%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU150+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:24 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 110 ( 75 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 132 ( 49 ~; 50 |; 27 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 65 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f87,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(f88,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)],[f87]) ).
fof(f89,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))],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f106,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)],[f10]) ).
fof(f107,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)],[f106]) ).
fof(f108,plain,
( ! [A,B,C] :
( ( ( sK3_skl(C,B,A) = B
| sK3_skl(C,B,A) = A
| in(sK3_skl(C,B,A),C) )
& ( ( sK3_skl(C,B,A) != B
& sK3_skl(C,B,A) != A )
| ~ in(sK3_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,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f107]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f272,plain,
? [A,B,C] :
( B != C
& singleton(A) = unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f273,plain,
? [B,C] :
( B != C
& ? [A] : singleton(A) = unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f272]) ).
fof(f274,plain,
( sK13_skl != sK14_skl
& singleton(sK15_skl) = unordered_pair(sK13_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK13_skl),skolemize(C,sK14_skl),skolemize(A,sK15_skl)],[f273]) ).
fof(f275,plain,
singleton(sK15_skl) = unordered_pair(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
sK13_skl != sK14_skl,
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f279,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f90]) ).
fof(f285,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f286,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f111]) ).
fof(f303,plain,
in(sK13_skl,singleton(sK15_skl)),
inference(paramodulation,[status(thm)],[f275,f285]) ).
fof(f306,plain,
in(sK14_skl,singleton(sK15_skl)),
inference(paramodulation,[status(thm)],[f275,f286]) ).
fof(f322,plain,
sK13_skl = sK15_skl,
inference(resolution,[status(thm)],[f303,f279]) ).
fof(f326,plain,
sK15_skl != sK14_skl,
inference(backward_demodulation,[status(thm)],[f322,f276]) ).
fof(f343,plain,
sK14_skl = sK15_skl,
inference(resolution,[status(thm)],[f306,f279]) ).
fof(f345,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f343,f326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:53:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.066107 seconds
% 0.11/0.42 % CPU time: 0.161758 seconds
% 0.11/0.42 % Total memory used: 105.169 MB
% 0.11/0.42 % Net memory used: 105.111 MB
%------------------------------------------------------------------------------