%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:31 PM UTC 2026
% Result : Theorem 0.06s 0.46s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 10 unt; 4 def)
% Number of atoms : 167 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 189 ( 70 ~; 65 |; 32 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 61 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [A] :
( ( ! [B] :
( ~ empty(B)
| element(B,A) )
& ! [B] :
( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ! [A] :
( ( ! [B] :
( ~ in(B,A)
| element(B,A) )
& ! [B] :
( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK0_skl(C,B,A),B)
& in(sK0_skl(C,B,A),A) )
| in(sK0_skl(C,B,A),C) )
& ( in(sK0_skl(C,B,A),B)
| ~ in(sK0_skl(C,B,A),A)
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f35]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f43,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f66,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,subset_complement(A,B))
& ~ in(C,B)
& element(C,A) )
& element(B,powerset(A)) )
& A != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f67,plain,
( ~ in(sK8_skl,subset_complement(sK6_skl,sK7_skl))
& ~ in(sK8_skl,sK7_skl)
& element(sK8_skl,sK6_skl)
& element(sK7_skl,powerset(sK6_skl))
& sK6_skl != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f66]) ).
fof(f68,plain,
sK6_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
element(sK7_skl,powerset(sK6_skl)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
element(sK8_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
~ in(sK8_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
~ in(sK8_skl,subset_complement(sK6_skl,sK7_skl)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f74,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f83,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f39]) ).
fof(f89,plain,
( in(sK8_skl,sK6_skl)
| empty(sK6_skl) ),
inference(resolution,[status(thm)],[f30,f70]) ).
fof(f97,definition,
( sQ2_spl
<=> empty(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ2_spl
| empty(sK6_skl) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ3_spl
<=> in(sK8_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ3_spl
| in(sK8_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f97,f100]) ).
fof(f109,plain,
( ~ sQ2_spl
| sK6_skl = empty_set ),
inference(resolution,[status(thm)],[f98,f74]) ).
fof(f110,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f68]) ).
fof(f111,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f164,plain,
subset_complement(sK6_skl,sK7_skl) = set_difference(sK6_skl,sK7_skl),
inference(resolution,[status(thm)],[f44,f69]) ).
fof(f199,plain,
! [X0] :
( ~ sQ3_spl
| in(sK8_skl,X0)
| in(sK8_skl,set_difference(sK6_skl,X0)) ),
inference(resolution,[status(thm)],[f83,f101]) ).
fof(f214,plain,
( ~ sQ3_spl
| in(sK8_skl,sK7_skl)
| in(sK8_skl,subset_complement(sK6_skl,sK7_skl)) ),
inference(paramodulation,[status(thm)],[f164,f199]) ).
fof(f221,definition,
( sQ9_spl
<=> in(sK8_skl,subset_complement(sK6_skl,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ9_spl
| in(sK8_skl,subset_complement(sK6_skl,sK7_skl)) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ10_spl
<=> in(sK8_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ10_spl
| in(sK8_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( ~ sQ3_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f214,f221,f224,f100]) ).
fof(f236,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f72]) ).
fof(f237,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f71]) ).
fof(f239,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
$false,
inference(sat_refutation,[status(thm)],[f103,f111,f227,f237,f239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.06/0.41 % CPULimit : 300
% 0.06/0.41 % WCLimit : 300
% 0.06/0.41 % DateTime : Mon Sep 21 05:54:20 UTC 2026
% 0.06/0.42 % CPUTime :
% 0.06/0.43 % Drodi V4.1.1
% 0.06/0.46 % Refutation found
% 0.06/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.56 % Elapsed time: 0.129599 seconds
% 0.24/0.56 % CPU time: 0.164586 seconds
% 0.24/0.56 % Total memory used: 26.253 MB
% 0.24/0.56 % Net memory used: 26.165 MB
%------------------------------------------------------------------------------