%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO554+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 : n014.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 12:25:13 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 15 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 141 ( 41 ~; 36 |; 50 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 271 ( 239 !; 32 ?)
% 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(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(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(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(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,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) )
=> coll(D,F,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ( circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) )
=> coll(D,F,G) ),
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(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(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(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,D,E,F,G,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9] :
( ~ coll(D,F,G)
& circle(B,C,G,NWPNT9)
& circle(A,C,G,NWPNT8)
& circle(B,C,F,NWPNT7)
& coll(B,E,F)
& circle(B,C,E,NWPNT6)
& coll(C,D,E)
& circle(A,C,D,NWPNT5)
& circle(B,C,NWPNT3,NWPNT4)
& circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [D,F,G] :
( ~ coll(D,F,G)
& ? [B,C] :
( ? [NWPNT9] : circle(B,C,G,NWPNT9)
& ? [A] :
( ? [NWPNT8] : circle(A,C,G,NWPNT8)
& ? [NWPNT7] : circle(B,C,F,NWPNT7)
& ? [E] :
( coll(B,E,F)
& ? [NWPNT6] : circle(B,C,E,NWPNT6)
& coll(C,D,E)
& ? [NWPNT5] : circle(A,C,D,NWPNT5)
& ? [NWPNT3,NWPNT4] : circle(B,C,NWPNT3,NWPNT4)
& ? [NWPNT1,NWPNT2] : circle(A,C,NWPNT1,NWPNT2)
& perp(C,A,C,B) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ coll(sK20_skl,sK21_skl,sK22_skl)
& circle(sK23_skl,sK24_skl,sK22_skl,sK35_skl)
& circle(sK25_skl,sK24_skl,sK22_skl,sK34_skl)
& circle(sK23_skl,sK24_skl,sK21_skl,sK33_skl)
& coll(sK23_skl,sK26_skl,sK21_skl)
& circle(sK23_skl,sK24_skl,sK26_skl,sK32_skl)
& coll(sK24_skl,sK20_skl,sK26_skl)
& circle(sK25_skl,sK24_skl,sK20_skl,sK31_skl)
& circle(sK23_skl,sK24_skl,sK29_skl,sK30_skl)
& circle(sK25_skl,sK24_skl,sK27_skl,sK28_skl)
& perp(sK24_skl,sK25_skl,sK24_skl,sK23_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,sK33_skl,sK34_skl,sK35_skl]),skolemize(D,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(B,sK23_skl),skolemize(C,sK24_skl),skolemize(A,sK25_skl),skolemize(E,sK26_skl),skolemize(NWPNT1,sK27_skl),skolemize(NWPNT2,sK28_skl),skolemize(NWPNT3,sK29_skl),skolemize(NWPNT4,sK30_skl),skolemize(NWPNT5,sK31_skl),skolemize(NWPNT6,sK32_skl),skolemize(NWPNT7,sK33_skl),skolemize(NWPNT8,sK34_skl),skolemize(NWPNT9,sK35_skl)],[f370]) ).
fof(f372,plain,
perp(sK24_skl,sK25_skl,sK24_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ coll(sK20_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f422,plain,
perp(sK24_skl,sK23_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f114,f372]) ).
fof(f426,plain,
perp(sK24_skl,sK23_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f422,f112]) ).
fof(f436,plain,
! [X0,X1] :
( para(sK24_skl,sK25_skl,X0,X1)
| ~ perp(sK24_skl,sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f372]) ).
fof(f685,plain,
para(sK24_skl,sK25_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f436,f426]) ).
fof(f865,plain,
para(sK25_skl,sK24_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f685,f107]) ).
fof(f884,plain,
para(sK25_skl,sK24_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f865,f105]) ).
fof(f1433,plain,
! [X0,X1] : eqangle(sK25_skl,sK24_skl,X0,X1,sK25_skl,sK24_skl,X0,X1),
inference(resolution,[status(thm)],[f189,f884]) ).
fof(f2283,plain,
! [X0,X1] : eqangle(X0,X1,sK25_skl,sK24_skl,X0,X1,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f1433,f140]) ).
fof(f2438,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f2283,f186]) ).
fof(f2453,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f2438,f256]) ).
fof(f2665,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f2453,f100]) ).
fof(f2849,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f2665,f98]) ).
fof(f2880,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2849,f103]) ).
fof(f2883,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f2880,f2849]) ).
fof(f2896,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f382,f2883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO554+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 17:22:19 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.46 % Refutation found
% 0.11/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.48 % Elapsed time: 0.111510 seconds
% 0.11/0.48 % CPU time: 0.608928 seconds
% 0.11/0.48 % Total memory used: 92.203 MB
% 0.11/0.48 % Net memory used: 91.593 MB
%------------------------------------------------------------------------------