%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO585+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 : n004.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 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 76 ( 19 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 161 ( 54 ~; 49 |; 42 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 301 ( 285 !; 16 ?)
% 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(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
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(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(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(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,U,D,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,U,V,NWPNT1] :
( ( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(A,U,D,V) ),
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(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(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(f369,plain,
? [A,B,C,O,D,U,V,NWPNT1] :
( ~ cyclic(A,U,D,V)
& perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,D,U,V] :
( ~ cyclic(A,U,D,V)
& ? [C] :
( perp(C,D,A,V)
& perp(A,D,C,V)
& perp(A,C,D,V)
& ? [B] :
( perp(B,D,A,U)
& perp(A,D,B,U)
& perp(A,B,D,U)
& ? [O] :
( ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cyclic(sK20_skl,sK22_skl,sK21_skl,sK23_skl)
& perp(sK24_skl,sK21_skl,sK20_skl,sK23_skl)
& perp(sK20_skl,sK21_skl,sK24_skl,sK23_skl)
& perp(sK20_skl,sK24_skl,sK21_skl,sK23_skl)
& perp(sK25_skl,sK21_skl,sK20_skl,sK22_skl)
& perp(sK20_skl,sK21_skl,sK25_skl,sK22_skl)
& perp(sK20_skl,sK25_skl,sK21_skl,sK22_skl)
& circle(sK26_skl,sK20_skl,sK21_skl,sK27_skl)
& circle(sK26_skl,sK20_skl,sK25_skl,sK24_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(A,sK20_skl),skolemize(D,sK21_skl),skolemize(U,sK22_skl),skolemize(V,sK23_skl),skolemize(C,sK24_skl),skolemize(B,sK25_skl),skolemize(O,sK26_skl),skolemize(NWPNT1,sK27_skl)],[f370]) ).
fof(f379,plain,
perp(sK24_skl,sK21_skl,sK20_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f380,plain,
~ cyclic(sK20_skl,sK22_skl,sK21_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f394,plain,
perp(sK20_skl,sK23_skl,sK24_skl,sK21_skl),
inference(resolution,[status(thm)],[f114,f379]) ).
fof(f516,plain,
! [X0,X1] :
( para(sK24_skl,sK21_skl,X0,X1)
| ~ perp(sK20_skl,sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f379]) ).
fof(f552,plain,
para(sK24_skl,sK21_skl,sK24_skl,sK21_skl),
inference(resolution,[status(thm)],[f516,f394]) ).
fof(f609,plain,
! [X0,X1] : eqangle(sK24_skl,sK21_skl,X0,X1,sK24_skl,sK21_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f552]) ).
fof(f617,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK21_skl,X0,X1,sK24_skl,sK21_skl),
inference(resolution,[status(thm)],[f140,f609]) ).
fof(f630,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f617,f186]) ).
fof(f634,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f630,f256]) ).
fof(f636,plain,
! [X0,X1] : para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[f630,f105]) ).
fof(f644,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f634,f100]) ).
fof(f652,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f644,f98]) ).
fof(f657,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f652,f103]) ).
fof(f660,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f657,f652]) ).
fof(f661,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
inference(resolution,[status(thm)],[f636,f189]) ).
fof(f682,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f660]) ).
fof(f685,plain,
! [X0,X1] : cyclic(X0,X1,X0,X0),
inference(resolution,[status(thm)],[f682,f661]) ).
fof(f700,plain,
! [X0,X1] : cyclic(X0,X0,X1,X0),
inference(resolution,[status(thm)],[f685,f131]) ).
fof(f711,plain,
! [X0,X1] : cyclic(X0,X0,X0,X1),
inference(resolution,[status(thm)],[f700,f129]) ).
fof(f718,plain,
! [X0,X1,X2] :
( cyclic(X0,X0,X2,X1)
| ~ cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f711,f136]) ).
fof(f722,plain,
! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f718,f711]) ).
fof(f735,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f722,f136]) ).
fof(f739,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f735,f722]) ).
fof(f747,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f380,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO585+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.38 % Computer : n004.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Sun Sep 20 17:40:09 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.14/5.40 % Drodi V4.1.1
% 0.14/5.43 % Refutation found
% 0.14/5.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.065238 seconds
% 0.14/5.45 % CPU time: 0.182847 seconds
% 0.14/5.45 % Total memory used: 85.521 MB
% 0.14/5.45 % Net memory used: 85.353 MB
%------------------------------------------------------------------------------