%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:40:25 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 11 unt; 4 def)
% Number of atoms : 143 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 150 ( 72 ~; 57 |; 12 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 83 ( 80 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f30,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f40,plain,
! [A] : element(sK0_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f5]) ).
fof(f41,plain,
! [X0] : element(sK0_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f84,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f85,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f91,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f94,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f97,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f99,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
? [A,B] :
( subset(B,A)
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f102,plain,
( subset(sK12_skl,sK11_skl)
& in(sK11_skl,sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f101]) ).
fof(f103,plain,
in(sK11_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
subset(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f110,plain,
~ empty(sK12_skl),
inference(resolution,[status(thm)],[f100,f103]) ).
fof(f111,plain,
! [X0] :
( in(X0,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f110,f85]) ).
fof(f112,plain,
in(sK0_skl(sK12_skl),sK12_skl),
inference(resolution,[status(thm)],[f111,f41]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f92,f89]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f95,f89]) ).
fof(f132,plain,
! [X0] :
( ~ empty(sK11_skl)
| ~ in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f130,f104]) ).
fof(f135,definition,
! [X0] :
( sQ0_spl
<=> ~ in(X0,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f136,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK12_skl) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ1_spl
<=> empty(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ1_spl
| ~ empty(sK11_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f132,f135,f138]) ).
fof(f143,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f112,f136]) ).
fof(f145,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f151,plain,
! [X0] :
( element(X0,sK11_skl)
| ~ in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f127,f104]) ).
fof(f160,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f97,f85]) ).
fof(f176,plain,
! [X0] :
( in(X0,sK11_skl)
| sK11_skl = empty_set
| ~ in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f151,f160]) ).
fof(f177,definition,
! [X0] :
( sQ2_spl
<=> ( in(X0,sK11_skl)
| ~ in(X0,sK12_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f178,plain,
! [X0] :
( ~ sQ2_spl
| in(X0,sK11_skl)
| ~ in(X0,sK12_skl) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ3_spl
<=> sK11_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ3_spl
| sK11_skl = empty_set ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f176,f177,f180]) ).
fof(f184,plain,
( ~ sQ2_spl
| in(sK11_skl,sK11_skl) ),
inference(resolution,[status(thm)],[f178,f103]) ).
fof(f187,plain,
( ~ sQ2_spl
| ~ in(sK11_skl,sK11_skl) ),
inference(resolution,[status(thm)],[f184,f31]) ).
fof(f188,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f184]) ).
fof(f189,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f192,plain,
( sQ1_spl
| ~ sQ3_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f181,f140]) ).
fof(f197,plain,
( sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f42]) ).
fof(f198,plain,
( sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
$false,
inference(sat_refutation,[status(thm)],[f141,f145,f183,f189,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:29:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.059400 seconds
% 0.12/0.43 % CPU time: 0.152089 seconds
% 0.12/0.43 % Total memory used: 80.955 MB
% 0.12/0.43 % Net memory used: 80.898 MB
%------------------------------------------------------------------------------