%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET787-1 : 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 02:10:36 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 14 unt; 7 def)
% Number of atoms : 101 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 42 ~; 41 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,V] :
( member(U,unionE_sk1(U,V))
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,V] :
( member(unionE_sk1(U,V),V)
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,V,W] :
( member(U,W)
| U = V
| ~ member(U,cons(V,W)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [C,A,B] :
( member(C,un(A,B))
| ~ member(C,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] :
( member(C,un(A,B))
| ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : ~ member(X,eptset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] :
( member(X0,unionE_sk1(X0,X1))
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( member(unionE_sk1(X0,X1),X1)
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [U,W] :
( member(U,W)
| ! [V] :
( U = V
| ~ member(U,cons(V,W)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,X2)
| X0 = X1
| ~ member(X0,cons(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [C,A] :
( ! [B] : member(C,un(A,B))
| ~ member(C,A) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,un(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [C,B] :
( ! [A] : member(C,un(A,B))
| ~ member(C,B) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] :
( member(X0,un(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] : ~ member(X0,eptset),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
~ member(sk2,un(a,b)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
~ member(sk2,a),
inference(resolution,[status(thm)],[f22,f32]) ).
fof(f34,plain,
~ member(sk2,b),
inference(resolution,[status(thm)],[f24,f32]) ).
fof(f35,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(resolution,[status(thm)],[f16,f31]) ).
fof(f51,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)],[f35,f20]) ).
fof(f52,definition,
( sQ0_spl
<=> unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f52,f55]) ).
fof(f60,plain,
( ~ sQ0_spl
| member(sk2,a)
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(paramodulation,[status(thm)],[f53,f15]) ).
fof(f61,definition,
( sQ2_spl
<=> member(sk2,union(cons(a,cons(b,eptset)))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ2_spl
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
( sQ3_spl
<=> member(sk2,a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ3_spl
| member(sk2,a) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( ~ sQ0_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64,f52]) ).
fof(f68,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f33]) ).
fof(f69,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f31]) ).
fof(f71,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f78,plain,
( ~ sQ1_spl
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ),
inference(resolution,[status(thm)],[f56,f20]) ).
fof(f79,definition,
( sQ4_spl
<=> unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ4_spl
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ5_spl
<=> member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ5_spl
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ sQ1_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f78,f79,f82,f55]) ).
fof(f89,plain,
( ~ sQ4_spl
| member(sk2,b)
| ~ member(sk2,union(cons(a,cons(b,eptset)))) ),
inference(paramodulation,[status(thm)],[f80,f15]) ).
fof(f90,definition,
( sQ6_spl
<=> member(sk2,b) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ6_spl
| member(sk2,b) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sQ4_spl
| sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f61,f90,f79]) ).
fof(f94,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f25]) ).
fof(f95,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f34]) ).
fof(f97,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f67,f69,f71,f85,f93,f95,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n014.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Mon Sep 21 05:38:04 UTC 2026
% 0.15/0.39 % CPUTime :
% 0.15/0.41 % Drodi V4.1.1
% 0.19/0.43 % Refutation found
% 0.19/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.51 % Elapsed time: 0.106206 seconds
% 0.19/0.51 % CPU time: 0.096638 seconds
% 0.19/0.51 % Total memory used: 2.582 MB
% 0.19/0.51 % Net memory used: 2.574 MB
%------------------------------------------------------------------------------