%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:11:00 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 4 unt; 4 def)
% Number of atoms : 118 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 46 ~; 49 |; 14 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,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)],[f8]) ).
fof(f26,plain,
( ! [A,B,C] :
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ! [A,B,C] :
( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<~> ( in(B,C)
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
? [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| set_difference(unordered_pair(A,B),C) != empty_set )
& ( ( in(B,C)
& in(A,C) )
| set_difference(unordered_pair(A,B),C) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( ( ~ in(sK3_skl,sK4_skl)
| ~ in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != empty_set )
& ( ( in(sK3_skl,sK4_skl)
& in(sK2_skl,sK4_skl) )
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f31]) ).
fof(f33,plain,
( in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( in(sK3_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
( ~ in(sK3_skl,sK4_skl)
| ~ in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,definition,
( sQ0_spl
<=> set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = empty_set ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != empty_set ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> in(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ1_spl
| ~ in(sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f36,f39]) ).
fof(f43,definition,
( sQ2_spl
<=> in(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f36,f43]) ).
fof(f47,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).
fof(f52,plain,
( ~ sQ0_spl
| set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl) = empty_set ),
inference(paramodulation,[status(thm)],[f13,f37]) ).
fof(f54,plain,
( ~ sQ0_spl
| subset(unordered_pair(sK3_skl,sK2_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f23,f52]) ).
fof(f55,plain,
( ~ sQ0_spl
| subset(unordered_pair(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f23,f37]) ).
fof(f58,definition,
( sQ3_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( sQ3_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f69,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f60]) ).
fof(f70,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f69]) ).
fof(f78,plain,
( ~ sQ0_spl
| in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f27,f55]) ).
fof(f79,plain,
( ~ sQ0_spl
| in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f27,f54]) ).
fof(f83,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f41]) ).
fof(f84,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ0_spl
| ~ subset(unordered_pair(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f38,f24]) ).
fof(f100,plain,
( sQ0_spl
| ~ subset(unordered_pair(sK3_skl,sK2_skl),sK4_skl) ),
inference(paramodulation,[status(thm)],[f13,f85]) ).
fof(f105,plain,
( sQ0_spl
| ~ in(sK2_skl,sK4_skl)
| ~ in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f29,f100]) ).
fof(f111,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f105,f43,f39,f36]) ).
fof(f113,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f79,f43,f36]) ).
fof(f114,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f46,f47,f70,f84,f111,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:44:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.044821 seconds
% 0.12/0.41 % CPU time: 0.124839 seconds
% 0.12/0.41 % Total memory used: 79.288 MB
% 0.12/0.41 % Net memory used: 78.989 MB
%------------------------------------------------------------------------------