%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.09s 0.53s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 93 ( 12 unt; 7 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 258 ( 121 ~; 130 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [Set1,Set2,Union] :
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
difference(c,a,cDa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
difference(c,b,cDb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,plain,
! [X0,X1,X2] :
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
! [X0,X1,X2] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f45,plain,
! [X0,X1,X2] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f46,plain,
! [Set1,Element] :
( member(Element,Set1)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set2] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [Set2,Element] :
( member(Element,Set2)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set1] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [Intersection,Element] :
( member(Element,Intersection)
| ! [Set1] :
( ~ member(Element,Set1)
| ! [Set2] :
( ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
! [Set1,Element] :
( member(Element,Set1)
| ! [Difference] :
( ~ member(Element,Difference)
| ! [Set2] : ~ difference(Set1,Set2,Difference) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [Set1,Set2] :
( ! [A_set] : ~ difference(A_set,Set1,Set2)
| ! [Element] :
( ~ member(Element,Set2)
| ~ member(Element,Set1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [Element,Set2] :
( member(Element,Set2)
| ! [Difference] :
( member(Element,Difference)
| ! [Set1] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f65,plain,
difference(c,a,cDa),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f66,plain,
difference(c,b,cDb),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
difference(c,aIb,cD_aIb),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
~ union(cDa,cDb,cD_aIb),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cDb)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[f43,f68]) ).
fof(f70,definition,
( sQ0_spl
<=> member(g(cDa,cDb,cD_aIb),cDa) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> member(g(cDa,cDb,cD_aIb),cDb) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ2_spl
<=> member(g(cDa,cDb,cD_aIb),cD_aIb) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ2_spl
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f73,f76]) ).
fof(f80,plain,
( ~ sQ2_spl
| union(cDa,cDb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolution,[status(thm)],[f77,f45]) ).
fof(f81,plain,
( ~ sQ2_spl
| union(cDa,cDb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[f77,f44]) ).
fof(f85,definition,
( sQ3_spl
<=> union(cDa,cDb,cD_aIb) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ3_spl
| union(cDa,cDb,cD_aIb) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ2_spl
| sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f80,f73,f85,f76]) ).
fof(f89,plain,
( ~ sQ2_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f70,f85,f76]) ).
fof(f90,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f68]) ).
fof(f91,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f141,plain,
! [X0] :
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[f49,f64]) ).
fof(f142,plain,
! [X0] :
( member(X0,c)
| ~ member(X0,cD_aIb) ),
inference(resolution,[status(thm)],[f56,f67]) ).
fof(f143,plain,
! [X0] :
( member(X0,c)
| ~ member(X0,cDb) ),
inference(resolution,[status(thm)],[f56,f66]) ).
fof(f144,plain,
! [X0] :
( member(X0,c)
| ~ member(X0,cDa) ),
inference(resolution,[status(thm)],[f56,f65]) ).
fof(f145,plain,
( ~ sQ0_spl
| member(g(cDa,cDb,cD_aIb),c) ),
inference(resolution,[status(thm)],[f144,f71]) ).
fof(f155,plain,
! [X0] :
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[f51,f64]) ).
fof(f201,plain,
! [X0] :
( ~ member(X0,cD_aIb)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[f58,f67]) ).
fof(f202,plain,
! [X0] :
( ~ member(X0,cDb)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[f58,f66]) ).
fof(f203,plain,
! [X0] :
( ~ member(X0,cDa)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[f58,f65]) ).
fof(f216,plain,
! [X0] :
( member(X0,aIb)
| member(X0,cD_aIb)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[f60,f67]) ).
fof(f217,plain,
! [X0] :
( member(X0,b)
| member(X0,cDb)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[f60,f66]) ).
fof(f218,plain,
! [X0] :
( member(X0,a)
| member(X0,cDa)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[f60,f65]) ).
