%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:10:56 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 7 unt; 2 def)
% Number of atoms : 59 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 54 ( 21 ~; 16 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f32,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,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)],[f11]) ).
fof(f35,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)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
? [A,B,C] :
( set_union2(unordered_pair(A,C),B) != B
& in(C,B)
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
( set_union2(unordered_pair(sK2_skl,sK4_skl),sK3_skl) != sK3_skl
& in(sK4_skl,sK3_skl)
& in(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)],[f39]) ).
fof(f41,plain,
in(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
in(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
set_union2(unordered_pair(sK2_skl,sK4_skl),sK3_skl) != sK3_skl,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f86,plain,
~ subset(unordered_pair(sK2_skl,sK4_skl),sK3_skl),
inference(resolution,[status(thm)],[f43,f33]) ).
fof(f89,plain,
( ~ in(sK4_skl,sK3_skl)
| ~ in(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f86,f38]) ).
fof(f90,definition,
( sQ0_spl
<=> in(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ0_spl
| ~ in(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ1_spl
<=> in(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ1_spl
| ~ in(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f89,f90,f93]) ).
fof(f97,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f41]) ).
fof(f98,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f42]) ).
fof(f100,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f101,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f98,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:43:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.046396 seconds
% 0.10/0.42 % CPU time: 0.140942 seconds
% 0.10/0.42 % Total memory used: 52.104 MB
% 0.10/0.42 % Net memory used: 51.788 MB
%------------------------------------------------------------------------------