%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU229+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:19:47 PM UTC 2026
% Result : Theorem 18.31s 2.81s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 12 unt; 1 def)
% Number of atoms : 168 ( 56 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 192 ( 76 ~; 76 |; 33 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 176 ( 166 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f28,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ( E = C
| E = B
| E = A ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f41,definition,
! [A,B,C,E] :
( sP0_prd(E,C,B,A)
<=> ( E = C
| E = B
| E = A ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f42,plain,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> sP0_prd(E,C,B,A) ) ),
inference(formula_renaming,[status(thm)],[f40,f41]) ).
fof(f43,plain,
! [A,B,C,D] :
( ( ? [E] :
( ( sP0_prd(E,C,B,A)
| in(E,D) )
& ( ~ sP0_prd(E,C,B,A)
| ~ in(E,D) ) )
| D = unordered_triple(A,B,C) )
& ( ! [E] :
( ( ~ sP0_prd(E,C,B,A)
| in(E,D) )
& ( sP0_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [A,B,C,D] :
( ? [E] :
( ( sP0_prd(E,C,B,A)
| in(E,D) )
& ( ~ sP0_prd(E,C,B,A)
| ~ in(E,D) ) )
| D = unordered_triple(A,B,C) )
& ! [A,B,C,D] :
( ( ! [E] :
( ~ sP0_prd(E,C,B,A)
| in(E,D) )
& ! [E] :
( sP0_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [A,B,C,D] :
( ( ( sP0_prd(sK0_skl(D,C,B,A),C,B,A)
| in(sK0_skl(D,C,B,A),D) )
& ( ~ sP0_prd(sK0_skl(D,C,B,A),C,B,A)
| ~ in(sK0_skl(D,C,B,A),D) ) )
| D = unordered_triple(A,B,C) )
& ! [A,B,C,D] :
( ( ! [E] :
( ~ sP0_prd(E,C,B,A)
| in(E,D) )
& ! [E] :
( sP0_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(D,C,B,A))],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( sP0_prd(X4,X3,X2,X1)
| ~ in(X4,X0)
| X0 != unordered_triple(X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP0_prd(X4,X3,X2,X1)
| in(X4,X0)
| X0 != unordered_triple(X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f90,plain,
? [A,B,C] :
( in(C,A)
& in(B,C)
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f91,plain,
? [A,C] :
( in(C,A)
& ? [B] :
( in(B,C)
& in(A,B) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
( in(sK12_skl,sK11_skl)
& in(sK13_skl,sK12_skl)
& in(sK11_skl,sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(A,sK11_skl),skolemize(C,sK12_skl),skolemize(B,sK13_skl)],[f91]) ).
fof(f93,plain,
in(sK11_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
in(sK13_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f95,plain,
in(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f101,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f102,plain,
! [B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [B] :
( ( ! [D] :
( ~ in(D,sK14_skl(B))
| ~ in(D,B) )
& in(sK14_skl(B),B) )
| ! [A] : ~ in(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(C,sK14_skl(B))],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( in(sK14_skl(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ in(X2,sK14_skl(X1))
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f109,plain,
! [A,B,C,E] :
( ( ( E != C
& E != B
& E != A )
| sP0_prd(E,C,B,A) )
& ( E = C
| E = B
| E = A
| ~ sP0_prd(E,C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f41]) ).
fof(f110,plain,
( ! [A,B,C,E] :
( ( E != C
& E != B
& E != A )
| sP0_prd(E,C,B,A) )
& ! [A,B,C,E] :
( E = C
| E = B
| E = A
| ~ sP0_prd(E,C,B,A) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| X0 = X2
| X0 = X3
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( X0 != X3
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( X0 != X2
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X0,X3,X2,X1)
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X0,X3,X2,X1)
| in(X0,unordered_triple(X1,X2,X3)) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f117,plain,
! [X0,X1,X2] : sP0_prd(X0,X1,X2,X0),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f118,plain,
! [X0,X1,X2] : sP0_prd(X0,X1,X0,X2),
inference(destructive_equality_resolution,[status(thm)],[f113]) ).
fof(f119,plain,
! [X0,X1,X2] : sP0_prd(X0,X0,X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f114]) ).
fof(f181,plain,
! [X0,X1,X2] : in(X0,unordered_triple(X0,X1,X2)),
inference(resolution,[status(thm)],[f117,f116]) ).
fof(f182,plain,
! [X0,X1,X2] : in(X0,unordered_triple(X1,X0,X2)),
inference(resolution,[status(thm)],[f118,f116]) ).
fof(f183,plain,
! [X0,X1,X2] : in(X0,unordered_triple(X1,X2,X0)),
inference(resolution,[status(thm)],[f119,f116]) ).
