%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET787-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:37 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 11 unt; 5 def)
% Number of atoms : 88 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 37 ~; 37 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [U,V,W] :
( member(U,un(W,V))
| ~ member(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U,V,W] :
( member(U,un(V,W))
| ~ member(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [U,V] :
( U = V
| ~ member(U,cons(V,eptset)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [U,V,W] :
( member(U,W)
| U = V
| ~ member(U,cons(V,W)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [U,V] :
( member(U,unionE_sk1(U,V))
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [U,V] :
( member(unionE_sk1(U,V),V)
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f148,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f149,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f170,plain,
! [U,V] :
( ! [W] : member(U,un(W,V))
| ~ member(U,V) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f171,plain,
! [X0,X1,X2] :
( member(X0,un(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [U,V] :
( ! [W] : member(U,un(V,W))
| ~ member(U,V) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f173,plain,
! [X0,X1,X2] :
( member(X0,un(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f282,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,cons(X1,eptset)) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f283,plain,
! [U,W] :
( member(U,W)
| ! [V] :
( U = V
| ~ member(U,cons(V,W)) ) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f284,plain,
! [X0,X1,X2] :
( member(X0,X2)
| X0 = X1
| ~ member(X0,cons(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f297,plain,
! [X0,X1] :
( member(X0,unionE_sk1(X0,X1))
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f298,plain,
! [X0,X1] :
( member(unionE_sk1(X0,X1),X1)
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f360,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f361,plain,
~ member(sk2,un(a,b)),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f369,plain,
~ member(sk2,b),
inference(resolution,[status(thm)],[f171,f361]) ).
fof(f370,plain,
~ member(sk2,a),
inference(resolution,[status(thm)],[f173,f361]) ).
fof(f518,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(resolution,[status(thm)],[f298,f360]) ).
fof(f530,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolution,[status(thm)],[f518,f284]) ).
fof(f531,definition,
( sQ10_spl
<=> unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( ~ sQ10_spl
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,definition,
( sQ11_spl
<=> member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ11_spl
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f530,f531,f534]) ).
fof(f539,plain,
( ~ sQ10_spl
| member(sk2,a)
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(paramodulation,[status(thm)],[f532,f297]) ).
fof(f540,definition,
( sQ12_spl
<=> member(sk2,union(cons(a,cons(b,eptset)))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( sQ12_spl
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,definition,
( sQ13_spl
<=> member(sk2,a) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ13_spl
| member(sk2,a) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( ~ sQ10_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f539,f540,f543,f531]) ).
fof(f547,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f370]) ).
fof(f548,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f360]) ).
fof(f550,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( ~ sQ11_spl
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ),
inference(resolution,[status(thm)],[f535,f282]) ).
fof(f580,plain,
( ~ sQ11_spl
| member(sk2,b)
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(paramodulation,[status(thm)],[f551,f297]) ).
fof(f588,definition,
( sQ18_spl
<=> member(sk2,b) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ18_spl
| member(sk2,b) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( ~ sQ11_spl
| sQ18_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f580,f540,f588,f534]) ).
fof(f592,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f369]) ).
fof(f593,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
$false,
inference(sat_refutation,[status(thm)],[f537,f546,f548,f550,f591,f593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET787-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 05:37:50 UTC 2026
% 0.20/0.41 % CPUTime :
% 0.20/0.44 % Drodi V4.1.1
% 0.20/0.47 % Refutation found
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54 % Elapsed time: 0.117363 seconds
% 0.20/0.54 % CPU time: 0.192852 seconds
% 0.20/0.54 % Total memory used: 30.716 MB
% 0.20/0.54 % Net memory used: 30.634 MB
%------------------------------------------------------------------------------