%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO082+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 : 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 12:24:00 PM UTC 2026
% Result : Theorem 0.17s 0.58s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 127 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 137 ( 46 ~; 57 |; 27 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 70 ( 64 !; 6 ?)
% 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(f17,conjecture,
! [C1,C2] :
( ( part_of(C2,C1)
& part_of(C1,C2) )
=> C1 = C2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C1,C2] :
( ( part_of(C2,C1)
& part_of(C1,C2) )
=> 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(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(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(f104,plain,
? [C1,C2] :
( C1 != C2
& part_of(C2,C1)
& part_of(C1,C2) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f105,plain,
( sK13_skl != sK14_skl
& part_of(sK14_skl,sK13_skl)
& part_of(sK13_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(C1,sK13_skl),skolemize(C2,sK14_skl)],[f104]) ).
fof(f106,plain,
part_of(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
part_of(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f108,plain,
sK13_skl != sK14_skl,
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0] :
( incident_c(X0,sK13_skl)
| ~ incident_c(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f23,f107]) ).
fof(f110,plain,
! [X0] :
( incident_c(X0,sK14_skl)
| ~ incident_c(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f23,f106]) ).
fof(f450,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(f457,plain,
! [X0,X1] :
( incident_c(sK1_skl(X1,X0,sK14_skl),sK13_skl)
| incident_c(sK1_skl(X1,X0,sK14_skl),X1)
| incident_c(sK1_skl(X1,X0,sK14_skl),X0)
| sK14_skl = sum(X0,X1) ),
inference(resolution,[status(thm)],[f34,f109]) ).
fof(f491,plain,
! [X0] :
( ~ incident_c(sK1_skl(X0,X0,X0),X0)
| X0 = sum(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f450]) ).
fof(f725,plain,
! [X0] :
( X0 = sum(X0,X0)
| X0 = sum(X0,X0) ),
inference(resolution,[status(thm)],[f491,f34]) ).
fof(f735,plain,
! [X0] : X0 = sum(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f725]) ).
fof(f1066,plain,
( incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK14_skl)
| sK14_skl = sum(sK13_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f457,f110]) ).
fof(f1116,plain,
( incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl)
| sK14_skl = sum(sK13_skl,sK13_skl) ),
inference(factoring,[status(thm)],[f457]) ).
fof(f1118,plain,
( incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK14_skl)
| sK14_skl = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f735,f1066]) ).
fof(f1119,plain,
incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1118,f108]) ).
fof(f1139,plain,
( incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl)
| sK14_skl = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f735,f1116]) ).
fof(f1140,plain,
incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1139,f108]) ).
fof(f1141,plain,
( ~ incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl)
| sK14_skl = sum(sK13_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f1119,f33]) ).
fof(f1152,plain,
( ~ incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl)
| sK14_skl = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f735,f1141]) ).
fof(f1153,plain,
~ incident_c(sK1_skl(sK13_skl,sK13_skl,sK14_skl),sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1152,f108]) ).
fof(f1165,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1153,f1140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 10:06:50 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.58 % Refutation found
% 0.17/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.62 % Elapsed time: 0.154015 seconds
% 0.17/0.62 % CPU time: 0.771090 seconds
% 0.17/0.62 % Total memory used: 87.950 MB
% 0.17/0.62 % Net memory used: 87.086 MB
%------------------------------------------------------------------------------