%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:08:48 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 8 unt; 5 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 152 ( 68 ~; 79 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Intersection] :
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
difference(a,b,aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
difference(a,aDb,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ intersection(a,b,aD_aDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0,X1,X2] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
! [Set1,Element] :
( member(Element,Set1)
| ! [Difference] :
( ~ member(Element,Difference)
| ! [Set2] : ~ difference(Set1,Set2,Difference) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [Set1,Set2] :
( ! [A_set] : ~ difference(A_set,Set1,Set2)
| ! [Element] :
( ~ member(Element,Set2)
| ~ member(Element,Set1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [Element,Set2] :
( member(Element,Set2)
| ! [Difference] :
( member(Element,Difference)
| ! [Set1] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
difference(a,b,aDb),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
difference(a,aDb,aD_aDb),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
~ intersection(a,b,aD_aDb),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
( member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolution,[status(thm)],[f35,f49]) ).
fof(f51,definition,
( sQ0_spl
<=> member(h(a,b,aD_aDb),aD_aDb) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ0_spl
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> member(h(a,b,aD_aDb),a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ1_spl
| member(h(a,b,aD_aDb),a) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f56,plain,
( sQ1_spl
| ~ member(h(a,b,aD_aDb),a) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sQ0_spl
| member(h(a,b,aD_aDb),X0)
| ~ difference(X0,X1,aD_aDb) ),
inference(resolution,[status(thm)],[f39,f52]) ).
fof(f74,plain,
( ~ sQ0_spl
| member(h(a,b,aD_aDb),a) ),
inference(resolution,[status(thm)],[f72,f48]) ).
fof(f82,plain,
! [X0] :
( ~ member(X0,aD_aDb)
| ~ member(X0,aDb) ),
inference(resolution,[status(thm)],[f41,f48]) ).
fof(f83,plain,
! [X0] :
( ~ member(X0,aDb)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[f41,f47]) ).
fof(f84,plain,
! [X0] :
( member(X0,aDb)
| member(X0,aD_aDb)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[f43,f48]) ).
fof(f85,plain,
! [X0] :
( member(X0,b)
| member(X0,aDb)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[f43,f47]) ).
fof(f103,definition,
( sQ2_spl
<=> member(h(a,b,aD_aDb),aDb) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ2_spl
| member(h(a,b,aD_aDb),aDb) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f107,plain,
( ~ sQ0_spl
| member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aDb) ),
inference(resolution,[status(thm)],[f85,f74]) ).
fof(f109,definition,
( sQ3_spl
<=> member(h(a,b,aD_aDb),b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ3_spl
| member(h(a,b,aD_aDb),b) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f107,f103,f109,f51]) ).
fof(f114,plain,
( ~ sQ1_spl
| member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolution,[status(thm)],[f55,f84]) ).
fof(f121,plain,
( ~ sQ1_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f114,f51,f103,f54]) ).
fof(f149,plain,
( ~ sQ2_spl
| ~ member(h(a,b,aD_aDb),b) ),
inference(resolution,[status(thm)],[f104,f83]) ).
fof(f150,plain,
( ~ sQ2_spl
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolution,[status(thm)],[f104,f82]) ).
fof(f158,plain,
( sQ1_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f74]) ).
fof(f159,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ2_spl
| member(h(a,b,aD_aDb),b)
| intersection(a,b,aD_aDb) ),
inference(resolution,[status(thm)],[f150,f36]) ).
fof(f162,definition,
( sQ4_spl
<=> intersection(a,b,aD_aDb) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ4_spl
| intersection(a,b,aD_aDb) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( ~ sQ2_spl
| sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f161,f162,f109,f103]) ).
fof(f176,plain,
( ~ sQ3_spl
| intersection(a,b,aD_aDb)
| ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolution,[status(thm)],[f110,f37]) ).
fof(f183,plain,
( ~ sQ3_spl
| sQ4_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f176,f51,f54,f162,f109]) ).
fof(f184,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f49]) ).
fof(f185,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f186,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f110]) ).
fof(f187,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f188,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f112,f121,f159,f165,f183,f185,f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n017.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Mon Sep 21 04:37:22 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.13/10.41 % Refutation found
% 0.13/10.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.43 % Elapsed time: 0.053165 seconds
% 0.13/10.43 % CPU time: 0.229462 seconds
% 0.13/10.43 % Total memory used: 18.933 MB
% 0.13/10.43 % Net memory used: 18.490 MB
%------------------------------------------------------------------------------