%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO093+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 : n001.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 12:24:03 PM UTC 2026
% Result : Theorem 0.23s 0.82s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 13 unt; 0 def)
% Number of atoms : 198 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 204 ( 68 ~; 88 |; 40 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 150 ( 138 !; 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(f2,axiom,
! [C,C1,C2] :
( C = sum(C1,C2)
<=> ! [Q] :
( incident_c(Q,C)
<=> ( incident_c(Q,C2)
| incident_c(Q,C1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [C,C1] :
( ( C1 != C
& part_of(C1,C) )
=> open(C1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [C,C1,C2,P] :
( ( meet(P,C1,C2)
& part_of(C2,C)
& part_of(C1,C)
& open(C) )
=> open(sum(C1,C2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C,C1,C2,P] :
( ( meet(P,C1,C2)
& part_of(C2,C)
& part_of(C1,C)
& open(C) )
=> open(sum(C1,C2)) ),
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(f26,plain,
! [C,C1,C2] :
( ( ? [Q] :
( ( incident_c(Q,C2)
| incident_c(Q,C1)
| incident_c(Q,C) )
& ( ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) )
| ~ incident_c(Q,C) ) )
| C = sum(C1,C2) )
& ( ! [Q] :
( ( ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) )
| incident_c(Q,C) )
& ( incident_c(Q,C2)
| incident_c(Q,C1)
| ~ incident_c(Q,C) ) )
| C != sum(C1,C2) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
( ! [C,C1,C2] :
( ? [Q] :
( ( incident_c(Q,C2)
| incident_c(Q,C1)
| incident_c(Q,C) )
& ( ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) )
| ~ incident_c(Q,C) ) )
| C = sum(C1,C2) )
& ! [C,C1,C2] :
( ( ! [Q] :
( ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) )
| incident_c(Q,C) )
& ! [Q] :
( incident_c(Q,C2)
| incident_c(Q,C1)
| ~ incident_c(Q,C) ) )
| C != sum(C1,C2) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [C,C1,C2] :
( ( ( incident_c(sK1_skl(C2,C1,C),C2)
| incident_c(sK1_skl(C2,C1,C),C1)
| incident_c(sK1_skl(C2,C1,C),C) )
& ( ( ~ incident_c(sK1_skl(C2,C1,C),C2)
& ~ incident_c(sK1_skl(C2,C1,C),C1) )
| ~ incident_c(sK1_skl(C2,C1,C),C) ) )
| C = sum(C1,C2) )
& ! [C,C1,C2] :
( ( ! [Q] :
( ( ~ incident_c(Q,C2)
& ~ incident_c(Q,C1) )
| incident_c(Q,C) )
& ! [Q] :
( incident_c(Q,C2)
| incident_c(Q,C1)
| ~ incident_c(Q,C) ) )
| C != sum(C1,C2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Q,sK1_skl(C2,C1,C))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ incident_c(X3,X2)
| incident_c(X3,X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ incident_c(sK1_skl(X2,X1,X0),X2)
| ~ incident_c(sK1_skl(X2,X1,X0),X0)
| X0 = sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f34,plain,
! [X0,X1,X2] :
( incident_c(sK1_skl(X2,X1,X0),X2)
| incident_c(sK1_skl(X2,X1,X0),X1)
| incident_c(sK1_skl(X2,X1,X0),X0)
| X0 = sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
! [C,C1] :
( open(C1)
| C1 = C
| ~ part_of(C1,C) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f75,plain,
! [C1] :
( open(C1)
| ! [C] :
( C1 = C
| ~ part_of(C1,C) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( open(X0)
| X0 = X1
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f104,plain,
? [C,C1,C2,P] :
( ~ open(sum(C1,C2))
& meet(P,C1,C2)
& part_of(C2,C)
& part_of(C1,C)
& open(C) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f105,plain,
? [C1,C2] :
( ~ open(sum(C1,C2))
& ? [P] : meet(P,C1,C2)
& ? [C] :
( part_of(C2,C)
& part_of(C1,C)
& open(C) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( ~ open(sum(sK13_skl,sK14_skl))
& meet(sK16_skl,sK13_skl,sK14_skl)
& part_of(sK14_skl,sK15_skl)
& part_of(sK13_skl,sK15_skl)
& open(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(C1,sK13_skl),skolemize(C2,sK14_skl),skolemize(C,sK15_skl),skolemize(P,sK16_skl)],[f105]) ).
fof(f107,plain,
open(sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
part_of(sK13_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
part_of(sK14_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,plain,
~ open(sum(sK13_skl,sK14_skl)),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f112,plain,
! [X0,X1,X2] :
( incident_c(X0,X2)
| incident_c(X0,X1)
| ~ incident_c(X0,sum(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ incident_c(X0,X1)
| incident_c(X0,sum(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ incident_c(X0,X2)
| incident_c(X0,sum(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( ~ incident_c(X0,X3)
| ~ part_of(X3,sum(X1,X2))
| incident_c(X0,X2)
| incident_c(X0,X1) ),
inference(resolution,[status(thm)],[f112,f23]) ).
fof(f126,plain,
! [X0,X1,X2] :
( incident_c(sK0_skl(sum(X0,X1),X2),X1)
| incident_c(sK0_skl(sum(X0,X1),X2),X0)
| part_of(sum(X0,X1),X2) ),
inference(resolution,[status(thm)],[f24,f112]) ).
