%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET162+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 : n015.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 08:35:56 AM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 24 ~; 24 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn 24 !; 2 ?)
% 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(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(thI18,conjecture,
! [A] : equal_set(union(A,empty_set),A),
file('theBenchmark.p',thI18) ).
fof(thI18_neg,negated_conjecture,
~ ! [A] : equal_set(union(A,empty_set),A),
inference(assume_negation,[status(cth)],[thI18]) ).
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_15,plain,
( ~ member(sK0(A,B),B)
| 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_24,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_25,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_27,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
fof(nnf_12,plain,
? [A] : ~ equal_set(union(A,empty_set),A),
inference(fof_nnf,[status(thm)],[thI18_neg]) ).
fof(sk_thI18_neg,plain,
~ equal_set(union(sK1,empty_set),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
~ equal_set(union(sK1,empty_set),sK1),
inference(split_conjunct,[status(thm)],[sk_thI18_neg]) ).
cnf(c_59,plain,
( subset(union(A,B),C)
| member(sK0(union(A,B),C),B)
| member(sK0(union(A,B),C),A) ),
inference(resolve,[status(thm)],[c_24,c_14]) ).
cnf(c_61,plain,
( subset(A,B)
| member(sK0(A,B),union(A,C)) ),
inference(resolve,[status(thm)],[c_25,c_14]) ).
cnf(c_980,plain,
( subset(A,union(A,B))
| subset(A,union(A,B)) ),
inference(resolve,[status(thm)],[c_61,c_15]) ).
cnf(c_759,plain,
subset(A,union(A,B)),
inference(copy,[status(thm)],[c_980]) ).
cnf(c_981,negated_conjecture,
( ~ subset(sK1,union(sK1,empty_set))
| ~ subset(union(sK1,empty_set),sK1) ),
inference(resolve,[status(thm)],[c_18,c_42]) ).
cnf(c_924,negated_conjecture,
~ subset(union(sK1,empty_set),sK1),
inference(resolve,[status(thm)],[c_981,c_759]) ).
cnf(c_982,plain,
( member(sK0(union(sK1,empty_set),sK1),empty_set)
| member(sK0(union(sK1,empty_set),sK1),sK1) ),
inference(resolve,[status(thm)],[c_924,c_59]) ).
cnf(c_975,plain,
member(sK0(union(sK1,empty_set),sK1),sK1),
inference(resolve,[status(thm)],[c_27,c_982]) ).
cnf(c_983,plain,
~ member(sK0(union(sK1,empty_set),sK1),sK1),
inference(resolve,[status(thm)],[c_15,c_924]) ).
cnf(c_979,plain,
$false,
inference(resolve,[status(thm)],[c_975,c_983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.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 07:18:13 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 3419880 was started by sandbox on n015,
% 0.08/0.36 % Sat Sep 26 07:18:13 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SZS status Theorem for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.12/0.42 % Length of proof is 18.
% 0.12/0.42 % Level of proof is 6.
% 0.12/0.42 % Maximum clause weight is 34.000.
% 0.12/0.42 % Given clauses 119.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------