%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO590+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 : n010.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 12:25:19 PM UTC 2026
% Result : Theorem 3.14s 0.90s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 162 ( 45 unt; 0 def)
% Number of atoms : 378 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 364 ( 148 ~; 145 |; 45 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 476 ( 464 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
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(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(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
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(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(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(f42,axiom,
! [A,B,P,Q] :
( ( ~ coll(P,Q,A)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
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(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(f54,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
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(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [C,D,E,O,A,F] :
( ( coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) )
=> cong(A,E,A,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [C,D,E,O,A,F] :
( ( coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) )
=> cong(A,E,A,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(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(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(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
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(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(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(f192,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| coll(P,Q,A)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| coll(X0,X3,X1)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
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(f223,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f224,plain,
! [A,B,C] :
( perp(A,B,B,C)
| ! [O] :
( ~ coll(O,A,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f223]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f228,plain,
! [A,B,M,O] :
( cong(O,A,O,B)
| ~ perp(O,M,A,B)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f229,plain,
! [A,B,O] :
( cong(O,A,O,B)
| ! [M] :
( ~ perp(O,M,A,B)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
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(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(f261,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f262,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f369,plain,
? [C,D,E,O,A,F] :
( ~ cong(A,E,A,F)
& coll(F,D,E)
& coll(F,C,A)
& perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,A,F] :
( ~ cong(A,E,A,F)
& ? [D] :
( coll(F,D,E)
& ? [C] :
( coll(F,C,A)
& ? [O] :
( perp(E,O,E,A)
& perp(C,D,C,A)
& midp(O,D,C)
& perp(E,C,E,D) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cong(sK21_skl,sK20_skl,sK21_skl,sK22_skl)
& coll(sK22_skl,sK23_skl,sK20_skl)
& coll(sK22_skl,sK24_skl,sK21_skl)
& perp(sK20_skl,sK25_skl,sK20_skl,sK21_skl)
& perp(sK24_skl,sK23_skl,sK24_skl,sK21_skl)
& midp(sK25_skl,sK23_skl,sK24_skl)
& perp(sK20_skl,sK24_skl,sK20_skl,sK23_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl]),skolemize(E,sK20_skl),skolemize(A,sK21_skl),skolemize(F,sK22_skl),skolemize(D,sK23_skl),skolemize(C,sK24_skl),skolemize(O,sK25_skl)],[f370]) ).
fof(f373,plain,
midp(sK25_skl,sK23_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
perp(sK24_skl,sK23_skl,sK24_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
perp(sK20_skl,sK25_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f377,plain,
coll(sK22_skl,sK23_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f378,plain,
~ cong(sK21_skl,sK20_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f413,plain,
! [X0] :
( coll(sK20_skl,X0,sK22_skl)
| ~ coll(sK22_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f103,f377]) ).
fof(f415,plain,
perp(sK24_skl,sK23_skl,sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f112,f374]) ).
fof(f416,plain,
perp(sK20_skl,sK25_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f112,f375]) ).
fof(f421,plain,
coll(sK25_skl,sK23_skl,sK24_skl),
inference(resolution,[status(thm)],[f262,f373]) ).
fof(f444,plain,
cong(sK25_skl,sK23_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f260,f373]) ).
fof(f446,plain,
perp(sK24_skl,sK21_skl,sK24_skl,sK23_skl),
inference(resolution,[status(thm)],[f114,f374]) ).
fof(f448,plain,
perp(sK20_skl,sK21_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f114,f375]) ).
fof(f451,plain,
! [X0,X1] :
( para(sK24_skl,sK23_skl,X0,X1)
| ~ perp(sK21_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f415]) ).
fof(f462,plain,
perp(sK24_skl,sK21_skl,sK23_skl,sK24_skl),
inference(resolution,[status(thm)],[f446,f112]) ).
fof(f466,plain,
! [X0,X1] :
( para(sK20_skl,sK21_skl,X0,X1)
| ~ perp(sK20_skl,sK25_skl,X0,X1) ),
inference(resolution,[status(thm)],[f448,f117]) ).
fof(f475,plain,
coll(sK20_skl,sK20_skl,sK22_skl),
inference(resolution,[status(thm)],[f413,f377]) ).
fof(f478,plain,
coll(sK20_skl,sK22_skl,sK20_skl),
inference(resolution,[status(thm)],[f475,f98]) ).
fof(f479,plain,
! [X0] :
( coll(sK20_skl,X0,sK20_skl)
| ~ coll(sK20_skl,sK22_skl,X0) ),
inference(resolution,[status(thm)],[f478,f103]) ).
fof(f488,plain,
! [X0,X1] :
( para(sK24_skl,sK21_skl,X0,X1)
| ~ perp(sK23_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f462,f117]) ).
