%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU307+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 : n004.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 02:20:06 PM UTC 2026
% Result : Theorem 0.22s 5.62s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 66 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 22 ~; 16 |; 7 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 38 ( 36 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f220,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = set_intersection2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f221,plain,
! [X0,X1,X2] :
( subset_intersection2(X1,X0,X2) = set_intersection2(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f222,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f223,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f227,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f228,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f231,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
? [A] :
( ? [B] :
( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) != B
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f234,plain,
( subset_intersection2(the_carrier(sK5_skl),sK6_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)],[f233]) ).
fof(f235,plain,
one_sorted_str(sK5_skl),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f236,plain,
element(sK6_skl,powerset(the_carrier(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f237,plain,
subset_intersection2(the_carrier(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl)) != sK6_skl,
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f239,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
cast_as_carrier_subset(sK5_skl) = the_carrier(sK5_skl),
inference(resolution,[status(thm)],[f232,f235]) ).
fof(f241,plain,
element(sK6_skl,powerset(cast_as_carrier_subset(sK5_skl))),
inference(backward_demodulation,[status(thm)],[f240,f236]) ).
fof(f251,plain,
subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl)) != sK6_skl,
inference(forward_demodulation,[status(thm)],[f240,f237]) ).
fof(f257,plain,
! [X0] :
( subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,X0) = set_intersection2(sK6_skl,X0)
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(resolution,[status(thm)],[f221,f241]) ).
fof(f258,plain,
element(cast_as_carrier_subset(sK5_skl),powerset(the_carrier(sK5_skl))),
inference(resolution,[status(thm)],[f223,f235]) ).
fof(f259,plain,
element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl))),
inference(forward_demodulation,[status(thm)],[f240,f258]) ).
fof(f313,plain,
subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl)) = set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl)),
inference(resolution,[status(thm)],[f257,f259]) ).
fof(f373,plain,
set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl)) != sK6_skl,
inference(backward_demodulation,[status(thm)],[f313,f251]) ).
fof(f1820,plain,
subset(sK6_skl,cast_as_carrier_subset(sK5_skl)),
inference(resolution,[status(thm)],[f229,f241]) ).
fof(f2004,plain,
set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl)) = sK6_skl,
inference(resolution,[status(thm)],[f1820,f239]) ).
fof(f2006,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2004,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.47 % Computer : n004.cluster.edu
% 0.17/5.47 % Model : x86_64 x86_64
% 0.17/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.47 % Memory : 8046.5625MB
% 0.17/5.47 % OS : Linux 6.8.0-71-generic
% 0.17/5.47 % CPULimit : 300
% 0.17/5.47 % WCLimit : 300
% 0.17/5.47 % DateTime : Mon Sep 21 06:09:55 UTC 2026
% 0.17/5.47 % CPUTime :
% 0.17/5.48 % Drodi V4.1.1
% 0.22/5.62 % Refutation found
% 0.22/5.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.64 % Elapsed time: 0.154402 seconds
% 0.22/5.64 % CPU time: 0.824822 seconds
% 0.22/5.64 % Total memory used: 118.715 MB
% 0.22/5.64 % Net memory used: 118.019 MB
%------------------------------------------------------------------------------