%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 02:51:41 PM UTC 2026
% Result : Theorem 96.73s 14.51s
% Output : Proof 96.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 59 ( 14 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 53 ( 23 ~; 17 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54,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',redefinition_k6_subset_1) ).
fof(f54_nnf,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [B,A,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c120,plain,
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
fof(f21,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f21_nnf,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c45,plain,
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f58,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',t22_pre_topc) ).
fof(f58_neg,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)],[f58]) ).
fof(f58_nnf,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(nnf_transformation,[status(thm)],[f58_neg]) ).
fof(f58_sk,plain,
( subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),sk6)) != sk6
& element(sk6,powerset(the_carrier(sk5)))
& one_sorted_str(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6])],[f58_nnf]) ).
cnf(c124,plain,
one_sorted_str(sk5),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(p317,plain,
element(cast_as_carrier_subset(sk5),powerset(the_carrier(sk5))),
inference(resolution,[status(thm)],[c45,c124]) ).
cnf(p583,plain,
( subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),X0) = set_difference(cast_as_carrier_subset(sk5),X0)
| ~ element(X0,powerset(the_carrier(sk5))) ),
inference(resolution,[status(thm)],[c120,p317]) ).
cnf(c125,plain,
element(sk6,powerset(the_carrier(sk5))),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(p4152,plain,
subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),sk6) = set_difference(cast_as_carrier_subset(sk5),sk6),
inference(resolution,[status(thm)],[p583,c125]) ).
fof(f25,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',dt_k6_subset_1) ).
fof(f25_nnf,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [B,A,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c49,plain,
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p360,plain,
( element(subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),X0),powerset(the_carrier(sk5)))
| ~ element(X0,powerset(the_carrier(sk5))) ),
inference(resolution,[status(thm)],[c49,p317]) ).
cnf(p2364,plain,
element(subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),sk6),powerset(the_carrier(sk5))),
inference(resolution,[status(thm)],[p360,c125]) ).
cnf(p4155,plain,
element(set_difference(cast_as_carrier_subset(sk5),sk6),powerset(the_carrier(sk5))),
inference(demodulation,[status(thm)],[p4152,p2364]) ).
cnf(p5784,plain,
subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),set_difference(cast_as_carrier_subset(sk5),sk6)) = sk6,
inference(resolution,[status(thm)],[p4155,p583]) ).
cnf(c126,plain,
subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),sk6)) != sk6,
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(p4153,plain,
subset_difference(the_carrier(sk5),cast_as_carrier_subset(sk5),set_difference(cast_as_carrier_subset(sk5),sk6)) != sk6,
inference(demodulation,[status(thm)],[p4152,c126]) ).
cnf(p5785,plain,
sk6 != sk6,
inference(demodulation,[status(thm)],[p5784,p4153]) ).
cnf(p5801,plain,
$false,
inference(equality_resolution,[status(thm)],[p5785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU309+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.40 % Computer : n015.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Thu Sep 24 13:41:57 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 96.73/14.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 96.73/14.51 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------