%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO658+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 12:25:29 PM UTC 2026
% Result : Theorem 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of formulae : 144 ( 11 unt; 2 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 413 ( 165 ~; 157 |; 65 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 576 ( 558 !; 18 ?)
% 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(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(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(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(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,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,H,I] :
( ( coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,F,H,I) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I] :
( ( coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,F,H,I) ),
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(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(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(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(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
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,H,I] :
( ~ para(G,F,H,I)
& coll(I,A,B)
& coll(I,E,F)
& coll(H,A,D)
& coll(H,E,G)
& coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [F,G,H,I] :
( ~ para(G,F,H,I)
& ? [A,B] :
( coll(I,A,B)
& ? [E] :
( coll(I,E,F)
& ? [D] :
( coll(H,A,D)
& coll(H,E,G)
& ? [C] :
( coll(G,B,C)
& perp(G,E,B,C)
& coll(F,C,D)
& perp(F,E,C,D)
& coll(E,A,C)
& para(A,C,B,D)
& para(A,B,C,D) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ para(sK21_skl,sK20_skl,sK22_skl,sK23_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& coll(sK23_skl,sK26_skl,sK20_skl)
& coll(sK22_skl,sK24_skl,sK27_skl)
& coll(sK22_skl,sK26_skl,sK21_skl)
& coll(sK21_skl,sK25_skl,sK28_skl)
& perp(sK21_skl,sK26_skl,sK25_skl,sK28_skl)
& coll(sK20_skl,sK28_skl,sK27_skl)
& perp(sK20_skl,sK26_skl,sK28_skl,sK27_skl)
& coll(sK26_skl,sK24_skl,sK28_skl)
& para(sK24_skl,sK28_skl,sK25_skl,sK27_skl)
& para(sK24_skl,sK25_skl,sK28_skl,sK27_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(F,sK20_skl),skolemize(G,sK21_skl),skolemize(H,sK22_skl),skolemize(I,sK23_skl),skolemize(A,sK24_skl),skolemize(B,sK25_skl),skolemize(E,sK26_skl),skolemize(D,sK27_skl),skolemize(C,sK28_skl)],[f370]) ).
fof(f373,plain,
para(sK24_skl,sK28_skl,sK25_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
perp(sK20_skl,sK26_skl,sK28_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f383,plain,
~ para(sK21_skl,sK20_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f507,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK27_skl)
| ~ para(X0,X1,sK24_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f373,f110]) ).
fof(f509,plain,
para(sK24_skl,sK28_skl,sK27_skl,sK25_skl),
inference(resolution,[status(thm)],[f373,f105]) ).
fof(f516,plain,
perp(sK20_skl,sK26_skl,sK27_skl,sK28_skl),
inference(resolution,[status(thm)],[f375,f112]) ).
fof(f521,plain,
! [X0,X1] :
( para(X0,X1,sK28_skl,sK27_skl)
| ~ perp(X0,X1,sK20_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f117,f375]) ).
fof(f532,plain,
para(sK27_skl,sK25_skl,sK24_skl,sK28_skl),
inference(resolution,[status(thm)],[f509,f107]) ).
fof(f534,plain,
! [X0,X1] :
( para(X0,X1,sK27_skl,sK28_skl)
| ~ perp(X0,X1,sK20_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f516,f117]) ).
fof(f692,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X1,X0,X4,X5)
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(resolution,[status(thm)],[f138,f189]) ).
fof(f693,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(f807,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(f979,plain,
para(sK27_skl,sK25_skl,sK25_skl,sK27_skl),
inference(resolution,[status(thm)],[f507,f532]) ).
fof(f986,plain,
para(sK27_skl,sK25_skl,sK27_skl,sK25_skl),
inference(resolution,[status(thm)],[f979,f105]) ).
fof(f1219,plain,
! [X0,X1,X2,X3] :
( para(X1,X0,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f692,f186]) ).
