%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% 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 08:35:44 AM UTC 2026
% Result : Theorem 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 59 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 55 ( 23 ~; 18 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 3 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('theBenchmark.p',union) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('theBenchmark.p',empty_set) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('theBenchmark.p',singleton) ).
fof(thI44,conjecture,
! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
file('theBenchmark.p',thI44) ).
fof(thI44_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(singleton(X),A) ),
inference(assume_negation,[status(cth)],[thI44]) ).
fof(nnf_12,plain,
? [A,X] :
( ~ subset(singleton(X),A)
& member(X,A) ),
inference(fof_nnf,[status(thm)],[thI44_neg]) ).
fof(sk_thI44_neg,plain,
( ~ subset(singleton(sK0),sK1)
& member(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(X,sK0)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
~ subset(singleton(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_thI44_neg]) ).
cnf(c_17,negated_conjecture,
member(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thI44_neg]) ).
cnf(c_28,plain,
( A = B
| ~ member(A,singleton(B)) ),
inference(clausify,[status(thm)],[singleton]) ).
cnf(c_32,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
cnf(c_34,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_35,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK2(A,B),B)
& member(sK2(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X,sK2(A,B))],[nnf_1]) ).
fof(sk_subset,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_sk]) ).
cnf(c_41,plain,
( ~ member(sK2(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_42,plain,
( member(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_75,plain,
member(sK0,union(sK1,A)),
inference(resolve,[status(thm)],[c_34,c_17]) ).
cnf(c_89,negated_conjecture,
~ member(sK2(singleton(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_41,c_16]) ).
cnf(c_91,plain,
member(sK2(singleton(sK0),sK1),singleton(sK0)),
inference(resolve,[status(thm)],[c_42,c_16]) ).
cnf(c_1219,plain,
( member(sK2(singleton(sK0),sK1),A)
| ~ member(sK2(singleton(sK0),sK1),union(sK1,A)) ),
inference(resolve,[status(thm)],[c_35,c_89]) ).
cnf(c_1198,plain,
~ member(sK2(singleton(sK0),sK1),union(sK1,empty_set)),
inference(resolve,[status(thm)],[c_1219,c_32]) ).
cnf(c_1213,plain,
sK2(singleton(sK0),sK1) = sK0,
inference(resolve,[status(thm)],[c_91,c_28]) ).
cnf(c_1220,plain,
~ member(sK0,union(sK1,empty_set)),
inference(paramod,[status(thm)],[c_1213,c_1198]) ).
cnf(c_1218,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_1220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 07:07:09 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3034530 was started by sandbox on n008,
% 0.18/0.45 % Sat Sep 26 07:07:09 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.64
% 0.23/0.64 % SZS status Theorem for theBenchmark
% 0.23/0.64
% 0.23/0.64 % Proof 1 at 0.11 (+ 0.06) seconds.
% 0.23/0.64 % Length of proof is 19.
% 0.23/0.64 % Level of proof is 4.
% 0.23/0.64 % Maximum clause weight is 23.000.
% 0.23/0.64 % Given clauses 138.
% 0.23/0.64
% 0.23/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------