%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 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 08:36:32 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 64 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 20 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_th50,conjecture,
! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
file('theBenchmark.p',prove_th50) ).
fof(prove_th50_neg,negated_conjecture,
~ ! [B,C] :
( subset(B,difference(C,B))
=> B = empty_set ),
inference(assume_negation,[status(cth)],[prove_th50]) ).
fof(nnf_7,plain,
? [B,C] :
( empty_set != B
& subset(B,difference(C,B)) ),
inference(fof_nnf,[status(thm)],[prove_th50_neg]) ).
fof(sk_prove_th50_neg,plain,
( empty_set != sK0
& subset(sK0,difference(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_7]) ).
cnf(c_11,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_th50_neg]) ).
cnf(c_12,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,negated_conjecture,
subset(sK0,difference(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_th50_neg]) ).
cnf(c_15,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_18,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_20,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
fof(nnf_1,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(sk_subset_defn_sk,plain,
! [B,C] :
( ( ( ~ member(sK2(B,C),C)
& member(sK2(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(D,sK2(B,C))],[nnf_1]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_defn_sk]) ).
cnf(c_23,plain,
( member(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_24,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_27,plain,
( ~ subset(B,A)
| A = B
| member(sK2(A,B),A) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_30,plain,
( member(A,difference(sK1,sK0))
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_24,c_13]) ).
cnf(c_60,plain,
( ~ subset(A,empty_set)
| empty_set = A ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_61,negated_conjecture,
empty_set != sK0,
inference(copy,[status(thm)],[c_12]) ).
cnf(c_37,negated_conjecture,
~ subset(sK0,empty_set),
inference(resolve,[status(thm)],[c_60,c_61]) ).
cnf(c_43,plain,
member(sK2(sK0,empty_set),sK0),
inference(resolve,[status(thm)],[c_37,c_23]) ).
cnf(c_47,plain,
member(sK2(sK0,empty_set),difference(sK1,sK0)),
inference(resolve,[status(thm)],[c_43,c_30]) ).
cnf(c_58,plain,
~ member(sK2(sK0,empty_set),difference(A,sK0)),
inference(resolve,[status(thm)],[c_20,c_43]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:58:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3761745 was started by sandbox2 on n009,
% 0.09/0.35 % Sat Sep 26 07:58:00 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 20.
% 0.13/0.37 % Level of proof is 6.
% 0.13/0.37 % Maximum clause weight is 11.000.
% 0.13/0.37 % Given clauses 29.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------