fof(f1227,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f693,f186]) ).
fof(f1228,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1229,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1228]) ).
fof(f1231,definition,
! [X2,X3] :
( sQ1_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1232,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1231]) ).
fof(f1234,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1227,f1228,f1231]) ).
fof(f1235,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f986,f1229]) ).
fof(f1241,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1235]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1232,f256]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f1232,f105]) ).
fof(f1285,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1245,f100]) ).
fof(f1323,plain,
! [X0,X1] :
( ~ sQ1_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1285,f98]) ).
fof(f1324,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1323,f103]) ).
fof(f1327,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1324,f1323]) ).
fof(f1331,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| perp(X1,X0,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1249,f120]) ).
fof(f1427,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,f1327]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1427,f807]) ).
fof(f1434,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1428,f1232]) ).
fof(f1451,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1434,f136]) ).
fof(f1455,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1451,f1434]) ).
fof(f1460,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,f1455]) ).
fof(f1461,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f1455]) ).
fof(f1462,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)],[f1460,f1455]) ).
fof(f1470,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| eqangle(X0,X1,X1,X2,X3,X0,X3,X2) ),
inference(resolution,[status(thm)],[f1461,f138]) ).
fof(f1499,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)],[f1462,f1455]) ).
fof(f1501,plain,
! [X0,X1] :
( ~ sQ1_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1499,f1470]) ).
fof(f1520,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1501,f232]) ).
fof(f1524,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1520,f1501]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ1_spl
| para(X0,X0,sK28_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f1524,f521]) ).
fof(f1547,plain,
! [X0] :
( ~ sQ1_spl
| para(sK28_skl,sK27_skl,X0,X0) ),
inference(resolution,[status(thm)],[f1525,f107]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ1_spl
| para(sK27_skl,sK28_skl,X0,X0) ),
inference(resolution,[status(thm)],[f1547,f1219]) ).
fof(f1709,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(sK27_skl,sK28_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1572,f120]) ).
fof(f1713,plain,
! [X0,X1] :
( ~ sQ1_spl
| perp(sK27_skl,sK28_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1709,f1524]) ).
fof(f2407,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f1455]) ).
fof(f2427,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f2407,f1501]) ).
fof(f2443,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2427,f1501]) ).
fof(f2490,plain,
! [X0] :
( ~ sQ1_spl
| para(X0,sK20_skl,sK27_skl,sK28_skl) ),
inference(resolution,[status(thm)],[f2443,f534]) ).
fof(f2561,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X2,sK20_skl,X0,X1)
| ~ perp(sK27_skl,sK28_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2490,f120]) ).
fof(f2565,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,sK20_skl,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2561,f1713]) ).
fof(f2572,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(sK20_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2565,f1331]) ).
fof(f2584,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| perp(X0,X1,sK20_skl,X2) ),
inference(resolution,[status(thm)],[f2572,f114]) ).
fof(f2593,plain,
! [X0,X1] :
( ~ sQ1_spl
| para(X0,X1,sK27_skl,sK28_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f534,f2584]) ).
fof(f2622,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| perp(X2,X3,X0,X1)
| ~ perp(sK27_skl,sK28_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2593,f120]) ).
fof(f2626,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2622,f1713]) ).
fof(f2627,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f2626]) ).
fof(f2631,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2627,f2626]) ).
fof(f2664,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f2631]) ).
fof(f2667,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f2664]) ).
fof(f2668,plain,
$false,
inference(sat_refutation,[status(thm)],[f1234,f1241,f2667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO658+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n002.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 18:17:23 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.58 % Refutation found
% 0.14/5.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.60 % Elapsed time: 0.222058 seconds
% 0.14/5.60 % CPU time: 1.486752 seconds
% 0.14/5.60 % Total memory used: 104.009 MB
% 0.14/5.60 % Net memory used: 101.729 MB
%------------------------------------------------------------------------------