%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET355+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 : n012.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 08:36:14 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% 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 : 47 ( 18 ~; 15 |; 9 &)
% ( 2 <=>; 3 =>; 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 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('theBenchmark.p',sum) ).
fof(thI43,conjecture,
! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
file('theBenchmark.p',thI43) ).
fof(thI43_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
inference(assume_negation,[status(cth)],[thI43]) ).
fof(nnf_12,plain,
? [A,X] :
( ~ subset(X,sum(A))
& member(X,A) ),
inference(fof_nnf,[status(thm)],[thI43_neg]) ).
fof(sk_thI43_neg,plain,
( ~ subset(sK0,sum(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(sK0,sum(sK1)),
inference(split_conjunct,[status(thm)],[sk_thI43_neg]) ).
cnf(c_17,negated_conjecture,
member(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thI43_neg]) ).
cnf(c_21,plain,
( ~ member(A,C)
| ~ member(C,B)
| member(A,sum(B)) ),
inference(clausify,[status(thm)],[sum]) ).
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_52,plain,
( ~ member(A,sK0)
| member(A,sum(sK1)) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_88,negated_conjecture,
~ member(sK2(sK0,sum(sK1)),sum(sK1)),
inference(resolve,[status(thm)],[c_41,c_16]) ).
cnf(c_90,plain,
member(sK2(sK0,sum(sK1)),sK0),
inference(resolve,[status(thm)],[c_42,c_16]) ).
cnf(c_585,plain,
member(sK2(sK0,sum(sK1)),sum(sK1)),
inference(resolve,[status(thm)],[c_52,c_90]) ).
cnf(c_584,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 07:34:20 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 15161 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 07:34:20 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.21/0.37
% 0.21/0.37 % SZS status Theorem for theBenchmark
% 0.21/0.37
% 0.21/0.37 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.21/0.37 % Length of proof is 12.
% 0.21/0.37 % Level of proof is 3.
% 0.21/0.37 % Maximum clause weight is 10.000.
% 0.21/0.37 % Given clauses 69.
% 0.21/0.37
% 0.21/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------