%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO543+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 : n015.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 12:25:12 PM UTC 2026
% Result : Theorem 0.13s 5.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 11 unt; 2 def)
% Number of atoms : 220 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 209 ( 70 ~; 65 |; 57 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 284 ( 264 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
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(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,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(f64,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
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,H,A1,P,Q] :
( ( midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(P,Q,H,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,H,A1,P,Q] :
( ( midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(P,Q,H,D) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
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(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(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(f369,plain,
? [A,B,C,D,E,F,H,A1,P,Q] :
( ~ cyclic(P,Q,H,D)
& midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [D,H,P,Q] :
( ~ cyclic(P,Q,H,D)
& ? [C,F] :
( midp(Q,F,C)
& ? [B,E] :
( midp(P,E,B)
& ? [A1] : midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& ? [A] :
( coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ cyclic(sK22_skl,sK23_skl,sK21_skl,sK20_skl)
& midp(sK23_skl,sK25_skl,sK24_skl)
& midp(sK22_skl,sK27_skl,sK26_skl)
& midp(sK29_skl,sK24_skl,sK26_skl)
& coll(sK21_skl,sK24_skl,sK25_skl)
& coll(sK21_skl,sK26_skl,sK27_skl)
& coll(sK25_skl,sK28_skl,sK26_skl)
& perp(sK25_skl,sK24_skl,sK28_skl,sK26_skl)
& coll(sK27_skl,sK28_skl,sK24_skl)
& perp(sK27_skl,sK26_skl,sK28_skl,sK24_skl)
& coll(sK20_skl,sK26_skl,sK24_skl)
& perp(sK20_skl,sK28_skl,sK26_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,sK28_skl,sK29_skl]),skolemize(D,sK20_skl),skolemize(H,sK21_skl),skolemize(P,sK22_skl),skolemize(Q,sK23_skl),skolemize(C,sK24_skl),skolemize(F,sK25_skl),skolemize(B,sK26_skl),skolemize(E,sK27_skl),skolemize(A,sK28_skl),skolemize(A1,sK29_skl)],[f370]) ).
fof(f382,plain,
midp(sK23_skl,sK25_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f383,plain,
~ cyclic(sK22_skl,sK23_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f698,plain,
! [X0,X1] :
( para(X0,sK25_skl,X1,sK24_skl)
| ~ midp(sK23_skl,X0,X1) ),
inference(resolution,[status(thm)],[f249,f382]) ).
fof(f703,plain,
! [X0,X1] :
( ~ midp(sK23_skl,X1,X0)
| para(X0,sK25_skl,X1,sK24_skl) ),
inference(resolution,[status(thm)],[f698,f122]) ).
fof(f732,plain,
para(sK24_skl,sK25_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f703,f382]) ).
fof(f737,plain,
para(sK24_skl,sK25_skl,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f732,f105]) ).
fof(f742,plain,
! [X0,X1] : eqangle(sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl,X0,X1),
inference(resolution,[status(thm)],[f737,f189]) ).
fof(f832,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK25_skl,X0,X1,sK24_skl,sK25_skl),
inference(resolution,[status(thm)],[f742,f140]) ).
fof(f836,definition,
( sQ0_spl
<=> coll(sK24_skl,sK24_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f838,plain,
( sQ0_spl
| ~ coll(sK24_skl,sK24_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f836]) ).
fof(f950,plain,
! [X0] :
( cyclic(X0,sK25_skl,sK24_skl,sK24_skl)
| ~ coll(sK24_skl,sK24_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f832,f195]) ).
fof(f953,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f832,f186]) ).
fof(f955,definition,
! [X0] :
( sQ12_spl
<=> cyclic(X0,sK25_skl,sK24_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f956,plain,
! [X0] :
( ~ sQ12_spl
| cyclic(X0,sK25_skl,sK24_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f955]) ).
fof(f958,plain,
( sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f950,f836,f955]) ).
fof(f963,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f953,f256]) ).
fof(f978,plain,
! [X0] :
( ~ sQ12_spl
| cyclic(sK25_skl,X0,sK24_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f956,f133]) ).
fof(f1014,plain,
! [X0] :
( ~ sQ12_spl
| cyclic(sK25_skl,sK24_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f978,f131]) ).
fof(f1018,plain,
! [X0] :
( sQ0_spl
| ~ coll(sK25_skl,X0,sK24_skl)
| ~ coll(sK25_skl,X0,sK24_skl) ),
inference(resolution,[status(thm)],[f838,f103]) ).
fof(f1022,plain,
! [X0] :
( sQ0_spl
| ~ coll(sK25_skl,X0,sK24_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1018]) ).
fof(f1024,plain,
( sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f1022,f963]) ).
fof(f1100,plain,
! [X0] :
( ~ sQ12_spl
| cyclic(sK25_skl,sK24_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f1014,f129]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ sQ12_spl
| cyclic(sK24_skl,sK24_skl,X0,X1)
| ~ cyclic(sK25_skl,sK24_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f1100,f136]) ).
fof(f1194,plain,
! [X0,X1] :
( ~ sQ12_spl
| cyclic(sK24_skl,sK24_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1181,f1100]) ).
fof(f1201,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| cyclic(sK24_skl,X0,X1,X2)
| ~ cyclic(sK24_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f1194,f136]) ).
fof(f1210,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| cyclic(sK24_skl,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1201,f1194]) ).
fof(f1217,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(sK24_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f1210,f136]) ).
fof(f1226,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1217,f1210]) ).
fof(f1228,plain,
( ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f1226]) ).
fof(f1233,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1228]) ).
fof(f1235,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1024]) ).
fof(f1236,plain,
$false,
inference(sat_refutation,[status(thm)],[f958,f1233,f1235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO543+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n015.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 17:30:10 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.13/5.46 % Refutation found
% 0.13/5.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.49 % Elapsed time: 0.115087 seconds
% 0.13/5.49 % CPU time: 0.671066 seconds
% 0.13/5.49 % Total memory used: 94.441 MB
% 0.13/5.49 % Net memory used: 93.797 MB
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