%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:45:02 AM UTC 2026
% Result : Theorem 96.01s 13.98s
% Output : CNFRefutation 96.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 92 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 90 ( 38 ~; 30 |; 10 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 55 ( 1 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t26_finsub_1,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('theBenchmark.p',t26_finsub_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t27_finsub_1,conjecture,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('theBenchmark.p',t27_finsub_1) ).
fof(t27_finsub_1_neg,negated_conjecture,
~ ! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
inference(assume_negation,[status(cth)],[t27_finsub_1]) ).
cnf(c_41,plain,
( ~ finite(C)
| ~ subset(C,B)
| in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_45,plain,
preboolean(finite_subsets(A)),
inference(clausify,[status(thm)],[dt_k5_finsub_1]) ).
cnf(c_82,plain,
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(clausify,[status(thm)],[cc2_finset_1]) ).
cnf(c_86,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
fof(nnf_8,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_8]) ).
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_88,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_89,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_117,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_118,plain,
subset(finite_subsets(A),powerset(A)),
inference(clausify,[status(thm)],[t26_finsub_1]) ).
cnf(c_120,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_35,plain,
? [A] :
( finite_subsets(A) != powerset(A)
& finite(A) ),
inference(fof_nnf,[status(thm)],[t27_finsub_1_neg]) ).
fof(sk_t27_finsub_1_neg,plain,
( finite_subsets(sK1) != powerset(sK1)
& finite(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_35]) ).
cnf(c_127,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t27_finsub_1_neg]) ).
cnf(c_128,negated_conjecture,
finite_subsets(sK1) != powerset(sK1),
inference(split_conjunct,[status(thm)],[sk_t27_finsub_1_neg]) ).
cnf(c_129,negated_conjecture,
powerset(sK1) != finite_subsets(sK1),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_133,plain,
( ~ finite(C)
| ~ subset(C,A)
| in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_16609,negated_conjecture,
( ~ subset(powerset(sK1),finite_subsets(sK1))
| ~ subset(finite_subsets(sK1),powerset(sK1)) ),
inference(resolve,[status(thm)],[c_86,c_129]) ).
cnf(c_249,negated_conjecture,
~ subset(powerset(sK1),finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_16609,c_118]) ).
cnf(c_403,plain,
in(sK0(powerset(sK1),finite_subsets(sK1)),powerset(sK1)),
inference(resolve,[status(thm)],[c_249,c_88]) ).
cnf(c_406,plain,
~ in(sK0(powerset(sK1),finite_subsets(sK1)),finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_89,c_249]) ).
cnf(c_3664,plain,
element(sK0(powerset(sK1),finite_subsets(sK1)),powerset(sK1)),
inference(resolve,[status(thm)],[c_403,c_117]) ).
cnf(c_16600,plain,
subset(sK0(powerset(sK1),finite_subsets(sK1)),sK1),
inference(resolve,[status(thm)],[c_3664,c_120]) ).
cnf(c_16610,plain,
( finite(sK0(powerset(sK1),finite_subsets(sK1)))
| ~ finite(sK1) ),
inference(resolve,[status(thm)],[c_3664,c_82]) ).
cnf(c_16601,negated_conjecture,
finite(sK0(powerset(sK1),finite_subsets(sK1))),
inference(resolve,[status(thm)],[c_127,c_16610]) ).
cnf(c_16611,plain,
( ~ finite(A)
| ~ subset(A,B)
| in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_133]) ).
cnf(c_16612,plain,
( ~ finite(sK0(powerset(sK1),finite_subsets(sK1)))
| ~ subset(sK0(powerset(sK1),finite_subsets(sK1)),sK1) ),
inference(resolve,[status(thm)],[c_16611,c_406]) ).
cnf(c_16613,plain,
~ subset(sK0(powerset(sK1),finite_subsets(sK1)),sK1),
inference(resolve,[status(thm)],[c_16612,c_16601]) ).
cnf(c_16608,plain,
$false,
inference(resolve,[status(thm)],[c_16600,c_16613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:37:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3229630 was started by sandbox on n008,
% 0.08/0.36 % Sat Sep 26 08:37:39 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 96.01/13.98
% 96.01/13.98 % given #500 (W,wt=11): 2206 -element(c2,f4(f7(c2))). [ur(119,b,333,a,c,1138,a)].
% 96.01/13.98
% 96.01/13.98 % given #1000 (T,wt=13): 1118 finite(f4(f7(f4(c4)))). [resolve(317,a,156,b),unit_del(a,320)].
% 96.01/13.98
% 96.01/13.98 % given #1500 (F,wt=12): 7497 -in(finite_subsets(c1),f7(powerset(c1))). [ur(213,b,7406,a,c,91,a)].
% 96.01/13.98
% 96.01/13.98 % SZS status Theorem for theBenchmark
% 96.01/13.98
% 96.01/13.98 % Proof 1 at 4.30 (+ 1.20) seconds.
% 96.01/13.98 % Length of proof is 29.
% 96.01/13.98 % Level of proof is 7.
% 96.01/13.98 % Maximum clause weight is 18.000.
% 96.01/13.98 % Given clauses 1865.
% 96.01/13.98
% 96.01/13.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------