%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO569+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 : 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 12:25:16 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 19 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 144 ( 49 ~; 44 |; 36 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 296 ( 277 !; 19 ?)
% 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(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(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(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(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,C1,B1,P,Q] :
( ( coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) )
=> cyclic(Q,B,C,P) ),
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(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(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(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(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(f331,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f332,plain,
! [A,O] :
( ? [P] : perp(P,A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(miniscoping,[status(thm)],[f331]) ).
fof(f333,plain,
! [A,O] :
( perp(sK11_skl(O,A),A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( perp(sK11_skl(X0,X1),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f369,plain,
? [A,B,C,O,C1,B1,P,Q] :
( ~ cyclic(Q,B,C,P)
& coll(Q,A,B)
& coll(Q,O,B1)
& coll(P,A,C)
& coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [B,C,P,Q] :
( ~ cyclic(Q,B,C,P)
& ? [A] :
( coll(Q,A,B)
& ? [O,B1] :
( coll(Q,O,B1)
& coll(P,A,C)
& ? [C1] :
( coll(P,O,C1)
& midp(B1,C,A)
& midp(C1,B,A)
& circle(O,A,B,C) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cyclic(sK23_skl,sK20_skl,sK21_skl,sK22_skl)
& coll(sK23_skl,sK24_skl,sK20_skl)
& coll(sK23_skl,sK25_skl,sK26_skl)
& coll(sK22_skl,sK24_skl,sK21_skl)
& coll(sK22_skl,sK25_skl,sK27_skl)
& midp(sK26_skl,sK21_skl,sK24_skl)
& midp(sK27_skl,sK20_skl,sK24_skl)
& circle(sK25_skl,sK24_skl,sK20_skl,sK21_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(B,sK20_skl),skolemize(C,sK21_skl),skolemize(P,sK22_skl),skolemize(Q,sK23_skl),skolemize(A,sK24_skl),skolemize(O,sK25_skl),skolemize(B1,sK26_skl),skolemize(C1,sK27_skl)],[f370]) ).
fof(f372,plain,
circle(sK25_skl,sK24_skl,sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
~ cyclic(sK23_skl,sK20_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f484,plain,
perp(sK11_skl(sK25_skl,sK24_skl),sK24_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f334,f372]) ).
fof(f486,plain,
! [X0,X1] :
( para(X0,X1,sK24_skl,sK25_skl)
| ~ perp(X0,X1,sK11_skl(sK25_skl,sK24_skl),sK24_skl) ),
inference(resolution,[status(thm)],[f484,f117]) ).
fof(f487,plain,
perp(sK24_skl,sK25_skl,sK11_skl(sK25_skl,sK24_skl),sK24_skl),
inference(resolution,[status(thm)],[f484,f114]) ).
fof(f517,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f486,f487]) ).
fof(f587,plain,
! [X0,X1] : eqangle(sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f517]) ).
fof(f601,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f587,f140]) ).
fof(f644,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f601,f186]) ).
fof(f660,plain,
! [X0,X1] : para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[f644,f105]) ).
fof(f661,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f644,f256]) ).
fof(f663,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
inference(resolution,[status(thm)],[f660,f189]) ).
fof(f687,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X3,X2),
inference(resolution,[status(thm)],[f663,f140]) ).
fof(f733,plain,
! [X0,X1] :
( cyclic(X1,X0,X0,X0)
| ~ coll(X0,X0,X0) ),
inference(resolution,[status(thm)],[f687,f195]) ).
fof(f737,plain,
! [X0,X1] : cyclic(X0,X1,X1,X1),
inference(forward_subsumption_resolution,[status(thm)],[f733,f661]) ).
fof(f740,plain,
! [X0,X1] : cyclic(X0,X1,X0,X0),
inference(resolution,[status(thm)],[f737,f133]) ).
fof(f746,plain,
! [X0,X1] : cyclic(X0,X0,X1,X0),
inference(resolution,[status(thm)],[f740,f131]) ).
fof(f752,plain,
! [X0,X1] : cyclic(X0,X0,X0,X1),
inference(resolution,[status(thm)],[f746,f129]) ).
fof(f753,plain,
! [X0,X1,X2] :
( cyclic(X0,X0,X1,X2)
| ~ cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f752,f136]) ).
fof(f758,plain,
! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f753,f752]) ).
fof(f759,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f758,f136]) ).
fof(f764,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f759,f758]) ).
fof(f769,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f379,f764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO569+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 17:32:53 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.48 % Elapsed time: 0.115453 seconds
% 0.12/0.48 % CPU time: 0.624342 seconds
% 0.12/0.48 % Total memory used: 92.094 MB
% 0.12/0.48 % Net memory used: 91.493 MB
%------------------------------------------------------------------------------