%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO631+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 : n019.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 12:25:25 PM UTC 2026
% Result : Theorem 0.82s 0.54s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 17 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 185 ( 54 ~; 49 |; 66 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 345 ( 319 !; 26 ?)
% 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(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(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(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(f95,conjecture,
! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ( coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(P,G,I,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ( coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> cyclic(P,G,I,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(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(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(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,P,F,G,H,E,I,NWPNT1,NWPNT2] :
( ~ cyclic(P,G,I,H)
& coll(I,H,E)
& coll(I,F,G)
& coll(E,C,D)
& perp(E,P,C,D)
& coll(H,B,C)
& perp(H,P,B,C)
& coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& circle(O,A,P,NWPNT2)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [P,G,H,I] :
( ~ cyclic(P,G,I,H)
& ? [E] :
( coll(I,H,E)
& ? [F] :
( coll(I,F,G)
& ? [C,D] :
( coll(E,C,D)
& perp(E,P,C,D)
& ? [B] :
( coll(H,B,C)
& perp(H,P,B,C)
& ? [A] :
( coll(G,A,B)
& perp(G,P,A,B)
& coll(F,A,D)
& perp(F,P,A,D)
& ? [O] :
( ? [NWPNT2] : circle(O,A,P,NWPNT2)
& ? [NWPNT1] : circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cyclic(sK20_skl,sK21_skl,sK23_skl,sK22_skl)
& coll(sK23_skl,sK22_skl,sK24_skl)
& coll(sK23_skl,sK25_skl,sK21_skl)
& coll(sK24_skl,sK26_skl,sK27_skl)
& perp(sK24_skl,sK20_skl,sK26_skl,sK27_skl)
& coll(sK22_skl,sK28_skl,sK26_skl)
& perp(sK22_skl,sK20_skl,sK28_skl,sK26_skl)
& coll(sK21_skl,sK29_skl,sK28_skl)
& perp(sK21_skl,sK20_skl,sK29_skl,sK28_skl)
& coll(sK25_skl,sK29_skl,sK27_skl)
& perp(sK25_skl,sK20_skl,sK29_skl,sK27_skl)
& circle(sK30_skl,sK29_skl,sK20_skl,sK32_skl)
& circle(sK30_skl,sK29_skl,sK27_skl,sK31_skl)
& circle(sK30_skl,sK29_skl,sK28_skl,sK26_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,sK29_skl,sK30_skl,sK31_skl,sK32_skl]),skolemize(P,sK20_skl),skolemize(G,sK21_skl),skolemize(H,sK22_skl),skolemize(I,sK23_skl),skolemize(E,sK24_skl),skolemize(F,sK25_skl),skolemize(C,sK26_skl),skolemize(D,sK27_skl),skolemize(B,sK28_skl),skolemize(A,sK29_skl),skolemize(O,sK30_skl),skolemize(NWPNT1,sK31_skl),skolemize(NWPNT2,sK32_skl)],[f370]) ).
fof(f375,plain,
perp(sK25_skl,sK20_skl,sK29_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f385,plain,
~ cyclic(sK20_skl,sK21_skl,sK23_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f391,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f256,f107]) ).
fof(f396,plain,
! [X0,X1,X2] :
( ~ para(X0,X2,X1,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f391,f105]) ).
fof(f402,plain,
! [X0,X1,X2] :
( ~ para(X1,X0,X0,X2)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f396,f107]) ).
fof(f409,plain,
! [X0,X1,X2] :
( ~ para(X1,X0,X2,X0)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f402,f105]) ).
fof(f416,plain,
! [X0,X1] :
( para(X0,X1,sK29_skl,sK27_skl)
| ~ perp(X0,X1,sK25_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f117,f375]) ).
fof(f435,plain,
! [X0,X1] :
( ~ perp(sK25_skl,sK20_skl,X0,X1)
| para(X0,X1,sK29_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f416,f114]) ).
fof(f491,plain,
para(sK29_skl,sK27_skl,sK29_skl,sK27_skl),
inference(resolution,[status(thm)],[f435,f375]) ).
fof(f518,plain,
! [X0,X1] : eqangle(sK29_skl,sK27_skl,X0,X1,sK29_skl,sK27_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f491]) ).
fof(f536,plain,
! [X0,X1] : eqangle(X0,X1,sK29_skl,sK27_skl,X0,X1,sK29_skl,sK27_skl),
inference(resolution,[status(thm)],[f518,f140]) ).
fof(f602,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f536,f186]) ).
fof(f612,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[f602,f189]) ).
fof(f613,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f602,f409]) ).
fof(f628,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
inference(resolution,[status(thm)],[f612,f138]) ).
fof(f647,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X0,X1,X3,X2),
inference(resolution,[status(thm)],[f628,f140]) ).
fof(f684,plain,
! [X0,X1] :
( cyclic(X1,X0,X0,X0)
| ~ coll(X0,X0,X0) ),
inference(resolution,[status(thm)],[f647,f195]) ).
fof(f686,plain,
! [X0,X1] : cyclic(X0,X1,X1,X1),
inference(forward_subsumption_resolution,[status(thm)],[f684,f613]) ).
fof(f695,plain,
! [X0,X1] : cyclic(X0,X1,X0,X0),
inference(resolution,[status(thm)],[f686,f133]) ).
fof(f707,plain,
! [X0,X1] : cyclic(X0,X0,X1,X0),
inference(resolution,[status(thm)],[f695,f131]) ).
fof(f719,plain,
! [X0,X1] : cyclic(X0,X0,X0,X1),
inference(resolution,[status(thm)],[f707,f129]) ).
fof(f726,plain,
! [X0,X1,X2] :
( cyclic(X0,X0,X1,X2)
| ~ cyclic(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f719,f136]) ).
fof(f736,plain,
! [X0,X1,X2] : cyclic(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f726,f719]) ).
fof(f755,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f736,f136]) ).
fof(f765,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f755,f736]) ).
fof(f770,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f385,f765]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 18:07:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.82/0.54 % Refutation found
% 0.82/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.82/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.82/0.55 % Elapsed time: 0.173517 seconds
% 0.82/0.55 % CPU time: 1.046750 seconds
% 0.82/0.55 % Total memory used: 98.272 MB
% 0.82/0.55 % Net memory used: 97.315 MB
%------------------------------------------------------------------------------