%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO580+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 : n012.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 12:25:17 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 89 ( 20 unt; 0 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 190 ( 62 ~; 57 |; 52 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 325 ( 309 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,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(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,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(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(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
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(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(f64,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
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,
! [A,B,C,D,E,F,G,H] :
( ( midp(H,C,B)
& coll(G,A,D)
& perp(G,C,A,D)
& coll(F,A,D)
& perp(F,B,A,D)
& coll(E,B,C)
& perp(E,A,B,C)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) )
=> cyclic(E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( midp(H,C,B)
& coll(G,A,D)
& perp(G,C,A,D)
& coll(F,A,D)
& perp(F,B,A,D)
& coll(E,B,C)
& perp(E,A,B,C)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) )
=> cyclic(E,F,G,H) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
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(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(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
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(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(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(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(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(f247,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f248,plain,
! [A,B,C,D] :
( para(A,C,B,D)
| ! [M] :
( ~ midp(M,C,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2,X3,X4] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
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,
? [A,B,C,D,E,F,G,H] :
( ~ cyclic(E,F,G,H)
& midp(H,C,B)
& coll(G,A,D)
& perp(G,C,A,D)
& coll(F,A,D)
& perp(F,B,A,D)
& coll(E,B,C)
& perp(E,A,B,C)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [E,F,G,H] :
( ~ cyclic(E,F,G,H)
& ? [B,C] :
( midp(H,C,B)
& ? [A,D] :
( coll(G,A,D)
& perp(G,C,A,D)
& coll(F,A,D)
& perp(F,B,A,D)
& coll(E,B,C)
& perp(E,A,B,C)
& eqangle(D,C,C,A,D,C,C,B)
& eqangle(D,B,B,C,D,B,B,A)
& eqangle(D,A,A,B,D,A,A,C) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cyclic(sK20_skl,sK21_skl,sK22_skl,sK23_skl)
& midp(sK23_skl,sK25_skl,sK24_skl)
& coll(sK22_skl,sK26_skl,sK27_skl)
& perp(sK22_skl,sK25_skl,sK26_skl,sK27_skl)
& coll(sK21_skl,sK26_skl,sK27_skl)
& perp(sK21_skl,sK24_skl,sK26_skl,sK27_skl)
& coll(sK20_skl,sK24_skl,sK25_skl)
& perp(sK20_skl,sK26_skl,sK24_skl,sK25_skl)
& eqangle(sK27_skl,sK25_skl,sK25_skl,sK26_skl,sK27_skl,sK25_skl,sK25_skl,sK24_skl)
& eqangle(sK27_skl,sK24_skl,sK24_skl,sK25_skl,sK27_skl,sK24_skl,sK24_skl,sK26_skl)
& eqangle(sK27_skl,sK26_skl,sK26_skl,sK24_skl,sK27_skl,sK26_skl,sK26_skl,sK25_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(E,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(H,sK23_skl),skolemize(B,sK24_skl),skolemize(C,sK25_skl),skolemize(A,sK26_skl),skolemize(D,sK27_skl)],[f370]) ).
fof(f381,plain,
midp(sK23_skl,sK25_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ cyclic(sK20_skl,sK21_skl,sK22_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f384,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f262,f122]) ).
fof(f385,plain,
coll(sK23_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f384,f381]) ).
fof(f394,plain,
! [X0,X1,X2] :
( ~ midp(X0,X1,X2)
| cong(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f149,f260]) ).
fof(f396,plain,
! [X0,X1,X2] :
( ~ midp(X0,X2,X1)
| cong(X0,X1,X2,X0) ),
inference(resolution,[status(thm)],[f394,f122]) ).
fof(f404,plain,
cong(sK23_skl,sK24_skl,sK25_skl,sK23_skl),
inference(resolution,[status(thm)],[f396,f381]) ).
fof(f406,plain,
cong(sK23_skl,sK24_skl,sK23_skl,sK25_skl),
inference(resolution,[status(thm)],[f404,f149]) ).
fof(f408,plain,
( midp(sK23_skl,sK24_skl,sK25_skl)
| ~ coll(sK23_skl,sK24_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f406,f258]) ).
fof(f413,plain,
midp(sK23_skl,sK24_skl,sK25_skl),
inference(forward_subsumption_resolution,[status(thm)],[f408,f385]) ).
fof(f522,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)],[f186,f140]) ).
fof(f650,plain,
! [X0,X1] :
( para(X0,sK24_skl,X1,sK25_skl)
| ~ midp(sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f249,f413]) ).
fof(f654,plain,
para(sK25_skl,sK24_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f650,f381]) ).
fof(f663,plain,
para(sK24_skl,sK25_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f654,f107]) ).
fof(f673,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f663,f105]) ).
fof(f684,plain,
! [X0,X1] : eqangle(sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl,X0,X1),
inference(resolution,[status(thm)],[f673,f189]) ).
fof(f732,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f522,f684]) ).
fof(f745,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[f732,f189]) ).
fof(f749,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f732,f256]) ).
fof(f789,plain,
! [X0,X1,X2] :
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f745,f195]) ).
fof(f960,plain,
! [X0,X1] : cyclic(X0,X1,X1,X1),
inference(resolution,[status(thm)],[f789,f749]) ).
fof(f973,plain,
! [X0,X1] : cyclic(X0,X1,X0,X0),
inference(resolution,[status(thm)],[f960,f133]) ).
fof(f986,plain,
! [X0,X1] : cyclic(X0,X0,X1,X0),
inference(resolution,[status(thm)],[f973,f131]) ).
fof(f1006,plain,
! [X0,X1] : cyclic(X0,X0,X0,X1),
inference(resolution,[status(thm)],[f986,f129]) ).
fof(f1013,plain,
! [X0,X1,X2] :
( cyclic(X0,X0,X1,X2)
| ~ cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f1006,f136]) ).
fof(f1022,plain,
! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f1013,f1006]) ).
fof(f1029,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1022,f136]) ).
fof(f1038,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f1029,f1022]) ).
fof(f1041,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f382,f1038]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO580+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sun Sep 20 17:36:52 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.30 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.156097 seconds
% 0.15/0.46 % CPU time: 1.028751 seconds
% 0.15/0.46 % Total memory used: 107.310 MB
% 0.15/0.46 % Net memory used: 105.441 MB
%------------------------------------------------------------------------------