%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:19:21 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 119 ( 82 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 145 ( 53 ~; 64 |; 24 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 69 ( 64 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,conjecture,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f77,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f78,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( sK0_skl(X0,X1) != X1
| ~ in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f89,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f90,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
( ! [A,B,C] :
( ( ( sK2_skl(C,B,A) = B
| sK2_skl(C,B,A) = A
| in(sK2_skl(C,B,A),C) )
& ( ( sK2_skl(C,B,A) != B
& sK2_skl(C,B,A) != A )
| ~ in(sK2_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f220,plain,
? [A] : unordered_pair(A,A) != singleton(A),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f221,plain,
unordered_pair(sK12_skl,sK12_skl) != singleton(sK12_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f220]) ).
fof(f222,plain,
unordered_pair(sK12_skl,sK12_skl) != singleton(sK12_skl),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f243,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f92]) ).
fof(f245,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f294,plain,
! [X0,X1,X2] :
( sK0_skl(unordered_pair(X0,X1),X2) = X1
| sK0_skl(unordered_pair(X0,X1),X2) = X0
| sK0_skl(unordered_pair(X0,X1),X2) = X2
| unordered_pair(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f83,f243]) ).
fof(f307,plain,
( sK0_skl(unordered_pair(sK12_skl,sK12_skl),sK12_skl) = sK12_skl
| sK0_skl(unordered_pair(sK12_skl,sK12_skl),sK12_skl) = sK12_skl
| sK0_skl(unordered_pair(sK12_skl,sK12_skl),sK12_skl) = sK12_skl ),
inference(resolution,[status(thm)],[f294,f222]) ).
fof(f324,plain,
sK0_skl(unordered_pair(sK12_skl,sK12_skl),sK12_skl) = sK12_skl,
inference(duplicate_literals_removal,[status(thm)],[f307]) ).
fof(f328,plain,
( sK0_skl(unordered_pair(sK12_skl,sK12_skl),sK12_skl) != sK12_skl
| ~ in(sK12_skl,unordered_pair(sK12_skl,sK12_skl))
| unordered_pair(sK12_skl,sK12_skl) = singleton(sK12_skl) ),
inference(paramodulation,[status(thm)],[f324,f82]) ).
fof(f330,plain,
( sK12_skl != sK12_skl
| ~ in(sK12_skl,unordered_pair(sK12_skl,sK12_skl))
| unordered_pair(sK12_skl,sK12_skl) = singleton(sK12_skl) ),
inference(forward_demodulation,[status(thm)],[f324,f328]) ).
fof(f331,plain,
( ~ in(sK12_skl,unordered_pair(sK12_skl,sK12_skl))
| unordered_pair(sK12_skl,sK12_skl) = singleton(sK12_skl) ),
inference(trivial_equality_resolution,[status(thm)],[f330]) ).
fof(f332,plain,
~ in(sK12_skl,unordered_pair(sK12_skl,sK12_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f331,f222]) ).
fof(f333,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f332,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n012.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 05:52:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.040409 seconds
% 0.12/0.41 % CPU time: 0.076531 seconds
% 0.12/0.41 % Total memory used: 16.676 MB
% 0.12/0.41 % Net memory used: 16.658 MB
%------------------------------------------------------------------------------