fof(f185,plain,
! [X0,X1,X2,X3] :
( sP0_prd(sK14_skl(unordered_triple(X1,X2,X3)),X3,X2,X1)
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f104,f115]) ).
fof(f330,plain,
! [X0,X1,X2,X3] :
( sK14_skl(unordered_triple(X1,X2,X3)) = X3
| sK14_skl(unordered_triple(X1,X2,X3)) = X2
| sK14_skl(unordered_triple(X1,X2,X3)) = X1
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f185,f111]) ).
fof(f452,plain,
! [X0,X1,X2] :
( sK14_skl(unordered_triple(X0,X1,X2)) = X2
| sK14_skl(unordered_triple(X0,X1,X2)) = X1
| sK14_skl(unordered_triple(X0,X1,X2)) = X0 ),
inference(resolution,[status(thm)],[f330,f183]) ).
fof(f539,plain,
! [X0,X1,X2,X3,X4] :
( sK14_skl(unordered_triple(X1,X2,X3)) = X3
| sK14_skl(unordered_triple(X1,X2,X3)) = X2
| ~ in(X4,X1)
| ~ in(X4,unordered_triple(X1,X2,X3))
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f452,f105]) ).
fof(f2462,plain,
! [X0,X1,X2,X3] :
( sK14_skl(unordered_triple(X1,X2,X3)) = X3
| sK14_skl(unordered_triple(X1,X2,X3)) = X2
| ~ in(X3,X1)
| ~ in(X0,unordered_triple(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f539,f183]) ).
fof(f3521,plain,
! [X0,X1,X2] :
( sK14_skl(unordered_triple(X1,X2,X0)) = X0
| sK14_skl(unordered_triple(X1,X2,X0)) = X2
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f2462,f183]) ).
fof(f3535,plain,
! [X0] :
( sK14_skl(unordered_triple(sK11_skl,X0,sK12_skl)) = sK12_skl
| sK14_skl(unordered_triple(sK11_skl,X0,sK12_skl)) = X0 ),
inference(resolution,[status(thm)],[f3521,f95]) ).
fof(f3558,plain,
! [X0,X1,X2] :
( sK14_skl(unordered_triple(sK11_skl,X1,sK12_skl)) = sK12_skl
| ~ in(X2,X1)
| ~ in(X2,unordered_triple(sK11_skl,X1,sK12_skl))
| ~ in(X0,unordered_triple(sK11_skl,X1,sK12_skl)) ),
inference(paramodulation,[status(thm)],[f3535,f105]) ).
fof(f11701,plain,
! [X0,X1] :
( sK14_skl(unordered_triple(sK11_skl,X1,sK12_skl)) = sK12_skl
| ~ in(sK11_skl,X1)
| ~ in(X0,unordered_triple(sK11_skl,X1,sK12_skl)) ),
inference(resolution,[status(thm)],[f3558,f181]) ).
fof(f12233,plain,
! [X0] :
( sK14_skl(unordered_triple(sK11_skl,sK13_skl,sK12_skl)) = sK12_skl
| ~ in(X0,unordered_triple(sK11_skl,sK13_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f11701,f93]) ).
fof(f12248,plain,
sK14_skl(unordered_triple(sK11_skl,sK13_skl,sK12_skl)) = sK12_skl,
inference(resolution,[status(thm)],[f12233,f183]) ).
fof(f12298,plain,
! [X0,X1] :
( ~ in(X1,sK12_skl)
| ~ in(X1,unordered_triple(sK11_skl,sK13_skl,sK12_skl))
| ~ in(X0,unordered_triple(sK11_skl,sK13_skl,sK12_skl)) ),
inference(paramodulation,[status(thm)],[f12248,f105]) ).
fof(f12431,plain,
! [X0] :
( ~ in(sK13_skl,unordered_triple(sK11_skl,sK13_skl,sK12_skl))
| ~ in(X0,unordered_triple(sK11_skl,sK13_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f12298,f94]) ).
fof(f12432,plain,
! [X0] : ~ in(X0,unordered_triple(sK11_skl,sK13_skl,sK12_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f12431,f182]) ).
fof(f12444,plain,
$false,
inference(resolution,[status(thm)],[f12432,f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU229+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:00:42 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 18.31/2.81 % Refutation found
% 18.31/2.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.31/2.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.41/2.95 % Elapsed time: 2.572384 seconds
% 1.41/2.95 % CPU time: 19.408337 seconds
% 1.41/2.95 % Total memory used: 242.615 MB
% 1.41/2.95 % Net memory used: 226.060 MB
%------------------------------------------------------------------------------