%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET347+4 : 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 : n003.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 08:36:13 AM UTC 2026
% Result : Theorem 0.16s 5.62s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 27 |; 14 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('theBenchmark.p',empty_set) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('theBenchmark.p',sum) ).
fof(thI38,conjecture,
equal_set(sum(empty_set),empty_set),
file('theBenchmark.p',thI38) ).
fof(thI38_neg,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(assume_negation,[status(cth)],[thI38]) ).
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(sK0(A,B),B)
& member(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(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_14,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_18,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
cnf(c_27,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
fof(nnf_10,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [X0] :
( member(X,X0)
& member(X0,A) )
| ~ member(X,sum(A)) ) ),
inference(fof_nnf,[status(thm)],[sum]) ).
fof(sk_sum_sk,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ( member(X,sK1(X,A))
& member(sK1(X,A),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(X,A))],[nnf_10]) ).
fof(sk_sum,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_0,VAR_2)
| ~ member(VAR_2,VAR_1)
| member(VAR_0,sum(VAR_1)) )
& ! [VAR_0,VAR_1] :
( member(VAR_0,sK1(VAR_0,VAR_1))
| ~ member(VAR_0,sum(VAR_1)) )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_0,VAR_1),VAR_1)
| ~ member(VAR_0,sum(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_sum_sk]) ).
cnf(c_36,plain,
( member(sK1(A,B),B)
| ~ member(A,sum(B)) ),
inference(split_conjunct,[status(thm)],[sk_sum]) ).
cnf(c_42,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(clausify,[status(thm)],[thI38_neg]) ).
cnf(c_50,plain,
( member(sK0(B,A),B)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_59,plain,
~ member(A,sum(empty_set)),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_97,negated_conjecture,
( member(sK0(empty_set,sum(empty_set)),empty_set)
| ~ subset(sum(empty_set),empty_set) ),
inference(resolve,[status(thm)],[c_50,c_42]) ).
cnf(c_86,negated_conjecture,
~ subset(sum(empty_set),empty_set),
inference(resolve,[status(thm)],[c_97,c_27]) ).
cnf(c_98,plain,
member(sK0(sum(empty_set),empty_set),sum(empty_set)),
inference(resolve,[status(thm)],[c_86,c_14]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET347+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n003.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Sat Sep 26 07:35:15 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.59 % Process 2336261 was started by sandbox2 on n003,
% 0.10/5.59 % Sat Sep 26 07:35:15 2026
% 0.10/5.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.60
% 0.16/5.60 % From the command line: assign(max_seconds, 300).
% 0.16/5.62
% 0.16/5.62 % SZS status Theorem for theBenchmark
% 0.16/5.62
% 0.16/5.62 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/5.62 % Length of proof is 14.
% 0.16/5.62 % Level of proof is 4.
% 0.16/5.62 % Maximum clause weight is 21.000.
% 0.16/5.62 % Given clauses 40.
% 0.16/5.62
% 0.16/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------