%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU325+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 : n011.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 02:51:44 PM UTC 2026
% Result : Theorem 25.46s 3.68s
% Output : Proof 25.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 25 unt; 0 def)
% Number of atoms : 175 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 61 ~; 52 |; 35 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 8 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f41_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c88,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f28,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f28_nnf,plain,
! [A] :
? [B] : element(B,A),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A] : element(sk4(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f28_nnf]) ).
cnf(c61,plain,
element(sk4(X0),X0),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p285,plain,
( in(sk4(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[c88,c61]) ).
fof(f44,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f44_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c92,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p472,plain,
( ~ empty(X1)
| ~ element(X0,powerset(X1))
| empty(X0) ),
inference(resolution,[status(thm)],[p285,c92]) ).
fof(f18,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(f18_nnf,plain,
! [A] :
( ! [B] :
( ( ( cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B)
| is_a_cover_of_carrier(A,B) )
& ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B)
| ~ is_a_cover_of_carrier(A,B) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( ( ( cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B)
| is_a_cover_of_carrier(A,B) )
& ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B)
| ~ is_a_cover_of_carrier(A,B) ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c50,plain,
( cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1)
| ~ is_a_cover_of_carrier(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f45,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tops_2) ).
fof(f45_neg,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [A] :
( ? [B] :
( B = empty_set
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
( sk11 = empty_set
& is_a_cover_of_carrier(sk10,sk11)
& element(sk11,powerset(powerset(the_carrier(sk10))))
& one_sorted_str(sk10)
& ~ empty_carrier(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11])],[f45_nnf]) ).
cnf(c94,plain,
one_sorted_str(sk10),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p267,plain,
( cast_as_carrier_subset(sk10) = union_of_subsets(the_carrier(sk10),X0)
| ~ is_a_cover_of_carrier(sk10,X0)
| ~ element(X0,powerset(powerset(the_carrier(sk10)))) ),
inference(resolution,[status(thm)],[c50,c94]) ).
cnf(c95,plain,
element(sk11,powerset(powerset(the_carrier(sk10)))),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p1052,plain,
( cast_as_carrier_subset(sk10) = union(empty_set)
| ~ is_a_cover_of_carrier(sk10,empty_set) ),
inference(resolution,[status(thm)],[p267,c95]) ).
cnf(c97,plain,
sk11 = empty_set,
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(c96,plain,
is_a_cover_of_carrier(sk10,sk11),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p106,plain,
is_a_cover_of_carrier(sk10,empty_set),
inference(superposition,[status(thm)],[c97,c96]) ).
cnf(p1739,plain,
cast_as_carrier_subset(sk10) = union(empty_set),
inference(resolution,[status(thm)],[p1052,p106]) ).
fof(f38,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f38_nnf,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [B,A] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c85,plain,
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f46,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f46_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c98,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f35,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f35_nnf,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A] :
( empty(sk7(A))
& element(sk7(A),powerset(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f35_nnf]) ).
cnf(c80,plain,
empty(sk7(X0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p121,plain,
sk7(X0) = empty_set,
inference(resolution,[status(thm)],[c98,c80]) ).
cnf(c79,plain,
element(sk7(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p122,plain,
element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[p121,c79]) ).
cnf(p341,plain,
union_of_subsets(X0,empty_set) = union(empty_set),
inference(resolution,[status(thm)],[c85,p122]) ).
fof(f23,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f23_nnf,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [B,A] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c56,plain,
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p295,plain,
element(union_of_subsets(X0,empty_set),powerset(X0)),
inference(resolution,[status(thm)],[c56,p122]) ).
cnf(p342,plain,
element(union(empty_set),powerset(X0)),
inference(demodulation,[status(thm)],[p341,p295]) ).
cnf(p1752,plain,
element(cast_as_carrier_subset(sk10),powerset(X0)),
inference(superposition,[status(thm)],[p1739,p342]) ).
cnf(p2250,plain,
( ~ empty(X0)
| empty(cast_as_carrier_subset(sk10)) ),
inference(resolution,[status(thm)],[p472,p1752]) ).
fof(f32,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f32_nnf,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c65,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p2278,plain,
empty(cast_as_carrier_subset(sk10)),
inference(resolution,[status(thm)],[p2250,c65]) ).
cnf(p2279,plain,
cast_as_carrier_subset(sk10) = empty_set,
inference(resolution,[status(thm)],[p2278,c98]) ).
fof(f16,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f16_nnf,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c40,plain,
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p153,plain,
cast_as_carrier_subset(sk10) = the_carrier(sk10),
inference(resolution,[status(thm)],[c40,c94]) ).
fof(f29,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f29_nnf,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c62,plain,
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p219,plain,
( ~ empty(the_carrier(sk10))
| empty_carrier(sk10) ),
inference(resolution,[status(thm)],[c62,c94]) ).
cnf(p222,plain,
( ~ empty(cast_as_carrier_subset(sk10))
| empty_carrier(sk10) ),
inference(superposition,[status(thm)],[p153,p219]) ).
cnf(p2281,plain,
( ~ empty(empty_set)
| empty_carrier(sk10) ),
inference(demodulation,[status(thm)],[p2279,p222]) ).
cnf(p2622,plain,
empty_carrier(sk10),
inference(resolution,[status(thm)],[p2281,c65]) ).
cnf(c93,plain,
~ empty_carrier(sk10),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p2623,plain,
$false,
inference(resolution,[status(thm)],[p2622,c93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 13:42:28 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.46/3.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.46/3.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------