%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 08:45:49 AM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 160 ( 36 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 167 ( 65 ~; 55 |; 33 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 12 sgn 51 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d8_pre_topc,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('theBenchmark.p',d8_pre_topc) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_pre_topc) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t5_tops_2,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('theBenchmark.p',t5_tops_2) ).
fof(t5_tops_2_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(assume_negation,[status(cth)],[t5_tops_2]) ).
fof(nnf_49,plain,
? [A] :
( ? [B] :
( empty_set = B
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t5_tops_2_neg]) ).
fof(sk_t5_tops_2_neg,plain,
( empty_set = sK1
& is_a_cover_of_carrier(sK0,sK1)
& element(sK1,powerset(powerset(the_carrier(sK0))))
& one_sorted_str(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_49]) ).
cnf(c_51,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_54,plain,
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[fc2_pre_topc]) ).
cnf(c_59,plain,
( union_of_subsets(the_carrier(A),B) = cast_as_carrier_subset(A)
| ~ is_a_cover_of_carrier(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d8_pre_topc]) ).
cnf(c_60,plain,
( the_carrier(A) = cast_as_carrier_subset(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
cnf(c_65,negated_conjecture,
empty_set = sK1,
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_66,negated_conjecture,
is_a_cover_of_carrier(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_68,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_70,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_71,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_72,plain,
( sK1 = A
| ~ empty(A) ),
inference(paramod,[status(thm)],[c_65,c_71]) ).
cnf(c_75,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_77,plain,
( union_of_subsets(B,A) = union(A)
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(nnf_36,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(sk_rc2_subset_1,plain,
! [A] :
( empty(sK2(A))
& element(sK2(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(B,sK2(A))],[nnf_36]) ).
cnf(c_79,plain,
empty(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
cnf(c_80,plain,
element(sK2(A),powerset(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
fof(nnf_29,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK3(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(B,sK3(A))],[nnf_29]) ).
cnf(c_102,plain,
element(sK3(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
fof(nnf_18,plain,
! [A,B] :
( ( ? [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) )
& ( ? [X3] :
( in(X3,A)
& in(C,X3) )
| in(C,B) ) )
| union(A) = B )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,A)
| ~ in(X0,X2) )
| in(X0,B) )
& ( ? [X1] :
( in(X1,A)
& in(X0,X1) )
| ~ in(X0,B) ) )
| union(A) != B ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(sk_d4_tarski_sk,plain,
! [A,B] :
( ( ( ( ! [D] :
( ~ in(D,A)
| ~ in(sK5(A,B),D) )
| ~ in(sK5(A,B),B) )
& ( ( in(sK6(A,B),A)
& in(sK5(A,B),sK6(A,B)) )
| in(sK5(A,B),B) ) )
| union(A) = B )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,A)
| ~ in(X0,X2) )
| in(X0,B) )
& ( ( in(sK4(A,B,X0),A)
& in(X0,sK4(A,B,X0)) )
| ~ in(X0,B) ) )
| union(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(A,B,X0)),skolemize(C,sK5(A,B)),skolemize(X3,sK6(A,B))],[nnf_18]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,VAR_0)
| ~ in(sK5(VAR_0,VAR_1),VAR_2)
| ~ in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK6(VAR_0,VAR_1),VAR_0)
| in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( in(sK5(VAR_0,VAR_1),sK6(VAR_0,VAR_1))
| in(sK5(VAR_0,VAR_1),VAR_1)
| union(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_0)
| ~ in(VAR_2,VAR_3)
| in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK4(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,sK4(VAR_0,VAR_1,VAR_2))
| ~ in(VAR_2,VAR_1)
| union(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_tarski_sk]) ).
cnf(c_108,plain,
( in(sK4(A,B,C),A)
| ~ in(C,B)
| union(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_145,negated_conjecture,
( ~ empty(cast_as_carrier_subset(sK0))
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_54,c_51]) ).
cnf(c_146,negated_conjecture,
~ empty(cast_as_carrier_subset(sK0)),
inference(resolve,[status(thm)],[c_68,c_145]) ).
