%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO587+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 : n008.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 12:25:18 PM UTC 2026
% Result : Theorem 4.56s 1.02s
% Output : CNFRefutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 26
% Syntax : Number of formulae : 127 ( 6 unt; 4 def)
% Number of atoms : 338 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 358 ( 147 ~; 140 |; 44 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 485 ( 467 !; 18 ?)
% 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(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
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(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
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(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(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,C,B,D,P,Q,R,S,O] :
( ( coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) )
=> cong(O,S,O,R) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,C,B,D,P,Q,R,S,O] :
( ( coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) )
=> cong(O,S,O,R) ),
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(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(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(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(f148,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f152,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f153,plain,
! [A,B,E,F] :
( cong(A,B,E,F)
| ! [C,D] :
( ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
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(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(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,C,B,D,P,Q,R,S,O] :
( ~ cong(O,S,O,R)
& coll(O,Q,S)
& coll(O,P,R)
& midp(S,A,D)
& midp(R,D,C)
& midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [R,S,O] :
( ~ cong(O,S,O,R)
& ? [Q] :
( coll(O,Q,S)
& ? [P] :
( coll(O,P,R)
& ? [A,D] :
( midp(S,A,D)
& ? [C] :
( midp(R,D,C)
& ? [B] :
( midp(Q,C,B)
& midp(P,B,A)
& perp(A,C,B,D) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cong(sK22_skl,sK21_skl,sK22_skl,sK20_skl)
& coll(sK22_skl,sK23_skl,sK21_skl)
& coll(sK22_skl,sK24_skl,sK20_skl)
& midp(sK21_skl,sK25_skl,sK26_skl)
& midp(sK20_skl,sK26_skl,sK27_skl)
& midp(sK23_skl,sK27_skl,sK28_skl)
& midp(sK24_skl,sK28_skl,sK25_skl)
& perp(sK25_skl,sK27_skl,sK28_skl,sK26_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]),skolemize(R,sK20_skl),skolemize(S,sK21_skl),skolemize(O,sK22_skl),skolemize(Q,sK23_skl),skolemize(P,sK24_skl),skolemize(A,sK25_skl),skolemize(D,sK26_skl),skolemize(C,sK27_skl),skolemize(B,sK28_skl)],[f370]) ).
fof(f372,plain,
perp(sK25_skl,sK27_skl,sK28_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
~ cong(sK22_skl,sK21_skl,sK22_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f417,plain,
perp(sK28_skl,sK26_skl,sK25_skl,sK27_skl),
inference(resolution,[status(thm)],[f114,f372]) ).
fof(f548,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK27_skl)
| ~ perp(X0,X1,sK28_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f417,f117]) ).
fof(f576,plain,
! [X0,X1,X2,X3,X4] :
( cong(X3,X4,X0,X2)
| ~ cong(X3,X4,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f260,f154]) ).
fof(f583,plain,
! [X0,X1,X2] :
( cong(X0,X1,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f260,f149]) ).
fof(f694,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X2,X3)
| ~ midp(X2,X0,X3)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f583,f576]) ).
fof(f898,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(f900,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(f975,plain,
para(sK25_skl,sK27_skl,sK25_skl,sK27_skl),
inference(resolution,[status(thm)],[f548,f372]) ).
fof(f1751,plain,
( ~ midp(sK22_skl,sK22_skl,sK20_skl)
| ~ midp(sK22_skl,sK21_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f694,f379]) ).
fof(f1775,definition,
( sQ56_spl
<=> midp(sK22_skl,sK21_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1777,plain,
( sQ56_spl
| ~ midp(sK22_skl,sK21_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f1775]) ).
fof(f1778,definition,
( sQ57_spl
<=> midp(sK22_skl,sK22_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1780,plain,
( sQ57_spl
| ~ midp(sK22_skl,sK22_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f1778]) ).
fof(f1781,plain,
( ~ sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1751,f1775,f1778]) ).
fof(f3328,definition,
! [X4,X5] :
( sQ159_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f3329,plain,
! [X0,X1] :
( ~ sQ159_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3328]) ).
fof(f3410,plain,
( ~ sQ159_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f975,f3329]) ).
fof(f3424,plain,
~ sQ159_spl,
inference(contradiction_clause,[status(thm)],[f3410]) ).
fof(f3450,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f900,f186]) ).
fof(f3458,definition,
! [X2,X3] :
( sQ166_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f3459,plain,
! [X0,X1] :
( ~ sQ166_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3458]) ).
fof(f3461,plain,
( sQ166_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f3450,f3328,f3458]) ).
fof(f3570,plain,
! [X0,X1] :
( ~ sQ166_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3459,f256]) ).
fof(f3573,plain,
! [X0,X1] :
( ~ sQ166_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f3459,f105]) ).
fof(f3605,plain,
! [X0,X1] :
( ~ sQ166_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3570,f100]) ).
fof(f3638,plain,
! [X0,X1] :
( ~ sQ166_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3605,f98]) ).
fof(f3640,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3638,f103]) ).
fof(f3643,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3640,f3638]) ).
fof(f3645,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ166_spl
| midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f3643]) ).
fof(f3647,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f3643]) ).
fof(f3651,plain,
! [X0,X1,X2,X3] :
( ~ sQ166_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3643]) ).
fof(f3696,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| midp(X2,X1,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3645,f3573]) ).
fof(f3778,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3651,f898]) ).
fof(f3788,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3778,f3459]) ).
fof(f3798,plain,
! [X0,X1,X2,X3] :
( ~ sQ166_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3788,f136]) ).
fof(f3802,plain,
! [X0,X1,X2,X3] :
( ~ sQ166_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3798,f3788]) ).
fof(f3822,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ166_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,f3802]) ).
fof(f3823,plain,
! [X0,X1,X2,X3] :
( ~ sQ166_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3802]) ).
fof(f3825,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ166_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)],[f3822,f3802]) ).
fof(f4008,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ166_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3825,f3802]) ).
fof(f4019,plain,
! [X0,X1] :
( ~ sQ166_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3823,f4008]) ).
fof(f4032,plain,
! [X0,X1] :
( ~ sQ166_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4019,f3647]) ).
fof(f4720,plain,
! [X0,X1] :
( ~ sQ166_spl
| midp(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3696,f4032]) ).
fof(f4730,plain,
! [X0,X1] :
( ~ sQ166_spl
| midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f4720,f122]) ).
fof(f4751,plain,
( sQ56_spl
| ~ sQ166_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1777,f4730]) ).
fof(f4758,plain,
( sQ56_spl
| ~ sQ166_spl ),
inference(contradiction_clause,[status(thm)],[f4751]) ).
fof(f4760,plain,
( sQ57_spl
| ~ sQ166_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1780,f4720]) ).
fof(f4761,plain,
( sQ57_spl
| ~ sQ166_spl ),
inference(contradiction_clause,[status(thm)],[f4760]) ).
fof(f4762,plain,
$false,
inference(sat_refutation,[status(thm)],[f1781,f3424,f3461,f4758,f4761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO587+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 17:41:09 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 4.56/1.02 % Refutation found
% 4.56/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.56/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.56/1.06 % Elapsed time: 0.675871 seconds
% 4.56/1.06 % CPU time: 4.983340 seconds
% 4.56/1.06 % Total memory used: 139.498 MB
% 4.56/1.06 % Net memory used: 133.294 MB
%------------------------------------------------------------------------------