%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU151+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 : n001.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 02:19:25 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 2 def)
% Number of atoms : 95 ( 64 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 114 ( 47 ~; 38 |; 25 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 55 ( 45 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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(f39,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
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) )
& ( ! [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(f108,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)],[f107]) ).
fof(f109,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))],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f197,plain,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f198,plain,
? [A,D] :
( A != D
& ? [C] :
( A != C
& ? [B] : unordered_pair(A,B) = unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f199,plain,
( sK10_skl != sK11_skl
& sK10_skl != sK12_skl
& unordered_pair(sK10_skl,sK13_skl) = unordered_pair(sK12_skl,sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(A,sK10_skl),skolemize(D,sK11_skl),skolemize(C,sK12_skl),skolemize(B,sK13_skl)],[f198]) ).
fof(f200,plain,
unordered_pair(sK10_skl,sK13_skl) = unordered_pair(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f201,plain,
sK10_skl != sK12_skl,
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f202,plain,
sK10_skl != sK11_skl,
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f289,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f290,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f111]) ).
fof(f304,plain,
in(sK10_skl,unordered_pair(sK12_skl,sK11_skl)),
inference(paramodulation,[status(thm)],[f200,f290]) ).
fof(f343,plain,
( sK10_skl = sK11_skl
| sK10_skl = sK12_skl ),
inference(resolution,[status(thm)],[f289,f304]) ).
fof(f350,definition,
( sQ2_spl
<=> sK10_skl = sK12_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ2_spl
| sK10_skl = sK12_skl ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,definition,
( sQ3_spl
<=> sK10_skl = sK11_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ3_spl
| sK10_skl = sK11_skl ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f343,f350,f353]) ).
fof(f358,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f201]) ).
fof(f359,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f202]) ).
fof(f361,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
$false,
inference(sat_refutation,[status(thm)],[f356,f359,f361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:58:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.063555 seconds
% 0.10/0.44 % CPU time: 0.159821 seconds
% 0.10/0.44 % Total memory used: 105.263 MB
% 0.10/0.44 % Net memory used: 105.193 MB
%------------------------------------------------------------------------------