%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO088+1 : TPTP v9.3.1. Released v2.4.0.
% 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 12:24:02 PM UTC 2026
% Result : Theorem 129.00s 16.79s
% Output : CNFRefutation 129.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 233 ( 82 ~; 98 |; 45 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 83 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [C,Cpp,P] :
( ( incident_c(P,Cpp)
& end_point(P,C)
& part_of(Cpp,C) )
=> end_point(P,Cpp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C,Cpp,P] :
( ( incident_c(P,Cpp)
& end_point(P,C)
& part_of(Cpp,C) )
=> end_point(P,Cpp) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [C,C1] :
( ( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ! [C,C1] :
( ? [P] :
( ~ incident_c(P,C)
& incident_c(P,C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [C,C1] :
( ( ~ incident_c(sK0_skl(C1,C),C)
& incident_c(sK0_skl(C1,C),C1) )
| part_of(C1,C) )
& ! [C,C1] :
( ! [P] :
( incident_c(P,C)
| ~ incident_c(P,C1) )
| ~ part_of(C1,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(P,sK0_skl(C1,C))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( incident_c(sK0_skl(X0,X1),X0)
| part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ incident_c(sK0_skl(X0,X1),X1)
| part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [P,C] :
( ( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ! [P,C] :
( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [P,C] :
( ( ~ part_of(sK3_skl(C,P),sK2_skl(C,P))
& ~ part_of(sK2_skl(C,P),sK3_skl(C,P))
& incident_c(P,sK3_skl(C,P))
& incident_c(P,sK2_skl(C,P))
& part_of(sK3_skl(C,P),C)
& part_of(sK2_skl(C,P),C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f37]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( part_of(sK2_skl(X1,X0),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( part_of(sK3_skl(X1,X0),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( incident_c(X0,sK2_skl(X1,X0))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( incident_c(X0,sK3_skl(X1,X0))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f45,plain,
! [X0,X1] :
( ~ part_of(sK2_skl(X1,X0),sK3_skl(X1,X0))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( ~ part_of(sK3_skl(X1,X0),sK2_skl(X1,X0))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f104,plain,
? [C,Cpp,P] :
( ~ end_point(P,Cpp)
& incident_c(P,Cpp)
& end_point(P,C)
& part_of(Cpp,C) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f105,plain,
? [Cpp,P] :
( ~ end_point(P,Cpp)
& incident_c(P,Cpp)
& ? [C] :
( end_point(P,C)
& part_of(Cpp,C) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( ~ end_point(sK14_skl,sK13_skl)
& incident_c(sK14_skl,sK13_skl)
& end_point(sK14_skl,sK15_skl)
& part_of(sK13_skl,sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(Cpp,sK13_skl),skolemize(P,sK14_skl),skolemize(C,sK15_skl)],[f105]) ).
fof(f107,plain,
part_of(sK13_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
end_point(sK14_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
incident_c(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
~ end_point(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ incident_c(sK0_skl(X0,X1),X2)
| ~ part_of(X2,X1)
| part_of(X0,X1) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f200,plain,
! [X0] :
( ~ incident_c(sK0_skl(X0,sK15_skl),sK13_skl)
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f179,f107]) ).
fof(f204,plain,
! [X0,X1] :
( ~ incident_c(sK0_skl(X0,sK15_skl),X1)
| ~ part_of(X1,sK13_skl)
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f200,f23]) ).
fof(f277,plain,
( part_of(sK2_skl(sK13_skl,sK14_skl),sK13_skl)
| end_point(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f41,f109]) ).
fof(f283,plain,
part_of(sK2_skl(sK13_skl,sK14_skl),sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f277,f110]) ).
fof(f285,plain,
! [X0] :
( ~ incident_c(sK0_skl(X0,sK15_skl),sK2_skl(sK13_skl,sK14_skl))
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f283,f204]) ).
fof(f302,plain,
( part_of(sK2_skl(sK13_skl,sK14_skl),sK15_skl)
| part_of(sK2_skl(sK13_skl,sK14_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f285,f24]) ).
fof(f306,plain,
part_of(sK2_skl(sK13_skl,sK14_skl),sK15_skl),
inference(duplicate_literals_removal,[status(thm)],[f302]) ).
fof(f341,plain,
! [X0,X1] :
( part_of(sK2_skl(sK13_skl,sK14_skl),X1)
| part_of(X1,sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(X0,sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(X0,X1)
| ~ part_of(X1,sK15_skl)
| ~ end_point(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f306,f40]) ).
fof(f356,plain,
( part_of(sK3_skl(sK13_skl,sK14_skl),sK13_skl)
| end_point(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f42,f109]) ).
fof(f362,plain,
part_of(sK3_skl(sK13_skl,sK14_skl),sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f356,f110]) ).
fof(f378,plain,
! [X0] :
( ~ incident_c(sK0_skl(X0,sK15_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f362,f204]) ).
fof(f395,plain,
( part_of(sK3_skl(sK13_skl,sK14_skl),sK15_skl)
| part_of(sK3_skl(sK13_skl,sK14_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f378,f24]) ).
fof(f399,plain,
part_of(sK3_skl(sK13_skl,sK14_skl),sK15_skl),
inference(duplicate_literals_removal,[status(thm)],[f395]) ).
fof(f441,plain,
! [X0] :
( part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(X0,sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(X0,sK3_skl(sK13_skl,sK14_skl))
| ~ end_point(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f399,f341]) ).
fof(f468,plain,
( part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(sK14_skl,sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(sK14_skl,sK3_skl(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f441,f108]) ).
fof(f475,plain,
( ~ incident_c(sK14_skl,sK13_skl)
| end_point(sK14_skl,sK13_skl)
| part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl))
| ~ incident_c(sK14_skl,sK3_skl(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f468,f43]) ).
fof(f479,plain,
( ~ incident_c(sK14_skl,sK13_skl)
| end_point(sK14_skl,sK13_skl)
| part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f44]) ).
fof(f489,plain,
( ~ incident_c(sK14_skl,sK13_skl)
| part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f110]) ).
fof(f490,plain,
( part_of(sK2_skl(sK13_skl,sK14_skl),sK3_skl(sK13_skl,sK14_skl))
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f489,f109]) ).
fof(f502,plain,
( ~ incident_c(sK14_skl,sK13_skl)
| end_point(sK14_skl,sK13_skl)
| part_of(sK3_skl(sK13_skl,sK14_skl),sK2_skl(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f490,f45]) ).
fof(f517,plain,
( ~ incident_c(sK14_skl,sK13_skl)
| end_point(sK14_skl,sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f46]) ).
fof(f536,plain,
~ incident_c(sK14_skl,sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f517,f110]) ).
fof(f537,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f109,f536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO088+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n008.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 20 10:29:38 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 129.00/16.79 % Refutation found
% 129.00/16.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 129.00/16.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.46/17.11 % Elapsed time: 16.668897 seconds
% 19.46/17.11 % CPU time: 129.621973 seconds
% 19.46/17.11 % Total memory used: 303.376 MB
% 19.46/17.11 % Net memory used: 265.900 MB
%------------------------------------------------------------------------------