fof(f128,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(f130,plain,
! [X0,X1,X2] :
( part_of(X0,sum(X1,X2))
| ~ incident_c(sK0_skl(X0,sum(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f113,f25]) ).
fof(f135,plain,
! [X0,X1,X2] :
( part_of(X0,sum(X1,X2))
| ~ incident_c(sK0_skl(X0,sum(X1,X2)),X2) ),
inference(resolution,[status(thm)],[f114,f25]) ).
fof(f137,plain,
! [X0] :
( ~ incident_c(sK0_skl(X0,sK15_skl),sK14_skl)
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f128,f109]) ).
fof(f138,plain,
! [X0] :
( ~ incident_c(sK0_skl(X0,sK15_skl),sK13_skl)
| part_of(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f128,f108]) ).
fof(f180,plain,
! [X0] :
( ~ incident_c(sK1_skl(X0,X0,X0),X0)
| X0 = sum(X0,X0)
| X0 = sum(X0,X0) ),
inference(resolution,[status(thm)],[f34,f33]) ).
fof(f196,plain,
! [X0] :
( ~ incident_c(sK1_skl(X0,X0,X0),X0)
| X0 = sum(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f180]) ).
fof(f344,plain,
! [X0,X1] :
( part_of(X0,sum(X0,X1))
| part_of(X0,sum(X0,X1)) ),
inference(resolution,[status(thm)],[f130,f24]) ).
fof(f352,plain,
! [X0,X1] : part_of(X0,sum(X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f344]) ).
fof(f371,plain,
! [X0,X1] :
( open(X0)
| X0 = sum(X0,X1) ),
inference(resolution,[status(thm)],[f352,f76]) ).
fof(f374,plain,
! [X0] : sum(sK13_skl,sK14_skl) = sum(sum(sK13_skl,sK14_skl),X0),
inference(resolution,[status(thm)],[f371,f111]) ).
fof(f458,plain,
! [X0,X1] :
( part_of(X0,sum(X1,X0))
| part_of(X0,sum(X1,X0)) ),
inference(resolution,[status(thm)],[f135,f24]) ).
fof(f466,plain,
! [X0,X1] : part_of(X0,sum(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f458]) ).
fof(f513,plain,
! [X0] : part_of(X0,sum(sK13_skl,sK14_skl)),
inference(paramodulation,[status(thm)],[f374,f466]) ).
fof(f535,plain,
! [X0,X1] :
( ~ incident_c(X0,X1)
| incident_c(X0,sK14_skl)
| incident_c(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f513,f118]) ).
fof(f604,plain,
! [X0] :
( X0 = sum(X0,X0)
| X0 = sum(X0,X0) ),
inference(resolution,[status(thm)],[f196,f34]) ).
fof(f614,plain,
! [X0] : X0 = sum(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f604]) ).
fof(f710,plain,
! [X0,X1] :
( part_of(X0,sK15_skl)
| ~ incident_c(sK0_skl(X0,sK15_skl),X1)
| incident_c(sK0_skl(X0,sK15_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f535,f137]) ).
fof(f712,plain,
! [X0,X1] :
( part_of(X0,sK15_skl)
| ~ incident_c(sK0_skl(X0,sK15_skl),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f138]) ).
fof(f713,plain,
! [X0] :
( part_of(sum(X0,X0),sK15_skl)
| part_of(sum(X0,X0),sK15_skl) ),
inference(resolution,[status(thm)],[f712,f126]) ).
fof(f725,plain,
! [X0] :
( part_of(sum(X0,X0),sK15_skl)
| part_of(X0,sK15_skl) ),
inference(forward_demodulation,[status(thm)],[f614,f713]) ).
fof(f726,plain,
! [X0] :
( part_of(X0,sK15_skl)
| part_of(X0,sK15_skl) ),
inference(forward_demodulation,[status(thm)],[f614,f725]) ).
fof(f727,plain,
! [X0] : part_of(X0,sK15_skl),
inference(duplicate_literals_removal,[status(thm)],[f726]) ).
fof(f743,plain,
! [X0] :
( open(X0)
| X0 = sK15_skl ),
inference(resolution,[status(thm)],[f727,f76]) ).
fof(f750,plain,
sum(sK13_skl,sK14_skl) = sK15_skl,
inference(resolution,[status(thm)],[f743,f111]) ).
fof(f788,plain,
~ open(sK15_skl),
inference(backward_demodulation,[status(thm)],[f750,f111]) ).
fof(f803,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f788,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50 % Computer : n001.cluster.edu
% 0.18/0.50 % Model : x86_64 x86_64
% 0.18/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.50 % Memory : 8046.5625MB
% 0.18/0.50 % OS : Linux 6.8.0-71-generic
% 0.18/0.50 % CPULimit : 300
% 0.18/0.50 % WCLimit : 300
% 0.18/0.50 % DateTime : Sun Sep 20 10:42:13 UTC 2026
% 0.18/0.50 % CPUTime :
% 0.23/0.53 % Drodi V4.1.1
% 0.23/0.82 % Refutation found
% 0.23/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.86 % Elapsed time: 0.331654 seconds
% 0.23/0.86 % CPU time: 2.171980 seconds
% 0.23/0.86 % Total memory used: 98.834 MB
% 0.23/0.86 % Net memory used: 97.052 MB
%------------------------------------------------------------------------------