%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET148+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 : 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 08:35:54 AM UTC 2026
% Result : Theorem 0.76s 0.62s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 58 ( 23 ~; 23 |; 8 &)
% ( 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 23 !; 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(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('theBenchmark.p',intersection) ).
fof(thI13,conjecture,
! [A] : equal_set(intersection(A,A),A),
file('theBenchmark.p',thI13) ).
fof(thI13_neg,negated_conjecture,
~ ! [A] : equal_set(intersection(A,A),A),
inference(assume_negation,[status(cth)],[thI13]) ).
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_21,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_23,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
fof(nnf_12,plain,
? [A] : ~ equal_set(intersection(A,A),A),
inference(fof_nnf,[status(thm)],[thI13_neg]) ).
fof(sk_thI13_neg,plain,
~ equal_set(intersection(sK1,sK1),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
~ equal_set(intersection(sK1,sK1),sK1),
inference(split_conjunct,[status(thm)],[sk_thI13_neg]) ).
cnf(c_44,plain,
( ~ member(A,B)
| member(A,intersection(B,B)) ),
inference(factor,[status(thm)],[c_23]) ).
cnf(c_55,plain,
( subset(intersection(A,B),C)
| member(sK0(intersection(A,B),C),A) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_119,plain,
( subset(A,B)
| member(sK0(A,B),intersection(A,A)) ),
inference(resolve,[status(thm)],[c_44,c_14]) ).
cnf(c_1968,plain,
( subset(intersection(A,B),A)
| subset(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_55,c_15]) ).
cnf(c_429,plain,
subset(intersection(A,B),A),
inference(copy,[status(thm)],[c_1968]) ).
cnf(c_1969,negated_conjecture,
( ~ subset(sK1,intersection(sK1,sK1))
| ~ subset(intersection(sK1,sK1),sK1) ),
inference(resolve,[status(thm)],[c_18,c_42]) ).
cnf(c_603,negated_conjecture,
~ subset(sK1,intersection(sK1,sK1)),
inference(resolve,[status(thm)],[c_1969,c_429]) ).
cnf(c_1970,plain,
( subset(A,intersection(A,A))
| subset(A,intersection(A,A)) ),
inference(resolve,[status(thm)],[c_119,c_15]) ).
cnf(c_1966,plain,
subset(A,intersection(A,A)),
inference(copy,[status(thm)],[c_1970]) ).
cnf(c_1967,plain,
$false,
inference(resolve,[status(thm)],[c_1966,c_603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET148+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.33 % Computer : n012.cluster.edu
% 0.04/0.33 % Model : x86_64 x86_64
% 0.04/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.33 % Memory : 8046.5625MB
% 0.04/0.33 % 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 07:13:34 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 4171900 was started by sandbox on n012,
% 0.04/0.34 % Sat Sep 26 07:13:34 2026
% 0.04/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.34
% 0.08/0.34 % From the command line: assign(max_seconds, 300).
% 0.76/0.62
% 0.76/0.62 % SZS status Theorem for theBenchmark
% 0.76/0.62
% 0.76/0.62 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.76/0.62 % Length of proof is 17.
% 0.76/0.62 % Level of proof is 5.
% 0.76/0.62 % Maximum clause weight is 27.000.
% 0.76/0.62 % Given clauses 233.
% 0.76/0.62
% 0.76/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------