%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU309+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 : n010.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 1.25s 0.64s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 25 unt; 0 def)
% Number of atoms : 99 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 37 ~; 28 |; 7 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 59 ( 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,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(f55,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(f57,axiom,
! [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,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f65,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f131,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f132,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f134,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f138,plain,
! [X0,X1,X2] :
( element(subset_difference(X1,X0,X2),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f244,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)],[f54]) ).
fof(f245,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)],[f244]) ).
fof(f246,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)],[f55]) ).
fof(f247,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)],[f246]) ).
fof(f250,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)],[f57]) ).
fof(f251,plain,
! [X0,X1] :
( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f254,plain,
? [A] :
( ? [B] :
( subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) != B
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f255,plain,
( subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_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)],[f254]) ).
fof(f256,plain,
one_sorted_str(sK5_skl),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
element(sK6_skl,powerset(the_carrier(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,plain,
subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl)) != sK6_skl,
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f267,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f283,plain,
cast_as_carrier_subset(sK5_skl) = the_carrier(sK5_skl),
inference(resolution,[status(thm)],[f132,f256]) ).
fof(f284,plain,
subset_difference(the_carrier(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl)) != sK6_skl,
inference(backward_demodulation,[status(thm)],[f283,f258]) ).
fof(f285,plain,
element(sK6_skl,powerset(cast_as_carrier_subset(sK5_skl))),
inference(backward_demodulation,[status(thm)],[f283,f257]) ).
fof(f286,plain,
subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl)) != sK6_skl,
inference(forward_demodulation,[status(thm)],[f283,f284]) ).
fof(f287,plain,
element(cast_as_carrier_subset(sK5_skl),powerset(the_carrier(sK5_skl))),
inference(resolution,[status(thm)],[f134,f256]) ).
fof(f288,plain,
element(cast_as_carrier_subset(sK5_skl),powerset(cast_as_carrier_subset(sK5_skl))),
inference(forward_demodulation,[status(thm)],[f283,f287]) ).
fof(f296,plain,
! [X0] :
( subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),X0) = set_difference(cast_as_carrier_subset(sK5_skl),X0)
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(resolution,[status(thm)],[f288,f247]) ).
fof(f297,plain,
! [X0] :
( element(subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),X0),powerset(cast_as_carrier_subset(sK5_skl)))
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(resolution,[status(thm)],[f288,f138]) ).
fof(f305,plain,
! [X0] :
( subset_intersection2(the_carrier(sK5_skl),X0,cast_as_carrier_subset(sK5_skl)) = X0
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl)))
| ~ one_sorted_str(sK5_skl) ),
inference(paramodulation,[status(thm)],[f283,f251]) ).
fof(f308,plain,
! [X0] :
( subset_intersection2(cast_as_carrier_subset(sK5_skl),X0,cast_as_carrier_subset(sK5_skl)) = X0
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl)))
| ~ one_sorted_str(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f283,f305]) ).
fof(f309,plain,
! [X0] :
( subset_intersection2(cast_as_carrier_subset(sK5_skl),X0,cast_as_carrier_subset(sK5_skl)) = X0
| ~ element(X0,powerset(cast_as_carrier_subset(sK5_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f256]) ).
fof(f326,plain,
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)],[f296,f285]) ).
fof(f327,plain,
subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl)) != sK6_skl,
inference(backward_demodulation,[status(thm)],[f326,f286]) ).
fof(f340,plain,
element(subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),sK6_skl),powerset(cast_as_carrier_subset(sK5_skl))),
inference(resolution,[status(thm)],[f297,f285]) ).
fof(f342,plain,
element(set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl),powerset(cast_as_carrier_subset(sK5_skl))),
inference(forward_demodulation,[status(thm)],[f326,f340]) ).
fof(f408,plain,
subset_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl,cast_as_carrier_subset(sK5_skl)) = sK6_skl,
inference(resolution,[status(thm)],[f309,f285]) ).
fof(f1253,plain,
subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl)) = set_difference(cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl)),
inference(resolution,[status(thm)],[f342,f296]) ).
fof(f1294,plain,
set_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl) != sK6_skl,
inference(backward_demodulation,[status(thm)],[f1296,f327]) ).
fof(f1296,plain,
subset_difference(cast_as_carrier_subset(sK5_skl),cast_as_carrier_subset(sK5_skl),set_difference(cast_as_carrier_subset(sK5_skl),sK6_skl)) = set_intersection2(cast_as_carrier_subset(sK5_skl),sK6_skl),
inference(forward_demodulation,[status(thm)],[f267,f1253]) ).
fof(f1300,plain,
set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl)) != sK6_skl,
inference(paramodulation,[status(thm)],[f128,f1294]) ).
fof(f1696,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)],[f245,f285]) ).
fof(f1744,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)],[f1696,f288]) ).
fof(f1861,plain,
sK6_skl = set_intersection2(sK6_skl,cast_as_carrier_subset(sK5_skl)),
inference(forward_demodulation,[status(thm)],[f408,f1744]) ).
fof(f1862,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1861,f1300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 06:10:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.25/0.64 % Refutation found
% 1.25/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.25/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.25/0.65 % Elapsed time: 0.286937 seconds
% 1.25/0.65 % CPU time: 2.022658 seconds
% 1.25/0.65 % Total memory used: 155.810 MB
% 1.25/0.65 % Net memory used: 152.971 MB
%------------------------------------------------------------------------------