fof(f549,plain,
! [X0] :
( circle(sK25_skl,sK23_skl,sK24_skl,X0)
| ~ cong(sK25_skl,sK23_skl,sK25_skl,X0) ),
inference(resolution,[status(thm)],[f124,f444]) ).
fof(f810,plain,
coll(sK20_skl,sK20_skl,sK20_skl),
inference(resolution,[status(thm)],[f479,f478]) ).
fof(f1303,plain,
para(sK20_skl,sK21_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f466,f416]) ).
fof(f1313,plain,
para(sK21_skl,sK20_skl,sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f1303,f107]) ).
fof(f1341,plain,
para(sK21_skl,sK20_skl,sK21_skl,sK20_skl),
inference(resolution,[status(thm)],[f1313,f105]) ).
fof(f1407,plain,
circle(sK25_skl,sK23_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f549,f444]) ).
fof(f1561,plain,
! [X0,X1] : eqangle(sK21_skl,sK20_skl,X0,X1,sK21_skl,sK20_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f1341]) ).
fof(f2656,plain,
( perp(sK23_skl,sK24_skl,sK24_skl,sK24_skl)
| ~ coll(sK25_skl,sK23_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f225,f1407]) ).
fof(f2658,plain,
perp(sK23_skl,sK24_skl,sK24_skl,sK24_skl),
inference(forward_subsumption_resolution,[status(thm)],[f2656,f421]) ).
fof(f2671,plain,
para(sK24_skl,sK21_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f2658,f488]) ).
fof(f2695,plain,
! [X0,X1] : eqangle(sK24_skl,sK21_skl,X0,X1,sK24_skl,sK24_skl,X0,X1),
inference(resolution,[status(thm)],[f2671,f189]) ).
fof(f2831,plain,
! [X0] :
( cong(sK20_skl,X0,sK20_skl,X0)
| ~ cyclic(sK20_skl,X0,sK21_skl,sK21_skl)
| ~ cyclic(sK20_skl,X0,sK21_skl,X0)
| ~ cyclic(sK20_skl,X0,sK21_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f1561,f198]) ).
fof(f2836,plain,
! [X0,X1] : eqangle(sK21_skl,sK20_skl,sK21_skl,sK20_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1561,f144]) ).
fof(f3253,plain,
! [X0] :
( cong(sK21_skl,X0,sK24_skl,X0)
| ~ cyclic(sK21_skl,X0,sK24_skl,sK24_skl)
| ~ cyclic(sK21_skl,X0,sK24_skl,X0)
| ~ cyclic(sK21_skl,X0,sK24_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f2695,f198]) ).
fof(f3260,plain,
! [X0] :
( cong(sK21_skl,X0,sK24_skl,X0)
| ~ cyclic(sK21_skl,X0,sK24_skl,X0)
| ~ cyclic(sK21_skl,X0,sK24_skl,sK24_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f3253]) ).
fof(f3363,plain,
! [X0,X1] :
( cong(sK20_skl,sK20_skl,X0,X0)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X1)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X0)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X0) ),
inference(resolution,[status(thm)],[f2836,f198]) ).
fof(f3364,plain,
! [X0] :
( cyclic(sK20_skl,sK20_skl,sK21_skl,X0)
| ~ coll(sK21_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f2836,f195]) ).
fof(f3365,plain,
! [X0] :
( cyclic(sK20_skl,sK20_skl,sK21_skl,X0)
| coll(sK21_skl,X0,sK20_skl) ),
inference(resolution,[status(thm)],[f2836,f193]) ).
fof(f3373,plain,
! [X0,X1] :
( cong(sK20_skl,sK20_skl,X0,X0)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X1)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3363]) ).
fof(f3374,plain,
! [X0] :
( cong(sK20_skl,sK20_skl,X0,X0)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3373,f3375]) ).
fof(f3375,plain,
! [X0] : cyclic(sK20_skl,sK20_skl,sK21_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3365,f3364]) ).
fof(f3376,plain,
! [X0] : cong(sK20_skl,sK20_skl,X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3374,f3375]) ).
fof(f3379,plain,
( midp(sK20_skl,sK20_skl,sK20_skl)
| ~ coll(sK20_skl,sK20_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f3376,f258]) ).
fof(f3386,plain,
midp(sK20_skl,sK20_skl,sK20_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3379,f810]) ).
fof(f3389,plain,
! [X0,X1] :
( midp(X0,sK20_skl,X1)
| ~ coll(X0,sK20_skl,X1)
| ~ para(sK20_skl,X0,sK20_skl,X1) ),
inference(resolution,[status(thm)],[f3386,f204]) ).
fof(f3502,plain,
! [X0,X1] :
( cyclic(sK20_skl,sK21_skl,X1,X0)
| ~ cyclic(sK20_skl,sK20_skl,sK21_skl,X0) ),
inference(resolution,[status(thm)],[f3375,f136]) ).
