%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET027+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 : n017.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 08:35:24 AM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 20 ~; 16 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 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(thI03,conjecture,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',thI03) ).
fof(thI03_neg,negated_conjecture,
~ ! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
inference(assume_negation,[status(cth)],[thI03]) ).
fof(nnf_12,plain,
? [A,B,C] :
( ~ subset(A,C)
& subset(B,C)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[thI03_neg]) ).
fof(sk_thI03_neg,plain,
( ~ subset(sK0,sK1)
& subset(sK2,sK1)
& subset(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK1)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
~ subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thI03_neg]) ).
cnf(c_17,negated_conjecture,
subset(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_thI03_neg]) ).
cnf(c_18,negated_conjecture,
subset(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_thI03_neg]) ).
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(sK3(A,B),B)
& member(sK3(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X,sK3(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(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_42,plain,
( ~ member(sK3(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_43,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_44,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_82,negated_conjecture,
~ member(sK3(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_42,c_16]) ).
cnf(c_84,plain,
member(sK3(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_43,c_16]) ).
cnf(c_86,plain,
( member(A,sK2)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_44,c_18]) ).
cnf(c_485,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_426,negated_conjecture,
~ member(sK3(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_485,c_82]) ).
cnf(c_486,plain,
member(sK3(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_86,c_84]) ).
cnf(c_484,plain,
$false,
inference(resolve,[status(thm)],[c_426,c_486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:50:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 77492 was started by sandbox on n017,
% 0.09/0.37 % Sat Sep 26 06:50:18 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.42
% 0.09/0.42 % SZS status Theorem for theBenchmark
% 0.09/0.42
% 0.09/0.42 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.09/0.42 % Length of proof is 13.
% 0.09/0.42 % Level of proof is 4.
% 0.09/0.42 % Maximum clause weight is 9.000.
% 0.09/0.42 % Given clauses 67.
% 0.09/0.42
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------