%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO660+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 : n005.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 1.42s 0.70s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 134 ( 7 unt; 2 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 377 ( 153 ~; 143 |; 54 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 544 ( 530 !; 14 ?)
% 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(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(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(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/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(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
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(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
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(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) )
=> para(E,F,C,B) ),
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(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(f141,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
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(f150,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
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(f205,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f206,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
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(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f369,plain,
? [A,B,C,D,E,F,G] :
( ~ para(E,F,C,B)
& coll(G,A,E)
& coll(G,B,C)
& eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,C,E,F] :
( ~ para(E,F,C,B)
& ? [A,G] :
( coll(G,A,E)
& coll(G,B,C)
& ? [D] :
( eqangle(D,C,C,F,F,C,C,B)
& eqangle(B,A,A,E,E,A,A,C)
& coll(F,A,B)
& coll(E,C,D)
& coll(D,A,B)
& perp(D,C,A,B)
& perp(C,A,C,B) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK22_skl,sK23_skl,sK21_skl,sK20_skl)
& coll(sK25_skl,sK24_skl,sK22_skl)
& coll(sK25_skl,sK20_skl,sK21_skl)
& eqangle(sK26_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK20_skl)
& eqangle(sK20_skl,sK24_skl,sK24_skl,sK22_skl,sK22_skl,sK24_skl,sK24_skl,sK21_skl)
& coll(sK23_skl,sK24_skl,sK20_skl)
& coll(sK22_skl,sK21_skl,sK26_skl)
& coll(sK26_skl,sK24_skl,sK20_skl)
& perp(sK26_skl,sK21_skl,sK24_skl,sK20_skl)
& perp(sK21_skl,sK24_skl,sK21_skl,sK20_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(C,sK21_skl),skolemize(E,sK22_skl),skolemize(F,sK23_skl),skolemize(A,sK24_skl),skolemize(G,sK25_skl),skolemize(D,sK26_skl)],[f370]) ).
fof(f372,plain,
perp(sK21_skl,sK24_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f381,plain,
~ para(sK22_skl,sK23_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f489,plain,
perp(sK21_skl,sK20_skl,sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f114,f372]) ).
fof(f514,plain,
! [X0,X1] :
( para(X0,X1,sK21_skl,sK20_skl)
| ~ perp(X0,X1,sK21_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f117,f372]) ).
fof(f533,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f151,f260]) ).
fof(f730,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(f732,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(f854,plain,
! [X0] :
( ~ midp(sK23_skl,X0,sK20_skl)
| ~ midp(sK22_skl,X0,sK21_skl) ),
inference(resolution,[status(thm)],[f201,f381]) ).
fof(f950,plain,
para(sK21_skl,sK20_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f514,f489]) ).
fof(f990,plain,
! [X0,X1] :
( para(X0,X0,X0,X1)
| ~ cong(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f206,f186]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ midp(X0,X1,X0)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f990,f533]) ).
fof(f1035,plain,
! [X0,X1] :
( para(X0,X1,X0,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1021,f107]) ).
fof(f2173,definition,
! [X4,X5] :
( sQ79_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f2174,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2173]) ).
fof(f2381,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f732,f186]) ).
fof(f2387,definition,
! [X2,X3] :
( sQ83_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f2388,plain,
! [X0,X1] :
( ~ sQ83_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f2387]) ).
fof(f2390,plain,
( sQ83_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f2381,f2173,f2387]) ).
fof(f2392,plain,
( ~ sQ79_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f950,f2174]) ).
fof(f2406,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f2392]) ).
fof(f2410,plain,
! [X0,X1] :
( ~ sQ83_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2388,f256]) ).
fof(f2449,plain,
! [X0,X1] :
( ~ sQ83_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2410,f100]) ).
fof(f2486,plain,
! [X0,X1] :
( ~ sQ83_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2449,f98]) ).
fof(f2489,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2486,f103]) ).
fof(f2492,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2489,f2486]) ).
fof(f2495,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2492]) ).
fof(f2496,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ83_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f2492]) ).
fof(f2513,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f2492]) ).
fof(f2555,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2495,f730]) ).
fof(f2564,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2555,f2388]) ).
fof(f2574,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2564,f136]) ).
fof(f2578,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2574,f2564]) ).
fof(f2585,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ83_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,f2578]) ).
fof(f2586,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2578]) ).
fof(f2588,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ83_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)],[f2585,f2578]) ).
fof(f2597,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X2,X1,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2586,f144]) ).
fof(f2612,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X2,X0,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2597,f138]) ).
fof(f2634,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X2,X1,X3,X0,X2,X3) ),
inference(resolution,[status(thm)],[f2612,f142]) ).
fof(f2673,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X2,X1,X0,X3,X3,X2) ),
inference(resolution,[status(thm)],[f2634,f140]) ).
fof(f2756,plain,
! [X0,X1,X2,X3] :
( ~ sQ83_spl
| eqangle(X0,X1,X2,X0,X1,X3,X3,X2) ),
inference(resolution,[status(thm)],[f2673,f138]) ).
fof(f2794,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| midp(X2,X1,X2)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2496,f2388]) ).
fof(f2834,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ83_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2588,f2578]) ).
fof(f2835,plain,
! [X0,X1] :
( ~ sQ83_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2834,f2756]) ).
fof(f2869,plain,
! [X0,X1] :
( ~ sQ83_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f2835,f2513]) ).
fof(f2879,plain,
! [X0,X1] :
( ~ sQ83_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2869,f2794]) ).
fof(f2884,plain,
! [X0,X1] :
( ~ sQ83_spl
| para(X0,X1,X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1035,f2879]) ).
fof(f2992,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f2884,f2496]) ).
fof(f2998,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2992,f2879]) ).
fof(f3001,plain,
! [X0] :
( ~ sQ83_spl
| ~ midp(sK23_skl,X0,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f854,f2998]) ).
fof(f3029,plain,
( ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3001,f2998]) ).
fof(f3030,plain,
~ sQ83_spl,
inference(contradiction_clause,[status(thm)],[f3029]) ).
fof(f3031,plain,
$false,
inference(sat_refutation,[status(thm)],[f2390,f2406,f3030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO660+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 18:16:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.42/0.70 % Refutation found
% 1.42/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.42/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.42/0.72 % Elapsed time: 0.352212 seconds
% 1.42/0.72 % CPU time: 2.490086 seconds
% 1.42/0.72 % Total memory used: 113.136 MB
% 1.42/0.72 % Net memory used: 110.373 MB
%------------------------------------------------------------------------------