%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU267+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 : 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 02:19:58 PM UTC 2026
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 5 unt; 2 def)
% Number of atoms : 105 ( 90 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 122 ( 51 ~; 47 |; 14 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 88 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f325,conjecture,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f326,negated_conjecture,
~ ! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(negated_conjecture,[status(cth)],[f325]) ).
fof(f470,plain,
! [A] :
( ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( B = C
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f471,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != C
& A = ordered_pair(C,D) )
| B = pair_first(A) )
& ( ! [C,D] :
( B = C
| A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f470]) ).
fof(f472,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( B != C
& ? [D] : A = ordered_pair(C,D) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f471]) ).
fof(f473,plain,
! [A] :
( ( ! [B] :
( ( B != sK17_skl(B,A)
& A = ordered_pair(sK17_skl(B,A),sK18_skl(B,A)) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(C,sK17_skl(B,A)),skolemize(D,sK18_skl(B,A))],[f472]) ).
fof(f474,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X4
| X0 != ordered_pair(X4,X5)
| X3 != pair_first(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f537,plain,
! [A] :
( ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( B = D
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f538,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != D
& A = ordered_pair(C,D) )
| B = pair_second(A) )
& ( ! [C,D] :
( B = D
| A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f537]) ).
fof(f539,plain,
! [A] :
( ( ! [B] :
( ? [D] :
( B != D
& ? [C] : A = ordered_pair(C,D) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f538]) ).
fof(f540,plain,
! [A] :
( ( ! [B] :
( ( B != sK30_skl(B,A)
& A = ordered_pair(sK31_skl(B,A),sK30_skl(B,A)) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(D,sK30_skl(B,A)),skolemize(C,sK31_skl(B,A))],[f539]) ).
fof(f541,plain,
! [X0,X1,X2,X3,X4,X5] :
( X3 = X5
| X0 != ordered_pair(X4,X5)
| X3 != pair_second(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f540]) ).
fof(f1526,plain,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
| pair_first(ordered_pair(A,B)) != A ),
inference(pre_NNF_transformation,[status(thm)],[f326]) ).
fof(f1527,plain,
( ? [A,B] : pair_second(ordered_pair(A,B)) != B
| ? [A,B] : pair_first(ordered_pair(A,B)) != A ),
inference(miniscoping,[status(thm)],[f1526]) ).
fof(f1528,plain,
( pair_second(ordered_pair(sK133_skl,sK134_skl)) != sK134_skl
| pair_first(ordered_pair(sK131_skl,sK132_skl)) != sK131_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131_skl,sK132_skl,sK133_skl,sK134_skl]),skolemize(A,sK131_skl),skolemize(B,sK132_skl),skolemize(A,sK133_skl),skolemize(B,sK134_skl)],[f1527]) ).
fof(f1529,plain,
( pair_second(ordered_pair(sK133_skl,sK134_skl)) != sK134_skl
| pair_first(ordered_pair(sK131_skl,sK132_skl)) != sK131_skl ),
inference(cnf_transformation,[status(thm)],[f1528]) ).
fof(f1628,definition,
( sQ2_spl
<=> pair_first(ordered_pair(sK131_skl,sK132_skl)) = sK131_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1630,plain,
( sQ2_spl
| pair_first(ordered_pair(sK131_skl,sK132_skl)) != sK131_skl ),
inference(component_clause,[status(thm)],[f1628]) ).
fof(f1631,definition,
( sQ3_spl
<=> pair_second(ordered_pair(sK133_skl,sK134_skl)) = sK134_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1633,plain,
( sQ3_spl
| pair_second(ordered_pair(sK133_skl,sK134_skl)) != sK134_skl ),
inference(component_clause,[status(thm)],[f1631]) ).
fof(f1634,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1529,f1628,f1631]) ).
fof(f1659,plain,
! [X0,X1,X2,X3] :
( pair_first(ordered_pair(X0,X1)) = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f474]) ).
fof(f1675,plain,
! [X0,X1,X2,X3] :
( pair_second(ordered_pair(X0,X1)) = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f541]) ).
fof(f1738,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(equality_resolution,[status(thm)],[f1659]) ).
fof(f1739,plain,
( sQ2_spl
| sK131_skl != sK131_skl ),
inference(backward_demodulation,[status(thm)],[f1738,f1630]) ).
fof(f1741,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1739]) ).
fof(f1742,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1741]) ).
fof(f1744,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(equality_resolution,[status(thm)],[f1675]) ).
fof(f1745,plain,
( sQ3_spl
| sK134_skl != sK134_skl ),
inference(backward_demodulation,[status(thm)],[f1744,f1633]) ).
fof(f1747,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1745]) ).
fof(f1748,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1747]) ).
fof(f1749,plain,
$false,
inference(sat_refutation,[status(thm)],[f1634,f1742,f1748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:04:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.40 % Drodi V4.1.1
% 0.15/0.43 % Refutation found
% 0.15/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.090527 seconds
% 0.15/0.46 % CPU time: 0.239367 seconds
% 0.15/0.46 % Total memory used: 135.149 MB
% 0.15/0.46 % Net memory used: 134.644 MB
%------------------------------------------------------------------------------