%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:32 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 18 unt; 0 def)
% Number of atoms : 189 ( 27 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 209 ( 88 ~; 78 |; 25 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 114 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [A,B] :
( ! [C] :
( ( C = complements_of_subsets(A,B)
<=> ! [D] :
( ( in(D,C)
<=> in(subset_complement(A,D),B) )
| ~ element(D,powerset(A)) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( ( in(subset_complement(A,D),B)
| in(D,C) )
& ( ~ in(subset_complement(A,D),B)
| ~ in(D,C) )
& element(D,powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ! [D] :
( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [A,B] :
( ! [C] :
( ( ( ( ( in(subset_complement(A,sK1_skl(C,B,A)),B)
| in(sK1_skl(C,B,A),C) )
& ( ~ in(subset_complement(A,sK1_skl(C,B,A)),B)
| ~ in(sK1_skl(C,B,A),C) )
& element(sK1_skl(C,B,A),powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ! [D] :
( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( in(subset_complement(X1,X3),X0)
| ~ in(X3,X2)
| ~ element(X3,powerset(X1))
| X2 != complements_of_subsets(X1,X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f48,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f49,plain,
! [X0,X1] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] : element(sK2_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl(A))],[f9]) ).
fof(f51,plain,
! [X0] : element(sK2_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f56,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f57,plain,
! [X0,X1] :
( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f64,plain,
! [A] :
( empty(sK5_skl(A))
& element(sK5_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(B,sK5_skl(A))],[f16]) ).
fof(f65,plain,
! [X0] : element(sK5_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0] : empty(sK5_skl(X0)),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f71,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f72,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f74,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
? [A,B] :
( complements_of_subsets(A,B) = empty_set
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f80,plain,
( complements_of_subsets(sK7_skl,sK8_skl) = empty_set
& sK8_skl != empty_set
& element(sK8_skl,powerset(powerset(sK7_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f79]) ).
fof(f81,plain,
element(sK8_skl,powerset(powerset(sK7_skl))),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
sK8_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
complements_of_subsets(sK7_skl,sK8_skl) = empty_set,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f90,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f93,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f98,plain,
! [X0,X1,X2] :
( in(subset_complement(X1,X2),X0)
| ~ in(X2,complements_of_subsets(X1,X0))
| ~ element(X2,powerset(X1))
| ~ element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(destructive_equality_resolution,[status(thm)],[f41]) ).
fof(f103,plain,
( complements_of_subsets(sK7_skl,empty_set) = sK8_skl
| ~ element(sK8_skl,powerset(powerset(sK7_skl))) ),
inference(paramodulation,[status(thm)],[f83,f57]) ).
fof(f104,plain,
complements_of_subsets(sK7_skl,empty_set) = sK8_skl,
inference(forward_subsumption_resolution,[status(thm)],[f103,f81]) ).
fof(f109,plain,
! [X0] : sK5_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f66,f91]) ).
fof(f111,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f109,f65]) ).
fof(f120,plain,
! [X0,X1,X2] :
( in(subset_complement(X1,X2),X0)
| ~ in(X2,complements_of_subsets(X1,X0))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f49]) ).
fof(f127,plain,
! [X0] :
( in(subset_complement(sK7_skl,X0),empty_set)
| ~ in(X0,sK8_skl)
| ~ element(X0,powerset(sK7_skl))
| ~ element(empty_set,powerset(powerset(sK7_skl))) ),
inference(paramodulation,[status(thm)],[f104,f120]) ).
fof(f129,plain,
! [X0] :
( in(subset_complement(sK7_skl,X0),empty_set)
| ~ in(X0,sK8_skl)
| ~ element(X0,powerset(sK7_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f111]) ).
fof(f132,plain,
! [X0] :
( ~ empty(empty_set)
| ~ in(X0,sK8_skl)
| ~ element(X0,powerset(sK7_skl)) ),
inference(resolution,[status(thm)],[f129,f94]) ).
fof(f134,plain,
! [X0] :
( ~ in(X0,sK8_skl)
| ~ element(X0,powerset(sK7_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f53]) ).
fof(f161,plain,
subset(sK8_skl,powerset(sK7_skl)),
inference(resolution,[status(thm)],[f77,f81]) ).
fof(f164,plain,
! [X0] :
( in(X0,powerset(sK7_skl))
| ~ in(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f161,f35]) ).
fof(f215,plain,
! [X0] :
( element(X0,powerset(sK7_skl))
| ~ in(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f164,f72]) ).
fof(f218,plain,
! [X0] : ~ in(X0,sK8_skl),
inference(forward_subsumption_resolution,[status(thm)],[f215,f134]) ).
fof(f262,plain,
! [X0] :
( empty(sK8_skl)
| ~ element(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f74,f218]) ).
fof(f271,plain,
empty(sK8_skl),
inference(resolution,[status(thm)],[f262,f51]) ).
fof(f273,plain,
sK8_skl = empty_set,
inference(resolution,[status(thm)],[f271,f91]) ).
fof(f274,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f273,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 05:55:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.070495 seconds
% 0.14/0.45 % CPU time: 0.277726 seconds
% 0.14/0.45 % Total memory used: 60.667 MB
% 0.14/0.45 % Net memory used: 60.281 MB
%------------------------------------------------------------------------------