%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:11:03 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 3 unt; 9 def)
% Number of atoms : 200 ( 41 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 230 ( 93 ~; 95 |; 25 &)
% ( 13 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 60 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
? [A,B] :
( A != B
& ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,B) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
? [A,B] :
( A != B
& ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,B) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
? [A,B] :
( A != B
& ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,B) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( sK2_skl != sK3_skl
& ! [C,D] :
( ~ in(ordered_pair(C,D),sK3_skl)
| in(ordered_pair(C,D),sK2_skl) )
& ! [C,D] :
( in(ordered_pair(C,D),sK3_skl)
| ~ in(ordered_pair(C,D),sK2_skl) )
& ! [C] :
( C = ordered_pair(sK6_skl(C),sK7_skl(C))
| ~ in(C,sK3_skl) )
& ! [C] :
( C = ordered_pair(sK4_skl(C),sK5_skl(C))
| ~ in(C,sK2_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(D,sK4_skl(C)),skolemize(E,sK5_skl(C)),skolemize(D,sK6_skl(C)),skolemize(E,sK7_skl(C))],[f21]) ).
fof(f23,plain,
! [X0] :
( X0 = ordered_pair(sK4_skl(X0),sK5_skl(X0))
| ~ in(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( X0 = ordered_pair(sK6_skl(X0),sK7_skl(X0))
| ~ in(X0,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),sK3_skl)
| ~ in(ordered_pair(X0,X1),sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK3_skl)
| in(ordered_pair(X0,X1),sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
sK2_skl != sK3_skl,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f28,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK8_skl(B,A),B)
| ~ in(sK8_skl(B,A),A) )
& ( in(sK8_skl(B,A),B)
| in(sK8_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( X1 = X0
| in(sK8_skl(X0,X1),X0)
| in(sK8_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( X1 = X0
| ~ in(sK8_skl(X0,X1),X0)
| ~ in(sK8_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f49,plain,
! [X0] :
( sK8_skl(X0,sK3_skl) = ordered_pair(sK6_skl(sK8_skl(X0,sK3_skl)),sK7_skl(sK8_skl(X0,sK3_skl)))
| sK3_skl = X0
| in(sK8_skl(X0,sK3_skl),X0) ),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f53,plain,
( sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl)))
| sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl)))
| sK3_skl = sK2_skl ),
inference(resolution,[status(thm)],[f49,f23]) ).
fof(f62,definition,
( sQ2_spl
<=> sK3_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( ~ sQ2_spl
| sK3_skl = sK2_skl ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ3_spl
<=> sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ3_spl
| sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ4_spl
<=> sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ4_spl
| sK8_skl(sK2_skl,sK3_skl) = ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f53,f62,f65,f68]) ).
fof(f144,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f27]) ).
fof(f145,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f148,plain,
( ~ sQ3_spl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK3_skl)
| in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
inference(paramodulation,[status(thm)],[f66,f26]) ).
fof(f149,plain,
( ~ sQ3_spl
| in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl)
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(paramodulation,[status(thm)],[f66,f25]) ).
fof(f150,definition,
( sQ11_spl
<=> in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ11_spl
| in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ12_spl
<=> in(sK8_skl(sK2_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ12_spl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f148,f150,f153,f65]) ).
fof(f157,definition,
( sQ13_spl
<=> in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ13_spl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
( sQ14_spl
<=> in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( ~ sQ14_spl
| in(ordered_pair(sK6_skl(sK8_skl(sK2_skl,sK3_skl)),sK7_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ sQ3_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f149,f157,f160,f65]) ).
fof(f164,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f66,f151]) ).
fof(f167,plain,
( sQ13_spl
| ~ sQ11_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f164]) ).
fof(f168,plain,
( sQ13_spl
| ~ sQ11_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| in(sK8_skl(sK2_skl,sK3_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f66,f161]) ).
fof(f171,plain,
( sQ12_spl
| sK3_skl = sK2_skl
| in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f155,f31]) ).
fof(f172,plain,
( sQ12_spl
| sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f171,f157,f62,f153]) ).
fof(f173,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| sK3_skl = sK2_skl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f169,f32]) ).
fof(f176,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| sQ2_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f173,f157,f62,f65,f160]) ).
fof(f207,plain,
( ~ sQ4_spl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK3_skl)
| in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
inference(paramodulation,[status(thm)],[f69,f26]) ).
fof(f208,plain,
( ~ sQ4_spl
| in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl)
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(paramodulation,[status(thm)],[f69,f25]) ).
fof(f209,definition,
( sQ19_spl
<=> in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ19_spl
| in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f207,f209,f153,f68]) ).
fof(f213,definition,
( sQ20_spl
<=> in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ20_spl
| in(ordered_pair(sK4_skl(sK8_skl(sK2_skl,sK3_skl)),sK5_skl(sK8_skl(sK2_skl,sK3_skl))),sK3_skl) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( ~ sQ4_spl
| sQ20_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f208,f157,f213,f68]) ).
fof(f217,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f69,f210]) ).
fof(f224,plain,
( sQ13_spl
| ~ sQ19_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f217]) ).
fof(f225,plain,
( sQ13_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| in(sK8_skl(sK2_skl,sK3_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f69,f214]) ).
fof(f229,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| sK3_skl = sK2_skl
| ~ in(sK8_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f226,f32]) ).
fof(f232,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f229,f157,f62,f68,f213]) ).
fof(f234,plain,
$false,
inference(sat_refutation,[status(thm)],[f71,f145,f156,f163,f168,f172,f176,f212,f216,f225,f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:45:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.044195 seconds
% 0.08/0.42 % CPU time: 0.105938 seconds
% 0.08/0.42 % Total memory used: 26.703 MB
% 0.08/0.42 % Net memory used: 26.673 MB
%------------------------------------------------------------------------------