,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK26_skl)
| ~ perp(X0,X1,sK20_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f117,f372]) ).
fof(f923,plain,
para(sK26_skl,sK25_skl,sK25_skl,sK26_skl),
inference(resolution,[status(thm)],[f543,f481]) ).
fof(f950,plain,
para(sK26_skl,sK25_skl,sK26_skl,sK25_skl),
inference(resolution,[status(thm)],[f923,f105]) ).
fof(f1416,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(f1417,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(f1419,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(f1645,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1419,f186]) ).
fof(f1654,definition,
! [X0,X1] :
( sQ2_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1654]) ).
fof(f1657,definition,
! [X2,X3] :
( sQ3_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1658,plain,
! [X0,X1] :
( ~ sQ3_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1660,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1645,f1654,f1657]) ).
fof(f1661,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f950,f1655]) ).
fof(f1668,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1661]) ).
fof(f1670,plain,
! [X0,X1] :
( ~ sQ3_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1658,f256]) ).
fof(f1706,plain,
! [X0,X1] :
( ~ sQ3_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1670,f100]) ).
fof(f1741,plain,
! [X0,X1] :
( ~ sQ3_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1706,f98]) ).
fof(f1743,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1741,f103]) ).
fof(f1746,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1743,f1741]) ).
fof(f1747,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f1746]) ).
fof(f1780,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1747,f1417]) ).
fof(f1789,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1780,f1658]) ).
fof(f1808,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1789,f136]) ).
fof(f1812,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1808,f1789]) ).
fof(f1817,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_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,f1812]) ).
fof(f1818,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f1812]) ).
fof(f1819,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_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)],[f1817,f1812]) ).
fof(f1845,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f1819,f1812]) ).
fof(f1857,plain,
! [X0,X1] :
( ~ sQ3_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1818,f1845]) ).
fof(f2328,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f232,f1857]) ).
fof(f2339,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2328,f1857]) ).
fof(f2378,plain,
! [X0] :
( ~ sQ3_spl
| para(X0,X0,sK21_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2339,f525]) ).
fof(f2386,plain,
! [X0] :
( ~ sQ3_spl
| para(X0,X0,sK24_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f2339,f541]) ).
fof(f2504,plain,
! [X0] :
( ~ sQ3_spl
| para(sK21_skl,sK25_skl,X0,X0) ),
inference(resolution,[status(thm)],[f2378,f107]) ).
fof(f2534,plain,
! [X0] :
( ~ sQ3_spl
| para(sK24_skl,sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f2386,f107]) ).
fof(f2547,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| perp(sK21_skl,sK25_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2504,f120]) ).
fof(f2551,plain,
! [X0,X1] :
( ~ sQ3_spl
| perp(sK21_skl,sK25_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2547,f2339]) ).
fof(f2615,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| perp(sK24_skl,sK26_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2534,f120]) ).
fof(f2619,plain,
! [X0,X1] :
( ~ sQ3_spl
| perp(sK24_skl,sK26_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2615,f2339]) ).
fof(f2645,plain,
! [X0,X1] :
( ~ sQ3_spl
| perp(X0,X1,sK21_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f2551,f114]) ).
fof(f2820,plain,
! [X0,X1] :
( ~ sQ3_spl
| para(X0,X1,sK24_skl,sK26_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f541,f2645]) ).
fof(f2997,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK24_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2820,f120]) ).
fof(f3001,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2997,f2619]) ).
fof(f3002,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f3001]) ).
fof(f3005,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3002,f3001]) ).
fof(f3012,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1417,f3005]) ).
fof(f3013,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ3_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)],[f1416,f3005]) ).
fof(f3469,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ3_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f3013,f3012]) ).
fof(f3818,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f380,f3469]) ).
fof(f3819,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f3818]) ).
fof(f3820,plain,
$false,
inference(sat_refutation,[status(thm)],[f1660,f1668,f3819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO560+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 17:30:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 1.15/0.77 % Refutation found
% 1.15/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.15/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.15/0.79 % Elapsed time: 0.410882 seconds
% 1.15/0.79 % CPU time: 2.973268 seconds
% 1.15/0.79 % Total memory used: 111.696 MB
% 1.15/0.79 % Net memory used: 107.425 MB
%------------------------------------------------------------------------------