%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU110+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 : n010.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 39.24s 5.50s
% Output : CNFRefutation 39.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 90 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 97 ( 42 ~; 37 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 63 ( 4 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t23_finsub_1,conjecture,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('theBenchmark.p',t23_finsub_1) ).
fof(t23_finsub_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
inference(assume_negation,[status(cth)],[t23_finsub_1]) ).
cnf(c_37,plain,
( subset(C,B)
| ~ in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_38,plain,
( finite(C)
| ~ in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_39,plain,
( ~ finite(C)
| ~ subset(C,B)
| in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_43,plain,
preboolean(finite_subsets(A)),
inference(clausify,[status(thm)],[dt_k5_finsub_1]) ).
fof(nnf_7,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_7]) ).
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_83,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_84,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_112,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
fof(nnf_33,plain,
? [A,B] :
( ~ subset(finite_subsets(A),finite_subsets(B))
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t23_finsub_1_neg]) ).
fof(sk_t23_finsub_1_neg,plain,
( ~ subset(finite_subsets(sK1),finite_subsets(sK2))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_33]) ).
cnf(c_121,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t23_finsub_1_neg]) ).
cnf(c_122,negated_conjecture,
~ subset(finite_subsets(sK1),finite_subsets(sK2)),
inference(split_conjunct,[status(thm)],[sk_t23_finsub_1_neg]) ).
cnf(c_126,plain,
( ~ finite(C)
| ~ subset(C,A)
| in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_127,plain,
( finite(C)
| ~ in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_43,c_38]) ).
cnf(c_128,plain,
( finite(A)
| ~ in(A,finite_subsets(B)) ),
inference(copy,[status(thm)],[c_127]) ).
cnf(c_129,plain,
( subset(C,A)
| ~ in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_43,c_37]) ).
cnf(c_246,plain,
( subset(A,sK2)
| ~ subset(A,sK1) ),
inference(resolve,[status(thm)],[c_121,c_112]) ).
cnf(c_249,plain,
in(sK0(finite_subsets(sK1),finite_subsets(sK2)),finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_122,c_83]) ).
cnf(c_251,negated_conjecture,
~ in(sK0(finite_subsets(sK1),finite_subsets(sK2)),finite_subsets(sK2)),
inference(resolve,[status(thm)],[c_84,c_122]) ).
cnf(c_262,plain,
( ~ finite(A)
| ~ subset(A,B)
| in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_126]) ).
cnf(c_269,plain,
( subset(A,B)
| ~ in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_129]) ).
cnf(c_1918,plain,
subset(sK0(finite_subsets(sK1),finite_subsets(sK2)),sK1),
inference(resolve,[status(thm)],[c_249,c_269]) ).
cnf(c_1921,plain,
finite(sK0(finite_subsets(sK1),finite_subsets(sK2))),
inference(resolve,[status(thm)],[c_249,c_128]) ).
cnf(c_18909,plain,
( ~ finite(sK0(finite_subsets(sK1),finite_subsets(sK2)))
| ~ subset(sK0(finite_subsets(sK1),finite_subsets(sK2)),sK2) ),
inference(resolve,[status(thm)],[c_262,c_251]) ).
cnf(c_13639,plain,
~ subset(sK0(finite_subsets(sK1),finite_subsets(sK2)),sK2),
inference(resolve,[status(thm)],[c_18909,c_1921]) ).
cnf(c_18910,plain,
subset(sK0(finite_subsets(sK1),finite_subsets(sK2)),sK2),
inference(resolve,[status(thm)],[c_1918,c_246]) ).
cnf(c_18908,plain,
$false,
inference(resolve,[status(thm)],[c_13639,c_18910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n010.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 08:37:00 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 2925447 was started by sandbox on n010,
% 0.18/0.46 % Sat Sep 26 08:37:00 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 39.24/5.50
% 39.24/5.50 % given #500 (T,wt=16): 2528 in(A,finite_subsets(A)) | -finite(A). [resolve(262,b,110,a)].
% 39.24/5.50
% 39.24/5.50 % given #1000 (A,wt=29): 329 finite_subsets(A) != c2 | in(f3(finite_subsets(B)),c2) | -subset(f3(finite_subsets(B)),A). [resolve(144,a,139,d)].
% 39.24/5.50
% 39.24/5.50 % given #1500 (T,wt=20): 8531 finite(f7(c6)) | finite(A) | element(f1(A,c5),A). [resolve(4333,c,111,a)].
% 39.24/5.50
% 39.24/5.50 % given #2000 (W,wt=21): 4749 -subset(powerset(finite_subsets(c4)),f8(c4)). [ur(480,b,4721,a)].
% 39.24/5.50
% 39.24/5.50 % SZS status Theorem for theBenchmark
% 39.24/5.50
% 39.24/5.50 % Proof 1 at 3.59 (+ 1.36) seconds.
% 39.24/5.50 % Length of proof is 27.
% 39.24/5.50 % Level of proof is 6.
% 39.24/5.50 % Maximum clause weight is 24.000.
% 39.24/5.50 % Given clauses 2490.
% 39.24/5.50
% 39.24/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------