%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET704+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 : n016.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 08:36:51 AM UTC 2026
% Result : Theorem 0.69s 0.59s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 48 ( 19 ~; 15 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(product,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('theBenchmark.p',product) ).
fof(thI42,conjecture,
! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
file('theBenchmark.p',thI42) ).
fof(thI42_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
inference(assume_negation,[status(cth)],[thI42]) ).
fof(nnf_12,plain,
? [A,X] :
( ~ subset(product(A),X)
& member(X,A) ),
inference(fof_nnf,[status(thm)],[thI42_neg]) ).
fof(sk_thI42_neg,plain,
( ~ subset(product(sK0),sK1)
& member(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK0),skolemize(X,sK1)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
~ subset(product(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_thI42_neg]) ).
cnf(c_17,negated_conjecture,
member(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_thI42_neg]) ).
cnf(c_20,plain,
( member(A,C)
| ~ member(C,B)
| ~ member(A,product(B)) ),
inference(clausify,[status(thm)],[product]) ).
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_50,plain,
( member(A,sK1)
| ~ member(A,product(sK0)) ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_88,negated_conjecture,
~ member(sK2(product(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_41,c_16]) ).
cnf(c_90,plain,
member(sK2(product(sK0),sK1),product(sK0)),
inference(resolve,[status(thm)],[c_42,c_16]) ).
cnf(c_1118,plain,
~ member(sK2(product(sK0),sK1),product(sK0)),
inference(resolve,[status(thm)],[c_50,c_88]) ).
cnf(c_1117,plain,
$false,
inference(resolve,[status(thm)],[c_90,c_1118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET704+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.34 % Computer : n016.cluster.edu
% 0.04/0.34 % Model : x86_64 x86_64
% 0.04/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.34 % Memory : 8046.5625MB
% 0.04/0.34 % OS : Linux 6.8.0-71-generic
% 0.04/0.34 % CPULimit : 300
% 0.04/0.34 % WCLimit : 300
% 0.04/0.34 % DateTime : Sat Sep 26 08:11:14 UTC 2026
% 0.04/0.34 % CPUTime :
% 0.04/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.34 % Process 382828 was started by sandbox on n016,
% 0.04/0.34 % Sat Sep 26 08:11:14 2026
% 0.04/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.35
% 0.04/0.35 % From the command line: assign(max_seconds, 300).
% 0.69/0.59
% 0.69/0.59 % SZS status Theorem for theBenchmark
% 0.69/0.59
% 0.69/0.59 % Proof 1 at 0.06 (+ 0.04) seconds.
% 0.69/0.59 % Length of proof is 12.
% 0.69/0.59 % Level of proof is 3.
% 0.69/0.59 % Maximum clause weight is 22.000.
% 0.69/0.59 % Given clauses 126.
% 0.69/0.59
% 0.69/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------