fof(f3506,plain,
! [X0,X1] : cyclic(sK20_skl,sK21_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3502,f3375]) ).
fof(f3509,plain,
! [X0,X1,X2] :
( cyclic(sK21_skl,X0,X2,X1)
| ~ cyclic(sK20_skl,sK21_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3506,f136]) ).
fof(f3511,plain,
! [X0,X1] : cyclic(sK20_skl,X0,sK21_skl,X1),
inference(resolution,[status(thm)],[f3506,f131]) ).
fof(f3514,plain,
! [X0] :
( cong(sK21_skl,X0,sK24_skl,X0)
| ~ cyclic(sK21_skl,X0,sK24_skl,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3260,f3517]) ).
fof(f3517,plain,
! [X0,X1,X2] : cyclic(sK21_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3509,f3506]) ).
fof(f3518,plain,
! [X0] :
( cong(sK20_skl,X0,sK20_skl,X0)
| ~ cyclic(sK20_skl,X0,sK21_skl,X0)
| ~ cyclic(sK20_skl,X0,sK21_skl,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f2831,f3511]) ).
fof(f3520,plain,
! [X0] : cong(sK21_skl,X0,sK24_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3514,f3517]) ).
fof(f3523,plain,
! [X0] :
( cong(sK20_skl,X0,sK20_skl,X0)
| ~ cyclic(sK20_skl,X0,sK21_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3518,f3511]) ).
fof(f3526,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK21_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3517,f136]) ).
fof(f3530,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3557]) ).
fof(f3540,plain,
! [X0] : cong(sK20_skl,X0,sK20_skl,X0),
inference(backward_subsumption_resolution,[status(thm)],[f3523,f3557]) ).
fof(f3557,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3526,f3517]) ).
fof(f3571,plain,
! [X0,X1] :
( perp(sK21_skl,sK24_skl,X1,X0)
| ~ cong(sK21_skl,X0,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f3520,f232]) ).
fof(f3575,plain,
! [X0,X1] : para(sK24_skl,sK23_skl,X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f451,f3582]) ).
fof(f3582,plain,
! [X0,X1] : perp(sK21_skl,sK24_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3571,f3520]) ).
fof(f3654,plain,
! [X0,X1] :
( perp(X1,sK20_skl,sK20_skl,X0)
| ~ cong(sK20_skl,X0,sK20_skl,X0) ),
inference(resolution,[status(thm)],[f3540,f3530]) ).
fof(f3662,plain,
! [X0,X1] : perp(X0,sK20_skl,sK20_skl,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3654,f3540]) ).
fof(f3667,plain,
! [X0,X1] : perp(X0,X1,sK21_skl,sK24_skl),
inference(resolution,[status(thm)],[f3582,f114]) ).
fof(f3693,plain,
! [X0] : coll(sK24_skl,sK23_skl,X0),
inference(resolution,[status(thm)],[f3575,f256]) ).
fof(f3701,plain,
! [X0,X1] :
( coll(X1,X0,sK24_skl)
| ~ coll(sK24_skl,sK23_skl,X0) ),
inference(resolution,[status(thm)],[f3693,f103]) ).
fof(f3733,plain,
! [X0,X1] : coll(X0,X1,sK24_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3701,f3693]) ).
fof(f3885,plain,
! [X0,X1] : coll(X0,sK24_skl,X1),
inference(resolution,[status(thm)],[f3733,f98]) ).
fof(f3928,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,sK24_skl,X1) ),
inference(resolution,[status(thm)],[f3885,f103]) ).
fof(f3959,plain,
! [X0,X1] :
( midp(X0,sK20_skl,X1)
| ~ para(sK20_skl,X0,sK20_skl,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f3389,f3987]) ).
fof(f3987,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3928,f3885]) ).
fof(f4224,plain,
! [X0,X1] :
( cong(X1,sK20_skl,X1,X0)
| ~ midp(sK20_skl,sK20_skl,X0) ),
inference(resolution,[status(thm)],[f3662,f230]) ).
fof(f4251,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ perp(sK21_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3667,f117]) ).
fof(f4258,plain,
! [X0,X1] : midp(X0,sK20_skl,X1),
inference(backward_subsumption_resolution,[status(thm)],[f3959,f4276]) ).
fof(f4276,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4251,f3582]) ).
fof(f4282,plain,
! [X0,X1] : cong(X0,sK20_skl,X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f4224,f4258]) ).
fof(f4307,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f378,f4282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO590+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 17:41:09 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 3.14/0.90 % Refutation found
% 3.14/0.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.14/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.96/0.94 % Elapsed time: 0.552828 seconds
% 2.96/0.94 % CPU time: 3.966832 seconds
% 2.96/0.94 % Total memory used: 123.016 MB
% 2.96/0.94 % Net memory used: 118.711 MB
%------------------------------------------------------------------------------