%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:45:18 AM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 68 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 28 ~; 21 |; 9 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(l71_subset_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l71_subset_1_neg,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(assume_negation,[status(cth)],[l71_subset_1]) ).
cnf(c_21,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_25,plain,
( ~ in(B,A)
| element(B,A)
| empty(A) ),
inference(clausify,[status(thm)],[d2_subset_1]) ).
fof(nnf_4,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_4]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_29,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_30,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_32,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
fof(nnf_18,plain,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1_neg]) ).
fof(sk_l71_subset_1_neg,plain,
( ~ element(sK1,powerset(sK2))
& ! [C] :
( in(C,sK2)
| ~ in(C,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_18]) ).
cnf(c_44,negated_conjecture,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_l71_subset_1_neg]) ).
cnf(c_45,negated_conjecture,
~ element(sK1,powerset(sK2)),
inference(split_conjunct,[status(thm)],[sk_l71_subset_1_neg]) ).
cnf(c_49,plain,
( ~ subset(A,B)
| in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_21]) ).
cnf(c_139,plain,
( ~ in(A,powerset(B))
| element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_25,c_32]) ).
cnf(c_82,negated_conjecture,
~ in(sK1,powerset(sK2)),
inference(resolve,[status(thm)],[c_139,c_45]) ).
cnf(c_98,plain,
~ subset(sK1,sK2),
inference(resolve,[status(thm)],[c_49,c_82]) ).
cnf(c_100,plain,
in(sK0(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_98,c_29]) ).
cnf(c_101,plain,
~ in(sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_30,c_98]) ).
cnf(c_140,negated_conjecture,
in(sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_100,c_44]) ).
cnf(c_138,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_101,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n009.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 08:44:29 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.39 % Process 3884468 was started by sandbox2 on n009,
% 0.14/0.39 % Sat Sep 26 08:44:29 2026
% 0.14/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.43 % Length of proof is 18.
% 0.14/0.43 % Level of proof is 5.
% 0.14/0.43 % Maximum clause weight is 20.000.
% 0.14/0.43 % Given clauses 66.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------