%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU308+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 : n006.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 02:20:07 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 12 unt; 2 def)
% Number of atoms : 71 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 25 ~; 18 |; 5 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f54,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f185,plain,
! [X0,X1,X2] :
( subset_difference(X1,X0,X2) = set_difference(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f186,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f187,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f197,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f198,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
? [A] :
( ? [B] :
( subset_complement(the_carrier(A),B) != subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f200,plain,
( subset_complement(the_carrier(sK5_skl),sK6_skl) != subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl)
& element(sK6_skl,powerset(the_carrier(sK5_skl)))
& one_sorted_str(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f199]) ).
fof(f201,plain,
one_sorted_str(sK5_skl),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
element(sK6_skl,powerset(the_carrier(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f203,plain,
subset_complement(the_carrier(sK5_skl),sK6_skl) != subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f204,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f205,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
cast_as_carrier_subset(sK5_skl) = the_carrier(sK5_skl),
inference(resolution,[status(thm)],[f198,f201]) ).
fof(f207,plain,
subset_complement(the_carrier(sK5_skl),sK6_skl) != subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(backward_demodulation,[status(thm)],[f206,f203]) ).
fof(f208,plain,
element(sK6_skl,powerset(cast_as_carrier_subset(sK5_skl))),
inference(backward_demodulation,[status(thm)],[f206,f202]) ).
fof(f209,plain,
subset_complement(cast_as_carrier_subset(sK5_skl),sK6_skl) != subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(forward_demodulation,[status(thm)],[f206,f207]) ).
fof(f210,plain,
( element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl)))
| ~ one_sorted_str(sK5_skl) ),
inference(paramodulation,[status(thm)],[f206,f187]) ).
fof(f211,definition,
( sQ0_spl
<=> one_sorted_str(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ0_spl
| ~ one_sorted_str(sK5_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
( sQ1_spl
<=> element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ1_spl
| element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f210,f211,f214]) ).
fof(f218,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f201]) ).
fof(f219,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f223,plain,
! [X0] :
( subset_difference(cast_as_carrier_subset(sK5_skl),X0,sK6_skl) = set_difference(X0,sK6_skl)
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(resolution,[status(thm)],[f185,f208]) ).
fof(f228,plain,
subset_complement(cast_as_carrier_subset(sK5_skl),sK6_skl) = set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(resolution,[status(thm)],[f205,f208]) ).
fof(f240,plain,
set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl) != subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(backward_demodulation,[status(thm)],[f228,f209]) ).
fof(f261,plain,
( ~ sQ1_spl
| subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl) = set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f223,f215]) ).
fof(f263,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f240]) ).
fof(f264,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f265,plain,
$false,
inference(sat_refutation,[status(thm)],[f217,f219,f264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 06:09:43 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.053519 seconds
% 0.14/0.42 % CPU time: 0.152301 seconds
% 0.14/0.42 % Total memory used: 104.830 MB
% 0.14/0.42 % Net memory used: 104.763 MB
%------------------------------------------------------------------------------