%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 147 ( 25 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 167 ( 60 ~; 57 |; 32 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 71 ( 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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(f17,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(f18,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,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(f96,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)],[f95]) ).
fof(f101,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f145,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)],[f144]) ).
fof(f146,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)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f203,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)],[f17]) ).
fof(f204,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)],[f203]) ).
fof(f205,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK15_skl(C,B,A),B)
& in(sK15_skl(C,B,A),A) )
| in(sK15_skl(C,B,A),C) )
& ( in(sK15_skl(C,B,A),B)
| ~ in(sK15_skl(C,B,A),A)
| ~ in(sK15_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,[sK15_skl]),skolemize(D,sK15_skl(C,B,A))],[f204]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f212,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f213,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f281,plain,
empty(sK18_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f56]) ).
fof(f282,plain,
empty(sK18_skl),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f386,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)],[f96]) ).
fof(f387,plain,
( ~ in(sK27_skl,subset_complement(sK25_skl,sK26_skl))
& ~ in(sK27_skl,sK26_skl)
& element(sK27_skl,sK25_skl)
& element(sK26_skl,powerset(sK25_skl))
& sK25_skl != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl]),skolemize(A,sK25_skl),skolemize(B,sK26_skl),skolemize(C,sK27_skl)],[f386]) ).
fof(f388,plain,
sK25_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f389,plain,
element(sK26_skl,powerset(sK25_skl)),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f390,plain,
element(sK27_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f391,plain,
~ in(sK27_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f392,plain,
~ in(sK27_skl,subset_complement(sK25_skl,sK26_skl)),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f403,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f101]) ).
fof(f404,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f466,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f208]) ).
fof(f504,plain,
subset_complement(sK25_skl,sK26_skl) = set_difference(sK25_skl,sK26_skl),
inference(resolution,[status(thm)],[f213,f389]) ).
fof(f519,plain,
sK18_skl = empty_set,
inference(resolution,[status(thm)],[f404,f282]) ).
fof(f522,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f404,f147]) ).
fof(f534,plain,
sK25_skl != sK18_skl,
inference(backward_demodulation,[status(thm)],[f519,f388]) ).
fof(f1350,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| X0 = sK18_skl ),
inference(forward_demodulation,[status(thm)],[f519,f522]) ).
fof(f1355,plain,
( in(sK27_skl,sK25_skl)
| sK25_skl = sK18_skl ),
inference(resolution,[status(thm)],[f1350,f390]) ).
fof(f1359,plain,
in(sK27_skl,sK25_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1355,f534]) ).
fof(f1748,plain,
! [X0] :
( in(X0,sK26_skl)
| ~ in(X0,sK25_skl)
| in(X0,subset_complement(sK25_skl,sK26_skl)) ),
inference(paramodulation,[status(thm)],[f504,f466]) ).
fof(f2140,plain,
( in(sK27_skl,sK26_skl)
| in(sK27_skl,subset_complement(sK25_skl,sK26_skl)) ),
inference(resolution,[status(thm)],[f1748,f1359]) ).
fof(f2161,plain,
in(sK27_skl,sK26_skl),
inference(forward_subsumption_resolution,[status(thm)],[f2140,f392]) ).
fof(f2166,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2161,f391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU171+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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 05:59:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.49 % Elapsed time: 0.115168 seconds
% 0.12/0.49 % CPU time: 0.665335 seconds
% 0.12/0.49 % Total memory used: 118.445 MB
% 0.12/0.49 % Net memory used: 117.068 MB
%------------------------------------------------------------------------------