%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO657+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 : n014.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 0.14s 5.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 134 ( 12 unt; 2 def)
% Number of atoms : 346 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 373 ( 161 ~; 151 |; 36 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 513 ( 499 !; 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(f6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
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(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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
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] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) )
=> para(B,D,G,F) ),
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(f108,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f109,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ para(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
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(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(f199,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f200,plain,
! [B,C,E,F] :
( para(E,F,B,C)
| ! [A] :
( ~ midp(F,A,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f217,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f218,plain,
! [B,C,M] :
( midp(M,B,C)
| ! [A,O] :
( ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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] :
( ~ para(B,D,G,F)
& coll(G,B,C)
& coll(F,C,D)
& para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,D,F,G] :
( ~ para(B,D,G,F)
& ? [C] :
( coll(G,B,C)
& coll(F,C,D)
& ? [A,E] :
( para(A,D,F,E)
& para(A,B,G,E)
& coll(E,A,C) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK20_skl,sK21_skl,sK23_skl,sK22_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& coll(sK22_skl,sK24_skl,sK21_skl)
& para(sK25_skl,sK21_skl,sK22_skl,sK26_skl)
& para(sK25_skl,sK20_skl,sK23_skl,sK26_skl)
& coll(sK26_skl,sK25_skl,sK24_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(B,sK20_skl),skolemize(D,sK21_skl),skolemize(F,sK22_skl),skolemize(G,sK23_skl),skolemize(C,sK24_skl),skolemize(A,sK25_skl),skolemize(E,sK26_skl)],[f370]) ).
fof(f373,plain,
para(sK25_skl,sK20_skl,sK23_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
para(sK25_skl,sK21_skl,sK22_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
~ para(sK20_skl,sK21_skl,sK23_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f420,plain,
para(sK25_skl,sK21_skl,sK26_skl,sK22_skl),
inference(resolution,[status(thm)],[f105,f374]) ).
fof(f421,plain,
para(sK25_skl,sK20_skl,sK26_skl,sK23_skl),
inference(resolution,[status(thm)],[f105,f373]) ).
fof(f436,plain,
para(sK26_skl,sK22_skl,sK25_skl,sK21_skl),
inference(resolution,[status(thm)],[f107,f420]) ).
fof(f437,plain,
para(sK22_skl,sK26_skl,sK25_skl,sK21_skl),
inference(resolution,[status(thm)],[f107,f374]) ).
fof(f438,plain,
para(sK26_skl,sK23_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f107,f421]) ).
fof(f453,plain,
! [X0,X1] :
( para(X0,X1,sK22_skl,sK26_skl)
| ~ para(X0,X1,sK25_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f110,f374]) ).
fof(f687,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(f709,plain,
para(sK22_skl,sK26_skl,sK22_skl,sK26_skl),
inference(resolution,[status(thm)],[f453,f437]) ).
fof(f816,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(resolution,[status(thm)],[f144,f189]) ).
fof(f1007,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f687,f186]) ).
fof(f1008,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1008]) ).
fof(f1011,definition,
! [X2,X3] :
( sQ1_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1012,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1011]) ).
fof(f1014,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1007,f1008,f1011]) ).
fof(f1015,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f709,f1009]) ).
fof(f1017,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1015]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1012,f256]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1023,f100]) ).
fof(f1068,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1045,f98]) ).
fof(f1070,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1068,f103]) ).
fof(f1073,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1070,f1068]) ).
fof(f1286,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f1073]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1286,f816]) ).
fof(f1293,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1288,f1012]) ).
fof(f1318,plain,
! [X0,X1,X2,X3,X4] :
( para(X2,X4,X0,X3)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f201,f107]) ).
fof(f1353,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1293,f136]) ).
fof(f1357,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1353,f1293]) ).
fof(f1363,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_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,f1357]) ).
fof(f1364,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f1357]) ).
fof(f1366,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_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)],[f1363,f1357]) ).
fof(f1374,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f1364,f138]) ).
fof(f1391,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X2,X0,X3,X1,X3,X2) ),
inference(resolution,[status(thm)],[f1374,f140]) ).
fof(f1403,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f1366,f1357]) ).
fof(f1405,plain,
! [X0,X1] :
( ~ sQ1_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1403,f1374]) ).
fof(f1424,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| circle(X0,X1,X2,X1)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f1405,f124]) ).
fof(f1449,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X2,X1,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f1391,f138]) ).
fof(f1521,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f1073]) ).
fof(f1531,plain,
! [X0] :
( ~ sQ1_spl
| midp(sK23_skl,X0,sK20_skl)
| ~ midp(sK26_skl,X0,sK25_skl) ),
inference(resolution,[status(thm)],[f1521,f438]) ).
fof(f1533,plain,
! [X0] :
( ~ sQ1_spl
| midp(sK22_skl,X0,sK21_skl)
| ~ midp(sK26_skl,X0,sK25_skl) ),
inference(resolution,[status(thm)],[f1521,f436]) ).
fof(f1541,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1521,f1012]) ).
fof(f1775,plain,
! [X0] :
( ~ midp(sK22_skl,X0,sK21_skl)
| ~ midp(sK23_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f1318,f377]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ sQ1_spl
| circle(X0,X1,X1,X1) ),
inference(resolution,[status(thm)],[f1424,f1405]) ).
fof(f1840,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f1073]) ).
fof(f1849,plain,
! [X0,X1] :
( ~ sQ1_spl
| midp(X1,X1,X1)
| ~ circle(X0,X1,X1,X1) ),
inference(resolution,[status(thm)],[f1840,f1449]) ).
fof(f1868,plain,
! [X0] :
( ~ sQ1_spl
| midp(X0,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1849,f1814]) ).
fof(f1942,plain,
! [X0,X1] :
( ~ sQ1_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1868,f1541]) ).
fof(f1954,plain,
! [X0,X1] :
( ~ sQ1_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1942,f122]) ).
fof(f1964,plain,
( ~ sQ1_spl
| midp(sK22_skl,sK26_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f1954,f1533]) ).
fof(f1965,plain,
( ~ sQ1_spl
| midp(sK23_skl,sK26_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f1954,f1531]) ).
fof(f2169,plain,
( ~ sQ1_spl
| ~ midp(sK22_skl,sK26_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f1965,f1775]) ).
fof(f2173,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2169,f1964]) ).
fof(f2174,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f2173]) ).
fof(f2175,plain,
$false,
inference(sat_refutation,[status(thm)],[f1014,f1017,f2174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO657+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n014.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 18:16:40 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.60 % Refutation found
% 0.14/5.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.62 % Elapsed time: 0.229319 seconds
% 0.14/5.62 % CPU time: 1.577753 seconds
% 0.14/5.62 % Total memory used: 100.454 MB
% 0.14/5.62 % Net memory used: 98.458 MB
%------------------------------------------------------------------------------