%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU159+3 : TPTP v9.3.1. Released v3.2.0.
% 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 02:19:27 PM UTC 2026
% Result : Theorem 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 4 unt; 6 def)
% Number of atoms : 193 ( 50 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 210 ( 76 ~; 92 |; 28 &)
% ( 12 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 79 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,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)],[f3]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
( ! [A,B,C] :
( ( ( sK0_skl(C,B,A) = B
| sK0_skl(C,B,A) = A
| in(sK0_skl(C,B,A),C) )
& ( ( sK0_skl(C,B,A) != B
& sK0_skl(C,B,A) != A )
| ~ in(sK0_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,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f22,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ in(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f35,plain,
? [A,B,C] :
( subset(unordered_pair(A,B),C)
<~> ( in(B,C)
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
? [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| ~ subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| subset(unordered_pair(A,B),C) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ( ~ in(sK5_skl,sK6_skl)
| ~ in(sK4_skl,sK6_skl)
| ~ subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) )
& ( ( in(sK5_skl,sK6_skl)
& in(sK4_skl,sK6_skl) )
| subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f36]) ).
fof(f38,plain,
( in(sK4_skl,sK6_skl)
| subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( in(sK5_skl,sK6_skl)
| subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
( ~ in(sK5_skl,sK6_skl)
| ~ in(sK4_skl,sK6_skl)
| ~ subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,definition,
( sQ0_spl
<=> subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ0_spl
| subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( sQ0_spl
| ~ subset(unordered_pair(sK4_skl,sK5_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ1_spl
<=> in(sK4_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ1_spl
| ~ in(sK4_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f41,f44]) ).
fof(f48,definition,
( sQ2_spl
<=> in(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f41,f48]) ).
fof(f52,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f41,f44,f48]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f55,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f62,plain,
( ~ sQ0_spl
| subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f12,f42]) ).
fof(f76,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f26,f55]) ).
fof(f78,plain,
( ~ sQ0_spl
| in(sK4_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f76,f62]) ).
fof(f79,plain,
( ~ sQ0_spl
| in(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f76,f42]) ).
fof(f83,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f46]) ).
fof(f84,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f89,plain,
( sQ0_spl
| ~ subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f12,f43]) ).
fof(f93,plain,
! [X0,X1,X2] :
( sK1_skl(X2,unordered_pair(X0,X1)) = X1
| sK1_skl(X2,unordered_pair(X0,X1)) = X0
| subset(unordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f27,f53]) ).
fof(f106,plain,
( sQ0_spl
| sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK4_skl
| sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK5_skl ),
inference(resolution,[status(thm)],[f93,f89]) ).
fof(f112,definition,
( sQ3_spl
<=> sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ3_spl
| sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK5_skl ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
( sQ4_spl
<=> sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ4_spl
| sK1_skl(sK6_skl,unordered_pair(sK5_skl,sK4_skl)) = sK4_skl ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ0_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f106,f112,f115,f41]) ).
fof(f126,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f79,f48,f41]) ).
fof(f173,plain,
( ~ sQ3_spl
| ~ in(sK5_skl,sK6_skl)
| subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f113,f28]) ).
fof(f175,definition,
( sQ7_spl
<=> subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ7_spl
| subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f182,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f173,f175,f48,f112]) ).
fof(f187,plain,
( ~ sQ7_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f89]) ).
fof(f188,plain,
( ~ sQ7_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f208,plain,
( ~ sQ4_spl
| ~ in(sK4_skl,sK6_skl)
| subset(unordered_pair(sK5_skl,sK4_skl),sK6_skl) ),
inference(paramodulation,[status(thm)],[f116,f28]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f208,f175,f44,f115]) ).
fof(f219,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f51,f52,f84,f118,f126,f182,f188,f214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU159+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 05:53:40 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.060585 seconds
% 0.13/5.43 % CPU time: 0.186650 seconds
% 0.13/5.43 % Total memory used: 102.500 MB
% 0.13/5.43 % Net memory used: 102.050 MB
%------------------------------------------------------------------------------