cnf(c_163,negated_conjecture,
( union_of_subsets(the_carrier(sK0),A) = cast_as_carrier_subset(sK0)
| ~ is_a_cover_of_carrier(sK0,A)
| ~ element(A,powerset(powerset(the_carrier(sK0)))) ),
inference(resolve,[status(thm)],[c_59,c_51]) ).
cnf(c_166,negated_conjecture,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(resolve,[status(thm)],[c_60,c_51]) ).
cnf(c_765,negated_conjecture,
( union_of_subsets(the_carrier(sK0),A) = cast_as_carrier_subset(sK0)
| ~ is_a_cover_of_carrier(sK0,A)
| ~ element(A,powerset(powerset(cast_as_carrier_subset(sK0)))) ),
inference(paramod,[status(thm)],[c_166,c_163]) ).
cnf(c_176,negated_conjecture,
( union_of_subsets(cast_as_carrier_subset(sK0),A) = cast_as_carrier_subset(sK0)
| ~ is_a_cover_of_carrier(sK0,A)
| ~ element(A,powerset(powerset(cast_as_carrier_subset(sK0)))) ),
inference(paramod,[status(thm)],[c_166,c_765]) ).
cnf(c_766,plain,
sK1 = sK2(A),
inference(resolve,[status(thm)],[c_79,c_72]) ).
cnf(c_183,plain,
sK2(A) = sK1,
inference(copy,[status(thm)],[c_766]) ).
cnf(c_767,plain,
~ in(A,sK2(B)),
inference(resolve,[status(thm)],[c_79,c_70]) ).
cnf(c_184,plain,
~ in(A,sK1),
inference(paramod,[status(thm)],[c_183,c_767]) ).
cnf(c_186,plain,
element(sK1,powerset(A)),
inference(paramod,[status(thm)],[c_183,c_80]) ).
cnf(c_768,negated_conjecture,
( union_of_subsets(cast_as_carrier_subset(sK0),sK1) = cast_as_carrier_subset(sK0)
| ~ element(sK1,powerset(powerset(cast_as_carrier_subset(sK0)))) ),
inference(resolve,[status(thm)],[c_176,c_66]) ).
cnf(c_521,negated_conjecture,
union_of_subsets(cast_as_carrier_subset(sK0),sK1) = cast_as_carrier_subset(sK0),
inference(resolve,[status(thm)],[c_186,c_768]) ).
cnf(c_769,plain,
( in(sK4(B,union(B),A),B)
| ~ in(A,union(B)) ),
inference(xxres,[status(thm)],[c_108]) ).
cnf(c_572,plain,
~ in(A,union(sK1)),
inference(resolve,[status(thm)],[c_769,c_184]) ).
cnf(c_652,plain,
union_of_subsets(A,sK1) = union(sK1),
inference(resolve,[status(thm)],[c_186,c_77]) ).
cnf(c_663,negated_conjecture,
union(sK1) = cast_as_carrier_subset(sK0),
inference(paramod,[status(thm)],[c_652,c_521]) ).
cnf(c_678,plain,
~ in(A,cast_as_carrier_subset(sK0)),
inference(paramod,[status(thm)],[c_663,c_572]) ).
cnf(c_770,negated_conjecture,
( in(A,cast_as_carrier_subset(sK0))
| ~ element(A,cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_75,c_146]) ).
cnf(c_763,negated_conjecture,
~ element(A,cast_as_carrier_subset(sK0)),
inference(resolve,[status(thm)],[c_770,c_678]) ).
cnf(c_764,plain,
$false,
inference(resolve,[status(thm)],[c_763,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU325+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 09:17:30 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 535647 was started by sandbox on n016,
% 0.19/0.44 % Sat Sep 26 09:17:30 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/0.46
% 0.23/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.56
% 0.23/0.56 % SZS status Theorem for theBenchmark
% 0.23/0.56
% 0.23/0.56 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.23/0.56 % Length of proof is 42.
% 0.23/0.56 % Level of proof is 9.
% 0.23/0.56 % Maximum clause weight is 26.000.
% 0.23/0.56 % Given clauses 107.
% 0.23/0.56
% 0.23/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------