fof(f223,plain,
( ~ sQ0_spl
| member(g(cDa,cDb,cD_aIb),aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolution,[status(thm)],[f216,f145]) ).
fof(f224,definition,
( sQ8_spl
<=> member(g(cDa,cDb,cD_aIb),aIb) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ8_spl
| member(g(cDa,cDb,cD_aIb),aIb) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( ~ sQ0_spl
| sQ8_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f223,f76,f224,f70]) ).
fof(f235,plain,
( ~ sQ8_spl
| member(g(cDa,cDb,cD_aIb),b) ),
inference(resolution,[status(thm)],[f225,f141]) ).
fof(f237,plain,
! [X0,X1] :
( ~ sQ8_spl
| member(g(cDa,cDb,cD_aIb),X0)
| ~ intersection(X0,X1,aIb) ),
inference(resolution,[status(thm)],[f225,f47]) ).
fof(f263,definition,
( sQ10_spl
<=> member(g(cDa,cDb,cD_aIb),a) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f273,definition,
( sQ11_spl
<=> member(g(cDa,cDb,cD_aIb),b) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ11_spl
| member(g(cDa,cDb,cD_aIb),b) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f285,plain,
( ~ sQ8_spl
| member(g(cDa,cDb,cD_aIb),a) ),
inference(resolution,[status(thm)],[f237,f64]) ).
fof(f288,plain,
( ~ sQ8_spl
| ~ member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[f285,f203]) ).
fof(f294,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f71]) ).
fof(f295,plain,
( ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f298,plain,
( ~ sQ2_spl
| ~ member(g(cDa,cDb,cD_aIb),aIb) ),
inference(resolution,[status(thm)],[f77,f201]) ).
fof(f299,plain,
( ~ sQ2_spl
| member(g(cDa,cDb,cD_aIb),c) ),
inference(resolution,[status(thm)],[f77,f142]) ).
fof(f312,plain,
( ~ sQ2_spl
| member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa) ),
inference(resolution,[status(thm)],[f299,f218]) ).
fof(f313,plain,
( ~ sQ2_spl
| member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb) ),
inference(resolution,[status(thm)],[f299,f217]) ).
fof(f322,plain,
( ~ sQ2_spl
| sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f312,f70,f263,f76]) ).
fof(f323,plain,
( ~ sQ2_spl
| sQ11_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f313,f73,f273,f76]) ).
fof(f328,plain,
( ~ sQ11_spl
| member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),a) ),
inference(resolution,[status(thm)],[f274,f155]) ).
fof(f336,plain,
( ~ sQ11_spl
| sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f328,f263,f224,f273]) ).
fof(f337,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f298]) ).
fof(f338,plain,
( ~ sQ8_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f339,plain,
( ~ sQ1_spl
| ~ member(g(cDa,cDb,cD_aIb),b) ),
inference(resolution,[status(thm)],[f74,f202]) ).
fof(f340,plain,
( ~ sQ1_spl
| member(g(cDa,cDb,cD_aIb),c) ),
inference(resolution,[status(thm)],[f74,f143]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f274]) ).
fof(f349,plain,
( ~ sQ1_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f352,plain,
( ~ sQ1_spl
| member(g(cDa,cDb,cD_aIb),aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb) ),
inference(resolution,[status(thm)],[f340,f216]) ).
fof(f362,plain,
( ~ sQ1_spl
| sQ8_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f352,f76,f224,f73]) ).
fof(f363,plain,
( ~ sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f235,f273,f224]) ).
fof(f364,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f88,f89,f91,f227,f295,f322,f323,f336,f338,f349,f362,f363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:42:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.53 % Refutation found
% 0.09/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.35/0.54 % Elapsed time: 0.175357 seconds
% 0.35/0.54 % CPU time: 1.181110 seconds
% 0.35/0.54 % Total memory used: 30.789 MB
% 0.35/0.54 % Net memory used: 28.795 MB
%------------------------------------------------------------------------------