%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO083+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 : n011.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 12:24:01 PM UTC 2026
% Result : Theorem 5.19s 16.34s
% Output : CNFRefutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 132 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 151 ( 54 ~; 56 |; 34 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 89 !; 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(f17,conjecture,
! [C1,C2,C3,P] :
( ( meet(P,C1,C3)
& meet(P,C1,C2)
& part_of(C2,C3) )
=> part_of(sum(C1,C2),sum(C1,C3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C1,C2,C3,P] :
( ( meet(P,C1,C3)
& meet(P,C1,C2)
& part_of(C2,C3) )
=> part_of(sum(C1,C2),sum(C1,C3)) ),
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(f104,plain,
? [C1,C2,C3,P] :
( ~ part_of(sum(C1,C2),sum(C1,C3))
& meet(P,C1,C3)
& meet(P,C1,C2)
& part_of(C2,C3) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f105,plain,
? [C1,C2,C3] :
( ~ part_of(sum(C1,C2),sum(C1,C3))
& ? [P] :
( meet(P,C1,C3)
& meet(P,C1,C2)
& part_of(C2,C3) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( ~ part_of(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl))
& meet(sK16_skl,sK13_skl,sK15_skl)
& meet(sK16_skl,sK13_skl,sK14_skl)
& part_of(sK14_skl,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(C3,sK15_skl),skolemize(P,sK16_skl)],[f105]) ).
fof(f107,plain,
part_of(sK14_skl,sK15_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
~ part_of(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,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(f112,plain,
! [X0,X1,X2] :
( ~ incident_c(X0,X1)
| incident_c(X0,sum(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ incident_c(X0,X2)
| incident_c(X0,sum(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f115,plain,
! [X0] :
( incident_c(X0,sK15_skl)
| ~ incident_c(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f23,f107]) ).
fof(f118,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,f111]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ incident_c(sK0_skl(X0,sum(X1,X2)),X2)
| part_of(X0,sum(X1,X2)) ),
inference(resolution,[status(thm)],[f25,f113]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ incident_c(sK0_skl(X0,sum(X1,X2)),X1)
| part_of(X0,sum(X1,X2)) ),
inference(resolution,[status(thm)],[f25,f112]) ).
fof(f533,plain,
( incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK14_skl)
| incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f118,f110]) ).
fof(f550,plain,
~ incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK15_skl),
inference(resolution,[status(thm)],[f120,f110]) ).
fof(f565,plain,
~ incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK13_skl),
inference(resolution,[status(thm)],[f121,f110]) ).
fof(f575,plain,
incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK14_skl),
inference(backward_subsumption_resolution,[status(thm)],[f533,f565]) ).
fof(f586,plain,
~ incident_c(sK0_skl(sum(sK13_skl,sK14_skl),sum(sK13_skl,sK15_skl)),sK14_skl),
inference(resolution,[status(thm)],[f550,f115]) ).
fof(f589,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f586,f575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.64 % CPULimit : 300
% 0.09/15.64 % WCLimit : 300
% 0.09/15.64 % DateTime : Sun Sep 20 10:12:51 UTC 2026
% 0.09/15.64 % CPUTime :
% 0.09/15.65 % Drodi V4.1.1
% 5.19/16.34 % Refutation found
% 5.19/16.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.19/16.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.19/16.37 % Elapsed time: 0.714138 seconds
% 5.19/16.37 % CPU time: 5.462488 seconds
% 5.19/16.37 % Total memory used: 125.627 MB
% 5.19/16.37 % Net memory used: 119.821 MB
%------------------------------------------------------------------------------