%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET928+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 : n020.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 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 5 unt; 5 def)
% Number of atoms : 120 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 56 ~; 48 |; 12 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [A,C] :
( ~ in(A,C)
| ! [B] : ~ disjoint(unordered_pair(A,B),C) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(C,B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] :
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<~> ( ~ in(B,C)
& ~ in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
? [A,B,C] :
( ( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
( ( in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != unordered_pair(sK2_skl,sK3_skl) )
& ( ( ~ in(sK3_skl,sK4_skl)
& ~ in(sK2_skl,sK4_skl) )
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = unordered_pair(sK2_skl,sK3_skl) ) ),
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)],[f26]) ).
fof(f28,plain,
( ~ in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = unordered_pair(sK2_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ~ in(sK3_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = unordered_pair(sK2_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
( in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != unordered_pair(sK2_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
( ! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) )
& ! [A,B] :
( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ0_spl
<=> set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = unordered_pair(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = unordered_pair(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != unordered_pair(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ1_spl
<=> in(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f35,f38]) ).
fof(f42,definition,
( sQ2_spl
<=> in(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ2_spl
| in(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f35,f42]) ).
fof(f46,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f35,f38,f42]) ).
fof(f59,definition,
( sQ4_spl
<=> unordered_pair(sK2_skl,sK3_skl) = unordered_pair(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ4_spl
| unordered_pair(sK2_skl,sK3_skl) != unordered_pair(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f66,definition,
( sQ6_spl
<=> unordered_pair(sK2_skl,sK3_skl) = unordered_pair(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ6_spl
| unordered_pair(sK2_skl,sK3_skl) != unordered_pair(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f70,plain,
( ~ sQ0_spl
| disjoint(unordered_pair(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f34,f36]) ).
fof(f76,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f13]) ).
fof(f77,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
( sQ0_spl
| ~ disjoint(unordered_pair(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f37,f33]) ).
fof(f81,plain,
( sQ0_spl
| ~ disjoint(unordered_pair(sK3_skl,sK2_skl),sK4_skl) ),
inference(paramodulation,[status(thm)],[f13,f78]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f13,f22]) ).
fof(f87,plain,
( sQ0_spl
| in(sK2_skl,sK4_skl)
| in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f24,f81]) ).
fof(f94,plain,
( sQ0_spl
| sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f87,f42,f38,f35]) ).
fof(f96,plain,
( sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f68]) ).
fof(f97,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( ~ sQ0_spl
| ~ in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f70,f83]) ).
fof(f100,plain,
( ~ sQ0_spl
| ~ in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f70,f22]) ).
fof(f104,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f100,f38,f35]) ).
fof(f105,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f99]) ).
fof(f106,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f107,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f45,f46,f77,f94,f97,f104,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET928+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 : n020.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 05:45:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.36 % Refutation found
% 0.09/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.040940 seconds
% 0.09/0.40 % CPU time: 0.064208 seconds
% 0.09/0.40 % Total memory used: 9.566 MB
% 0.09/0.40 % Net memory used: 9.562 MB
%------------------------------------------------------------------------------